Sample | Curriculum for the Digital SAT by MasteryPrep

Curriculum for the Digital SAT®

How Curriculum for the Digital SAT® Works:

How Mastery for the Digital SAT Works

Welcome to Mastery for the Digital SAT, a new take on improving SAT scores.

Students have three paths to boosting their scores: time management

Students have three paths to boosting their scores:

• Time management

• Test-taking skills

• Content

• test-taking skills

• content

Traditional test preparation provides a review of content. It discusses test-taking skills. It reminds students about time management. Students who are already strong test-takers, who already perform well academically, benefit. Most students, however, forget the content, don’t change their test-taking behaviors, and continue to struggle against the clock.

Our approach is different. We call it the Mastery Pyramid. It works even for students who need the most help in these areas.

• Content Mastery: Engaging direct instruction based on modern best practices helps students bridge the gap between classroom learning and the SAT’s assessed standard. By isolating skills, we make each topic easier to learn. Later, mixed practice with authentic SAT question emulations prepares students for a real testing environment.

• Test Mastery: Test-taking is a skill that can be learned like any other. Our lessons simplify key test-taking strategies, provide many opportunities to practice them, and reinforce the fundamentals again and again until test-taking behavior actually improves.

Time Mastery: It’s one thing to memorize the time limits. It takes practice to improve pacing and decisionmaking skills. In each lesson, students practice with timed test sections and mini-tests until they’re genuinely able to beat the clock.

Our approach is different. We call it the Mastery Pyramid. It works even for students who need the most help in these areas.

Three Paths to Boosting Scores:

Content Mastery:

Engaging direct instruction based on modern best practices helps students bridge the gap between classroom learning and the SAT’s assessed standard. By isolating skills, we make each topic easier to learn. Later, mixed practice with authentic SAT question emulations prepares students for a real testing environment.

Test Mastery:

Test-taking is a skill that can be learned like any other. Our lessons simplify key test-taking strategies, provide many opportunities to practice them, and reinforce the fundamentals again and again until testtaking behavior actually improves.

Time Mastery:

It’s one thing to memorize the time limits. It takes practice to improve pacing and decision-making skills. In each lesson, students practice with timed test sections and mini-tests until they’re genuinely able to beat the clock.

HOW MASTERY FOR THE DIGITAL SAT WORKS I

Curriculum for the Digital SAT®

The Mastery for the Digital SAT Difference

Authentic Practice

Each math book features hundreds of SAT Math questions that are extremely similar to what students will face on the SAT. If they can answer the questions correctly in this book, they’ll get them correct on the test. Other test prep programs don’t come close to the amount of authentic practice we provide.

Lots of Authentic Practice

Did we mention Mastery for the Digital SAT provides students a lot of authentic “at-bats”? For each content dimension, we include literally dozens of practice questions to ensure your students have enough runway to master the skills. With traditional test prep programs, the average number of practice questions provided per skill is 3 (compared to more than 40 in Mastery for the Digital SAT).

Isolation

We break the test down one content dimension at a time. Students are given the opportunity to master each skill, and given plenty of practice with each skill in isolation, before applying what they have learned to mixed practice. The result is that students better consolidate what they learn and don’t get overwhelmed. Traditional test prep programs fail to provide sufficient practice in isolation.

Interleaving

Mastery for the Digital SAT’s mini-tests bridge the gap between isolated practice and the real SAT experience by interspersing questions related to the topic at hand with a wide range of question types. This helps students improve their problem-solving and time management skills. Mastery for the Digital SAT Math has 23 mini-tests, nearly five times more than traditional test prep programs.

Scripted Lessons

Mastery for the Digital SAT is the only SAT prep program that provides comprehensive, scripted lesson plans. The result is a consistent, score-raising experience for students and minimal planning time for teachers.

Pre-Built Hooks

Traditional test prep programs are dry and follow the old “drill and kill” philosophy. If this is your first time running a test prep program, it can be challenging to introduce the content while bringing it to life. We’ve designed the program with hooks and activities built in, making each lesson interesting and engaging.

Learning by Doing

Unlike traditional test prep programs that resort to “sage on the stage” demonstrations, Mastery for the Digital SAT students learn from what they do in the lessons, not from what you read them from a slide deck. Every instructional unit is centered around student activity and engagement.

Scaffolded Instruction

SAT items are highly rigorous. Traditional test prep aims directly at rehearsing the items, which can leave many students behind. Mastery for the Digital SAT is designed to start at a more remedial level and rapidly scaffold students to higher levels of attainment. We don’t assume students know the basics, and the result is greater student engagement and achievement.

Detailed Test-Taking Approaches and Guessing Strategies

Traditional test prep programs are built for highperforming students who are already solid testtakers. Students who struggle with tests also struggle in these programs. Mastery for the Digital SAT radically simplifies key strategies and walks students through each concept step-by-step.

Integrated Time Management Coaching

By embedding time management coaching into every section, Mastery for the Digital SAT is by far the most reliable program for improving your students’ time management skills.

Slide Decks and Teacher Resources

Unlike traditional test prep designed for tutors to use for weekend programs, we provide everything you need to run an Mastery for the Digital SAT class during the school day, right out of the box, including lesson plans, slide decks, and entrance and exit tickets.

Complete

Mastery for the Digital SAT provides the most comprehensive coverage of SAT content dimensions for students at all score ranges.

Curriculum for the Digital SAT®

What Mastery for the Digital SAT Includes

Student Workbooks

(4)

• Mastery for ther Digital SAT Writing

• Mastery for ther Digital SAT Reading

• Mastery for ther Digital SAT Math: Algebra and Geometry

• Mastery for ther Digital SAT Math: Advanced Math and Data Analysis

Students work directly in their workbooks. The workbooks allow students to follow along with the classroom activities and include all of the practice materials needed for success on the SAT. No printing required!

Teacher Manuals (4)

• Mastery for ther Digital SAT Writing

• Mastery for ther Digital SAT Reading

• Mastery for ther Digital SAT Math: Algebra and Geometry

• Mastery for ther Digital SAT Math: Advanced Math and Data Analysis

Teacher manuals (like this one) provide everything you need to facilitate over 40 Mastery for ther Digital SAT lessons, including answer explanations, scripted lesson plans, and definitions of key terms.

Slide Decks (4 sets)

• Mastery for ther Digital SAT Writing

• Mastery for ther Digital SAT Reading

• Mastery for ther Digital SAT Math: Algebra and Geometry

• Mastery for ther Digital SAT Math: Advanced Math and Data Analysis

Every Mastery for ther Digital SAT chapter is accompanied by a slide deck to provide a visual focus for the class. Every exercise and question that appears in the student workbook also appears in the accompanying slide deck, along with its solution.

Missing a resource?

Contact your school support manager directly by emailing support@masteryprep.com

Mastery for the Digital SAT Page by Page

When you teach a Mastery for ther Digital SAT lesson, you’ll work from the teacher manual. Your students will be looking at their workbooks. On the projector will be the slide deck. There are a lot of moving parts. That’s why Mastery for ther Digital SAT uses a system to ensure that you and your class are always, literally, on the same page. For every page in the student workbook (for example, page 218 on the left in the figure below), there are two pages in the teacher manual (for example, pages 218a and 218b on the right). This is always an exact match. In the teacher manual, the “a” pages are always on the left, and the “b” pages are always on the right. The entire student workbook is reprinted in the teacher manuals, so you don’t need to have the student workbook open and in front of you to track what your students are looking at.

Curriculum for the Digital SAT®

Mastery for the Digital SAT Page by Page

Each page in the student workbook (page 219, for instance) can have one or more slides that go with it. Each slide number starts with the matching page number in the student workbook and teacher manual (for example, 219.1, 219.2, and 219.3).

If you want to start a lesson on pages 212a and 212b in your teacher manual, have your students turn to page 212 in their workbooks, and pull up slide 212.1 on the projector.

Curriculum for the Digital SAT®

Mastery for the Digital SAT Page by Page

As you go through the dialogue on page 212b, helpful slide call-outs tell you when the next slide is relevant (for example, 212.2 and 212.3).

Once you get to the bottom of page 212b, you’ll turn to the next pages in your teacher manual, 212a and 213b, while having your students look at page 213 in their workbooks. You’ll also click the slides to 213.1.

TEACHER MANUAL

Curriculum for the Digital SAT®

MEAN, MEDiAN, AND MODE

Foundation (17 minutes)

In this section, students will find the mean and median for a few sets.

Let’s review the difference between mean and median. To find the mean of a set of data, add all of the values in the set together, then divide by the number of values in the set. To find the median, list the numbers from least to greatest and locate the value in the middle of the set. If there are an even number of values in the set, take the mean of the middle two numbers to determine the median.

I like to pronounce “median” as “mid-dian” to remind myself that median is looking for the middle term in the set. Work on your own to answer questions 1 through 3. You have 2 minutes.

SLIDE 212.1

Review the answers when time is up.

ANSWER KEY

SLIDE 212.2

1. Mean: 12345 5 ++++ = 3

Median: 3

Number Line:

SLIDE 212.3

2. Mean: 11345 5 ++++ = 2.8

Median: 3

Number Line: 1 2 3 4 5 6 7 8 9 10

SLIDE 212.4

3. Mean: 1 2 3 4 10 5 ++++ == 4

Median: 3

Number Line: 1 2 3 4 5 6 7 8 9 10

In question 1, the median is 3. How are the other values spaced around that point?

They’re all evenly spaced.

Since they’re evenly spaced, that means the median and mean are the same value. How about question 2?

There are two values at 1, so there is a gap between 1 and 3.

The middle number, the median, is still the same at 3. With the uneven distribution to the left, though, the mean will get pulled to the left. That makes it smaller than the median. How are the points spread in question 3?

There is a big gap between 4 and 10, but the rest are spread evenly.

The value at 10 pulls the mean higher than the median, but the median still remains at 3. The point at 10 is called an outlier. It is farther away from the rest of the points and pulls the mean away from the median. It also stretches the range, or the difference between the highest and lowest number in the data set.

Question 2 also had a mean different from the median, but would you say it also had an outlier? No.

Even though we do see an effect on the mean in question 2, there isn’t an outlier. An outlier is much larger or much smaller than the other values in the data set.

Curriculum for the Digital SAT®

Structure of a Mastery for the Digital SAT Lesson

Every Mastery for ther Digital SAT lesson has the same structure. This sequence of content is designed to help students master SAT content dimensions. It also enables them to gradually build test-taking and time management skills until they’re second nature.

1. Warm-Up:

Three timed practice questions introduce your students to the topic and help you differentiate instruction.

2. Foundation:

A scaffolded lesson reviews the basics of the content dimension and provides students with skill-building activities that improve their grasp of content.

3. Practice Sets:

Three sets of authentic test items are interspersed throughout the lesson, providing isolated practice and a way to hone newly acquired skills.

4. Approach:

Students learn how to identify question types, eliminate incorrect answers, and double-check their work.

5. Strategy:

There is more than one way to earn points. Students learn test-taking strategies that help them arrive at the right answer even if they’re stuck.

At the bottom of many student workbook pages is this tracker that shows where you are in the lesson. Every lesson has the same tracker.

6. Mini-Test:

Students apply what they have learned to a timed emulation of a real SAT testing experience. Questions from the lesson are mixed with other SAT items.

7. Wrap-Up:

Three more timed questions, at the same difficulty level as the warm-up items, help you evaluate students’ progress.

8. Review:

A one-page cheat sheet provides a handy recap for students to study before test day.

Every section of an Mastery for ther Digital SAT lesson is designed to stand on its own.

You can use the lessons one after another for a onesemester or full-year course. However, you’re also free to pick and choose resources from lessons and

Curriculum for the Digital SAT®

individual sections to suit your students’ needs. For example, if you feel your students have mastered the instructional content but need additional practice, you could have them focus only on the Warm-Up, Practice Sets, Mini-Test, and Wrap-Up.

Or if you want to give your students a one-week cram just before test day, you could stick to Warm-Up, Strategy, and Wrap-Up for a lightning-fast review of tips and tricks.

ONE-WEEK CRAM

Teachers who want to avoid test-taking tips and focus on content might prefer the Foundation and Approach sections.

For more ideas about how to make the most of Mastery for ther Digital SAT’s modular lesson design, see “How to Use Mastery for ther Digital SAT” later in this guide.

Digital SAT®

Advanced Math and Data Analysis

Chapter

Ratios and Proportions

This chapter will teach students to solve problems using ratios and proportions. Specifically, students will learn how to apply proportional relationships and ratios to numerical and real-world problems.

RATIOS AND PROPORTIONS

CONTENT D i MENS i ONS

Rates, proportions, and units

Apply proportional relationships, ratios, rates, and units in a wide variety of contexts. Examples include, but are not limited to, scale drawings and problems in the natural and social sciences.

LEARN i NG TARGETS

1. Use proportions and ratios to solve word problems.

2. Implement the basic approach for ratios and proportions questions.

3. Apply the Estimate and Factor Elimination strategies to ratios and proportions questions.

SCORE D i FFERENT i AT i O N

Skip the Foundation segment if ...

Math above 500 Problem Solving and Data Analysis above 8

Math above 480 Problem Solving and Data Analysis above 8

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

MASTERY FOR THE D I G I TAL SAT: ADVANCED MATH AND DATA ANALYS I S

Warm-Up

Complete the warm-up. When you have finished, double-check your work.

The cost of a pair of shoes at Store B is approximately 7 8 of the cost at Store A. The cost of a pair of shoes at Store C is approximately 19 8 of the cost at Store A. If a pair of shoes costs $80 at Store A, approximately how much more does it cost at Store C than at Store B ?

A) $70

B) $91

C) $120

D) $190

Propagation Period versus Height Expectancy

Propagation period (days)

A botanist at a plant society created the scatterplot above to understand the relationship between the propagation period and height expectancy of 10 species of plants. Which labeled point represents the plant that has the greatest ratio of height expectancy to propagation period?

A) A

B) B C) C

D) D

A baker takes 3 cupcakes out of every 500 cupcakes home for his family. At this rate, how many cupcakes will be taken home if the baker makes 25,000 cupcakes?

A) 100

B) 150 C) 200 D) 250

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Warm-Up (12 minutes)

SLIDE 14.1

Give the class 6 minutes to complete the warm-up. Review the answers briefly before beginning the lesson.

SLIDE 14.2

1. The correct answer is C. Because the cost of a pair of shoes at Store B is approximately 7 8 of the cost at Store A, multiply 7 8 by 80 to find that the cost of the shoes at Store B is $70. Because the cost of a pair of shoes at Store C is approximately 19 8 of the cost at Store A, multiply 19 8 by 80 to find that the cost of shoes at Store C is $190. The question asks for the difference between the costs of the pairs of shoes at Store C and Store B. To find the answer, subtract the values as follows: $190 − $70 = $120.

SLIDE 14.3

2. The correct answer is A. Height expectancy is the y-axis, and propagation period is the x-axis. The ratio of height expectancy to propagation period for each point is the ratio of the y to x values. Calculating this for all points shows that point A has the highest ratio: 6 18 = 1 3

14.4

3. The correct answer is B. The ratio of cupcakes that the baker takes home is 3 500 . The ratio of cupcakes that the baker takes home out of 25,000 cupcakes, x, can be represented by 25,000 x Set the ratios equal to each other. 6 500 = 25,000 x Multiply both sides by 25,000.

x = 3 500 · 25,000 Simplify.

x = 150

SLIDE

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

Foundation

Complete the class activity following your teacher’s instructions.

1. Length of volunteer’s foot:

2. Length of statue’s foot:

3. Height of volunteer:

4. Height of statue:

Work with your teacher to identify the given ratio in the question. Do not solve.

5. At a ballpoint pen factory, an inspector randomly selects 12 pens for inspection from a batch of 500 pens. At this rate, how many pens will the inspector select for inspection from a day’s production of 15,000 pens?

Given ratio: _____________________________

Work on your own to identify the given ratio in the question. Do not solve.

6. For two similar right triangles, the hypotenuse of the smaller triangle is 5 inches, and the hypotenuse of the larger triangle is 10 inches. If the shorter side of the smaller triangle is 3 inches, what is the length of the shorter side of the larger triangle?

Given ratio: _____________________________

Foundation (17 minutes)

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

In this section, you will introduce students to the basics of ratios and proportions. Students will see how proportions can model word problems and how they can be solved by cross multiplication or scaling.

How tall would the action figure be?

65 ÷ 10 = 6.5 inches

We are going to build a statue in front of the school. One person in this class will be the inspiration. Hundreds of years from now, people will look at this heroic statue in awe and wonder. Whom should we honor with the statue?

Wait for a volunteer and have them come to the front of the class. We assume the student is “Michael” in this dialogue.

We want this statue to be majestic: 20 times as tall as Michael. However, we want it to be as accurate as possible in terms of Michael’s proportions. For example, we don’t want the feet to be too long or too short; that would look weird. How can we figure out how long the statue’s feet should be?

Measure the length of Michael’s foot, then make the statue’s foot 20 times as long.

Measure the length of the volunteer’s foot. If a ruler or measuring tape is not available, estimate.

How long should the statue’s feet be?

20 · (length of Michael’s foot)

Have the volunteer return to their seat.

The statue will represent Michael’s features without distorting him, but it will make him 20 times larger. This is because we used a ratio to solve this question. A ratio is a numerical way to describe the size relationship between two quantities. We often see ratios written as fractions.

Next, we decide to make a small action figure of Michael instead of a huge statue.

Ask the volunteer for their height and convert it to inches. Assume for this example that the volunteer is 65 inches tall.

Let’s design the action figure so the ratio of Michael’s foot length to the foot length of the action figure is 10 to 1, or 10 1 . What do you think we can figure out from this information? The height of the action figure.

These examples show how we can use ratios to scale the size of something up, like we did for the statue, or scale down, like we did for the action figure. Many SAT questions ask you to use this idea.

The keys to solving these problems are: 1) identifying a ratio from given information, 2) setting up a proportion, and 3) solving that proportion. A proportion is an equation stating that two ratios are equal. We’ll practice working through this process step by step. Look at question 5 in your workbook. There are three quantities given. A ratio relates two quantities at a time, so let’s relate 12 pens selected to 500 pens in the whole batch. Writing this ratio as a fraction, we get selected total : 12 500 .

Notice how we labeled the numerator (the top) and the denominator (the bottom).

15.3

Take 30 seconds to identify a ratio in question 6. Always label the numerator and denominator. What did your ratio look like?

small large : 5 10 or shorter hypotenuse : 3 5

There’s more than one way to correctly relate quantities with a ratio. Relating 5 inches to 10 inches is correct since those are both lengths of a hypotenuse. Relating 3 inches to 5 inches is also correct since those are side lengths of the same triangle.

Always relate “like with like.” Writing the ratio for this problem would be incorrect, since 3 inches is the short-side length of the smaller triangle, while 10 inches is the hypotenuse length of the larger triangle. There’s nothing alike about them.

SLIDE 15.2

SLIDE

SLIDE 15.1

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

MASTERY FOR THE D I G I TAL SAT: ADVANCED MATH AND DATA ANALYS I S

Foundation

Work with your teacher to write a proportion for the question. Do not solve.

Proportion: _______________________

Work on your own to write a proportion for the question. Do not solve.

