Sample - Curriculum for the ACT by MasteryPrep

Curriculum for the ACT®

Eliminate prep time and provide teachers with a sustainable sequence of instruction.

The first and only mastery-based prep curriculum for the ACT®. This program provides a course of study, with scaffolded course modules and instruction that aligns state standards to what’s measured on the ACT. Ready-touse materials include scripted lessons, PowerPoint slides, and student workbooks – eliminating prep time and allowing teachers to focus on the classroom.

Implementation Models:

Lesson plans for any session length (from 15 minutes to 1 hour 45 minutes) and any number of sessions (from a one-week prep program to a full-year class), tailored to your students’ predicted ACT scale scores.

What’s included:

• 4 student workbooks (English, Math, Reading, and Science)

• Over 150 hours of content

• Over 1,600 authentic practice questions

• Direct customer support

• Teacher manuals with scripted lessons for each subject

• Mini-tests

• Ebooks available

MasteryPrep “Master What Matters” Framework:

Content Mastery:

Time management and test-taking strategies can only take students so far. In the end, students must know the content to succeed on required assessments.

Test Mastery:

Test-taking is a skill that can be learned just like anything else. In every lesson, students learn essential techniques and tricks that help them master the required assessment.

Time Mastery:

Every lesson includes timed practice and pacing techniques, so students learn the time management habits they need to succeed.

English:

• 470 pages, 30 lessons, 550 practice questions, 45 test-taking tips.

• Tips and strategies for transitions questions, the most heavily weighted topic in ACT English

• Master crucial punctuation rules that comprise 15% of scores, but often haven’t been reviewed since middle school

• Essential review for sentence structure, reducing redundancy, identifying author purpose, and much more.

Math:

• 546 pages, 38 lessons, 575 practice questions, 45 test-taking tips.

• Time is of the essence in math. Demonstrates not only how to answer the questions, but also how to more quickly and more accurately.

• Pre-algebra and elementary algebra drive most ACT score

• Improvement; extensive review of the basics creates a firm foundation to build from.

• Shows how to reverse engineer word problems and dissect figures to maximum advantage.

Reading:

• 334 pages, 18 lessons, 325 practice questions, 25 test-taking tips.

• Lessons on context, prefixes, and stems mean that confusing terms and phrases have met their match.

• Learn to skim passages and scan for answers so that even if students run out of time or are challenged readers they can still get most of the questions right.

• One-third of the questions on the ACT Reading don’t require students to read the passage; we show students how to identify these items and answer them quickly and painlessly.

Science:

• 314 pages, 16 lessons, 220 practice questions, 20 test-taking tips.

• To score well on the science test, students have to think like a scientist, which is why we review the essentials of experimental design, controls, and the scientific method.

• So much of the ACT Science test boils down to one skill: interpreting charts and graphs. Our science lessons help students tame and master them.

• The only curriculum that provides a skill-by-skill breakdown of the ACT Science test, and the most rigorous ACT Science practice of any test prep program.

Chapter Anatomy

Entrance Ticket:

Role: The entrance ticket is designed for three purposes. First, it serves as a way to begin the class. Second, the activity provides a method for informal assessment. Third, it primes the students for the lesson content by exposing the skills and material they have not yet mastered.

Implementation: Direct students to complete the entrance ticket as they come into class each day. Have the question displayed on the slide so that students can begin as soon as they enter the classroom, even if the bell has not yet rung. Give them 2–5 minutes to complete the entrance ticket, depending on the activity. Review the activity together as a class before moving to the learning targets and self-assessment.

Learning Targets:

Role: The learning targets are designed to give students a goal for each lesson. They also serve as guideposts for the teacher as the lesson is taught.

Implementation: Review the learning targets at the beginning of each lesson. Refer to the learning targets as the lesson is taught to give the students a sense of progression. Be sure to review them one last time before the class ends.

Self-Assessment:

Role: The self-assessment serves as a moment of reflection for the students. It allows them to consider their incoming knowledge and encourages them to set a daily learning goal. It also functions as informal assessment of the students prior to the lesson, which can help guide the teaching depth.

Implementation: Have students rate their knowledge of the material on the self-assessment page after reviewing the learning targets. Instruct the students to reassess themselves after the completion of the exit ticket to chart their daily progress.

Quick Check:

Role: The quick check is designed to briefly review important material that is prerequisite knowledge for the lesson. Students should be familiar with this content. If they are not, the teacher will need to integrate the quick check concepts into the lesson content. The quick check also contains a review of vocabulary pertinent to the lesson.

Implementation: Review the quick check material after the students have assessed themselves. Spend no more than 5 minutes on the quick check, and focus on informally assessing students as they respond to the prompts. If students struggle during this portion, spend additional time reviewing the content during the lesson content.

Lesson Elements:

Role: The lesson elements contain the bulk of instructional time during any given lesson. They are designed to address the content of the ACT in ways that are approachable by students of all skill levels. The lesson elements contain enough content and flexibility to support differentiation in the class based on previous data and the informal assessments carried out at the start of class time during the entrance ticket, self-assessment, and quick check.

Implementation: Each lesson element has its own particular implementation, but in general, the lessons vary from teacher-led instruction or discussions to group activities or individual work. Each lesson element contains material designed to build up to the ACT practice sets contained at the end of the lesson.

Practice Sets:

Role: The practice sets are authentic recreations of ACT practice questions based on MasteryPrep’s research. They are designed to build subject mastery on the ACT. Each lesson contains five practice sets, which each contain three questions. Be sure to emphasize that these questions are at the ACT’s level of difficulty.

Implementation: The practice sets can be used in various ways. Primarily, the sets should be implemented throughout the lesson so that students can begin to measure their progress in a tangible, ACT-centric way. For example, after a lesson element is completed, have the students try a practice set. This will help them realize their progress and reveal any further skills needed that will be covered in the next lesson topic. You can also skip straight to the practice sets during the lesson should students exhibit mastery of the lesson content.