Proportion: _______________________

Foundation (17 minutes)

Turn to the next page in your workbook. Question 5 is there again, but now we’re going to set up a proportion. We already have the ratio selected total : 12 500 for the problem. Now we need to set up another ratio that relates the other known quantity, 15,000, and the unknown quantity, x pens selected for inspection. How should this ratio look if we’re staying consistent with the first ratio?

selected total : 15,000 x

It’s important to relate quantities the same way in both ratios. This lets us write a proportion, which is an equation between ratios: selected total : 12 500 = 15,000 x Why would 12 500 = 15,000 x be incorrect?

The numerators and denominators describe different kinds of quantities.

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Take 1 minute to set up a proportion for question 6. When time is up, review by calling on individual students.

Let’s say your given ratio for question 6 was small large : 5 10 . How would your proportion look?

small large : 5 10 = 3 x

How would your proportion look if you used shorter hypotenuse : 3 5 ?

shorter hypotenuse : 3 5 = 10 x

Both are correct, as long as your numerators and denominators mean the same thing.

SLIDE 16.2

SLIDE 16.1

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

MASTERY FOR THE D I G I TAL SAT: ADVANCED MATH AND DATA ANALYS I S

Foundation

Work with your teacher to write a proportion for the question. Do not solve.

Proportion: _______________________

Work on your own to write a proportion for the question. Do not solve.

Proportion: _______________________

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Practice Set 1 (12 minutes)

SLIDE 19.1

Give the class 6 minutes to complete the practice set. Review the answers before moving to the next section.

SLIDE 19.2

1. The correct answer is A. The number of students that were both in 8th grade and played golf is 5. The total number of students is 50, so the proportion is 51 5010 =

19.3

2. The correct answer is B Convert 5 4 9 to its approximate decimal form, 4.56. The proportion of vinyl records to inches is 70 4.56 , where b is the number of vinyl recordsin the stack, and h is the height of the stack. Set h = 9 and solve for

b = 70 4.56

Cross multiply.

4.56b = 70 9

Simplify the right side of the equation.

4.56b = 630

Divide both sides by 4.56 and simplify. b ≈ 138.16 or about 140.

SLIDE

19b

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

MASTERY FOR THE D I G I TAL SAT: ADVANCED MATH AND DATA ANALYS I S

ENTRANCE

Ratios and proportions questions can be identified by these terms:

• proportion

• rate

• ratio

... or by this feature:

• two related quantities being compared to each other

Review question 4 with your teacher. Circle the part of the question that identiﬁes it as a ratios and proportions question. Do not solve the question.

A wildlife biologist at a fishery checks 9 fish at random for disease out of every 200 fish caught. At this rate, how many fish will be checked if 10,000 fish are caught at the fishery?

A) 350

B) 400

C) 450

D) 500

Curriculum for the Digital SAT®

Approach (12 minutes)

In this section, you will illustrate how the Entrance step can help students identify ratios and proportions questions on the SAT.

SLIDE 22.1

Now that you know the basics of ratios and proportions, it’s time to see how these questions are asked on the SAT. The first step to answering any question is Entrance. During Entrance, you identify what kind of question you are being asked. No matter how good you are at answering ratios and proportions questions, you must be able to identify which questions they are on the SAT, so you know when to put your new knowledge and skills into action.

SLIDE 22.2

Look at question 4 for identifying language such as proportion or ratio or features such as related quantities being compared to each other. Do you notice any of those identifiers?

The question has the word rate and compares a subset of the population of fish with a larger population of fish.

Circle those identifiers with your pencil.

These questions often specifically ask for a ratio or proportion, but if they don’t, they will still compare related quantities. When you see these identifiers in a question, there’s a very good chance you need to set up a proportion.

Ratios and proportions questions sometimes look a lot like rate questions. They often will literally say the word rate, after all! It turns out that proportions and rates are mostly interchangeable, so you wonʼt be in a bad place if your entrance step sends you either way. Today weʼre going to focus on the ratio and proportion way of solving things. The rate way of doing it is covered in the Rates chapter.

Circle the identifying language in questions 5 and 6.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

FOR

SOLVE, STRATEGIZE, OR SKIP

Step 1: Can I solve this quickly and easily?

1. Relate relevant quantities as ratios.

2. If the question’s answer choices have fractions, choose the one relating the specified quantities. The quantity coming after to or of in the question should go in the denominator.

3. If the question’s answer choices are whole numbers, set the unknown’s ratio equal to another ratio and solve the proportion.

4. If the question asks you to compare ratios, convert them to decimals.

Step 2: If not, can I apply a strategy?

Estimate: Look for opportunities to estimate, use number sense, and rule out answer choices that are unreasonable based on the numbers in the problem.

Factor Elimination: Find where the row and column of the data table mentioned in the question intersect, and eliminate choices whose numerators don’t divide that number.

Step 3: Otherwise, I should skip

If the question is too tough to solve or strategize, skip it. Mark your best guess and move on.

Solve question 4 with your teacher.

A wildlife biologist at a fishery checks 9 fish at random for disease out of every 200 fish caught. At this rate, how many fish will be checked if 10,000 fish are caught at the fishery?

A) 350

B) 400

C) 450

D) 500

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Approach (12 minutes)

In this section, you will illustrate the steps to Solve, Strategize, or Skip for ratios and proportions questions using the three questions from the Entrance step.

SLIDE 24.1

Once you confirm you have a ratios and proportions question, it’s time to decide how to answer it. If you can solve the question quickly and easily, you should do so. If you’re stumped, you have other options: You will either need to strategize, using techniques such as Estimate or Factor Elimination, or skip the question. For now, we will focus on the solve part of the approach. We’ll discuss strategize later.

Note: The questions discussed in this chapter are similar to those covered in the Rates chapter. You might find that the approach we use here can also be helpful for those questions, and vice versa. If you have already covered rates with your students, it’s a good idea to mention this.

SLIDE 24.2

Look at question 4. The first thing to do is relate relevant quantities as ratios. Before we do that, let’s review what each of the given values specifically refers to.

For example, the 9 means 9 fish checked for disease. How would you describe the other two given values?

200 fish caught and 10,000 fish caught.

The 9 fish checked were out of the 200 fish caught, so it makes sense to relate them. How would this ratio look?

9 200

Are the answer choices fractions?

No, they’re whole numbers.

If they were fractions, you would just need to find the right fraction, and your work would be done. Flip back in your book to Practice Set 1, question 1. This is an example of a question that you answer using part 2 of the solve step.

With question 4, though, we skip part 2 of the solve step and go directly to part 3. Since the choices are whole numbers, what do we need to do?

Set the unknown’s ratio equal to another ratio and solve the proportion.

We know 10,000 fish are caught in the second case; let’s say x fish were checked out of that 10,000. How should this ratio look?

10,000 x

That gives us a proportion of 9 200 = 10,000 x .

How would it look if you solved by cross multiplication?

9 · 10,000 = 200x Divide both sides by 200.

x = 90,000 ÷ 200 x = 450 fish

You could also solve this with a scale factor. Since 200 fish are caught the first time and 10,000 fish are caught the second time, 10,000 ÷ 200 = 50 times as many fish are caught the second time. This means 9 · 50 = 450 fish would be checked the second time.

We didn’t get to part 4 with this problem. What is its advice?

If the question asks you to compare ratios, convert them to decimals.

That makes it easier to compare the fractions. This will help you with question 6 on the next page.

Now that we’ve reviewed the solve step for question 4, use it on questions 5 and 6 on your own.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

Solve questions 5 and 6 on your own.

In a group of 225 college students, 5 are majoring in education. At this rate, how many of 8,100 college students are majoring in education?

A) 130

B) 180

C) 230

D) 280

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Cashtown 3,522,549 4,070,2284,585,9505,879,718

Bill City375,497 360,236487,876490,185

Moneyville 12,456,280 10,900,0579,022,37812,776,495

Dollar Springs 297,854450,321402,397524,832

Los Pesos 1,364,4751,547,6651,430,4441,648,254

The table above lists the average home prices for each of six different cities from 2014 to 2017.

Of the following, which city’s ratio of its 2014 home price to its 2017 home price is closest to Dollar Springs's ratio of its 2014 home price to its 2017 home price?

A) Dough Hills

B) Cashtown

C) Moneyville

D) Los Pesos

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Approach (12 minutes)

SLIDE 25.1

Give the class 4 minutes to answer questions 5 and 6. Review the answers afterward.

SLIDE 25.2

5. The correct answer is B. Relate the given quantities using a ratio.

The ratio is number of college students majoring in education total number of college students or 5 225

Write a ratio using the given values. Let x represent the unknown value.

= 5 2258,100 x

Cross multiply to solve for x 8,100 · 5 = 225x Simplify.

40,500 = 225x Divide both sides by 225. x = 180 students majoring in education

25.3

6. The correct answer is B. Relate the given quantities using ratios. The ratio is cost of a home in 2014 cost of a home in 2017 Dollar Spring’s ratio of 2014 home price to 2017 home price is 297,854 524,832 ≈ 0.57.

Find the ratio of the 2014 to 2017 home price for the cities in the answer choices and convert to decimals.

Dough Hills: 2,357,268 3,275,766 ≈ 0.72

Cashtown: 3,522,549 5,879,718 ≈ 0.60

Moneyville: 12,456,280 12,776,495 ≈ 0.97

Los Pesos: 1,364,475 1,648,254 ≈ 0.83

The closest number to 0.57 is 0.60, Cashtown.

SLIDE

25b

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

If you solved the question …

Double-check your work to catch any mistakes. Did you …

• use values that aren’t relevant to the question?

• set up a proportion with mismatched numerators and denominators?

If you used a strategy …

Mark the problem so you can come back to it after you answer the remaining questions. On the second pass, you can double-check that you used the strategy correctly or try to solve the question.

If you skipped the question …

Check that you guessed an answer and marked the question.

Work with your teacher to double-check the math on question 7. Identify and correct any errors made by the student who attempted to solve it.

Taco Filling and Tortilla Selection Filling

The table above shows the type of taco filling and tortilla chosen by people at a party. Each person chose one filling and one tortilla. Of the people who chose flour tortillas, what fraction chose veggie as their filling?

Student reasoning:

In the chart, there are a total of 28 people picking tacos, but from that, 6 people chose veggie and flour, and 2 people chose veggie and corn. Therefore, 8 people from the 28 chose veggies. That means that the fraction of people who chose veggie as their filling is 8 28 or 2 7

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Approach (12 minutes)

In this section, you will illustrate the Exit step for ratios and proportions questions by double-checking an SAT item that has been solved incorrectly.

SLIDE 26.1

Once you’ve finished your calculations, you might think you’re done and ready for the next question. But don’t forget this important last step to every problem: the Exit step. If you solved the question, double-check your work. If you used a strategy or guessed, mark the question so you can review it on a second pass.

SLIDE 26.2

Since we are focusing on the solve part of the Approach, we’re going to practice doublechecking your work. Look at question 7 in your workbook. A student has already attempted to answer this question. Take 2 minutes to doublecheck the work on this problem and identify any errors made by the student.

What error did the student make?

The student found the ratio of all veggie-filled tacos to the total number of tacos. all veggie-filled tacos total number of tacos = (62) (12862) + +++ = 8 28 = 2 7

This type of error can happen easily if you use the wrong information from the table. Here, it happened because the student jumped straight to veggie and ignored an important part of the last sentence. What part did they ignore?

Of the people who chose flour tortillas.

The student should only consider people who chose flour tortillas. Any numbers involving corn tortillas are irrelevant to the question. How should they have answered the question?

The student should have set up a ratio of veggiefilled flour tortillas to the total number of flour tortillas.

veggie-filled flour all flour tortilla tacos = 6 18 = 1 3

Only use values relevant to the question. If the student had remembered to check this, they would have avoided this error and gotten another question right.

There is one other error to check for with this type of problem. What is it?

Setting up a proportion with mismatched numerators and denominators.

All of the denominators, the bottom numbers in the fractions, should be about the same thing. All of the top numbers, the numerators, should also be about the same thing. That’s why you should label your fractions. Always double-check this before moving on to the next problem.

Let’s apply the ratios and proportions approach to a practice set.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

MASTERY FOR THE D I G I TAL SAT: ADVANCED MATH AND DATA ANALYS I S

ESTIMATE

You can answer some ratios and proportions questions if you look for opportunities to estimate, use number sense, and rule out answer choices that are unreasonable based on the numbers in the problem.

1. Estimate the scale factor between two known values in the question. For example, is one value roughly two times as large as the other?

2. Scale the other known value up or down by the same approximate scale factor.

3. Choose the answer closest to the result.

Review question 11 with your teacher. Use the Estimate strategy to answer the question as a class.

If 20 pancakes were stacked on top of each other in a column, the column would be approximately 5 3 8 inches tall. At this rate, which of the following is closest to the number of pancakes it would take to make a 10-inch-tall column?

A) 30

B) 40

C) 80

D) 120

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Strategy (12 minutes)

In this section, you will demonstrate the Estimate strategy using three SAT items.

SLIDE 28.1

It can be easy to foul up ratios and proportions questions by messing up arithmetic, hitting the wrong button, or being unclear about whether you should multiply or divide.

If you are unsure how to solve a ratios and proportions problem, strategize instead. One of the best and quickest techniques to use is the Estimate strategy. This strategy will allow you to use an estimated relationship between two values, the ratio, to approximate the new value. Having an idea of about how big or small the new value should be will help you eliminate wrong answers and can even land you on the correct one.

SLIDE 28.2

What ratio is being asked for in question 11?

The number of pancakes in a stack compared to the stack’s height.

What is the unknown value in this question?

The number of pancakes in a 10-inch stack.

The first step is to estimate the scale factor between two known values in the question. What comparison can you make with the given heights?

The known height for 20 pancakes is a little more than 5 inches. This is about half the height of the requested 10-inch stack.

What’s the scale factor?

Itʼs 2, since we have to multiply 5 inches by 2 to get a 10-inch stack.

What’s the next step in the strategy?

Scale the other known value up or down by the same approximate scale factor.

If the height of the stack of pancakes roughly doubles, what do you think that means for the number of pancakes in the stack?

It means the number of pancakes should also roughly double.

How many pancakes would there be if the number doubled?

Now we choose the answer closest to the result. What choice is closest to 40?

Choice B.

That’s the correct answer.

You were able to solve this question without using your calculator because you applied your estimation skills.

You can always use this strategy to eliminate answer choices that don’t make sense with the given information.

This strategy is also used as a time saver. Even if you do know how to apply the solve step, when you are crunched for time, it’s often a good idea to use the Estimate strategy instead. Look out for obvious scale factors. That’s the clearest tipoff that Estimate is the way to go.

Try this strategy on questions 12 and 13. Fair warning: you can’t follow the exact Estimate procedure for question 12, but you can still use the concept of estimation to arrive at the correct answer.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ADVANCED MATH AND DATA ANALYSIS

Work on your own using the Estimate strategy to answer questions 12 and 13.

Nikki earned $30 for 4 hours of work at her job today. How many dollars will she earn tomorrow if she works 10 hours at the same hourly rate?

A) 40

B) 75

C) 120

D) 150

The number of cupcakes a baker sells is directly proportional to the number of people that come into the bakery. The baker sells 180 cupcakes when 10 people come into the bakery. How many cupcakes will the baker sell when 40 people come into the bakery?

A) 1,800

B) 900

C) 720

D) 360

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Strategy (12 minutes)

SLIDE 29.1

Give the class 4 minutes to complete questions 12 and 13. Review the answers when time has elapsed.

SLIDE 29.2

12. The correct answer is B. The estimated scale factor from 4 hours to 10 hours is 10 4 = 2.5.

Scale Nikki’s earnings for 4 hours up by 2.5 to estimate her earnings for 10 hours of work.

30 · 2.5 = 75

Since 75 is an answer, choice B is the correct answer.

29.3

13. The correct answer is C. The estimated scale factor from 10 people to 40 people is 40 ÷ 10 = 4. Scale the known number of cupcakes up by multiplying by 4 and estimating.

180 · 4 ≈ 200 · 4 ≈ 800

Since 720 is the answer closest to 800, choice C is the correct answer.

SLIDE

29b

Curriculum for the Digital SAT®

Mini-Test

Complete the mini-test. When you have finished, double-check your work.

Percent of University Students Who Studied Abroad

A survey was given to college seniors at 30 diﬀerent universities around the country asking if they had studied abroad during their sophomore or junior year. The table above shows the results from 7 of the universities. The median percent of students who studied abroad for all 30 universities was 38.92%. What is the diﬀerence between the median percent of students who studied abroad for these 7 universities and the median for all 30 universities?

A) 0.08% B) 0.98% C) 1.35%

U.S. Major City Populations, 2010 to 2013 City Year 2010201120122013

Atlanta

367,423352,490477,386479,645

Chicago2,276,9082,539,2222,392,5163,164,093

Dallas 1,489,217 1,689,1551,561,2171,798,939

Los Angeles4,067,068 4,115,2754,636,7055,944,791

Miami 273,109412,909368,966481,228

New York 13,589,00111,891,2629,842,83513,938,337

The table above lists the population for six diﬀerent major cities in the United States from 2010 to 2013.

Of the following, which city’s ratio of its 2011 population to its 2012 population is closest to Dallas’s ratio of its 2011 population to its 2012 population?

A) Atlanta

B) Chicago

C) Los Angeles

D) New York

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Mini-Test (30 minutes)

SLIDE 34.1

Give the class 20 minutes to complete the mini-test. Review the answers at the end and emphasize the ratios and proportions questions.

SLIDE 34.2 CENTER AND SPREAD

1. The correct answer is B. List the percentages of students given in the table from least to greatest.

26.5%, 32.8%, 33.4%, 39.9%, 40.5%, 44.1%, 46.8%

The median is the number found in the middle of the list. In this case, the median percentage of the 7 universities is 39.9%.

Subtract the reported median of all universities from the median percentage of the 7 given universities to find the difference.

39.9 − 38.92 = 0.98

SLIDE 34.3 RATES, PROPORTIONS, AND UNITS

2. The correct answer is B. Dallas’s population ratio from 2011 to 2012 is 1,689,155 1,561,217 ≈ 1.08. Find the ratio of the 2011 and 2012 population from each city in the answer choices and convert to decimals.

Atlanta: 352,490 477,386 ≈ 0.74

Chicago: 2,539,222 2,392,516 ≈ 1.06

Los Angeles: 4,115,275 4,636,705 ≈ 0.89

New York: 11,891,262 9,842,835 ≈ 1.21

The closest to 1.08 is 1.06, Chicago.

Curriculum for the Digital SAT®

Mini-Test (30 minutes)

SLIDE 35.1 LINEAR FUNCTIONS

3. The correct answer is A The given function is in the form of w(d) = md + n. This is a linear function in slope-intercept form, and the coefficient of d represents the slope, or the rate of change. Because slope can be interpreted as the amount of change in the y variable for each change in the x variable, m can be interpreted as the amount of change in the ounces the kitten gains on each day during the period.

SLIDE 35.2 RATES, PROPORTIONS, AND UNITS

4. The correct answer is B. Since the measure of distance on Map X is approximately 4 15 of the measure of distance on Map Y, multiply 4 15 by 150 to find that the measure of distance on Map X is 40.

Since the measure of distance on Map Z is approximately 17 15 of the measure of distance on Map Y, multiply 17 15 by 150 to find that the

measure of distance on Map Z is 170.

Subtract the two values to find how many more units the measure of distance on Map Z is to Map X.

170 – 40 = 130

RAT i OS AND PROPORT i ONS

SLIDE 35.3 RATES, PROPORTIONS, AND UNITS

5. The correct answer is B. A total of 8 + 7 = 15 customers bought paperback textbooks, and 7 of them bought composition notebooks. The ratio is 7 15

SLIDE 35.4 NONLINEAR FUNCTIONS

6. The correct answer is A. Plug in −3 for x

Wrap-Up

Curriculum for the Digital SAT®

Complete the wrap-up. When you have finished, double-check your work.

Diet and Exercise Information for Men and Women Diet onlyDiet and exercise

14 22

4 17 21

The table above shows the number of men and women trying to lose weight through diet only or through diet and exercise. What fraction of the women are only dieting?

A) 4 43 B) 4 21 C) 1 3 D) 4 7

5 If 75 sheets of paper are stacked on top of each other, the stack will be approximately 1 3 4 inches tall. At this rate, which of the following is closest to the number of sheets of paper it would take to make a 12-inch-tall stack of paper?

A) 280

B) 325

C) 575

D) 900

Question 6 is an example of a student-produced response question.

Furlongs and miles are units of measure of distance. They are directly proportional such that 8 miles is equal to 64 furlongs. What distance, in furlongs, is equal to 3 miles?

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Wrap-Up (12 minutes)

SLIDE 38.1

Give the class 6 minutes to complete the wrap-up. Review the answers afterward.

SLIDE 38.2

4. The correct answer is B. The number of women dieting only is 4. The total number of women in the group is 21. The ratio of women only dieting to the total number of women is 4 21

SLIDE 38.3

5. The correct answer is A. Convert 1 3 4 to its decimal form, 3.25. The ratio of sheets of paper in the shorter stack is 75 3.25 . The ratio of sheets of paper in the 12-inch stack, x, can be found by solving the proportion 75 3.25 = 12 x

Cross multiply.

3.25x = 75(12)

Simplify.

3.25x = 900

Divide both sides by 3.25 and simplify.

x ≈ 276.92

The closest answer choice is 280.

SLIDE 38.4

6. The correct answer is 24. Since 8 miles is equal to 64 furlongs, the proportional relationship between miles to furlongs is M F = 1 8 , where M is the number of miles and F is the number of furlongs. Set M = 3.

3 F = 1 8

Cross multiply.

3 · 8 = 1 · F

Simplify. F = 24

38b

ENTRANCE

Ratios and proportions questions can be identified by these terms:

• proportion • rate

• ratio

... or by this feature:

• two related quantities being compared to each other

SOLVE, STRATEGIZE, OR SKIP

Step 1: Can I solve this quickly and easily?

1. Relate relevant quantities as ratios.

2. If the question’s answer choices have fractions, choose the one relating the specified quantities. The quantity coming after to or of in the question should go in the denominator.

3. If the question’s answer choices are whole numbers, set the unknown’s ratio equal to another ratio and solve the proportion.

4. If the question asks you to compare ratios, convert them to decimals.

If you solved the question …

Double-check your work to catch any mistakes. Did you …

• use values that aren’t relevant to the question?

• set up a proportion with mismatched numerators and denominators?

Curriculum for the Digital SAT®

Step 2: If not, can I apply a strategy?

Estimate: Look for opportunities to estimate, use number sense, and rule out answer choices that are unreasonable based on the numbers in the problem.

Factor Elimination: Find where the row and column of the data table mentioned in the question intersect, and eliminate choices whose numerators don’t divide that number.

Step 3: Otherwise, I should skip If the question is too tough to solve or strategize, skip it. Mark your best guess and move on.

If you used a strategy or skipped the question … Mark the problem so you can come back to it after you answer the remaining questions. On a second pass, double-check that you guessed an answer or try to solve the question.

Algebra and Geometry

CHAPTER 2

Linear Equations

This chapter will teach students how to solve a linear equation in one variable, both for the variable and for other linear expressions involving the variable. Specifically, students will learn how to simplify a linear equation, apply inverse operations to solve for a variable, and find the value of another linear expression from the solution of the equation.

Linear Equations

LINEAR EQUATIONS

CONTENT D i MENS i ONS

Linear equations, one variable Solve a linear equation in one variable, making strategic use of algebraic structure.

LEARN i NG TARGETS

1. Strategically use algebraic structure to solve a linear equation in one variable.

2. Implement the basic approach for linear equations questions.

3. Apply the Solve for the Expression and Working Backward strategies to linear equations questions.

SCORE D i FFERENT i AT i O N

Skip the Foundation segment if ...

Math above 480

Heart of Algebra above 8

Math above 460

Heart of Algebra above 8

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

Warm-Up

Complete the warm-up. When you have finished, double-check your work.

Questions 2 and 3 are examples of student-produced response questions.

Warm-Up (12 minutes)

Curriculum for the Digital SAT®

LINEAR EQUATIONS

SLIDE 14.1

Give the class 6 minutes to complete the warm-up. Review the answers briefly before beginning the lesson.

SLIDE 14.2

1. The correct answer is C. Divide both sides of the equation by 5 to find q q = 9

Plug in 9 for q into 10q – 4.

10(9) – 4 = 90 – 4 = 86

SLIDE 14.3

2. The correct answer is 25. Distribute to eliminate the parentheses.

4x – 60 – 5 – x = 10

Combine like terms.

3x – 65 = 10

Add 65 to both sides of the equation.

3x = 75

Divide both sides of the equation by 3. x = 25

SLIDE 14.4

3. The correct answer is 3. Multiply both sides of the equation by 27.

12x – x = 24 + 9

Combine like terms.

11x = 33

Divide both sides by 11. x = 3

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

Write an equation modeling the story described in class.

Equation: ______________________________________________

Solve the equation you just wrote for x

Review these examples of linear and nonlinear equations with your teacher.

Nonlinear Equations 2x + 5 = 6 3,000 – 2x = 6 + 4x Linear Equations

Foundation (12 minutes)

In this section, you will introduce students to the parts of a linear equation.

SLIDE 15.1

Who would like an all-expenses paid trip to Las Vegas?

Pick a volunteer student. They will be referred to as Hannah here.

Sorry, Hannah, you’re not really getting a trip, but we’re going to pretend you are for an example. That’s just as good, right? Let’s say Hannah goes to Vegas and starts out hot, winning like crazy. Not just doubling or tripling the money she started with, but some other multiple—by how much do we think Hannah multiplied the money she took to Vegas?

Wait for responses and decide on a multiple. We will assume it is 10 here and on the slides.

So Hannah is winning big and decides to make one more big bet before calling it quits. All good things must come to an end, and that includes Hannah’s luck—she loses. How much money do you think Hannah lost on the last bet?

Wait for responses and decide on an amount lost. We will assume it is $500 here and on the slides.

Hannah isn’t flat broke, though. How much money did she have left?

Wait for responses and decide on an amount left. We will assume it is $1,000 here and on the slides.

To recap, Hannah multiplied her money by 10, then lost $500 on her last bet and was left with a total of $1,000. How can we figure out how much money Hannah started with?

Add $500 back to $1,000 to get $1,500, or how much money she had before losing on her last bet, then divide $1,500 by 10 to get $150.

To figure out the original amount of money Hannah had, we needed to work backward through the story and “undo” each step. Does the order in which we undo the steps matter?

Yes. If we divided $1,000 by 10 we would get $100, then adding $500 would give us $600 instead. This would have been incorrect.

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Great. Let’s represent the story using an equation, but let’s say that we don’t know yet how much money Hannah started with. Call that amount x. Go ahead and write the equation in your workbook. You have 30 seconds.

What did your equation look like?

10x – 500 = 1,000

This is an example of a linear equation in one variable. The only variable, x, is to the first power. It isn’t in a radical, like a square root.

Let’s solve this equation. Following the order of operations, we would multiply x by 10 first and then subtract 500, fitting with the steps of our story.

When we solve such an equation, we work back through the story and undo each step in reverse order, just as we did when we figured out how much money Hannah started with. Take 30 seconds to solve your equation.

How did you solve?

Add 500 to both sides of the equation, then divide both sides by 10. Hannah’s starting amount was $150.

Every time you “undid” a step, you applied an inverse operation. Addition and subtraction are inverse operations of each other, just as multiplication and division undo each other. Applying the correct inverse operations in the correct reverse order (that is, against the order of operations) is the key to solving linear equations.

SLIDE 15.2

There are two examples of linear equations in your workbook. x to the first power is just written as x, without an exponent. To the right are two examples of nonlinear equations. Why is each not linear?

The first equation has a variable raised to the second power. The second equation takes the square root of a variable.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

Review the Order of Operations chart with your teacher.

Order of Operations Parentheses Exponents Multiply/Divide Add/Subtract

Review this example with your teacher. 2(5 + 1)2 – 10 = _______________

For each question, write the sequence of operations applied to x in the correct order, then write the sequence of inverse operations that would cancel those operations.

1. 2x + 4

Operations:

Inverse operations:

2. 3x – 6

Operations:

Inverse operations:

3. –2 + 10x

Operations:

Inverse operations:

4. 3 x + 5

Operations:

Inverse operations:

Operations:

Inverse operations: 6. 3(x – 4)

Operations:

Inverse operations: 7. 2 3 x + 5

Operations:

Inverse operations:

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Foundation (12 minutes)

In this section, you will review identifying operations and their inverses in linear expressions.

SLIDE 16.1

I’ve mentioned “the order of operations” several times. You can see it illustrated in the diagram in your workbook. The arrow shows the general order you should use to apply operations in an expression. For example, if you see a minus sign and a multiplication sign, you should multiply before doing the subtraction, even if the minus sign comes first in the expression.

Addition and subtraction are grouped together in the diagram since they have the same importance: take care of plus and minus signs one by one, working left to right. Multiplication and division are grouped together this way, too. However, exponents come before any of those four operations. If you see something that needs to be squared, handle that before adding, subtracting, multiplying, or dividing.

Parentheses are the most important. If you see anything grouped in parentheses, the operations inside come before anything else.

Look at the example. In the expression 2(5 + 1)2 – 10, what is the first calculation?

Parentheses: 5 + 1 = 6

Next we have 2(6)2 – 10. What’s the next calculation?

Exponents: 62 = 36

Now we have 2(36) – 10. What’s the next calculation?

Multiplication: 2(36) = 72

That gives us 72 – 10. What’s the last calculation?

Subtraction: 72 – 10 = 62

SLIDE 16.2

Look at question 1. What happens to x in that expression, and in what order?

It gets multiplied by 2, then 4 is added.

Next to Operations, write ×2 and then +4.

Inverse operations also follow PEMDAS, in reverse. SADMEP. What operations would undo the operations in question 1, and in what order?

Subtract 4. Then divide by 2.

In the Inverse operations blank, write –4 and then ÷2.

Next look at question 2. What happens to x in that expression, and in what order?

It gets multiplied by 3, then 6 is subtracted.

Next to Operations, write ×3 and –6. What operations would undo those, and in what order?

Add 6. Then divide by 3.

In the Inverse operations blank, write +6 and ÷3. Take 3 minutes to complete questions 3–7.

When 3 minutes are up, review the answers.

ANSWER KEY

SLIDE 16.3

3. Operations: ×10, –2

Inverse operations: +2, ÷10

4. Operations: ÷3, +5

Inverse operations: –5, ×3

SLIDE 16.4

5. Operations: –2, ÷ 4

It might seem that this goes against the order of operations, but the expression is equivalent to (x – 2) ÷ 4. It’s like every fraction has invisible parentheses around its numerator and denominator.

Inverse operations: ×4, +2

6. Operations: –4, ×3

Subtract first because of the parentheses.

Inverse operations: ÷3, +4

7. Operations: × 2 3 , +5

Inverse operations: –5, ÷ 2 3 or –5, × 3 2

To divide by a fraction, flip it to get its reciprocal, then multiply.

Curriculum for the Digital SAT®

Practice Set 1

Complete

Question

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Practice Set 1 (12 minutes)

SLIDE 19.1

Give the class 6 minutes to complete the practice set. Review the answers before moving to the next section.

SLIDE 19.2

1. The correct answer is D Multiply both sides of the equation by 7 5

75 57 �� ÷ �� p = 67 55 �� ÷ �� p = 42 25

SLIDE 19.3

2. The correct answer is B. Cross-multiply to eliminate the fractions.

4(w + 24) = 16w

Distribute.

4w + 96 = 16w

Subtract 4w from both sides of the equation.

96 = 12w

Divide both sides of the equation by 12. w = 8

Plug in 8 for w into the expression.

2 w = 8 2 = 4

SLIDE 19.4

3. The correct answer is 15. Distribute to eliminate the parentheses.

9x + 18 – 3 – 6x = 60

Combine like terms.

3x + 15 = 60

Subtract 15 from both sides of the equation.

3x = 45

Divide both sides of the equation by 3. x = 15

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

Approach

Linear equations questions can be identified by this feature:

• one equation with a single variable raised to the first power ... and the question asks for the value of a variable or expression

Review question 4 with your teacher. Circle and underline the parts of the question that identify it as a linear equations question. Do not solve the question.

ENTRANCE EXIT SOLVE, STRATEGIZE, OR SKIP

Question 4 is an example of a student-produced response question.

2(3x – 30) – (17 + 4x) = 11

What value of x satisfies the equation above?

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Approach (12 minutes)

In this section, you will illustrate how the Entrance step can help students identify linear equations questions on the SAT.

SLIDE 20.1

OK everyone, pencils ready. You have 1 minute to solve this equation:

SLIDE 20.2

3 42 53 1 32 xx xx �+ � = 10 x

Just kidding; believe it or not, I’m not some kind of monster. What about this equation makes it intimidating? I know, “everything.” But specifically, what are the parts of it that are troubling?

The radical, the exponents, the fractions. Guess what—when you have a linear equations question, you don’t have to worry about any of these things. They’re some of the nicer, easierto-solve equations that you’ll see. The best part is, if you get stuck on one, you can work backward from the answer choices to see which one is right. We’ll talk about that strategy later; right now we’re going to discuss identifying these questions.

The first step to answering any linear equations question is Entrance. During Entrance, you identify what kind of question you are being asked. Look for terms, features, or question patterns that are common to linear equations questions.

Like with most question types, the clue is in the name. A linear equations problem presents one equation. That equation uses one variable (but, like in question 4, it might use that same variable more than once). And that equation is linear, meaning the variable is to the first power.

SLIDE 20.3

Why is question 4 a linear equations question?

There is one equation. It has only one variable, x The variable does not have an exponent or appear in a radical or fraction denominator.

Underline the equation. Circle the variables. These are your identifiers. When a variable has no exponent, it’s understood to be to the first power. It has a 1 as its exponent; it’s just not written. If the variable has a 2 as its exponent, it’s to the second power. A 3 means to the third power, and so on. When a variable is in a radical, like a square root, or in the denominator of a fraction, it’s not to the first power.

Quick question before you try this on your own. Look at question 6. Does it have two equations? No. It has one equation and one expression.

Find the identifiers for questions 5 and 6.

Underline the equations and circle the variables. Entrance steps are supposed to be very fast, so I’ll give you 30 seconds.

Curriculum for the Digital SAT®

Review questions 5 and 6 on your own. Circle and underline the parts of the question that identify it as a linear equations question. Do not solve the problems.

Approach (12 minutes)

Curriculum for the Digital SAT®

LINEAR EQUATIONS

SLIDE 21.1

Give the class 30 seconds to circle and underline the identifying language in questions 5 and 6. Review the answers afterward.

5. You can identify this as a linear equations question because it has one equation with one variable, y, to the first power

6. You can identify this as a linear equations question because it has one equation with one variable, x, to the first power.

SLIDE 21.3

SLIDE 21.2

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

Approach

SOLVE, STRATEGIZE, OR SKIP

Step 1: Can I solve this quickly and easily?

1. Simplify the equation by distributing across any parentheses and combining any like terms.

2. Use inverse operations to isolate the variable.

3. If the question asks for the value of the variable, find the answer choice matching the value you found. If the question asks for the value of another expression, plug in the value of the variable.

Step 2: If not, can I apply a strategy?

Solve for the Expression: When the question asks for the value of an expression, compare the coefficient of the expression with the coefficient of the equation. Look for multiples, factors, or any other way you can connect the two and use that connection to solve for the expression.

Working Backward: Relate the answers to the question and the rules, plug in each answer, and eliminate conflicts.

Step 3: Otherwise, I should skip If the question is too tough to solve or strategize, skip it. Mark your best guess and move on.

Solve question 4 with your teacher.

Question 4 is an example of a student-produced response question.

2(3x – 30) – (17 + 4x) = 11 What value of x satisfies the equation above?

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Approach (12 minutes)

In this section, you will illustrate the steps to Solve, Strategize, or Skip for linear equations questions using the three questions from the Entrance step.

SLIDE 22.1

Once you know you have a linear equations question, the next step is choosing the best way to solve it. I mentioned earlier that we’d talk about working backward from the answer choices, but it’s actually quicker to just solve these questions when you can. Otherwise, you will either need to strategize or skip the question. We’ll talk later about techniques to use when you’re stumped.

SLIDE 22.2

Look at question 4. What should we do first?

Simplify the equation. Distribute the 2 and the negative to get rid of the parentheses.

How does this change the equation? It is now 6x – 60 – 17 – 4x = 11.

When we distributed the negative, it changed the sign of the terms in the parentheses. What should be the next step?

Combine like terms.

2x – 77 = 11

What’s our next step?

Isolate the variable using inverse operations. The opposite of –77 is +77, so begin by adding 77 to both sides of the equation.

2x = 88

Note: Students may try to divide by 2 first. Remind them that inverse operations are applied in reverse order. Addition/subtraction is before multiplication/division.

What is the final step?

Divide both sides of the equation by 2.

x = 44

Some linear equations questions ask you to do more than just isolate the variable. They want you to use that value to solve for a new expression. We can see this in question 6. So after isolating the variable, you need to make sure you answered the question being asked. What does question 4 ask you to find?

The value of x

Since the question is asking for the value of x and not some other expression, we’re done.

These same three steps apply any time you need to solve a linear equations question on the SAT.

Now that we’ve reviewed this method for question 4, solve questions 5 and 6 on your own.

22b

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Approach (12 minutes)

SLIDE 23.1

SLIDE 23.2

5. The correct answer is B. The equation does not need to be simplified. Use inverse operations to isolate the variable.

Multiply both sides of the equation by 5 4

Give the class 4 minutes to answer questions 5 and 6. Review the answers afterward. ( ) ( )

35 44 y = 15 16

SLIDE 23.3

6. The correct answer is C. The equation does not need to be simplified. Use inverse operations to isolate the variable.

Subtract 5 from both sides of the equation.

4x = 3

Divide both sides of the equation by 4. x = 3 4 Plug in 3 4 for x in the expression.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

Approach

If you solved the question …

Double-check your work to catch any mistakes. Did you …

• subtract from both sides of an equation when you should have added?

• stop at solving for the variable when the question asked for an expression?

If you used a strategy …

Mark the problem so you can come back to it after you answer the remaining questions. On the second pass, double-check that you used the strategy correctly or try to solve the question.

If you skipped the question …

Check that you guessed an answer and marked the question for review.

Work with your teacher to double-check the math on question 7. Identify and correct any errors made by the student who attempted to solve it.

Question 7 is an example of a student-produced response question.

If 4p = 28, what is the value of 5p + 6 ?

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Approach (12 minutes)

In this section, you will illustrate the Exit step for linear equations questions by double-checking an SAT item that has been solved incorrectly.

SLIDE 24.1

The final step is Exit. At this point, you need to wrap up the question and move on to the next one. If you solved the question, double-check your work. If you used a strategy or guessed at the answer, mark the question so that you can review it on a second pass.