Each practice set should be timed for 2 minutes. Ultimately, no additional time should be given so that students can develop pacing skills in addition to content skills. If pacing is a major issue, though, students can be given extended time, gradually working up to ACT pacing. To ensure good pacing practice, be sure to monitor the time for each set and do not allow students to work on the next set.

Exit Ticket:

Role: The exit tickets are to be used as formal assessments of student progress. They can be scored and analyzed to assess overall student proficiency of each family of ACT questions, which allows teachers to adjust the class accordingly..

Implementation: After completing the lesson, students complete the exit ticket individually. Each ticket should be timed for 2 minutes. No additional time should be given in order to produce the most accurate results. Review the correct answers and demonstrate how to solve for them. After completing the questions, students should trade papers and grade each other’s answers as you provide the answers and explanations.

Learning Targets

ACT College Readiness Standards provide clear objectives for every lesson (with optional Common Core correlation).

Lesson 1 – Ambiguity and Series

1.2 Learning Targets

> Review learning objectives with your students, displayed on the slide and in their workbooks.

> After reviewing the learning objectives, ask students to assess their knowledge and confidence level on these objectives. They should rate themselves on a scale of 1 to 4, with 1 being not confident or uncertain, and 4 being completely confident or certain. They should circle this number in the designated section of their workbooks.

1.2 Learning Targets

1. Identify several different strategies to use in comma usage conflicts

2. Use commas for different purposes in several types of sentences

Self-Assessment

Circle the number that corresponds to your confidence level in your knowledge of this subject before beginning the lesson. A score of 1 means you are completely lost, and a score of 4 means you have mastered the skills. After you finish the lesson, return to the bottom of this page and circle your new confidence level to show your improvement.

Learning Targets, English Student Workbook

Learning Targets, English Slide Deck

Lesson 1 – Linear Equations

1.2 Learning Target

> Review the learning target with your students, displayed on the slide and in their workbooks.

> After reviewing the learning target, ask students to assess their knowledge and confidence level on this target. They should rate themselves on a scale of 1 to 4, with 1 being not confident or uncertain, and 4 being completely confident or certain. They should circle this number in the designated section of their workbooks.

Student Page 9

1.2 Learning Target

1. Solve equations with one unknown variable

Self-Assessment

Circle

Learning Targets, Math Student Workbook

Learning Targets, Math Slide Deck

Lesson 6 – Intent and Purpose

6.2 Learning Targets

Review learning targets with your students, displayed on the slide and in their workbooks.

After reviewing the learning targets, ask students to assess their knowledge and confidence level on these targets. They should rate themselves on a scale of 1 to 4, with 1 being not confident or uncertain, and 4 being completely confident or certain. They should circle this number in the designated section of their workbooks.

6.2

6.2 Learning Targets

 Identify the purpose of a detail and/or paragraphs in a passage

 Identify the author’s intent and purpose in a passage

 Identify how an author’s purpose shapes content and style

Self-Assessment

6.2 Learning Targets

1. Identify the purpose of a detail and/or paragraphs in a passage

2. Identify the author’s intent and purpose in a passage

3. Identify how an author’s purpose shapes content and style

Self-Assessment

Learning

Targets, Reading Student Workbook

Lesson 2 – Select Data and Features Part 2

2.2 Learning Targets

> Review learning targets with your students, displayed on the slide and in their workbooks.

> After reviewing the learning targets, ask students to assess their knowledge and confidence level on these targets. They should rate themselves on a scale of 1 to 4, with 1 being not confident or uncertain, and 4 being completely confident or certain. They should circle this number in the designated section of their workbooks.

2.2 Learning Targets

 Read charts and graphs to answer ACT questions

 Find information in the science passages and experimental descriptions needed to read complex charts and graphs

 Relate information given in the passage to the terminology used in the question items

Self-Assessment

2.2 Learning Targets

2.2 Learning Targets

1. Read charts and graphs to answer ACT questions

2. Find information in the science passages and experimental descriptions needed to read complex charts and graphs

3. Relate information given in the passage to the terminology used in the question items

Self-Assessment

Circle

Targets, Science Student Workbook

Entrance and Exit Tickets

Start and close each class period with an entrance/exit ticket combo that helps you remove dead time, differentiate instruction, and measure progress.

Lesson 1 – Ambiguity and Series

Ambiguity and Series

This lesson covers comma errors that frequently show up on the ACT English test. The errors covered include those that create basic sense problems, errors in series, and errors that create ambiguity. Students will learn when it is appropriate to delete or insert commas to best express the meaning of the sentence.

ACT Standards:

PUN 201. Delete commas that create basic sense problems (e.g., between verb and direct object)

PUN 302. Use appropriate punctuation in straightforward situations (e.g., simple items in a series)

PUN 403. Use commas to avoid obvious ambiguity (e.g., to set off a long introductory element from the rest of the sentence when a misreading is possible)

PUN 501. Delete commas in long or involved sentences when an incorrect understanding of the sentence suggests a pause that should be punctuated (e.g., between the elements of a compound subject or compound verb joined by and)

PUN 601. Use commas to avoid ambiguity when the syntax or language is sophisticated (e.g., to set off a complex series of items)

Ambiguity and Series

1.1 Entrance Ticket

How does the location of the comma affect the sentence’s meaning? Write a short paragraph explaining the image. Use complete sentences.

It’s raining, cats and dogs!

Entrance Ticket, English Student Workbook

Entrance Ticket, English Slide Deck

Mastery for the ACT® English Teacher Manual

1.5 Exit Ticket

> Students complete the three questions on their exit ticket.

Students are timed 2 minutes for the three questions (40 seconds per question). There is no break between questions.

Lesson 1 – Ambiguity and Series

Visual storage at the Louvre and other museums protects the sculptures, profits the community culture, and gives public access to art once kept in closed vaults.

With technology in the hands of so many people; we tend to forget that personal computers in the home were once rare.

1. A. NO CHANGE

B. sculptures; profits

C. sculptures profits

D. sculptures it also profits

2. F. NO CHANGE

G. people, we H. people, we, J. people we

It meanders through the grass like a worm curving, and bending near the sidewalk.