SLIDE 24.2

Since we are focusing on the solve part of the Approach, we’re going to practice doublechecking your work. Look at question 7. A student has already attempted to answer this question. Take 2 minutes to double-check the work on this problem and identify any errors made by the student.

What error did the student make?

The student selected the value of p, but the problem is asking for the value 5p + 6.

The student probably got excited when they found the value of p and forgot to plug it back in. How should the student have answered this question?

The student should have substituted 7 for p into 5p + 6.

Simplify.

5(7) + 6 = 35 + 6 = 41

Always double-check what the question is asking for instead of assuming it wants the value of the variable. You can bet that the SAT is going to give you questions meant to catch you in this kind of mistake!

There is another error to look out for. Students often subtract when they need to add, or vice versa. Look at question 10 in practice set 2. You need to add 30 to both sides, but if you’re going too quickly, you might think, “I need to get rid of the –30.” So you get rid of it and then subtract 30 from the right side. Whoops! This error is listed as the first bullet point in the Exit procedure.

We’ve covered all three parts of the Approach for linear equations questions. Let’s apply what we’ve learned to a practice set.

Curriculum for the Digital SAT®

Practice Set 2

Complete

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Practice Set 2 (12 minutes)

SLIDE 25.1

Give the class 6 minutes to complete the practice set. Review the answers before moving to the next section.

SLIDE 25.2

8. The correct answer is C. Combine like terms to simplify the equation.

7n – 11 = 4 + 2n

Subtract 2n from both sides of the equation.

5n – 11 = 4

Add 11 to both sides of the equation.

5n = 15

Divide both sides by 5. n = 3

SLIDE 25.3

9. The correct answer is D Multiply both sides of the equation by x – 6.

x + 6 = 12(x – 6)

Distribute.

x + 6 = 12x – 72

Subtract x from both sides of the equation.

6 = 11x – 72

Add 72 to both sides of the equation.

78 = 11x

Divide both sides of the equation by 11.

x = 78 11

SLIDE 25.4

10. The correct answer is 9. Add 30 to both sides of the equation.

5x = 75

Divide both sides of the equation by 5. x = 15

Plug in 15 for x into the expression.

x – 6 = 15 – 6 = 9

25b

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

SOLVE

FOR THE EXPRESSION

When the SAT asks you to solve for an expression, manipulate the equation instead of solving for a variable to save time. Make one side of the equation match the expression.

1. Compare the coefficients in the equation and the expression.

2. Make the coefficients equal by multiplying or dividing both sides of the equation.

3. If necessary, make the expression appear in the equation by adding or subtracting.

Review question 11 with your teacher. Use the Solve for the Expression strategy to answer the question as a class.

Question 11 is an example of a student-produced response question.

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Strategy (12 minutes)

In this section, you will demonstrate the Solve for the Expression strategy using three SAT items.

SLIDE 26.1

I’m going to give you a strategy that makes your work easier and quicker—who doesn’t like that? We call this Solve for the Expression.

SLIDE 26.2

With question 11, how would we normally solve this?

Find the value of q, then find the value of 8q + 2.

That works, but it turns out we can skip a step. When we need to find the value of an expression, we don’t actually have to find the value of the variable. We don’t have to solve for q. Instead, we can just find the value of 8q + 2. In other words, we’ll Solve for the Expression.

How do we do that? We make one side of the equation match the expression.

Usually we want to isolate q, to get it all alone on one side of the equation. Next we’re going to give it some friends. It can get lonely being a variable.

The first step is to make the coefficients match. A coefficient is the number multiplied by a variable. For example, in question 11, the 8 in the expression is a coefficient. What is the coefficient in the equation?

The coefficient in the equation is 4.

How can we make it match the expression?

Multiply both sides of the equation by 2.

8q = 36

Does one side of the equation match yet? What do we need to do?

No. Add 2 to both sides.

8q + 2 = 38

We still don’t know what q is, but we do know that 8q + 2 is 38. That’s all the SAT is asking for, so that’s all the work we’ll do.

Questions 12 and 13 are just like this. Use the Solve for the Expression strategy to solve them on your own.

Note: This strategy may not work as well when the coefficient in the expression is not a factor or multiple of the coefficient in the equation. In this case, it may be faster to use the standard Solve procedure.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT:

Work on your own using the Solve for the Expression strategy to answer questions 12 and 13.

Question 13 is an example of a student-produced

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Strategy (12 minutes)

SLIDE 27.1

Give the class 4 minutes to complete questions 12 and 13. Review the answers when time has elapsed.

SLIDE 27.2

12. The correct answer is C. Before calculating the answer, compare the expression to the equation. 6y in the expression is 2 times the value of 3y in the equation.

Make the coefficients equal by multiplying both sides of the equation by 2.

6y + 10 = 14

The question asks for 6y + 2, not 6y + 10, so the left-hand side must be reduced by 8. Subtract 8 from both sides of the equation.

6y + 2 = 6

SLIDE 27.3

13. The correct answer is 11. Before calculating the answer, compare the expression to the equation. The coefficient in the equation is 3, while the coefficient in the expression is 1. Make the coefficients equal by dividing both sides of the equation by 3.

x – 4 = 11

27b

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

WORKING BACKWARD

When given a multiple-choice linear equations question, check which answer satisfies the equation.

1. Relate the answers to the question and the rules.

2. Plug in each answer.

3. Eliminate conflicts.

Review question 14 with your teacher. Use the Working Backward strategy to answer the question as a class.

In the equation above, what is the value of p ?

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Strategy (12 minutes)

In this section, you will demonstrate the Working Backward strategy using three SAT items.

28.1

Let’s say you have a multiple-choice linear equations question. It’s asking you for the value of z, and you’re having a brain freeze.

Here’s where Working Backward is the way to go. This strategy is especially good for questions where solving for the variable algebraically could take a long time. Let’s look at question 14.

SLIDE 28.2

With this strategy, we try out each answer choice until we find one that doesn’t break the equation.

What’s the first step?

Relate the answers to the question and the rules. What’s the relationship between the answers and the question?

They are all possible values for p

There aren't really any rules to worry about for this question, since p could be any kind of number. What's the next step?

Plug in each answer.

Since the answers are all possible values for p, we will substitute each choice in for p in the equation and see what works. When you use Working Backward, always start with answer choices that look easy to work with. This saves you time. Which choices look easier to you and why?

Choices A and C because they are not fractions.

Let’s test choice A. What happens when you plug in 4 for p?

The equation becomes 4(4) + 4 + 4 + 6 + 2 = 4 + 4 + 4 – 7.

Simplify both sides of this equation and see if it’s true.

32 ≠ 5

This is what we’ll call a conflict in the Working Backward strategy, so that brings us to the third step: eliminate conflicts. We know that choice A leads to a conflict, so get rid of it.

Let’s try choice C. What happens when you plug in –5 for p?

The equation becomes 4(–5) + (–5) + (–5) + 6 + 2 = (–5) + (–5) + (–5) – 7.

Simplify both sides of this equation and see if it’s true.

–22 = –22 is true, so choice C is the correct answer.

If choice C didn’t result in a true statement, what could you do next?

You could either continue to test answer choices, or, if you’re out of time, guess from the remaining two options.

The other two choices would be pretty ugly to work with, so you might be better off guessing instead of spending a lot of time messing with fractions. This question is worth the same as any other multiple choice question, so you don’t want to spend too much time on it.

In any case, it’s always better to guess from two answer choices instead of four!

Try the Working Backward strategy on your own on the next page. Watch out: question 16 is trickier than the others.

SLIDE

28b

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Strategy (12 minutes)

SLIDE 29.1

Give the class 4 minutes to complete questions 15 and 16. Review the answers when time has elapsed.

SLIDE 29.2

15. The correct answer is D. All of the choices are values for p. Since all the answer choices are fractions, start with a middle value. Based on the result, you will know if you need to test a larger or smaller number, which can save you time. Start with choice B, and plug it into the equation for p

( ( ) )

57 �� ÷�÷ �� = 7 3

Since there is one 5 in the numerator and denominator, they cancel.

73 =

Since the side with the variable is too small, you need to pick a larger choice. Try choice D, and plug it in for p

335

59 �� ÷�÷ �� = 7 3

SLIDE 29.3

16. The correct answer is B. All of the choices are values for 6 x Start with choice C, and assume 6 x is equal to 6. This means x is 36.

Plug 36 into the equation for x and simplify.

6 36 = 24 3630 + 1 6 = 24 66

Cross-multiply.

1 · 66 = 6 · 24

66 = 6 · 24

Since 66 is smaller than 6 · 24, eliminate choice C. Assume choice D is correct, since it’s the only other whole number option.

Since 6 x is 10, x must be 60.

Factor the 35 and cancel the 5s and a pair of 3s.

57 3

533 �� × ��÷ �÷ × �� = 7 3

( ( ( ( ) ) ) ) 5 · 7 3 · 3

33 =

This is a true statement, so choice D is the correct answer.

Plug 60 into the equation for x and simplify.

6 60 = + 24 6030

1 10 = 24 90

Cross-multiply.

1 · 90 = 24 · 10

90 = 240

This is not a true statement, so eliminate choice D. The correct answer must be either choice A or choice B. In this case, it is choice B.

This question highlights the importance of the first step in the Working Backward procedure. If you don’t relate the answers to the question, then you might make the mistake of plugging in the choices as values for x. The right way to do Working Backward was to figure out what x was based on the answer choices, then plug that into the equation.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

Mini-Test

Complete the mini-test. When you have finished, double-check your work.

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Mini-Test (30 minutes)

SLIDE 32.1

SLIDE 32.2 LINEAR EQUATIONS, ONE VARIABLE

1. The correct answer is B. Cross-multiply to eliminate the fractions.

6(y + 10) = 12y

Distribute.

SLIDE 32.4 LINEAR EQUATIONS, ONE VARIAB LE

3. The correct answer is A. Multiply both sides of the equation by 5 9 .

Give the class 20 minutes to complete the mini-test. Review the answers at the end and emphasize the linear equations questions. ( ( ) )

6y + 60 = 12y

Subtract 6y from both sides of the equation.

60 = 6y

Divide both sides of the equation by 6.

y = 10

Plug in 10 for y in the expression.

2 y = 10 2 = 5

SLIDE 32.3 EQUIVALENT EXPRESSIONS

2. The correct answer is D Expand the exponent so that the fraction has 1 in the numerator. This will make it easier to reduce the expression later on.

59 95

x = 45 99

x = 20 81

SLIDE 32.5 LINEAR EQUATIONS, ONE VARIA BLE

4. The correct answer is C. Because the question asks for the value of t, the goal is to isolate the variable in the equation. Multiply both sides of the equation by t – 2.

t + 2 = 6(t – 2)

Distribute.

t + 2 = 6t – 12

Subtract t from both sides of the equation.

2 = 5t – 12

(25) 1 4 25 = ( 1 4 25 )3

Convert the 1 4 25 into ( 1 2 25 ) 1 2 25 since 1 2 25 can be reduced to a whole number.

( 1 2 25 ) 1 2 25 )3

1 2 25 is equal to 25 , which is equal to 5.

Therefore, 1 2 25 can be replaced with 5. 3 1 2 5

( ) 3 3 5

= ( 55 )3

55 · 55 · 55 = 55

Add 12 to both sides of the equation.

14 = 5t

Divide both sides of the equation by 5.

t = 14 5

The amount of money a landscaper earns is directly proportional to the number of lawns the landscaper mows. The landscaper earns $96 on a day when he mows 6 lawns.

How much money will the landscaper earn if he mows 20 lawns in a week?

A) $720

B) $480

C) $320

D) $200

If m = 4 5 p and p = 25, what is the value of

m + 1 ?

61 B) 46 C) 20 D) 15

Curriculum for the Digital SAT®

SLIDE 33.1 RATES, PROPORTIONS, AND U NITS

5. The correct answer is C. Since the landscaper earns $96 when he mows 6 lawns, he earns $96

6 = $16 per lawn. If the landscaper mows 20 lawns, he will earn 20 · $16 = $320.

SLIDE 33.2 SYSTEMS OF EQUATIONS

6. The correct answer is A. Plug in 25 for p

m = 4 5 (25) = 20

Plug in 20 for m into the expression.

3(20) + 1

60 + 1

SLIDE 33.3 LINEAR EQUATIONS, ONE VARI ABLE

7. The correct answer is C. Subtract 1 from both sides of the equation.

3x = 2

Divide both sides of the equation by 3.

x = 2 3

Plug in 2 3 for x into the expression.

15 2 3 �� ÷ �� + 2

Mini-Test (30 minutes) ( ) x ( ) ( )

10 + 2

LINEAR EQUATIONS

SLIDE 33.4 LINEAR EQUATIONS, ONE VARIAB LE

8. The correct answer is C. Multiply both sides of the equation by 7 2

27 �� ÷ �� x = 77 112 �� ÷ �� x = 49 22

Curriculum for the Digital SAT®

Wrap-Up

Complete the wrap-up. When you have finished, double-check your work.

Questions 5 and 6 are examples of student-produced response questions.

Curriculum for the Digital SAT®

LINEAR EQUATIONS

Wrap-Up (12 minutes)

SLIDE 36.1

SLIDE 36.2

4. The correct answer is C. Subtract 8 from both sides of the equation.

6x = 5

Divide both sides of the equation by 6.

x = 5 6

Plug in 5 6 for x into the expression.

12 5 6 �� ÷ �� + 4

10 + 4 = 14

SLIDE 36.3

5. The correct answer is .257 or 9 35 . Multiply both sides of the equation by 3 7

SLIDE 36.4

6. The correct answer is 4 3 Distribute to eliminate the parentheses.

2p + 4 + 4p – 8 = 3p

Combine like terms.

6p – 4 = 3p

Give the class 6 minutes to complete the wrap-up. Review the answers afterward. ( ) ( ( ) q )

37 73 �� ÷ ��q = 33 57 �� ÷ ��

Simplify.

q = 9 35

Either 9 35 or its decimal equivalent, .257, are acceptable answers to input.

Subtract 6p from both sides of the equation.

–4 = –3p

Divide both sides of the equation by –3.

p = 4 3

36b

MASTERY FOR THE DIGITAL SAT: ALGEBRA AND GEOMETRY

MASTERY FOR THE D I G I TAL SAT: ALGEBRA AND GEOMETRY

Curriculum for the Digital SAT®

ENTRANCE

Linear equations questions can be identified by this feature:

• one equation with a single variable raised to the first power ... and the question asks for the value of a variable or expression

SOLVE, STRATEGIZE, OR SKIP

Step 1: Can I solve this quickly and easily?

1. Simplify the equation by distributing across any parentheses and combining any like terms.

2. Use inverse operations to isolate the variable.

If you solved the question … Double-check your work to catch any mistakes. Did you …

• subtract from both sides of an equation when you should have added?

• stop at solving for the variable when the question asked for an expression?

Step 2: If not, can I apply a strategy?

Working Backward: Relate the answers to the question and the rules, plug in each answer, and eliminate conflicts.

Step 3: Otherwise, I should skip If the question is too tough to solve or strategize, skip it. Mark your best guess and move on.

Digital SAT®

CHAPTER 2

Reading Closely

This chapter explains how to recognize reading closely questions on the SAT and introduces a brief, step-by-step process to eliminate incorrect answers. This chapter also demonstrates how to apply the Predict the Future strategy to answer reading closely questions.

Reading Closely

READING CLOSELY

ILLUSTRATING CLAIMS

CONTENT DIMENSIONS

Determining implicit meaning

The student will draw reasonable inferences and logical conclusions from text.

LEARNING TARGETS

1. Draw reasonable inferences and make logical conclusions from information and ideas explicitly stated in the text.

2. Implement the basic approach for reading closely questions.

3. Apply the Predict the Future strategy and utilize pacing key words to improve scanning techniques on reading closely questions.

SCORE DIFFERENTIATION

Skip the Foundation segment if ...

Reading and Writing above 500 No subscore

Reading and Writing above 480 No subscore

Curriculum for the Digital SAT®

Complete the warm-up. When you have finished, double-check your work.

e following text is adapted from Frances Hodgson Burnett’s e Secret Garden:

She had begun to wonder why she had never seemed to belong to anyone even when her father and mother had been alive. Other children seemed to belong to their fathers and mothers, but she had never seemed to really be anyone’s little girl. She had had servants, and food and clothes, but no one had taken any notice of her. She did not know that this was because she was a disagreeable child; but then, of course, she did not know she was disagreeable. She o en thought that other people were, but she did not know that she was so herself.

According to the text, what is true about the main character?

A) She believes she has always belonged to her parents.

B) She acknowledges her own disagreeable nature.

C) She feels she has never truly belonged to anyone.

D) She is aware that she is the reason for her loneliness.

In 1901, Guglielmo Marconi and his team worked tirelessly to achieve the rst transatlantic radio transmission. Due to the Earth’s curvature, standard radio signals could not travel long distances without losing strength and clarity. Marconi’s team had to nd a way to overcome this limitation in order to successfully send a wireless message across the Atlantic Ocean.

A er much research and experimentation, they discovered that using lower-frequency radio waves, which could be refracted by the Earth’s ionosphere, would allow the signal to travel the required distance. In December 1901, Marconi’s groundbreaking achievement was realized when his team successfully transmitted a radio signal from Cornwall, England, to Newfoundland, Canada, revolutionizing long-distance communication.

According to the text, why was a standard radio signal unable to travel long distances without losing strength and clarity?

A) Because of the Earth’s curvature and the limitations of standard radio signals

B) Because Marconi’s team used the wrong type of equipment for their initial experiments

C) Because the Earth’s ionosphere was not yet discovered at the time of Marconi’s research

D) Because radio signals were too weak to penetrate the Earth’s atmosphere during long-distance transmission

Curriculum for the Digital SAT®

READING CLOSELY

Warm-Up (16 minutes)

Give students 9 minutes to complete the warm-up. Review the answers briefly before beginning the lesson.

SLIDE 14.1

1. The correct answer is C. Choice A is incorrect because the text states that the main character feels she never really belonged to her parents, even when they were alive.

Choice B is incorrect because the text specifically states that the main character does not know she is disagreeable.

Choice D is incorrect because while the main character is lonely, she does not realize that her own disagreeableness is the cause of her loneliness.

Choice C is correct because the text directly states that the main character feels she has never truly belonged to anyone, not even her own parents.

14.2

2. The correct answer is A. Choice B is incorrect because the text does not mention any issues with the equipment Marconi’s team used in their initial experiments. The limitation in the standard radio signals was due to the Earth’s curvature, not the equipment used.

Choice C is incorrect because the text does not state or imply when the ionosphere was discovered; the text only states that Marconi’s team discovered how low-frequency radio waves could be refracted by the Earth’s ionosphere.

Choice D is incorrect because the text does not mention the strength of radio signals being unable to penetrate the Earth’s atmosphere. Instead, it discusses the Earth’s curvature as the main reason for the limitation with standard radio signals.

Choice A is correct because the text clearly states that standard radio signals could not travel long distances without losing strength and clarity due to the Earth’s curvature. This limitation was what Marconi’s team had to overcome in order to successfully send a wireless message across the Atlantic Ocean.

SLIDE

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: READING

Fill in the blank with a distinguishing detail for each suspect. Then draw a line to the related piece of evidence from the crime scene.

Suspect:

Professor Reginald Smythe

A distinguished and slightly eccentric professor of archaeology, Professor Smythe is known for his extensive knowledge of ancient civilizations and artifacts. He is never seen without his tweed jacket.

Miss Penelope “Penny” Featherstone

A quiet and unassuming librarian, Penny often goes unnoticed by those around her. Those who do know her admire her compassion for animals—she owns four cats—and are enamored by her gentle, genial spirit.

Madeline “Maddie” LaRue

A young and ambitious reporter, Maddie is known for her nervous energy and obsessive note-taking. Her keen intuition and dogged determination often lead her to uncover secrets others would prefer to keep hidden.

Distinguishing detail: Evidence:

After securing the crime scene, a dimly lit gallery in a local art museum, investigators collected a number of intriguing clues.

1. Under a bench they found a half-eaten chocolate bar.

2. On a nail protruding from the wall where the painting had been stolen, they discovered a small scrap of wool woven in a diagonal pattern.

3. Out of the trash can, they recovered a crumpled exhibition brochure. It included meticulous notes on many of the paintings— but curiously, notes on the stolen piece were conspicuously absent.

4. Near the entrance of the gallery, they found a small gold locket with an engraved letter “M” on the front.

5. On the corner of a painting frame, they found a smattering of two- to three-inch hairs.

Foundation (18 minutes)

Curriculum for the Digital

READING CLOSELY

In this section, students will practice identifying the core points and key phrases of a given detail.

Have you ever been in a car that was driving through the fog? How far ahead could you see?

Ask 1–2 students to share.

What about the fog makes it harder to drive? It’s hard to see the road ahead of you.

SLIDE 16.1

Answering reading closely questions can be a little bit like driving in the fog. It can be hard to see where you’re going, but keeping an eye out for key details can keep you on the right track. Let’s practice! Take a look at the first Foundation exercise in your book. What do you think our goal is here?

To look at the evidence. To solve the crime! We’ve got a painting heist on our hands, and it would be nice to find the guilty suspect! But for the purposes of our test, our goal is to practice recognizing how the same ideas can be communicated with different words. In the exercise, you’ll match that detail to another short statement. For starters, what’s the first suspect’s name?

Professor Reginald Smythe.

Read over the professor’s description. What visual detail stands out?

His tweed jacket.

Under Distinguishing detail, next to letter A, write tweed jacket. Move on to the next column, Evidence, and look for something that could incriminate a person who wears a tweed jacket. What is it?

Number 2. It mentions a small scrap of wool woven in a diagonal pattern

Draw a line from letter A in the center column to number 2 in the right-hand column. Next, look back to the left-hand column with the suspect’s names. Who’s the second one, and what’s her distinguishing detail?

“Penny” Featherstone. She owns a whole bunch of cats.

For letter B, write owns four cats. Which piece of evidence could link to the cats?

Two- to three-inch hairs sounds like cat hairs.

Draw a line from letter B to number 5 in the evidence column. One more distinguishing detail to find. What stands out about “Maddie” LaRue?

Her nervous energy and obsessive note-taking.

Do either of those line up with something from the evidence column? Which number?

Number 3 talks about a brochure that somebody wrote meticulous notes on

Write obsessive note-taking down for letter C and draw a line to number 3. Learning to align details that describe the same thing or communicate the same ideas with different words is really at the heart of reading closely questions. Certain details jump out of both questions and passages like clues. Connect the dots between them, and you’ve often found your answer!

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: READING

READING CLOSELY

Match each sentence from the sentence banks to its correct description. Write each sentence’s letter in the space provided.

1. Sentence Bank

A. Watching extreme sports can be relaxing for some.

B. Drag racing is the ultimate sleep aid.

C. The sound of roaring engines makes some people more productive.

Original Some people watch drag racing to fall asleep.

Extreme

Reversal I could never fall asleep watching extreme sports.

Sounds Good

Half-WrongI watch street luge to fall asleep.

2. Sentence Bank

A. Interpretive dance is certainly a creative approach to communicating with squirrels.

B. Ballroom dance has been used to communicate with squirrels effectively.

C. Trained animals have been used in some ballet performances.

D. Interpretive dance is the ultimate squirrel communication technique.

Original Interpretive dance is an effective way to communicate with squirrels.

Extreme

Reversal Interpretive dance isn’t an effective way to communicate with squirrels at all.

Sounds Good

Half-Wrong

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

Practice Set 1

Complete the practice set. When you have finished, double-check your work.

In 1928, physicist Paul Dirac developed a groundbreaking equation that combined quantum mechanics and special relativity to describe the behavior of subatomic particles. His equation led to the prediction of the existence of antimatter, speci cally the antielectron, or positron. e discovery of the positron in 1932 by Carl David Anderson con rmed Dirac’s prediction and revolutionized the understanding of particle physics, ultimately earning Dirac the Nobel Prize in Physics in 1933.

According to the text, why was Paul Dirac’s equation signi cant to the eld of physics?

A) e equation established the fundamental principles of quantum mechanics for the rst time.

B) e equation combined quantum mechanics and special relativity to predict the existence of antimatter, which was later con rmed.

C) e equation provided an explanation for the behavior of subatomic particles at extremely high speeds.

D) e equation demonstrated that antimatter and matter behave in an identical manner.

e following text is adapted from L. Frank Baum’s e Wonderful Wizard of Oz: e sun had baked the plowed land into a gray mass, with little cracks running through it. Even the grass was not green, for the sun had burned the tops of the long blades until they were the same gray color to be seen everywhere. Once the house had been painted, but the sun blistered the paint and the rains washed it away, and now the house was as dull and gray as everything else.

According to the text, what is the description of the setting?

A) e house appears to be well-maintained.

B) All the surrounding grass has died.

C) e ground is covered in large cracks.

D) e environment lacks color.

Curriculum for the Digital SAT®

READING CLOSELY

Practice Set 1 (16 minutes)

Give students 9 minutes to complete the practice set. Review the answers before moving to the next section.

SLIDE 19.1

1. The correct answer is B. Choice A is incorrect because the text does not state that Dirac’s equation established the fundamental principles of quantum mechanics for the first time

Choice C is incorrect because it does not mention the prediction of antimatter, which was a significant aspect of Dirac’s equation according to the text.

Choice D is incorrect because the text does not mention any comparison between the behavior of antimatter and matter.

Choice B is correct because it accurately reflects the text’s description of Dirac’s equation as significant for combining quantum mechanics and special relativity to predict the existence of antimatter, which was later confirmed through the discovery of the positron.

SLIDE 19.2

2. The correct answer is D. Choice A is incorrect because it states that the house appears to be well-maintained, but the text indicates that the paint has been blistered and washed away, making the house dull and gray.

Choice B is incorrect because it claims that all the surrounding grass has died. The text does not say the grass is dead but rather that the sun has burned the tops of the long blades, making them gray in color.

Choice C is incorrect because it states that the ground is covered in large cracks. The text mentions there are little cracks running through the gray mass of plowed land but does not say the ground is covered in large cracks.

Choice D is correct because it says the environment lacks color. The text describes various aspects of the setting as gray, dull, and colorless, such as the plowed land, the grass, and the house.

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

Approach

ENTRANCE

Reading closely questions can be identified by this feature:

• a question that asks for specific information from the passage ... or one of the following phrases:

• according to the text

• based on the text

Review question 4 with your teacher. Do not answer the question.

ENTRANCE EXIT EVIDENCE AND ELIMINATION

The following text is adapted from Charlotte Brontë’s 1847 novel Jane Eyre. Jane Eyre is describing her first impression of Mr. Rochester.

[Mr. Rochester] had a dark face, with stern features and a heavy brow; his eyes and gathered eyebrows looked ireful and thwarted just now; he was past youth, but had not reached middle-age; perhaps he might be thirty-five. I felt no fear of him, and but little shyness. Had he been a handsome, heroic-looking young gentleman, I should not have dared to stand thus questioning him against his will, and offering my services unasked.

According to the text, what is true about Jane’s impression of Mr. Rochester?

A) She is intimidated by his appearance and demeanor.

B) She finds his appearance approachable and feels comfortable around him.

C) She believes he is too old to be an attractive gentleman.

D) She is unsure of his intentions and remains cautious.

Curriculum for the Digital SAT®

READING CLOSELY

Approach (30 minutes)

In this section, students will practice identifying a reading closely question using a key word or phrase.

The first step to answering any Reading question is Entrance. During Entrance, you identify what kind of question you are being asked.

Have a student read the identifying characteristics of a reading closely question aloud.

Imagine we’re on a birdwatching expedition, and we want to identify a red-tailed hawk. What would we need to know?

We’d need to know what that hawk looks like. Things like size, color, wing shape, unusual markings.

You can spot a red-tailed hawk by—get ready for it—their distinctive russet-red tails. But what do we know if we see a bird that has some of the features of a red-tailed hawk, but it has a whitebanded tail instead of a red one?

Then it’s not a red-tailed hawk. It must be some other kind of bird.

We can use the same kind of reasoning to identify a reading closely question. This type of question will always have a defining characteristic. If you see one of the key words from your book in the question, it’s a giveaway, but do you think they’ll always appear?

Probably not.

They won’t always show up, but they often will— and it’s super helpful when they do. It’s important to identify reading closely questions because it changes how you approach them. Unlike other Reading question types, when you come across a reading closely question, you should dive into the passage and dig for evidence as quickly as possible.

Let’s practice using question 4. Who can read the question text only for us?

Select a student to read.

What clue do you see in the question that tells you it’s a reading closely question?

According to the text. It asks for specific details about Jane’s impression

Take a moment now to find the identifying language in questions 5 and 6 on your own. Don’t answer the questions just yet.

SLIDE 22.2

SLIDE 22.1

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

Approach

EVIDENCE AND ELIMINATION

To answer a reading closely question, follow these steps:

1. Identify the key words and phrases in the question.

2. Scan the passage for related key words.

3. Eliminate answer choices not supported by evidence from the passage.

Answer question 4 with your teacher.

ENTRANCE EXIT EVIDENCE AND ELIMINATION

The following text is adapted from Charlotte Brontë’s 1847 novel Jane Eyre. Jane Eyre is describing her first impression of Mr. Rochester.

According to the text, what is true about Jane’s impression of Mr. Rochester?

A) She is intimidated by his appearance and demeanor.

B) She finds his appearance approachable and feels comfortable around him.

C) She believes he is too old to be an attractive gentleman.

D) She is unsure of his intentions and remains cautious.

Curriculum for the Digital SAT®

READING CLOSELY

Approach (30 minutes)

In this section, students will practice applying the steps of Evidence and Elimination to a reading closely question.

SLIDE 24.1

Once you know you have a reading closely question on your hands, it’s time to start Evidence and Elimination. Our first step says we need to identify key words and phrases. What do you think a key word is?

A key word is a unique word or phrase that helps us determine the main focus or topic of the question.

Will key words always appear exactly the same in the question and passage?

No, sometimes the SAT will use synonyms.

Where would be the best place to find key words? In the question.

SLIDE 24.2

Do you see anything in question 4 that could be a key word or phrase?

Jane’s impression of Mr. Rochester

In this case, the characters’ names appear to be the most important. We need to know something about Mr. Rochester. And specifically, we need to find details about Jane’s impression of him. We’re dealing with a short passage, so you won’t need to do any in-depth skimming. Mr. Rochester’s name shows up right at the beginning. But where is Jane’s name?

It isn’t there. It says I instead.

We’re getting the description from Jane’s point of view. Since the passage is from Jane’s point of view, we need a phrase where we see I telling us something about her impression of Mr. Rochester. What in the passage could fit that?

I felt no fear of him, and but little shyness.

We’re told that Jane felt no fear when it came to Mr. Rochester. Can you eliminate any answers based on that?

Answer choice A.

If she wasn’t afraid of him, then she wouldn’t be intimidated by him either. We can eliminate answer choice A. What about the but little shyness part? If she wasn’t feeling shy, what does that let us eliminate? Choice D.

Why can we eliminate choice D? Choice D says that she remains cautious. But the quote says she wasn’t feeling shy, so she probably isn’t being cautious.

Choices A and D are out. Each one contradicts at least part of the sentence, I felt no fear of him, and but little shyness. That leaves us with answer choices B and C. Which one isn’t completely supported by the passage?

Choice C.

Why isn’t choice C supported by evidence? In the passage, Jane mentions how old she thinks Mr. Rochester is. But she doesn’t specifically say that she thinks his age makes him too old to be attractive.

What about choice B? Any evidence to support the idea that she finds him approachable and feels comfortable around him? Jane says that she felt no fear of him. She also goes on to say that she was comfortable questioning him against his will

Both of these details support choice B, so we know it’s our answer. Use this same process of Elimination to help you answer questions 5 and 6. Find the key words in each question. Then use them to make eliminations and identify the correct answer.

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

READING CLOSELY

Approach

Answer questions 5 and 6 on your own. Focus on eliminating incorrect answers.

In 1905, physicist Albert Einstein developed the special theory of relativity, a revolutionary concept that transformed the understanding of space and time in the realm of physics. This innovative theory introduced the idea that time is relative and can vary depending on the observer’s speed, challenging previous notions of absolute time. The famous equation E = mc², derived from the theory, demonstrates the equivalence of mass and energy. Einstein’s work forever changed the field of physics, laying the foundation for advancements in nuclear research and shaping modern scientific thought.

According to the text, what made Einstein’s special theory of relativity a pivotal development in the field of physics?

A) The theory provided the first evidence of the existence of black holes.

B) The theory established that time is influenced by the observer’s speed.

C) The theory disproved the fundamental principles of Newtonian physics.

D) The theory explained the behavior of subatomic particles in the presence of strong magnetic fields.

The following text is adapted from Herman Melville’s 1851 novel Moby Dick. The scene takes place on a Saturday night aboard the whaling ship Pequod, where the sailors are engaged in their work as harpooneers under the leadership of the mysterious Captain Ahab.

It was a Saturday night, and such a Sabbath as followed! Ex officio professors of Sabbath breaking are all whalemen. The ivory Pequod was turned into what seemed a shamble; every sailor a butcher. You would have thought we were offering up ten thousand red oxen to the sea gods [...] And now suspended in stages over the side, Starbuck and Stubb, the mates, armed with their long spades, began cutting a hole in the body for the insertion of the hook just above the nearest of the two side-fins.

Based on the text, what can be inferred about the atmosphere on the Pequod on this particular Saturday night?

A) The sailors are focused on their work, even though it is the Sabbath and traditionally a time for rest.

B) The sailors are enjoying a festive celebration, even though their profession is typically serious and dangerous.

C) The sailors are participating in a religious ceremony, even though their primary concern is their work on the ship.

D) The sailors are engaged in a competition, even though their main responsibility is to serve as harpooneers.

Curriculum for the Digital SAT®

Approach (30 minutes)

Give the class 6 minutes to answer questions 5 and 6. Review the answers afterward.

5. The correct answer is B. Using the Evidence and Elimination process, first identify key words and phrases in the question. Here, the key phrases are Einstein’s special theory of relativity and pivotal development in the field of physics

Next, scan the passage for related key words

The special theory of relativity shows up in the first sentence and is defined in the second sentence: This innovative theory introduced the idea that time is relative and can vary depending on the observer’s speed, challenging previous notions of absolute time

Then we eliminate answer choices not supported by evidence from the passage

Choice A is incorrect because the term is not one of our key words, and the concept does not appear in the passage.

Choice C is incorrect because although the passage mentions physics and this word aligns with one of our key words, nothing in the passage states that Einstein’s theory disproved the fundamental principles of Newtonian physics

Choice D is incorrect because neither subatomic particles nor magnetic fields relate to our key words, and the concepts do not appear in the passage.

Choice B is correct because the passage states that Einstein’s special theory of relativity—one of our key phrases—introduced the idea that time is relative and can vary depending upon the observer’s speed

READING CLOSELY

6. The correct answer is A. Using the Evidence and Elimination process, first identify key words and phrases in the question. Here, the key phrases are Saturday night and Sabbath Next, scan the passage for related key words In the passage, we see that it was a Saturday night and that the sailors were working as butchers on the ship, despite it being the Sabbath, a traditional day of rest.

Then we eliminate answer choices not supported by evidence from the passage Choice B is incorrect because a festive celebration does not fit with our key phrases, nor does anything in the passage suggest that the sailors were celebrating.

Choice C is incorrect because while one of our key phrases, Saturday night, could imply the Sabbath, there is no mention of a religious ceremony taking place.

Choice D is incorrect because a competition is unrelated to our key phrases, and nothing else in the passage fits with that.

Choice A is correct because the sailors are employed on the Sabbath as butchers, confirming their focus on work.

SLIDE 25.2

SLIDE 25.1

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

Approach

If you’ve found the answer … Check to make sure that the answer matches the details of the passage. Mark your answer and continue to the next question.

If you’re stuck between two choices … Break the remaining answer choices into pieces and compare them to find the essential difference. Test each piece against the passage for accuracy.

If you have no idea what the answer is … Go with your gut. Select the choice that is the most consistent with the context and sounds best.

Review questions 7 and 8. Work with your teacher to choose the correct answer from the remaining choices.

The following text is adapted from Jonathan Swift’s 1726 satirical novel Gulliver’s Travels. The narrator, Gulliver, has just woken up and discovered himself in a strange land with a giant figure observing him.

In the midst of the discourse, I was awakened by the noise of a great shout, and found it was day. The first object I beheld was the figure of a man having no resemblance in any manner to those I had seen before; he was only twice my length, but ten times as broad, lying on his side, and leaning his head against his hand, with his eyes fixed earnestly upon me. I returned his look with equal observation, and found my senses struck with admiration, observing every part of him full of strength and comeliness, and comparing him with the Lilliputians, whose smallness had rendered their beauties almost imperceptible to me.

Based on the text, how does Gulliver respond to the giant figure?

A) He is initially frightened by the figure’s size, even though he later finds the figure’s appearance admirable

B) He makes eye contact with the figure, even though the figure’s size is intimidating.

C) He expresses curiosity about the figure’s intentions, even though the figure seems to be observing him peacefully

D) He compares the figure to the Lilliputians, even though the figure’s size is the only apparent difference between them. ENTRANCE EXIT EVIDENCE AND ELIMINATION

Curriculum for the Digital SAT®

READING CLOSELY

Approach (30 minutes)

In this section, students will practice using a variety of Exit strategies for reading closely questions.

SLIDE 26.1

When you’ve found an answer to a reading closely question, take a moment to doublecheck your choice before moving on. Make sure it supports the whole claim. But what if you’re stuck between two choices? What should you do?

Break the remaining answer choices into pieces and compare them to find the essential difference. Test each piece against the passage for accuracy

Maybe neither option feels like it fully matches the claim. But one of them will offer more support than the other. The more support in the evidence, the more likely you’ve found the right answer.

SLIDE 26.2

For instance, take a peek at question 7. What is it asking?

How does Gulliver respond to the giant figure?

We’ve got answer choices B and D left as options. If we start by taking answer choice B and breaking it up into pieces, what ideas do we have?

Gulliver makes eye contact with the figure. The figure’s size is intimidating

Do you see evidence for the first part? Does it ever tell us that Gulliver makes eye contact with the figure?

Yes, it says the giant fixed his eyes on Gulliver and that Gulliver returned his look

Is there evidence the figure’s size is intimidating? Maybe. He’s really big, in any case.

We’ll keep choice B in mind as we test answer choice D. What do we get when we break choice D into pieces?

Gulliver compares the figure to the Lilliputians. The figure’s size is the only apparent difference between them.

Do both of those claims hold up?

He does compare the figure to the Lilliputians, who are smaller. But it’s not clear that’s the only difference. He says some of the Lilliputians’ qualities weren’t visible to him.