3. A. NO CHANGE

B. worm, curving and bending

C. worm curving and bending,

D. worm, curving and bending,

Answered Correctly

1.1 Entrance Ticket

> Have students try the following three ACT practice questions. Students should work independently. Once the entrance ticket has been completed, review the questions with the students and have them share their answers. Give students the correct answers to the questions, as well as a step-by-step demonstration of how to solve the problems, but do not go into detailed explanation. This will serve as an introduction to the lesson content but is not intended to be the main lesson.

1. The correct answer is E. Solve for x by isolating it.

1.1 Entrance Ticket

Solve

Ticket, Math Student Workbook

1.5 Exit Ticket Lesson 1 –

> Students complete the three questions on their exit ticket. Students are timed 3 minutes for the three questions (60 seconds per question). There is no break between questions.

Lesson 1 – Linear Equations

1. For what value of x is the equation 2( x + 7) = 3( x + 11) true?

–19

–4

2. What is the value of x that satisfies the equation 3( x – 2) = 6 x + 5 ?

3. If 5( x – 3) + 11 = 6, what is the value of x ?

Answered Correctly

DO YOUR FIGURING HERE.

2.1 Entrance Ticket

Read the passage and answer the questions.

By “Cheat the Prophet,” the author refers to the phenomenon where people attentively listen to wise predictions about the future and “then go out and do something else.”

In the beginning of the 20th century, the game of Cheat the Prophet was made far more difficult than it had ever been before. There were so many prophets and so many prophecies that it was difficult to elude all their ingenuities. When a man did something free and frantic and entirely his own, a horrible thought struck him afterward; it might have been predicted. Whenever a duke climbed a lamppost, when a dean acted recklessly, he could not be really happy: he could not be certain that he was not fulfilling some prophecy.

In the beginning of the 20th century, you could not see the ground for clever men. They were so common that a stupid man was quite exceptional, and when they found him, they followed him in crowds down the street and treasured him up and gave him some high post in the state. And all these clever men were at work giving accounts of what would happen in the next age, all quite clear, all quite keen-sighted and ruthless, and all quite different. And it seemed that the good old game of hoodwinking your ancestors could not really be managed this time, because the ancestors neglected meat and sleep and practical politics, so that

they might meditate day and night on what their descendants would be likely to do.

But the way the prophets of the 20th century went to work was this: they took something or other that was certainly going on in their time and then said that it would go on more and more until something extraordinary happened. And, very often, they added that in some odd place that extraordinary thing had indeed happened and that it showed the signs of the times.

For instance, there were Mr. H. G. Wells and others who thought that science would take charge of the future; just as the motorcar was quicker than the coach, so some lovely thing would be quicker than the motorcar, and so on forever. And there arose from their ashes Dr. Quilp, who said that a man could be sent on his machine so fast around the world that he could keep up a long, chatty conversation in some old-world village by saying a word of a sentence each time he came ‘round. And it was said that the experiment had been tried on an apoplectic old major who was sent around the world so fast that there seemed to be (to the inhabitants of some other star) a continuous band ‘round the earth of white whiskers, a reddish complexion and tweeds—a thing like the ring of Saturn.

2.1 Entrance Ticket

1. In the fourth paragraph (lines 37–53), the predictions of H. G. Wells and Dr. Quilp could best be characterized as anticipating that:

A. scientific advances would dramatically improve transportation.

B. man would return to a more natural state.

C. the motorcar would be replaced by the carriage.

D. Earth would eventually become a planet more like Saturn.

2. The narrator claims that in the 20th century, it was difficult to play “Cheat the Prophet” because:

F. people were becoming far too cynical to believe in prophecies.

G. people were becoming more merciful, which meant they would do what the prophet said.

H. people were making so many predictions that it was inevitable some would come true.

J. so many people were making accurate predictions.

3. The first three paragraphs (lines 1–36) of the passage establish all of the following EXCEPT that:

A. the passage is discussing the beginning of the 20th century.

B. various people were engaged in hoodwinking their ancestors.

C. some of the predictions made in the 1900s were based on occurrences that were already taking place.

D. many people who thought themselves clever were predicting the future.

Entrance Ticket, Reading Student Workbook

2.1

Entrance Ticket

> Have students try the following ACT practice questions. Students should work independently. Once the entrance ticket has been completed, review the questions with the students and have them share their answers. Give students the correct answers to the questions, as well as a step-by-step demonstration of how to solve the problems, but do not go into detailed explanation. This will serve as an introduction to the lesson content but is not intended to be the main lesson.

1. The correct answer is A. Choices B and C are not mentioned, so they can be eliminated. Students may be tempted to choose choice D, since Saturn is explicitly mentioned. However, the passage does not state that the earth is becoming like Saturn but rather that the blur of the man traveling around the world so quickly would look like a ring around Saturn. It is also not predicted by the scientists. Lines 39–42 describe one scientist’s prediction that just as something more advanced than the coach had been developed, the motorcar, so would something even more advanced than the motorcar. He predicted this trend would continue, with more and more advances being made in transportation. The paragraph goes on to discuss another scientist with a machine that could send men traveling around the world at high speeds.

Entrance Ticket, Reading Teacher Manual

1.5 Exit Ticket

> Students complete the three questions on their exit ticket.

Students are timed 4 minutes per practice set or 2 minutes to read the passage and 2 minutes to answer the questions. There is no break between questions.

I stayed up way too late last night. Not quite late enough to see the sun come up, but almost. Believe it or not, it’s much easier for me to wake up now than when I was young; in college I’d easily sleep ten hours on school nights and fourteen on weekends. These days it just takes a few hours of sleep and a cup of strong coffee to get me up and at ‘em. Still, I’m not the active firecracker I used to be—just crouching down to lace up my boots makes me want to crawl back into bed. When I finally make it out the door, I’m running only a few minutes late.