It can be tricky when parts of your last two answers seem to work. But if part of an answer is wrong, the whole thing is wrong. Which answer choice, B or D, has part that we can confidently say is unsupported?

Choice D. It’s not clear that the figure’s size is the only difference with the Lilliputians.

We can eliminate answer choice D. Earlier when we looked at that answer choice, we didn’t feel like we had slam dunk evidence to prove it was right. So where does the elimination of answer choice D leave us?

With choice B as the last answer left.

Sometimes questions will be like that. You may not love the correct answer, but as long as the other answers are worse, what can you still be confident of?

It’s the right answer.

In this case, that’s answer choice B.

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

Strategy

PREDICT THE FUTURE

When you’re struggling to find evidence, the Predict the Future strategy is an excellent way to guide you toward a correct answer.

1. Cover the answers.

2. Read the question and come up with your own answer.

3. Select the answer that best matches your prediction.

Review question 12 with your teacher. Use the Predict the Future strategy to answer the question as a class.

The following text is from John Keats’s 1819 poem “Ode to a Nightingale.”

Thou wast not born for death, immortal Bird! No hungry generations tramp thee down; The voice I hear this passing night was heard In ancient days by emperor and clown: Perhaps the self-same song that found a path

Through the sad heart of Ruth, when, sick for home,

She stood in tears amid the alien corn; The same that oft-times hath Charm’d magic casements, opening on the foam

Of perilous seas, in faery lands forlorn. Based on the text, what quality does the nightingale symbolize?

A) The fleeting nature of life and beauty

B) The transformation brought by the passage of time

C) The timeless and unchanging nature of beauty

D) The complexity of human emotions and relationships

Curriculum for the Digital SAT®

READING CLOSELY

Strategy (30 minutes)

In this section, students will practice using the Predict the Future strategy to answer a reading closely question.

SLIDE 30.1

It’s easy to get bogged down in the details of the passage when you’re working on a reading closely question. What are some reasons that might happen?

Ask 1–2 students to share.

One possibility is you can’t find a good key word in the question. When you can’t find any evidence to either support or eliminate your answers, you can use the Predict the Future strategy. Granted, this isn’t as good as finding real evidence in the passage, but it’s much better than just a random guess.

SLIDE 30.2

Let’s try it with question 12. What’s the first step to Predict the Future?

Cover the answers. Using your hand to cover the answers on the computer screen lets you focus more.

This not only lets you focus more on the question, but it also keeps you from wasting time overanalyzing your options in search of the perfect one. What’s our next step?

Read the question and come up with your own answer.

As you do this, try to keep it loose. Making the answer too specific causes at least a couple of problems. For one, it will just take you longer. What else could go wrong if you’re getting too specific?

It could be so specific that it sounds like one of the answer choices.

With all that in mind, what descriptive word gives us some information about this nightingale or bird? Immortal

The poet is making some kind of connection between this bird and immortality, which essentially means living life without having to worry about dying. Cover your answer choices and look back over the poem with that in mind. What quality could this nightingale symbolize? Something timeless or without end. Which answer choice fits with that? Choice C.

How does that one match with our general prediction?

It’s the only answer choice that mentions anything timeless or enduring.

Practice using the Predict the Future strategy to answer questions 13 and 14. It’s okay if your predicted answer is short and sweet. You’re not trying out to be an SAT test writer. The more general it is, the easier it will be to match it up with a choice.

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

Work on your own using the Predict the Future strategy to answer questions 13 and 14.

13

Nikola Tesla, a Serbian American inventor, played a pivotal role in developing alternating current (AC) electrical systems, foundational to modern AC power transmission. His inventive prowess wasn’t limited to electricity; he also ventured into early wireless communication concepts and imagined machines with a degree of automation. While not directly the father of robotics or computer science, his forward-thinking ideas hinted at these future fields. Tesla’s groundbreaking work undeniably shaped the trajectory of technological advancement, leaving an indelible mark on the world.

Which choice best describes Tesla’s impact on various fields, as presented in the text?

A) His influence extended only to electrical systems.

B) His work directly led to the development of modern telecommunications systems.

C) He explored early concepts of electricity, wireless communication, and automated machines.

D) He collaborated extensively with other inventors to develop new technologies.

The following text is adapted from Kate Chopin’s 1899 novel The Awakening Mrs. Pontellier was beginning to realize her position in the universe as a human being, and to recognize her relations as an individual to the world within and about her. This may seem like a ponderous weight of wisdom to descend upon the soul of a young woman of twenty-eight—perhaps more wisdom than the Holy Ghost is usually pleased to vouchsafe.

Based on the text, what is true about Mrs. Pontellier’s self-awareness?

A) She is hesitant to explore her thoughts and emotions.

B) She is overwhelmed by the sudden surge of introspection.

C) She is gaining a deeper understanding of her place in the world.

D) She is resentful of the wisdom being granted to her by the Holy Ghost.

Curriculum for the Digital SAT®

READING CLOSELY

Strategy (30 minutes)

Give the class 6 minutes to complete questions 13 and 14. Review the answers when time has elapsed.

13. The correct answer is C. Using the Predict the Future strategy, begin by reading the question and coming up with your own answer: Tesla’s impact includes developments in electricity, wireless communication, and automated machines.

Choice A is incorrect because it says his influence extended only to electrical systems. But we know from our answer that Tesla’s impact affected a variety of other kinds of technology, including wireless communication and automated machines.

Choice B is incorrect because it says his work directly led to the development of modern telecommunications systems, but that doesn’t particularly align well with our answer, which describes a variety of innovations. Additionally, while the passage says Tesla ventured into early wireless communication concepts, it does not go as far as choice B does.

Choice D is incorrect because it says he collaborated extensively with other inventors to develop new technologies, but our answer doesn’t reflect that kind of collaboration, and the text doesn’t mention any other inventors.

Choice C is the correct answer. It says he explored early concepts of electricity, wireless communication, and automated machines These three categories of innovation match with our answer.

14. The correct answer is C. Using the Predict the Future strategy, begin by reading the question and coming up with your own answer: Mrs. Pontellier is gaining a deeper understanding of her place in the world.

Choice A is incorrect because it says she is hesitant to explore her thoughts and emotions, but our answer doesn’t mention hesitation and neither does the text.

Choice B is incorrect because neither our answer nor the text implies that she’s overwhelmed; the passage states that she’s beginning to understand her position.

Choice D is incorrect because neither our answer nor the text mentions any resentment. Rather, the passage discusses her gaining wisdom and understanding.

Choice C is the correct answer. The text describes Mrs. Pontellier’s growing realization of her individuality and her relationship with the world. The passage clearly indicates her developing insight into her own existence and role, underscoring the idea that she is, indeed, gaining a deeper understanding of her place in the world.

SLIDE 31.2

SLIDE 31.1

MASTERY FOR THE DIGITAL SAT: READING

Curriculum for the Digital SAT®

Strategy

SCANNING FOR EVIDENCE

Answer reading closely questions more accurately and quickly by identifying the most relevant evidence in the passage.

1. Find the key word or short phrase in the question that seems to be the most important. Use the electronic highlighter to mark it.

2. In the passage, look for synonyms and concepts related to the words you highlighted.

3. Choose the answer that aligns with the meaning of the sentence that includes the key word.

Review question 15 with your teacher. Use the Scanning for Evidence strategy to answer the question as a class.

People can estimate the passage of time without the use of clocks or watches, relying on their internal sense of time. Many psychologists, including John Wearden, have explored this phenomenon. In various experiments, participants were tasked with judging durations based on their internal clocks, often without external cues. The findings generally indicate that participants can estimate time intervals with reasonable accuracy, although deviations can occur. This suggests that humans possess an innate ability to gauge time even without external reference points.

Based on the passage, how did the researchers determine the participants’ ability to estimate time in the studies?

A) They asked each participant to judge the passage of time without using any tools.

B) They examined how participants reacted to changes in the environment.

C) They studied the accuracy of participants pressing a button after a specific duration.

D) They tracked the participants’ physical movements during the experiment.

Curriculum for the Digital SAT®

READING CLOSELY

Strategy (30 minutes)

In this section, students will practice using the Scanning for Evidence strategy to evaluate answer choices while answering a reading closely question.

SLIDE 32.1

The passages for reading closely questions aren’t wildly long. Many of them are under a hundred words. What do we call our strategy that will help us sift through those hundred-or-so words to find the exact ones we need?

Scanning for Evidence

What’s our first step?

Find the word or short phrase in the question that seems to be the most important. Use the electronic highlighter to mark it

Let’s start with key words or phrases in the question. What do you see?

Estimate time.

The correct answer is almost certainly going to have something to do with estimating time. You can underline the phrase in your book. On the actual test, you’ll use a digital highlighter. Moving to step 2, what does it say?

In the passage, look for synonyms and concepts related to the words you highlighted

Let’s turn to our passage now. How close of a match can you find for estimate time?

The third sentence mentions judging durations. And the fourth sentence directly says estimate time

What does it say about how they were judging durations?

It says their judging of durations is based on their internal clocks.

And what does the fourth sentence say about estimating time?

It says a lot of people can do it with reasonable accuracy

Step 3 says to choose the answer that aligns with the meaning of the sentence that includes the key word. Does that apply to answer choice A? Yes, it fits with answer choice A.

Answer choice A says they asked each participant to judge the passage of time without using any tools. What idea have we mentioned that fits with that?

Judging durations based on their internal clocks

The fourth sentence has an exact match for our phrase, but how is the overall information in that sentence just a little different from what the question is asking?

The fourth sentence talks about the results of the experiment. The question is asking about how the research was conducted.

And the third sentence also describes the research. Even though judging durations isn’t a word-for-word match, do we have the evidence we need to feel confident in our answer?

Yes.

We can see the importance of step 2, look for synonyms and concepts, not just exact word matches. Estimating time means the same thing as judging durations. So, we have the evidence we need.

Use these tips to help you answer questions 16 and 17 on your own.

Curriculum for the Digital SAT®

MASTERY

FOR THE DIGITAL SAT: READING

Work on your own using the Scanning for Evidence strategy to answer questions 16 and 17.

Hopi-Tewa potter Nathan Begaye reimagines vessels of clay by intertwining both traditional Hopi and Navajo techniques. These methods incorporate Hopi coiling and Navajo corrugated patterns, creating textures that evoke the rich artistic traditions found in many Native communities. Moreover, Begaye integrates natural clay pigments, capturing the vibrant and earthy hues cherished in many Native art pieces. In this fusion, he not only challenges the distinctions between Hopi and Navajo cultures but also redefines pottery craftsmanship, blurring the lines between distinct tribal styles and techniques.

Which choice best describes Begaye’s approach to pottery, as presented in the text?

A) He combines techniques from both Hopi and Navajo pottery traditions to create his unique pieces.

B) He focuses solely on Hopi coiling methods while ignoring other pottery techniques.

C) He disregards the use of natural clay pigments and minerals in favor of synthetic materials.

D) He is equally influenced by Native American pottery and contemporary Western ceramics.

The following text is adapted from Upton Sinclair’s 1906 novel The Jungle Jurgis had come there, and thought he was going to make himself useful, and rise and become a skilled man; but he would soon find out his error—for nobody rose in Packingtown by doing good work. You could lay that down for a rule—if you met a man who was rising in Packingtown, you met a knave.

Based on the text, what is true about people who succeed in Packingtown?

A) They become successful through their dedication and hard work.

B) They struggle to find meaningful work but are ultimately rewarded.

C) They focus on their individual goals and ignore the needs of others.

D) They are likely using dishonest means to achieve their success.

Curriculum for the Digital SAT®

READING CLOSELY

Strategy (30 minutes)

Give the class 6 minutes to complete questions 16 and 17. Review the answers when time has elapsed.

SLIDE 33.1

16. The correct answer is A. Using the Scanning for Evidence strategy, begin by underlining the most important word or short phrase in the question. In this case, it’s Begaye’s approach to pottery

Next, look for synonyms and concepts related to the words you underlined in the passage. Examples include:

• reimagines vessels of clay

• incorporate Hopi coiling and Navajo corrugated patterns

• integrates natural clay pigments

• blurring the lines between distinct tribal styles

Choice B says that Begaye focuses solely on Hopi coiling methods, but we found evidence that Begaye also incorporates Navajo patterns, so this answer choice can be eliminated.

Choice C focuses on the idea that he disregards the use of natural clay pigments

This contradicts the passage, which states that he integrates natural clay pigments. It can also be eliminated.

Choice D focuses on his influence from Western ceramics, but as we found, the passage only focuses on his fusion of Hopi and Navajo techniques.

Choice A is correct because the text emphasizes that Begaye combines both Hopi and Navajo pottery techniques in his work, including the use of Hopi coiling and Navajo corrugated patterns, as well as the integration of natural clay pigments. This choice best captures Begaye’s approach to pottery, which involves blending elements from these two distinct Native American traditions to create unique, innovative pieces.

17. The correct answer is D. Using the Scanning for Evidence strategy, begin by underlining the most important word or short phrase in the question. In this case, it’s people who succeed in Packingtown

Next, scan the passage for synonyms and concepts related to the phrase you underlined in the question. For example, nobody rose in Packingtown by doing good work and if you met a man who was rising in Packingtown, you met a knave.

Choice A focuses on people becoming successful through their dedication and hard work. This contradicts the statement about how only knaves, or dishonest people, were able to rise in Packingtown, so it can be eliminated.

Choice B focuses on people ultimately being rewarded for their hard work, but this also contradicts the idea that only knaves were rising or seeing rewards. This choice can be eliminated.

Choice C focuses on those who are attentive to their individual goals and ignore the needs of others. The passage doesn’t mention how successful people in Packingtown interact with others, so it can be eliminated.

Choice D is correct because it focuses on the fact that people are likely using dishonest means to achieve their success. This answer aligns with the meaning of the sentence that includes the key word (knave) and is supported by the passage’s statement about nobody rising in Packingtown by doing good work.

SLIDE 33.2

Curriculum for the Digital SAT®

Wrap-Up

Complete the wrap-up. When you have finished, double-check your work.

e following text is from Jane Austen’s 1813 novel Pride and Prejudice. Elizabeth lives with her parents, Mr. and Mrs. Bennet, and her four sisters at Longbourn estate.

Elizabeth, feeling all the more than common awkwardness and anxiety of his situation, now forced herself to speak; and immediately, though not very uently, gave him to understand that her sentiments had undergone so material a change since the period to which he alluded, as to make her receive with gratitude and pleasure his present assurances. e happiness which this reply produced was such as he had probably never felt before; and he expressed himself on the occasion as sensibly and as warmly as a man violently in love can be supposed to do.

Based on the excerpt, what is true about Elizabeth?

A) Elizabeth is usually hesitant to express her emotions to others.

B) Elizabeth has always been open about her feelings toward the man in question.

C) Elizabeth believes the man’s happiness is super cial and temporary.

D) Elizabeth had experienced a signi cant change in her emotions. 5

According to the text, why are geologists intrigued by Crater Lake?

D) It provides a habitat for rare species of sh and plants. MASTERY

Oregon hosts Mount Mazama, a volcanic crater that now contains Crater Lake, the deepest lake in the United States. Formed approximately 7,700 years ago by the eruption and subsequent collapse of Mount Mazama, Crater Lake has a depth of 1,949 feet. Geologists are intrigued by the lake’s clarity and purity, as it is solely fed by rain and snowfall. ey believe that studying Crater Lake could provide valuable insights into the natural ltration processes of water.

A) It is unusually deep for a lake in the United States.

B) It was formed by a unique volcanic event that took place 7,700 years ago.

C) e water from rain and snowfall that lls the lake is exceptionally clear and pure.

Curriculum for the Digital SAT®

READING CLOSELY

Wrap-Up (16 minutes)

Give students 9 minutes to complete the wrap-up. Review the answers afterward.

4. The correct answer is D. Choice A is incorrect because the text does not provide enough information to support the idea that Elizabeth is generally hesitant to express her emotions to others. It only describes her awkwardness and anxiety in this specific situation.

Choice B is incorrect because the excerpt actually indicates the opposite. Elizabeth informs the man that her sentiments had undergone a significant change since the period he referred to. This suggests that her feelings toward him were not always as positive as they are at the moment of their conversation.

Choice C is incorrect because the text does not provide any information to suggest that Elizabeth believes the man’s happiness is superficial and temporary. Instead, it describes the man’s happiness in response to Elizabeth’s assurances.

Choice D is correct because the text clearly states that Elizabeth’s sentiments had undergone so material a change. This indicates that her emotions or feelings toward the man in question had significantly changed, leading her to receive his present assurances with gratitude and pleasure. The passage doesn’t indicate the nature of this change in sentiment, but it is clear that a substantial change has occurred.

5. The correct answer is C. Choice A is incorrect because although the text mentions that Crater Lake is the deepest lake in the United States, it doesn’t specifically state that geologists are intrigued by its depth.

Choice B is incorrect because while the text does explain that Crater Lake was formed by a unique volcanic event, it doesn’t state that this event is the reason geologists are interested in the lake.

Choice D is incorrect because the text does not mention anything about rare species of fish and plants being present in Crater Lake or being a reason for geologists’ interest.

Choice C is correct because the text specifically states that geologists are intrigued by the lake’s clarity and purity, as it is solely fed by rain and snowfall. This indicates that the exceptional clarity and purity of the water from rain and snowfall is the reason for their interest in Crater Lake.

SLIDE 36.1

SLIDE 36.2

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: READING

Review

ENTRANCE

Reading closely questions can be identified by this feature:

• a question that asks for specific information from the passage ... or one of the following phrases:

• according to the text

• based on the text

EVIDENCE AND ELIMINATION

To answer a reading closely question, follow these steps:

1. Identify the key words and phrases in the question.

2. Scan the passage for related key words.

3. Eliminate answer choices not supported by evidence from the passage.

EXIT

If you’ve found the answer ... Check to make sure that the answer matches the details of the passage. Mark your answer and continue to the next question.

If you’re stuck between two choices ... Break the remaining answer choices into pieces and compare them to find the essential difference. Test each piece against the passage for accuracy.

If you have no idea what the answer is ... Go with your gut. Select the choice that is the most consistent with the context and sounds best.

If you used a strategy or skipped a question ... Mark the question so you can come back to it after you answer the remaining questions. On a second pass, double-check that you guessed an answer or try to answer the question.

STRATEGY

Predict the Future

When you’re struggling to find evidence, the Predict the Future strategy is an excellent way to guide you toward a correct answer.

Scanning for Evidence

Answer reading closely questions more accurately and quickly by identifying the most relevant evidence in the passage.

Digital SAT® WRITING

Verbs

This chapter explains how to recognize verbs questions on the SAT and introduces a brief, stepby-step process to eliminate incorrect answers. This chapter also demonstrates how to apply the Tune Out and Sounds Wrong Is Wrong strategies to answer questions about verb tense and usage.

Curriculum for the Digital SAT®

CONTENT DIMENSIONS

Verb tense, mood, and voice

The student will recognize and correct inappropriate shifts in verb tense, voice, and mood within and between sentences.

LEARNING TARGETS

1. Identify verbs and their correct tenses.

2. Implement the basic approach for verb tense questions.

3. Identify time references when dealing with conflicting tenses.

SCORE DIFFERENTIATION

Skip the Foundation segment if ...

Reading and Writing above 500 No subscore

Reading and Writing above 480 No subscore

Curriculum for the Digital SAT®

Warm-Up

Complete the warm-up. When you have finished, double-check your work.