When I pull into my parking spot, I breathe a sigh of relief when I see there isn’t a crowd waiting along the street. Of course that’s yet to be the case in the five years I’ve owned the place, so I’m not sure why I worry. I unlock the door and flip on the lights. The fluorescents flicker on panel by panel, all the way to the back of the store.

Maybe it’s just because I have an affinity for doit-yourself projects, but there’s no smell in the world like an arts and craft store. The combined scents of unvarnished wood, clay, glue, silk flowers, and, of course,

1. According to the passage, which of the following craft materials does the man need from the narrator’s store?

A. Sequins

B. Flowers

C. Pillowcases

D. Yarn

2. The narrator states that although it has not yet happened, she worries:

F. her shop will be robbed.

G. people will be lined up, waiting for her to open.

H. people will leave her negative feedback online.

J. her shop will be vandalized.

potpourri make me feel like I can conquer any project, even though my do-it-yourself attempts usually end up cluttering my workshop—or as I prefer to call it, my laboratory. I giggle as I compare myself to a mad scientist, gluing sequins onto flip-flops, tie-dying cotton pillowcases, and creating tiny plastic terrariums. It’s a pretty accurate picture.

Around 10:30 a.m. a man opens the door and pauses, looking like he just stepped out of a space shuttle and onto another planet. Doing my best to seem as little like a craft-obsessed maniac as possible, I smile and ask if he’s looking for anything specific.

“Do you have any, um, alpaca?” he asks, but the way he pronounces the word makes it clear it was the first time he ever said it. I conclude that he was definitely sent here by someone far more knowledgeable about yarn, and whoever sent him agrees with me that alpaca is the best kind. I instantly warm to his mission.

“Sure do,” I respond. “Do you have a color preference?”

3. According to the passage, compared to her younger years, the narrator’s need for sleep is:

A. much greater now than before.

B. much less now than before.

C. about the same as before.

D. a bit less now than before.

12.1 Entrance Ticket

Many nutritionists have different ideas about dieting—whether low-carbohydrate diets or low-fat diets are most effective for weight loss. Write a short paragraph (5–7 sentences) describing which method you think would be more effective. Do you think low-carbohydrate diets or low-fat diets help people lose weight faster? Be sure to include details to support your stance. What information would you need to know to prove your hypothesis?

Mastery for the ACT® Science Teacher Manual

1.1 Entrance Ticket

> Show students the entrance ticket in their workbooks. Give them up to 5 minutes to work on this activity independently.

> Come together as a class. Display the answers and demonstrate how to use the information in the table to answer the questions.

Elena lives in Portland, Oregon. The average March temperature in Austin, Texas was 62°F, which is lower than the average September temperature there, 82°F. The average March temperature in Portland, Oregon was 52°F, which is higher than the average September temperature there, 47°F.

Darren lives in Burlington, Vermont. The average March temperature in Cleveland, Ohio is 39°F. Four degrees lower than this is 35°F, which is the average March temperature in Burlington, Vermont.

Tiana lives in Los Angeles, California. The average September temperature in Portland, Oregon was 47°F, which is below 60°F. The average September temperature in Los Angeles, California was 61°F, which is above 60°F.

> This chapter focuses on the skill of reading charts and graphs. The purpose of this activity is to introduce students to using critical thinking skills to analyze data in a table.

2.5 Exit Ticket

> Students complete the three questions on their exit ticket.

Students are timed 3 minutes for the three questions. There is no break between questions. We strongly recommend providing your students with a physical copy of the exit ticket PDF, or alternately sending them the digital PDF to view on their devices at their desks. The powerpoint slides of the questions are provided for instructional purposes only.

Name Date

Passage IV

Consisting of three stages, cellular respiration is a common chemical process used to generate energy in the form of ATP. This study was conducted to examine the effects of temperature on cellular respiration in yeast. Yeast uses a specific pathway called anaerobic respiration. This pathway does not require oxygen in order to generate ATP molecules for energy.

Experiment 1

A gas pressure sensor, which measures pressure in kilopascals (kPa), was turned on. A hot water bath containing 50 mL of water was warmed, and 2.0 mL of glucose was poured inside a properly labeled test tube (see Figure 1).

Experiment 2

The rate of cellular respiration is determined by the change in pressure (ΔP) over the change in time (ΔT). The seconds required to reach the designated temperature was recorded. This measurement and the pressure difference were used to calculate the cellular respiration rate (see Table 2).

Table 2

2.0 mL of glucose

Figure 1

An equal volume of 2.0 mL of yeast solution was also poured into the test tube. Enough drops of oil were added to ensure the top of the solution was fully covered. After shaking the mixture, the initial pressure was determined using the pressure probe from the gas pressure sensor. Initial pressure recordings were noted.

After the mixed solution was re-shaken, the test tube was placed in a hot water bath. The temperature of the hot water bath was monitored. For each temperature, the final pressure was measured using the pressure probe on the gas pressure sensor. Final pressure recordings for each temperature range were noted (see Table 1).

Table 1

1. In Experiment 1, what was the final gas pressure sensor recording at a temperature range of 15–25°C?

A. 102.4 kPa

B. 110.5 kPa

C. 123.1 kPa

D. 128.9 kPa

2. In Table 2, what was the rate of cellular respiration at 30–42°C?

F. 0.0145 kPa/s

G. 0.0525 kPa/s

H. 0.1170 kPa/s

J. 0.1455 kPa/s

3. In Experiment 2, what initial pressure recording was used to calculate a slope of 0.1170 kPa/s?

A. 99.5 kPa

B. 99.8 kPa

C. 99.7 kPa

D. 100.0 kPa

Answered Correctly

Each lesson includes a PowerPoint slide deck that provides a visual focus for the class and illustrates key concepts.

English Slide Decks

Math Slide Decks

Reading Slide Decks

Step-by-Step

Instructions

Scripted lessons walk you through every step of the program. No matter your comfort level with the material, you have the tools to boost scores.

Lesson 2 – Unnecessary Commas

2.3.2 Deleting Commas

> Show the picture and ask for student commentary.

> Teacher Dialogue: Commas are not always when you pause. Imagine you are reading a passage aloud. You may pause or take a breath in certain places, but it does not mean a comma needs to go there in writing. Only put commas where you know they are grammatically necessary. Otherwise, bulldoze the commas!

> Teacher Dialogue: Some people put commas where they are not needed. When you write, it is impor tant not to go comma crazy. Remember these two rules:

> Review the rules on the slide and have students write them in the space provided in the workbook.

1. Do not use commas that disrupt sentence structure. A single comma cannot ever come between a subject and a verb, a verb and an object, a preposition and an object, an adjective and the noun it modifies, or an adverb and the verb it modifies, etc.

2. Only put commas where you know you need them. Otherwise, the sentence flow can be disrupted, or the meaning can be confused.

Go with the Flow: When you read, you should be able to go with the flow. There should be a normal rhythm and cadence to the writing. Remove commas that disrupt the flow of a sentence or confuse its meaning.

Step-by-Step Instructions, English Teacher Manual

Step-by-Step Instructions, English Slide Deck

Mastery for the ACT® English

2.3.2 Deleting Commas

Comma Rule 1:

Comma Rule 2:

1. So, biologists decided, to dissect the mutated frogs themselves.

2. Growing up, on the beaches of Australia, Adrian Buchan would one day become a world-renowned surfer.

3. Athletes, typically, find, that getting enough sleep at night plays a huge role in their endurance.

English Tip

Go With the Flow: When you read, you should be able to go with the flow. There should be a normal rhythm and cadence to the writing. Remove commas that disrupt the flow of a sentence or confuse its meaning.

Step-by-Step Instructions, English Student Workbook

13.3.2 Advanced Volume

> Teacher Dialogue: Now Hungry Dave is craving his favorite sandwich, the PB&J. But Hungry Dave is a very peculiar boy. Unlike some kids who want the crust cut off their sandwiches, Hungry Dave ONLY likes to eat the crust. What do you need to know to figure out how many sandwich crusts Hungry Dave can eat?

Possible answers include volume of sandwich, dimensions of sandwich, dimensions of crust to be cut off, etc.

> Reveal the measurement values on the slide. Students solve the problem, showing their work on the blank space provided in their workbooks.

> Teacher Dialogue: How would you solve this problem?

Find the volume of the entire sandwich. Subtract the volume of the sandwich to be removed. Divide Hungry Dave’s stomach capacity by the volume of the crust-only sandwich.

Find the volume of the sandwich before the middle is cut out. Remind the students that volume is the area of the main shape multiplied by the thickness or height. The square that is the bread has an area of 5 5 = 25. Multiply this by the thickness. 25 ⋅ 1 = 25 in3

Find the volume of the sandwich without the crust. If 0.5 inches is removed on every side, the new dimensions of the sandwich are 4 4. (Show picture or draw it out for students. 5 – 0.5 – 0.5 = 4 for both sides.) Find the volume in the same way. The area of the main shape, a square, is 4 4 = 16. Multiply it by the height of the sandwich. 16 ⋅ 1 = 16 in3

Subtract the volume of the crustless sandwich from the volume of the whole sandwich to find the volume of just the crust. 25 – 16 = 9 in3

How many crusts can Hungry Dave eat? Divide his stomach capacity by the volume of the crust of one sandwich. 61 ÷ 9 = 6.777. Hungry Dave can eat 6 sandwich crusts.

Step-by-Step Instructions, Math Teacher Manual

Step-by-Step Instructions, Math Student Workbook

Step-by-Step Instructions, Math Slide Deck

Lesson 5 – Drawing Conclusions Part 2

5.3.1 Inference vs. Exact Details

> Show the students the following questions. Read each one aloud and have students try to identify which ones are looking for word for word matches in a passage and which ones ask the reader to make an inference.

1. Inference because of the word suggest

2. Inference because of the words most likely

3. Word for word because of the words according to the author

4. Word for word because of the word indicates

5. Inference because of the words reasonably inferred

6. Word for word because of the word indicates

> Teacher Dialogue: What is the difference between indicates and suggests? Indicates means there will be a straightforward fact described, while suggests means something is implied or inferred.

> Make a list on the board of words from these examples that suggest you will have to make an inference. Have students volunteer the words. Add the words in the context of the passage (because we usually have to draw conclusions from context, think context clues) and help establish

> Tell students that they will know to make inferences when they see these words.

Scanning: The only difference between scanning for an exact detail and scanning for an inference is how students should use the passage. In both cases, students need to go back to the passage using their scanning skills. For an inference question, they should not expect an exact match. Instead, they should scan for general supporting details from the passage.

5.3.1 Inferences vs. Exact Details

1. Details in the passage most strongly suggest that: word for word or inference

Keyword:

2. When the narrator refers to “cheating the prophet,” he is most likely making a statement about: word for word or inference

Keyword:

3. According to the author, the scientists encountered which of the following as a result of their theories? word for word or inference

Keyword:

4. Information in the passage indicates that which type of terrain can be found between Toronto and Ottawa? word for word or inference

Keyword:

5. It can be reasonably inferred from the passage that the main character most strongly desires to: word for word or inference

Keyword:

6. In the passage, the author indicates that he believes that the main cause for the decline in interest is: word for word or inference

Keyword:

Reading Tip

Scanning: The only difference between scanning for an exact detail and scanning for an inference is how you use the passage. For an inference, do not expect an exact match. Instead, scan for general supporting details from the passage.

Step-by-Step Instructions, Reading Student Workbook

Step-by-Step Instructions, Reading Slide Deck

1.3.1

Road Signs

> Teacher Dialogue: Both the reading and science tests involve a passage followed by questions. You may have already learned how to approach passages on the reading test.

> Teacher Dialogue: What do you do on an ACT reading test when you see a passage and a set of questions?

First, skim the passage to get an idea of it as a whole; for each question, identify the key details and scan the passage for them.

> Tell students that they can approach science passages in a similar way. Here, however, the steps are the following:

1. Preview the passage

2. Follow the road signs

> Have students write these two steps in the designated section of their workbooks.