In the 1930s, a man named Wallace Carothers was struggling to nd a breakthrough in synthetic materials at DuPont when his colleague Julian Hill advised him to develop a new kind of ber from their experimental polymer, leading to the creation of a strong, elastic material. In addition, Hill ______ marketing the material for use in clothing and other industries under a memorable name: nylon.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) proposed

B) proposes

C) had proposed

D) was proposing

In the Large Hadron Collider, protons are accelerated close to the speed of light until they ______ a speci c energy level, at which point they are guided to collide with each other, enabling scientists to study the fundamental particles and forces of nature.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) will attain

B) attain

C) had attained

D) are attaining

e card game Uno, developed in 1971 by Merle Robbins in Ohio, is a variation of the classic card game Crazy Eights. In both games, players take turns to match cards with similar attributes, such as color or number, and using speci c cards like “Draw Two” or “Skip” cards _______ a player's chances of emptying their hand and winning the game.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) improves

B) are improving

C) have improved

D) improve

Curriculum for the Digital

Warm-Up (12 minutes)

Give students 6 minutes to complete the warm-up. Review the answers briefly before beginning the lesson.

SLIDE 14.1

1. The correct answer is A. Choice B is incorrect because proposes is in the present tense, while the rest of the passage is in the past tense.

Choice C is incorrect because had proposed is in the past perfect tense, which would indicate that the action happened before another past action, but there is no other action in the passage that would require this tense.

Choice D is incorrect because was proposing is in the past continuous tense, which would indicate that the action was ongoing, but there is no indication in the passage that the proposing was ongoing or continuous; it is more logical to assume that Hill proposed the idea once.

Choice A is correct because proposed is in the simple past tense, which is consistent with the tense used in the rest of the passage.

SLIDE 14.2

2. The correct answer is A. Choice B is incorrect because are improving is in the present continuous tense, which suggests an ongoing action. In this context, we need a verb form that shows the general effect of using specific cards, not an ongoing action.

Choice C is incorrect because have improved is in the present perfect tense, which is used to describe an action that began in the past and affects the present. In this context, we need a verb form that shows the general effect of using specific cards, not a past action that affects the present.

Choice D is incorrect because although improve is in the present tense, which is correct, it does not match the singular subject of the sentence, using

Choice A is correct because improves is in the simple present tense, which is appropriate for this context since the action of using specific cards has a general effect on a player’s chances of emptying their hand and winning the game. The verb improves correctly pairs with using to complete the sentence in Standard English.

14.3

3. The correct answer is B. Choice A is incorrect because will attain is in the future tense. In this context, a present tense verb is more suitable because it describes a general, ongoing action that occurs during the operation of the Large Hadron Collider.

Choice C is incorrect because had attained is in the past perfect tense. This tense is typically used to describe an action completed before another action in the past. Since the sentence describes a recurring, present action in the operation of the collider, the past perfect tense is not appropriate.

Choice D is incorrect because are attaining is in the present continuous tense. The action of attaining, or reaching, an energy level is something that happens at a single point in time, rather than an ongoing or continuing action. Once the protons attain the level, they can't keep attaining it over and over again. Thus, the simple present makes more sense than the present continuous tense here.

Choice B is correct because attain is in the simple present tense, which is appropriate for the context since the rest of the sentence is also in the present tense.

SLIDE

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: WRITING

Work with your teacher to ﬁll in chart number 1.

Subject Past Present Future I kangarooed kangaroo will kangaroo he/she/it kangarooed kangaroos will kangaroo they kangarooed kangaroo will kangaroo

1. Verb: learn

Subject Past Present Future I learned

he/she/it learns they will learn

Fill in chart number 2 with your favorite verb following the same model.

2. Write your favorite verb: ___________________________________________

Subject Past Present Future I he/she/it they

Foundation (26 minutes)

Curriculum for the Digital

In this section, students will complete the tables with verbs in different tenses.

SLIDE 15.1

Picture two animals side by side: a kangaroo and a snail. Which one would you associate with action?

The kangaroo.

Kangaroos jump, they kick, and they run. Snails, not so much. In that spirit, we've turned the word kangaroo into a verb. Why is that a little strange?

A kangaroo is an animal. It’s a noun, not a verb.

The word kangaroo isn’t actually a verb, but that's fine for this exercise because it makes the verb tense patterns clear. What do you notice about all the “kangaroo” verbs in the past tense? What do they have in common?

They all end with –ed

That –ed ending is super common on verbs that describe things that took place in the past. What about things that are going to happen in the future? What do all of our future kangaroo verbs have in common?

They all have the word will at the beginning. The word will is about as strong a clue as you can get that the verb tense is in the future. It’s describing something that’s going to happen. Looking to move ahead, which tense haven’t we talked about yet? Present.

Here, we’re dealing with things that are happening right now. What slight difference do you notice between the verb forms in that middle column?

Two of the examples are just the word kangaroo But if the subject is he, she, or it, then the verb has the letter s on the end.

With these patterns in mind, fill in table 1. Give students 1 minute to complete the task. Let’s look first at the past tense verbs. What did you put in the two blank spaces in that column? Learned.

It’s the same word that’s at the top of the column. Past tense verbs usually end with –ed, and that’s definitely true of learned. What about that middle column? Did you copy what’s in the middle row and put learns for both of those? No, those should be learn, not learns

Only with he, she, or it—the singular subjects— would we use learns. No s needed at the end for pairing with I and they. What about future tense? What did you put for that? Will learn both times.

That helping word will usually tells us we’re dealing with the future. Moving on to table 2, choose your favorite verb and complete it. Use the patterns we’ve learned but know there are exceptions.

Give students 3 minutes to complete the task. Take a look at the verbs you just used to fill out table 2. Does the pattern generally follow what came before in the tables above?

Yes.

On the other hand, not every verb forms its tenses in the exact same way. Does anyone have an example of that?

Ask 1–2 students to share.

Since we all have different responses for table 2, trade with a classmate to check answers. Raise your hand if you need my help.

Give students 2 minutes to complete this task. The bottom line is that verb tenses can seem complicated. But if you think in three big categories—past, present, and future—it will make your life a lot easier. Look for clues whether you're dealing with things that have already happened, are happening now, or are yet to happen in the future.

TABLE 1: ANSWER KEY

Subject Past Present Future

I learned learn will learn he/she/it learned learns will learn they learned learn will learn

Table 2: Answers will vary depending on the verb chosen by each student.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: WRITING

Circle the correct “clue” verb in each numbered sentence in the paragraph. Complete the paragraph by selecting the correct conjugation of the missing verbs.

(1) When I first began taking singing lessons at a studio near my house, I _______________ (was/is/will be) excited. I couldn’t wait to practice my scales, record short tracks, and basically become the next big pop star. The excitement of singing in a semi-professional environment, however, soon wore off. (2) The daily practice, which involved singing the same pieces over and over again, _______________ (became/becomes/will become) a chore, and all that late-night practicing annoyed a lot of my family members, and my cat. (3) After six months, I felt no closer to my dream of becoming a major recording artist than when I first _______________ (started/start/will start). Luckily, though, I was about to get my big break.

Foundation (26 minutes)

Curriculum for the Digital SAT®

In this section, students will identify “clue” verbs to determine the correct tenses in a paragraph.

SLIDE 16.1

When we talk about verb tense, we’re talking about the action described by the verb that is taking place. In broad strokes, we’re talking about past tense, present tense, and—what’s the other main category?

Future tense.

One key to finding the correct tense in a question is to get in the habit of spotting other verbs in the sentence and the paragraph. Why might this help?

The verbs we need for our answers are probably in the same tense.

If you can figure out the tense of the verbs you’re given, you won’t feel so, well, tense, when you’re trying to answer this kind of question. Sorry, I couldn’t help myself. Look in your book. Would someone please read sentence 1 aloud?

When I first began taking singing lessons at a studio near my house, I ______________ excited

What’s the first verb you see in that sentence? It will give us a clue about the tense we should pick.

Began.

Is began a past, present, or future tense verb? Past tense.

Look at the options for the missing verb that will go in the first blank. We have was/is/will be. The correct verb tense of the missing verb should match the tense of began, our “clue” verb. Which of our options is also a past tense verb? Was.

Write the verb was in the blank after number 1. Using these same steps, complete sentences 2 and 3 on your own.

Give students 1 minute to complete the exercise. Afterward, review the answers.

What is a “clue” verb in sentence 2? What is its tense?

Involved or annoyed. Past tense.

So, what is the missing past tense verb? Became.

What is the verb that gives us a clue in sentence 3? What is its tense? Felt. Past tense.

Based on that, what is our missing verb here? Started.

Look for “clue” verbs when you need to find the correct tense on SAT verb tense questions. Practice the skills we’ve covered in this section on the following practice set.

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: WRITING

Practice Set 1

Complete the practice set. When you have finished, double-check your work. 1

e Civil Rights Movement in the United States was driven by various organizations and activists who fought for racial equality. Among the prominent gures __________ Rosa Parks, a key participant in the Montgomery Bus Boycott.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) was

B) were C) are

D) have been

When writing her Pulitzer Prize-winning novel To Kill a Mockingbird (1960), author Harper Lee drew on her own childhood experiences growing up in the Deep South. e classic book was Lee's rst published novel, but her writing __________ recognized even before its publication. In 1956, she received a generous Christmas gi from friends to support her writing for a year, allowing her to complete the manuscript.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) were B) have been C) had been D) are

In his 1917 work Fountain, French-American artist Marcel Duchamp challenged the concept of art by presenting a signed urinal as a sculpture. Today, Duchamp __________ considered a pioneer of conceptual art.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) will be

B) had been C) was D) is

Curriculum for the Digital SAT®

Practice Set 1 (12 minutes)

Give students 6 minutes to complete the practice set. Review the answers before moving to the next section.

18.1

1. The correct answer is A. Choice B is incorrect because were is the plural past tense form of the verb to be. In this sentence, the word order is inverted. It can be rearranged to Rosa Parks was among the prominent figures. Then, it's clear that the subject is Rosa Parks, which requires the singular past tense verb was Thus, the verb should be in singular form, making were an inappropriate choice.

Choice C is incorrect because are is in the present tense. The sentence is discussing historical events and figures, specifically the Civil Rights Movement and Rosa Parks, which requires a past tense verb to indicate that these events and individuals were prominent in the past.

Choice D is incorrect because have been is in the present perfect tense. This tense is not appropriate here because the sentence is referring to a specific historical context, requiring a simple past tense verb to align with the time frame of the Civil Rights Movement.

Choice A is correct because was is the singular past tense form of the verb to be. It agrees with the singular subject Rosa Parks and is appropriate for discussing historical contexts, such as the Civil Rights Movement. In this sentence, was effectively links the singular noun Rosa Parks to the phrase among the prominent figures, indicating her inclusion in that group in the past.

SLIDE 18.2

2. The correct answer is D Choice A is incorrect because will be is in the future tense. The sentence is making a statement about Duchamp’s current reputation, not something that will happen in the future, so the future tense is not appropriate here.

Choice B is incorrect because had been is in the past perfect tense. It’s used to describe an action completed before another action in the past. In this context, we are discussing Duchamp’s present status in the art world, so a

verb in the present tense is needed.

Choice C is incorrect because was is in the past tense. Although Duchamp’s action of presenting the urinal as a sculpture occurred in the past, the sentence is describing his current reputation. Therefore, a present tense verb is required.

Choice D is correct because is is in the present tense. The sentence is discussing Duchamp’s current standing in the world of art. He is considered a pioneer of conceptual art now, as people continue to evaluate and appreciate his contributions to the art world. The use of the present tense is appropriate for indicating a present state or condition.

18.3

3. The correct answer is C. Choice A is incorrect because were is a plural past tense verb. The subject her writing is singular, so a singular verb form is needed for correct subject-verb agreement.

Choice B is incorrect because have been is a plural present perfect tense verb. The singular subject her writing requires a singular verb. Additionally, the sentence is discussing a past event, specifically the recognition of Lee's writing before the publication of her novel, so a past tense verb form would be more appropriate.

Choice D is incorrect because are is a present tense verb and it’s plural. The sentence is discussing past events and requires a singular verb to agree with the singular subject her writing

Choice C is correct because had been is in the past perfect continuous tense, which is used to describe an action that began in the past, continued for a period of time, and was completed in the past. It is singular, matching the singular subject her writing. In this context, it suggests that the recognition of Lee’s writing began before the publication of To Kill a Mockingbird and continued until the book was published.

SLIDE

Curriculum for the Digital SAT®

Verb questions can be identified by this feature: • variations of similar verbs in the answer choices

Review question 4 with your teacher. Do not answer the question.

A survey conducted by political scientist Robert Putnam in his book Bowling Alone: The Collapse and Revival of American Community found that the level of civic engagement in the United States, measured by participation in community organizations, experienced a decline, with parent-teacher associations witnessing a drop in membership of about 61% between 1965 and 1995, indicating that social ties among Americans __________ significantly weaker.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) becoming B) to become C) to have become D) had become

Curriculum for the Digital SAT®

Approach (24 minutes)

In this section, students will practice identifying a verbs question by considering the answer choices.

SLIDE 20.1

Finish the well-known phrase: “Lights, camera, ...”

Action.

Whether or not you’ve ever been on the set of a movie, you can spot action words in a question’s answer choices. Sometimes they have to do with physical action like running or jumping or flying. What do we call words that describe things like that?

Verbs.

And of course, not all verbs describe actions that are visible to us. What are some actions you could take that are invisible?

Ask 1–2 students to share. (Examples include verbs describing mental or emotional processes like think, believe, know, love, or want.)

There are also state-of-being verbs like the word is that more or less tell you that someone or something, well, exists. And a state-of-being verb can be connected to a descriptive word, like in the sentence She is tall. Why would we bother thinking through all these kinds of verbs?

We’ll need to be able to spot them to recognize verb questions.

If your answer choices are filled up with one verb or verb phrase after another, it’s gotta be a verb question. There are a couple of different kinds of verb questions the SAT may throw at you, but we can spare you those details for now. The bottom line: how do you know you’re dealing with a verb question?

You’ll see verbs for every answer choice.

Keep an eye out for the action words—or verbs of another kind—in the answer choices, and this step won’t trip you up!

Curriculum for the Digital SAT®

Review questions 5–8 on your own. Circle the two questions that test knowledge of verbs. 5

An economic analysis by economist Thomas Piketty in his book Capital in the Twenty-First Century revealed that the wealth inequality in the United States in 2010, measured by the share of total income going to the top 1% of earners, __________ 1.6 times greater than the level of inequality observed in 1980.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) being B) was C) to have been D) will be

The internet has made communication faster and more accessible than ever before. ____________, it has also led to concerns about privacy and security in the digital age.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) However B) For instance C) Consequently D) In the same vein

Photography was originally a laborious process, requiring hours of exposure and careful handling of chemicals. ____________, early photographers had to be both skilled artists and chemists.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) Therefore B) Conversely C) Similarly D) On the contrary

The Women’s Suffrage Movement in the United States saw the emergence of many influential women leaders, advocating for women’s right to vote. Among these leaders __________ Susan B. Anthony, cofounder of the National Woman Suffrage Association.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) was B) were C) are D) have been

MASTERY FOR THE DIGITAL SAT: WRITING

Curriculum for the Digital SAT®

VERBS

Approach (24 minutes)

Give the class 1 minute to circle the identifying language in questions 5–8. Review the answers afterward.

SLIDE 21.1

5. Question 5 is a verbs question. Each answer choice offers a different tense for the verb to be

SLIDE 21.2

6. Question 6 is not a verbs question. The question instead tests transitional words and phrases.

SLIDE 21.3

7. Question 7 is not a verbs question. The question instead tests transitional words and phrases.

SLIDE 21.4

8. Question 8 is a verbs question. Each answer choice offers a different tense for the verb to be

Curriculum for the Digital

Approach (24 minutes)

In this section, students will practice applying the steps in Elimination to a verbs question.

22.1

Verbs questions can be a little puzzling because there are two different kinds you can run into. But our Elimination step will help us cut right through the fog. What does our first step say?

Determine what kinds of verbs appear in the answer choices.

What kind of verbs might we find? Steps 2 and 3 will help us to see what we’re looking for. We’re talking about answer choices that fall into two different buckets. What are you going to see with the first kind of answer choices?

Different verb tenses.

And the second kind?

They have singular and plural verbs

Our answer choices should point us in one of two directions. Look in your book at question 4. Specifically, look over the answer choices. Which of the two kinds of verbs questions do we have here?

Different verb tenses.

How do you know they’re different tenses? They all have to do with the same verb, to become. But some have to do with different times, like the present and the past.

Look at our second Elimination step. It begins with: If you’re dealing with different verb tenses. We’ve decided that’s what we’re dealing with, so what does step 2 say we should we do next?

Eliminate answers that don’t reflect the tense of other verbs in the sentence.

We’re dealing with a long sentence here. Wind your way through it looking for the verbs that are already there. What do you see?

Conducted. Found. Measured. Experienced. Witnessing. Indicating.

We want to know, at least in a basic sense, what tense those verbs are. One way to think about that is to ask: do the actions that most of them describe take place in the past, the present, or the future?

They’re mostly in the past.

Other than witnessing and indicating, they’re all past tense verbs. Knowing that, what do we need to do next?

Eliminate answer choices that aren’t in the past tense.

Choice A is becoming. What should we do with that choice?

It isn’t in the past, so we can eliminate it.

Choice A is out. What about choice B? What does it say, and what should we do with it?

It says to become. That doesn’t sound like it’s describing something in the past, so we can eliminate it too.

We’ve eliminated choices A and B. That leaves us with choice C, to have become, and choice D, had become. Which of those two answer choices most clearly describes something happening in the past?

Choice D, had become

Choice C might be tempting because it describes something that takes place partly in the past. But the kind of action it describes continues up to the present, or at least happened very recently. Why does choice D seem to line up better with the other verbs in the sentence?

It’s totally in the past.

Let’s make sure to check it. If you plug choice D, had become, into the sentence, does it make sense when you read it?

It sounds good.

Choice D is correct. When you run into a verbs question on your test, ask: are the answer choices offering up different verb tenses? If they are, checking the tense of the other verbs in the sentence can give you a big clue to the answer.

SLIDE

Curriculum for the Digital SAT®

Approach

Answer questions 5 and 8 on your own. Focus on eliminating incorrect answers.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) being B) was C) to have been D) will be

Photography was originally a laborious process, requiring hours of exposure and careful handling of chemicals. ____________, early photographers had to be both skilled artists and chemists.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) Therefore B) Conversely C) Similarly D) On the contrary

The internet has made communication faster and more accessible than ever before. ____________, it has also led to concerns about privacy and security in the digital age

Which choice completes the text so that it conforms to the conventions of Standard English?

A) However B) For instance C) Consequently D) In the same vein

Which choice completes the text so that it conforms to the conventions of Standard English?

A) was B) were C) are D) have been

MASTERY FOR THE DIGITAL SAT: WRITING

Curriculum for the Digital SAT®

Approach (24 minutes)

Give the class 4 minutes to answer questions 5 and 8. Review the answers afterward.

SLIDE 23.1

5. The correct answer is B. First, we determine whether the answer choices present different verb tenses or whether they alternate singular and plural verbs. Since the answer choices are being, was, to have been, and will be, they offer different verb tenses.

Our next step is to eliminate answers that don’t reflect the tense of other verbs in the sentence. Since the verbs in the sentence are revealed and measured, we need to eliminate answers that are not in the past tense.

Choice A is incorrect and can be eliminated because being is not in the past tense. It’s a present participle, and it does not provide a clear or complete thought in this context.