> Teacher Dialogue: The first step for every science passage is to make sense of the passage before answering the questions. We call this previewing the passage.

> Teacher Dialogue: Think back to your practice test. How many of the answers came from the passage text? How many came from the char ts and graphs?

Most questions can be answered directly from the charts and graphs. (If the students have not taken a practice test yet, they will have to take your word for it.)

> Teacher Dialogue: If that is the case, how should you approach previewing the passage?

Focus primarily on the information in the figures and tables.

> Teacher Dialogue: Look at the passage in your workbooks. What can you gather from the figures?

In the dialogue here and on the next page of this manual, prompt students with questions to elicit observations and conclusions. Questions such as “Do you notice any trends in the data?” can get students thinking.

Figure 1 measures the sulfur content for each of the days in both Spring 1 and Spring 2. Figure 2 measures the water flow. Spring 2’s values in the figures are almost always lower than Spring 1’s values. Table 1 records the temperature of both springs on each day, while Table 2 gives the average of those temperatures.

Step-by-Step Instructions, Science Teacher Manual

1.3.1 Road Signs

Step #1 when approaching a science passage: ______________________________________________

Step #2 when approaching a science passage: ______________________________________________

Two measurements are taken of the water in a hot spring: the sulfur content and the temperature. Both of these measurements can be affected by water flow.

Sulfur content in hot springs is thought to have medicinal and therapeutic effects for those relaxing in the springs. Figure 1 shows the sulfur levels in parts per million (ppm) on 5 collection days at two different hot springs, Spring 1 and Spring 2.

Table 1 shows the temperature in Fahrenheit of the water in Spring 1 and Spring 2 on each of the 5 collection days. Table 2 shows the average water temperature in Fahrenheit of Spring 1 and Spring 2 during this time.

Figure 2 shows the water flow of each spring in cubic feet per second on the 5 collection days.

Step-by-Step

Instructions, Science Student Workbook

Step-by-Step Instructions, Science Slide Deck

Engaging Activities

Lesson 5 – Apostrophes

5.3.1 Apostrophe Rules

> Have students briefly pair up with students next to them and try to come up with at least two rules for when to use apostrophes with possessives. After approximately five minutes, allow the students to share their rules with you. Work with the class to include the following rules for possession.

(Possessives are the focus of the lesson. As long as students are comfortable with contractions, focus on rules for possessives only here.)

1. A singular noun with no s on the end – add ’s (dog’s collar)

2. A singular noun with an s on the end – also add ’s (bus’s route)

3. Plural nouns with no s on the end – add ’s (children’s group)

4. Plural nouns with an s on the end – only add ’ (all the trees’ leaves)

Students may get bogged down and confused by all these rules. Help them narrow it down. Which forms need ’s, and which forms only need an apostrophe?

Add only an apostrophe  plurals ending in s (all the trees’ rings, all the dogs’ food bowls)

Add an apostrophe and the letter s  all the others (this is the normal rule, the above is the exception)

> Have the students write down these rules on the lines provided in this section of their workbooks.

Engaging Activities, English Student Workbook

Engaging Activities, English Slide Deck

The Circonian Martians travel the outermost ring of Saturn three times before realizing they are going in circles. How far out of their way have they traveled before they get back on the route toward their destination?

Engaging Activities, Math Slide Deck

Mastery for the ACT® Math Teacher Manual

12.3.1 Circumference

> Teachers read this story aloud for the students.

In a galaxy far, far away, the Circonian martians have made a monumental discovery—a planet not unlike their own—inhabited by a strange race of creatures. There are no corners in the Circonian world, and no straight edges either. Their bodies are round, their food is round, and they live in circular dwellings. Every geographic feature on their planet is made of soft curves and spheres. However, this new planet is full of other shapes. The harsh edges and bold corners of this unknown planet worry the Circonians, who are headed to the planet to deliver a message to its strange and lanky inhabitants.

The Circonian martians board their spaceship ready for voyage to this newfound land. They enter the Milky Way galaxy near Pluto and stop there to greet their distant allies, the Icekan aliens, who live on the cold and rocky planet. Eventually the Circonians reach Saturn, a planet they are rather unfamiliar with. They mistake the rings of Saturn for roads the inhabitants of Saturn have constructed. The captain of the spaceship believes the road is a shortcut to their destination and steers the ship along its direction. Before long, the spaceship crew starts to complain. It seems like this road is never ending!

> Present the students with this problem.

> Teacher Dialogue: The Circonian martians travel the outermost ring of Saturn three times before realizing they are going in circles! How far out of their way have they traveled before they get back on the route toward their destination?

Ask the students what the answer is. If they can’t answer it, ask them what they need to do to find the answer. What other information do you need to know? What formula do you need to know? What is the formula for circumference? If the students say radius, ask them: If I gave you the radius of just the planet Saturn, would that be enough? (Answer: No, they need the radius of the ring.)

> Generate some discussion on what combinations of information they could use to solve the problem. Eventually, concede to give them the radius of Saturn and the measurement of the distance between the largest ring and the surface of Saturn.

The radius of Saturn is 36,184 miles. The outermost ring of Saturn is 8,000,000 miles from the surface of the planet. The formula for circumference is 2πr Have students use 3.14 for π and round to the nearest whole number.

Engaging Activities, Reading Student Workbook

Engaging Activities, Reading Slide Deck

5.3.2

Mastery for the ACT® Reading Teacher Manual

Identifying Incorrect Answers

> Teacher Dialogue: Sometimes it is easier to “back into” the correct answer. If you are not sure what the correct inference is, use the process of elimination to get rid of answers you know are wrong.

> Teacher Dialogue: Imagine you are on a dating game looking for the perfect partner. Identifying wrong answers on the ACT reading test is like identifying the people who are not the right match for you. They may all look good on the outside—just like some ACT answers use fancy words or even words from the passage—but are still not right.

> Teacher Dialogue: Can you think of any common incorrect answers you’ve seen?

Answers will vary, but students should talk about some common incorrect answers, such as answers that are not supported or answers that are only partially correct.

> Show the common incorrect answers on the slides and have the students copy them into their workbooks.

Answer options that look or sound good but are not supported by the passage These answer options sometimes add details not in the passage, so they have no support.

This contestant is always making up stories.

Answer options that are contradicted by the passage These answer options say the opposite of what the passage implies. This contestant is the opposite of what you are looking for once you get to know them.

Engaging Activities, Science Slide Deck

10.3.1 Variables and Controls

1. You want to know whether boys or girls are better at throwing a paper ball into a trash can.

Test:

Variable:

Constants:

2. You want to know if exposure to sunlight affects plant growth.

Test:

Variable:

Constants:

3. You want to know if the year a car was made affects its crash test results.

Test:

Variable:

Constants:

4. You want to know if amount of time spent studying affects how well a student performs on a test.

Test:

Variable:

Constants:

Engaging Activities, Science Student Workbook

10.3.1 Variables and Controls

> The following activity takes the concept of controlling variables and brings it to life by making it personal for your students. Begin by crumpling a piece of paper and placing a trash can at the front of the room.

> Teacher Dialogue: It is time for an experiment! Let’s find out whether the boys or the girls in this class are better at throwing this paper ball into the trash can. Before we start, there are a few rules.

1. The student who goes first must remain seated while making a shot.

2. The student who goes second is allowed to stand up while making a shot. The third student must sit, and so on. Students alternate between sitting and standing on each turn.

3. Each student only gets one shot.

> Keep a tally on the board of the number of girls and boys who make the shot. Expect the students to complain about the rules not being fair. (That is the point of this activity.) You can keep the activity from getting off track by saying something like, “Let’s see what happens. It is just an experiment.”

> Keep score as each student shoots, making sure to let every other student stand for the shot. Students should notice that those sitting closer to the trash can and those who get to stand up have an unfair advantage. Do not let students move closer or adjust the trash can. Once all students have taken a turn, tally the scores and announce the winner.

> Teacher Dialogue: Is this an accurate result? Was this experiment fair? More than likely, the losing group will already begin to complain about how the activity was unfair.

> Teacher Dialogue: How was this experiment unfair?

> Count the students’ reasons or write the issues on the board. Help them determine the exact elements that made the experiment unfair or inaccurate.

> Teacher Dialogue: In science, you would say there are too many variables.

Detailed Answer Explanations

A comprehensive walkthrough of every single test item in each book makes even the toughest ACT questions approachable.

6.4.1 Set One

Its not easy growing up in a world where perspectives shift constantly and information bombards the senses; one hardly knows what to think of as right or wrong. 1.

In actuality, the association could not defend it’s inane argument that the puppy compromised the child’s safety. 2. F. NO CHANGE

Selma High School simultaneously gives back to the community and raises funds for its field trips by organizing community activities throughout the year in exchange for small donations.

END OF SET ONE

DO NOT GO ON TO THE NEXT PAGE UNTIL TOLD TO DO SO.

Detailed Answer Explanations, English Student Workbook

Mastery for the ACT® English Teacher Manual

6.4.1 Set One

Its not easy growing up in a world where perspectives shift constantly and information bombards the senses; one hardly knows what to think of as right or wrong.

1. A. NO CHANGE

B. It’s

C. Its’ D. That’s

1. The correct answer is B. We are using it’s as a contraction of it is to say, It is not easy growing up. It is the subject and is is the verb. Choice A is incorrect because a possessive pronoun is unnecessary; there is nothing in this part of the sentence to possess. Choice C is incorrect because its’ is not a word. Choice D is incorrect because there is nothing for that to refer to.

In actuality, the association could not defend it’s inane argument that the puppy compromised the child’s safety.

2. F. NO CHANGE

G. they are H. it is J. its

2. The correct answer is J. The argument belongs to the association, so we use the possessive pronoun its. Choice F is incorrect because it’s is the contraction of it is, which does not make sense in the context of the sentence. This also eliminates choice H. Choice G is incorrect because the association is singular and they is a plural pronoun.

Selma High School simultaneously gives back to the community and raises funds for its field trips by organizing community activities throughout the year in exchange for small donations.

3. A. NO CHANGE

B. it’s

C. its’ D. its’s

3. The correct answer is A. The field trips belong to Selma High School, so we use the possessive pronoun its. Choice B is incorrect because we need the possessive form, not the contraction of it is. Choice C is incorrect because its’ is not a word. Choice D is incorrect because its’s is not a word.

2.4.1 Set One

DO YOUR FIGURING HERE.

1. If p + q = 36, and p – q = 20, then q = ?

A. –8

B. 8

C. 16 D. 28 E. 56

2. Which of the following ( a , b ) pairs is the solution for the system of equations 2 a + b = 3 and a – 3 b = 5 ?

F. (–2, 7 )

G. ( 0, 3 )

H. ( 3 4 , 6 4 )

J. ( 2,–1 )

K. ( 3,–3 )

3. What is the v alue of y in the solution to the following system of equations? x – 4y – 8 = 20 2 x + y = 20

–4 B. –1.8

END OF SET ONE

STOP! DO NOT GO ON TO THE NEXT PAGE UNTIL TOLD TO DO SO.

Detailed Answer Explanations, Math Student Workbook

1. If p + q = 36, and p – q = 20, then q = ?

A. –8

B. 8

C. 16

D. 28

E. 56

2.4.1 Set One

1. The correct answer is B. Combine the two equations to solve for p, then plug it back in to solve for q

2p = 56

p = 28

p + q = 36

28 + q = 36

q = 8

2. Which of the following ( a , b ) pairs is the solution for the system of equations 2 a + b = 3 and a – 3 b = 5 ?

F. (–2, 7 )

G. ( 0, 3 )

H. ( 3 4 , 6 4 )

J. ( 2,–1 )

K. ( 3,–3 )

3. What is the v alue of y in the solution to the following system of equations?

x – 4y – 8 = 20 2 x + y = 20

A. –4

B. –1.8

C. 8

D. 10

E. 14

2. The correct answer is J. Combine the two equations to solve for one variable, then plug it back in to find the other.

a – 3b = 5  –2(a – 3b) = –2(5)  –2a + 6b = –10

–2a + 6b = –10

+ 2a + b = 3

7b = –7

b = –1

2a + (–1) = 3

2a = 4

a = 2

So the solution is (2,–1).