Choice C is incorrect and can be eliminated because to have been is not in the past tense. It’s in the present perfect tense and does not provide a clear or complete thought in this context.

Choice D is incorrect and can be eliminated because will be is in the future tense, not the past tense. In addition, the sentence is discussing a comparison of wealth inequality levels between two specific years in the past (1980 and 2010). Using the future tense is not appropriate for this context.

Choice B is correct because was completes the sentence by providing a simple past tense verb that aligns with the time frame being discussed. It creates a clear and concise statement that the level of wealth inequality in 2010 was 1.6 times greater than that in 1980. The sentence is discussing a completed action in the past, so the simple past tense is the appropriate choice.

8. The correct answer is A. First, we determine whether the answer choices present different verb tenses or whether they alternate singular and plural verbs. Although not all answer choices are in the same tense, the first two answers, was and were, are both in the past tense. Because of that, we’re looking at singular and plural verbs.

Our next step is to eliminate answers that don’t agree with the subject.

Choice B is incorrect and can be eliminated because, while Susan B. Anthony is one person and therefore singular, were is a plural verb.

Choice C is incorrect and can be eliminated because are is a plural verb.

Choice D is incorrect and can be eliminated because have been is a plural verb.

Choice A is correct because was is a singular verb that fits grammatically with Susan B. Anthony

SLIDE 23.2

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT:

Approach

If you’ve found the answer ...

Plug it into the sentence and confirm that it sounds right. Mark your answer and continue to the next question.

If you’re stuck between two choices ...

Go with your gut. Select the choice that is most consistent with the context and sounds best.

If you have no idea what the answer is ...

Watch out for doubles in your answer choices. Look for the choice that stands out from the rest.

• If you see more than one answer with the same helping verb, you can likely eliminate both.

• If you see two past tense options and one present tense, choose the present tense one.

• If you see two singular options and one plural option, pick the plural one.

Review questions 9 and 10. Work with your teacher to choose the correct answer from the remaining choices.

Similar to other Arctic insects, the Arctic woolly bear caterpillar (Gynaephora groenlandica) cannot produce its own heat in the extreme cold; therefore, during the freezing winter months, it __________ by producing natural antifreeze called a cryoprotectant in its body, which prevents its cells from freezing and rupturing.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) had adapted

B) adapted

C) would adapt D) adapts

American inventor Richard James developed a well-known playful novelty item. In the 1940s, he invented the Slinky, which __________ of a traditional metallic spring.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) were a flexible, walking version

B) are flexible, walking versions

C) were flexible, walking versions

D) is a flexible, walking version

Curriculum for the Digital SAT®

Approach (24 minutes)

In this section, students will practice answering verbs questions using various Exit strategies, depending on how many answers they are initially able to eliminate before becoming stuck.

SLIDE 24.1

When you’ve found an answer to a verbs question, take a moment to double-check your choice before you move on. Plug the answer into the sentence and confirm that it sounds right. But what if you can’t narrow your options down to one answer choice? What should you do if you get stuck between two options?

Go with your gut. Select the choice that is most consistent with the context and sounds best

You might not have known there’s a direct connection between your ear and your gut. Okay, you might not want to put that on a biology test. But with verbs questions, it’s okay to let your ear and your gut be your guide.

SLIDE 24.2

For instance, take a look at question 9. What’s the subject of this long, winding sentence?

The Arctic woolly bear caterpillar.

I wonder if it turns into an Arctic woolly bear butterfly. Well, that’s beside the point. We can see that choices A and B have been eliminated— looks like that was because they’re both past tense. We’re down to options C and D. Try plugging each one in and reading the sentence to yourself. Which one passes the gut test?

Choice D.

Choice C would have us say that during the freezing winter months this caterpillar would adapt. That almost makes it sound like it stopped adapting at some point along the way. But choice D just says it adapts. That describes a process that it continues to do, which only makes sense with natural behavior. Are you feeling confident about choice D?

Yes.

Choice D is correct. Down to those two possibilities, just plugging the remaining answers in and going with our gut led to the right answer. Take a look at question 10. What’s the difference between the two answer choices that are left?

One says are flexible. The other says is a flexible

The sentence is talking about the toy called the Slinky. Does it sound right to say that a Slinky is a flexible, walking version or that a Slinky are flexible, walking versions? Go with your gut.

The first one sounds right: A Slinky is a flexible, walking version

And which choice does that make correct? Choice D.

Once again, choice D is correct. When it comes to this kind of question, the convenient thing is that we use words every day. Even just talking, without knowing it, we’re practicing using verbs correctly. So, any time you get stuck after a couple of answer eliminations, try the ear-andgut check. Usually, the answer that sounds right really is!

24b

Curriculum for the Digital SAT®

MASTERY FOR THE DIGITAL SAT: WRITING

Practice Set 2

Complete the practice set. When you have finished, double-check your work.

Electrons in a cathode ray tube, a component used in older television sets, are accelerated by electric elds until they __________ a desired velocity, at which point they are directed to strike a phosphorescent screen, creating an image.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) will achieve

B) achieve

C) had achieved

D) are achieving

Established in 1945 to promote international cooperation and maintain peace and security, the United Nations initially consisted of 51 member countries. By 1980, the organization __________ its original membership.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) has tripled

B) had tripled

C) triples

D) will triple

In his renowned series of water lily paintings from the late 1800s and early 1900s, French Impressionist painter Claude Monet sought to depict the ethereal quality of his own garden in Giverny, employing dappled brushstrokes and vivid colors to render the water’s surface and the oating vegetation. Interestingly, the iconic water lilies themselves __________ the central focus in many of these works.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) are

B) have been

C) were

D) is

Curriculum for the Digital SAT®

Practice Set 2 (12 minutes)

Give students 6 minutes to complete the practice set. Review the answers before moving to the next section.

SLIDE 25.1

11. The correct answer is B. Choice A is incorrect because will achieve is in the future tense. In this sentence, a present tense verb is needed to indicate an action that occurs whenever electrons are accelerated by electric fields in the context of a cathode ray tube’s operation.

Choice C is incorrect because had achieved is in the past perfect tense. This tense is used to describe an action that was completed before another past action. However, the sentence describes a process that happens in general terms whenever a cathode ray tube is in operation, so a simple present tense verb is appropriate.

Choice D is incorrect because are achieving is in the present continuous tense. It suggests an ongoing process, but in this context, the simple present tense is more appropriate to describe a general fact related to the functioning of a cathode ray tube.

Choice B is correct because achieve is in the simple present tense. This choice is appropriate because it describes an action that occurs once in the operation of a cathode ray tube. Electrons are accelerated until they achieve a desired velocity as a regular part of the device’s operation, making the simple present tense the correct option.

SLIDE 25.2

12. The correct answer is B. Choice A is incorrect because has tripled is in the present perfect tense, which is used to describe actions that have been completed at an unspecified time in the past. However, the text is referring to a specific time period by 1980, so the present perfect tense is not appropriate.

Choice C is incorrect because triples is in the simple present tense, which is used to describe habitual or general actions. However, the text is referring to a specific event that happened in the past, so the simple present tense is not appropriate.

Choice D is incorrect because will triple is in the future tense, which is used to describe actions that will take place after the present moment. However, the text is referring to a past event, so the future tense is not appropriate.

Choice B is correct because had tripled is in the past perfect tense, which is used to describe actions that were completed before another past action or event. In this case, the United Nations tripled its membership by 1980 after its establishment in 1945, so the past perfect tense is the most appropriate choice.

25.3

13. The correct answer is A. Choice B is incorrect because have been is in the present perfect tense, suggesting a condition or state that originated in the past and is still relevant or continuing into the present. While it’s technically correct to refer to the paintings in the present perfect since they still exist and are observed today, the use of present simple can be more straightforward and customary in discussing the content or thematic elements of artwork.

Choice C is incorrect because were is in the past tense. While it might seem appropriate given that the paintings were made in the past, discussing the thematic and content elements of artworks, especially those that continue to be viewed and studied, is often done in the present tense.

Choice D is incorrect because is doesn’t agree in number with the plural subject water lilies We need a plural verb to match the plural subject for correct subject-verb agreement.

Choice A is correct because are is in the present tense and agrees with the plural subject water lilies. When discussing the content, themes, or elements within artworks, it is conventional to use the present tense, as these aspects of the art continue to be observed and interpreted in the present every time the works are viewed.

25b

SLIDE

Strategy (28 minutes)

Curriculum for the Digital SAT®

In this section, students will practice using the Tune Out strategy to answer a verbs question.

SLIDE 26.1

These verbs questions from the SAT can feel like they’re scrambling your brain. The answer choices usually have only small differences and sound a lot alike. Fortunately, we’ve got a strategy that “cuts to the chase,” so to speak. It will help you focus on just the parts of the question you really need. What’s this strategy called?

Tune Out

The bottom line is that we want to tune out all the words that come between the subject and the verb. That’s the first step of our strategy. Why do you think we’d want to do that?

It will make it clearer which verb fits with the subject.

Let’s practice using question 14. What’s the subject of the sentence?

Waiting for Godot.

That’s kind of an unusual subject. What is Waiting for Godot?

It’s the name of a play.

Since our verb is going to go in the blank, what do we need to cross out or tune out?

The phrase between the commas, a tragicomedy originally written in French.

Keep in mind that when you’re actually taking the SAT, you’ll be on a computer. On a screen, you won’t be able to cross words out the way you can in your book. What do you think you might have available that you could write on?

Scratch paper?

You’ll have scratch paper, so one option would be to jot down the words that remain after you “tune out” the phrase we don’t need. If you did that, what might you write down?

Waiting for Godot (blank) scholars’ understanding What does step 2 of our strategy say to do?

Plug each answer into the underlined portion. What do you get when you plug choice A in?

Waiting for Godot has expanded scholars’ understanding

How does that sound?

Pretty good.

Plug in each of the other three answer choices. See how those sound.

Give students 1 minute to complete the task. Did any of those other answer choices sound good?

No, they sounded weird.

Step 3 for our strategy says Eliminate answers that don’t agree with the subject. Did choices B, C, and D sound wrong enough that you’d be confident to eliminate them?

Yes.

And you’re feeling good about choice A as the correct answer?

Totally.

Choice A is the correct answer. It’s the only answer that is a singular verb—meaning it fits with one single play—and it’s also the right verb tense. Yet we arrived at the answer without focusing too much on those details. By tuning out the words we didn’t need, it became clear which verb fit with our subject.

Strategy (28 minutes)

Curriculum for the Digital

Give students 4 minutes to complete questions 15 and 16. Review the answers afterward.

SLIDE 27.1

15. The correct answer is B. Using the Tune Out strategy, cross out all the words in the sentence that come between the subject and the verb That leaves us with Suite Española (blank) researchers’ understanding of the cross-cultural and innovative musical styles Next, plug each answer into the underlined portion.

Choice A is incorrect because it does not make logical or grammatical sense to say Suite Española [are deepening] researchers’ understanding of the cross-cultural and innovative musical styles

Choice C is incorrect because it does not make logical or grammatical sense to say Suite Española [have deepened] researchers’ understanding of the cross-cultural and innovative musical styles.

Choice D is incorrect because it does not make logical or grammatical sense to say Suite Española [deepen] researchers’ understanding of the cross-cultural and innovative musical styles

Choice B is correct because it makes sense to say Suite Española [has deepened] researchers’ understanding of the cross-cultural and innovative musical styles. Furthermore, the singular noun a collection of piano pieces pairs correctly with the singular helping verb has

16. The correct answer is D. Using the Tune Out strategy, cross out all the words in the sentence that come between the subject and the verb That leaves us with Vera Rubin (blank) data about galaxy rotation curves when she made a groundbreaking discovery Next, plug each answer into the underlined portion.

Choice A is incorrect because although both actions (analyzing data and making the discovery) did occur in the past, using simple past for both verbs (analyzed and made) doesn't quite work. The intended meaning of this sentence is that Rubin made her discovery (a one-time occurrence) while she was in the process of analyzing the data (an ongoing action), and using simple past for both verbs does not convey this idea.

Choice B is incorrect because has been analyzing implies an action that is continuing up to the present time, but that doesn't work with the simple past verb made a discovery, which describes an action that was completed in the past.

Choice C is incorrect because will analyze describes an action that will take place in the future, but that doesn't work with the simple past verb made a discovery, which describes an action that was completed in the past.

Choice D is correct because it clearly and correctly conveys the idea that Rubin was in the process of analyzing data (an ongoing action that took place in the past) when she made a groundbreaking discovery (a one-time action that occurred in the past).

SLIDE 27.2

Curriculum for the Digital SAT®

FOR THE DIGITAL SAT: WRITING

Work on your own using the Sounds Wrong Is Wrong strategy to answer questions 18 and 19. 18

Throughout the 1930s and 1940s, American artist Georgia O’Keeffe famously depicted the rugged landscapes of New Mexico in her art, using bold shapes and rich colors to represent the region’s distinct geological features and expansive skies. The evocative animal skulls that often __________ a recurring motif in these paintings are particularly striking.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) are B) have been C) were D) is 19

American architect Alfred M. Butts invented a popular word game. In 1938, he developed the game of Scrabble, which __________ of the simpler word-based board games of that era.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) were an enhanced, scoring version

B) are enhanced, scoring versions

C) were enhanced, scoring versions

D) is an enhanced, scoring version

MASTERY

Strategy (28 minutes)

Curriculum for the Digital SAT®

Give students 4 minutes to complete questions 18 and 19. Review the answers afterward.

18. The correct answer is A. Using the Sounds Wrong Is Wrong strategy, plug each answer choice into the blank and see if it sounds wrong or incomplete.

Choice B is incorrect because it reads The evocative animal skulls that often [have been] a recurring motif in these paintings are particularly striking. This creates a verb tense mismatch between have been and are

Choice C is incorrect because it reads The evocative animal skulls that often [were] a recurring motif in these paintings are particularly striking. This creates a verb tense mismatch between were and are

Choice D is incorrect because it reads The evocative animal skulls that often [is] a recurring motif in these paintings are particularly striking. This creates a subject-verb agreement mismatch.

Choice A is correct because it creates a complete, correct sentence: The evocative animal skulls that often [are] a recurring motif in these paintings are particularly striking

19. The correct answer is D. Using the Sounds Wrong Is Wrong strategy, plug each answer choice into the blank and see if it sounds wrong or incomplete.

Choice A is incorrect because it reads In 1938, he developed the game of Scrabble, which [were an enhanced, scoring version] of the simpler word-based board games of that era. It creates a mismatch between the singular Scrabble and the plural verb were

Choice B is incorrect because it reads In 1938, he developed the game of Scrabble, which [are enhanced, scoring versions] of the simpler word-based board games of that era. It creates a mismatch between the singular Scrabble and the plural verb are

Choice C is incorrect because it reads In 1938, he developed the game of Scrabble, which [were enhanced, scoring versions] of the simpler word-based board games of that era. It creates a mismatch between the singular Scrabble and the plural verb were

Choice D is correct because it creates a complete, correct sentence: In 1938, he developed the game of Scrabble, which [is an enhanced, scoring version] of the simpler word-based board games of that era. The singular noun Scrabble fits correctly with the singular noun is

SLIDE 29.2

SLIDE 29.1

Curriculum for the Digital SAT®

Practice Set 3

D) providing MASTERY

Complete the practice set. When you have finished, double-check your work.

A study led by Dr. Jane Lubchenco, a marine ecologist, found that the rate of kelp forest recovery in marine protected areas __________ three times faster than in areas open to shing, highlighting the e ectiveness of these conservation zones in promoting ecosystem resilience.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) is B) being C) to be D) will be

American composer Amy Beach’s Gaelic Symphony (1896), the rst symphony composed by an American woman, __________ scholars’ understanding of the signi cant contributions of women to classical music in the late 19th century. Which choice completes the text so that it conforms to the conventions of Standard English?

A) has broadened B) are broadening C) have broadened D) broaden

British archaeologist Howard Carter’s discovery of Tutankhamun’s tomb (1922), one of the most intact ancient Egyptian burial sites ever found, __________ signi cant insights into the art, burial customs, and royal history of the New Kingdom period in ancient Egypt.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) provide

B) provides

C) have provided

Wrap-Up

Complete the wrap-up. When you have finished, double-check your work.

Architecture and the sensation of space are central to Frank Lloyd Wright’s designs. In Fallingwater, for example, the integration of the house with its natural surroundings creates a seamless connection to the outdoors, while in the Guggenheim Museum, the character of the spiral layout __________ a form of spatial experience whereby the visitor’s path evokes a sense of continuous movement.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) presented B) has presented C) presents D) will be presenting

Inventor omas Edison and entrepreneur George Westinghouse were key players in the “War of the Currents,” a period of intense competition that __________ the development and adoption of alternating current (AC) and direct current (DC) electrical power systems.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) have in uenced

B) were in uencing

C) in uenced

D) in uence

When developing the revolutionary e-commerce platform Amazon (1994), entrepreneur Je Bezos was inspired by his interest in the internet’s potential. e successful businessman has founded multiple companies, but his entrepreneurial spirit __________ evident early on. At the age of 12, he started his rst business venture, a summer camp for young students. Which choice completes the text so that it conforms to the conventions of Standard English?

A) were

B) was C) have been D) are

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Sample | Curriculum for the Digital SAT

Curriculum for the Digital SAT®

How Curriculum for the Digital SAT® Works:

How Mastery for the Digital SAT Works

Three Paths to Boosting Scores:

Content Mastery:

Test Mastery:

Time Mastery:

Curriculum for the Digital SAT®

The Mastery for the Digital SAT Difference

Authentic Practice

Lots of Authentic Practice

Interleaving

Curriculum for the Digital SAT®

What Mastery for the Digital SAT Includes

Student Workbooks

Teacher Manuals (4)

Mastery for the Digital SAT Page by Page

Curriculum for the Digital SAT®

Mastery for the Digital SAT Page by Page

Curriculum for the Digital SAT®

Mastery for the Digital SAT Page by Page

Curriculum for the Digital SAT®

ANSWER KEY

Curriculum for the Digital SAT®

Structure of a Mastery for the Digital SAT Lesson

Curriculum for the Digital SAT®

Digital SAT®

Advanced Math and Data Analysis

Table of Contents

Ratios and Proportions

RATIOS AND PROPORTIONS

Curriculum for the Digital SAT®

Warm-Up

Curriculum for the Digital SAT®

Warm-Up (12 minutes)

Curriculum for the Digital SAT®

Foundation (17 minutes)

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

RAT i OS AND PROPORT i ONS

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

Practice Set 1 (12 minutes)

Curriculum for the Digital SAT®

ENTRANCE

Curriculum for the Digital SAT®

Approach (12 minutes)

Curriculum for the Digital SAT®

SOLVE, STRATEGIZE, OR SKIP

Curriculum for the Digital SAT®

Approach (12 minutes)

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

Approach (12 minutes)

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

Approach (12 minutes)

Curriculum for the Digital SAT®

ESTIMATE

Curriculum for the Digital SAT®

Strategy (12 minutes)

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

Mini-Test

Curriculum for the Digital SAT®

Mini-Test (30 minutes)

Curriculum for the Digital SAT®

Mini-Test (30 minutes)

Wrap-Up

Curriculum for the Digital SAT®

Curriculum for the Digital SAT®

Wrap-Up (12 minutes)

ENTRANCE

SOLVE, STRATEGIZE, OR SKIP

Curriculum for the Digital SAT®

Algebra and Geometry

Table of Contents