3. The correct answer is A. Combine the equations and solve for y

x – 4y – 8 = 20  x – 4y = 28  –2(x – 4y) = –2(28)  –2x + 8y = –56 –2x + 8y = –56 + 2x + y = 20 9y = –36 y = –4

Answer Explanations, Math Teacher Manual Student Page 28

5.4.1 Set One Answer Explanations

1. The correct answer is A. Choices C and D are unsupported by the passage. Choice B cannot be inferred from the information provided in the passage. Lines 43–44 discuss how the creation of the transatlantic line would require a cable of nearly 2,000 nautical miles, by far the longest in the world. Thus, it is possible to infer that all others prior were shorter than this distance, as seen in choice A.

2. The correct answer is F. Choices G and H are unsupported by the passage. Choice J is opposite, since the discovery actually aided the project in determining where to lay the cable. The passage discusses Newfoundland and Ireland in lines 24–28, stating that the narrow bandwidth made the project seem even theoretically possible. Thus, choice F is correct.

3. The correct answer is C. Lines 55–62 discuss the failed 1857 attempt. After, Field manufactured more cable to replace what had been lost and devised a new system of paying it out from the back of the ship. Choice D is opposite, since Field was not defeated. Choice A is unsupported by the passage, while choice B is possible but also unsupported. Choice C is the best option, since Field persevered despite several setbacks.

4. The correct answer is H. Lines 68–70 describe how the cable stopped working, and public confidence hit a new low Choices F, G, and J are all unsupported by the passage, since these lines only imply that the public felt disillusioned and doubtful about the project, as stated in choice H.

5. The correct answer is A. The final paragraph discusses the cable’s greatest legacy, laying the foundation for modern computer science, as businesses on either end quickly recognized the value of condensing frequently repeated terms into code. It does not mention London’s prominence, stock markets, or other public works, so choices B, C, and D can be eliminated. Choice A is correct since this paragraph is focused on computer science and the condensing of data.

Lesson 5 – Drawing Conclusions Part 2

5.4.1 Set One

Passage II

The length of time it took to deliver a message had been a limiting factor in transatlantic communication ever since Europeans made landfall in the New World. Any relay of information between North America and Europe was subject to the snaillike pace of ocean travel, along with its attendant delays. The effect was that business and political transactions on both sides of the Atlantic were hampered by long lulls in conversation.

The telegraph’s debut in the late 1830s revolutionized overland communication, but water remained a barrier since it dissipated the wires’ electric signal. In 1845 Charles Wheatstone hit upon the solution of coating underwater cables in gutta-percha, the adhesive juice of the Palaquium gutta tree. This breakthrough allowed the first successful undersea cable to link Dover and Calais via the English Channel in 1851, and plans were soon underway to connect Newfoundland and Nova Scotia across the Cabot Strait.

But channels and straits were not oceans, and major obstacles remained to connect two continents on opposite sides of the Atlantic. Aside from the incredible expense of manufacturing thousands of miles of conductive cable, the ocean’s sheer depth complicated the engineering.

Along the entire expanse between Newfoundland and Ireland (the shortest possible distance for the cable), there was a single narrow bandwidth—an undersea plateau two miles deep—that made the project seem even theoretically possible.

Samuel Morse, the telegraph pioneer, had publicly advocated for the construction of a transatlantic line as early as 1840, but more than a decade had passed with no serious attempts made. Then in 1856, Cyrus West Field decided to take on the project. A prominent and vastly successful New York businessman, he had already financed completion of the Newfoundland-Nova Scotia telegraph after it stalled due to bankruptcy. Though he had little knowledge of telegraphy or the deep sea, Field was savvy enough to enlist the help of experts, among them Morse, the oceanographer Matthew Maury, and British engineer Charles Tilston Bright.

Even armed with such brainpower, the challenge before the newly formed Atlantic Telegraph Company was immense. At nearly 2,000 nautical miles, the cable would be by far the longest in the world. It would

consist of seven copper wires covered with three coats of gutta-percha and wound with tarred hemp inside a sheath of flexible iron strands. Heavy-duty in the literal sense, the cables weighed more than a ton per nautical mile. The enormous cost of manufacture required funding from an army of investors, as well as the British and American governments, who also furnished naval warships to trail the cable across the sea. On August 5, 1857, the U.S.S. Niagara and the HMS Agamemnon finally set sail from Valentia Bay, Ireland, cable in tow.

But success proved elusive. The 1857 attempt was aborted when the cable snapped more than 400 miles out at sea. Undaunted, Field manufactured more cable to replace what had been lost and devised a new system of paying it out from the back of the ship. A second try in the spring of 1858 also failed, but the third attempt, later that summer, proved to be the charm. On August 5, 1858, the first transatlantic telegraph cable was finally laid.

Jubilation erupted on both sides of the ocean as people realized the profound change that had occurred. Queen Victoria sent a message of congratulations to President James Buchanan, who replied that the cable was “a triumph more glorious [than any] on the field of battle.” The elation was short-lived though, as the cable stopped working after just three weeks. Public confidence hit a new low, and Field was vilified by the press.

The Civil War’s outbreak in 1861 stalled the project’s renewal, but by 1865, Field had a new cable design and a single massive ship to lay its entire length. After yet another unsuccessful bid, a final attempt in July 1866 went smoothly, and this time the cable remained operational. At first, the high price of sending a message limited clientele to governments, corporations, and the very wealthy, but this exclusivity faded with technological advances. By 1900, fifteen transatlantic cables were in use, and the process was on its way to full democratization. The cable also revolutionized stock trading between New York and London, further solidifying those cities as preeminent global financial centers.

1. It is reasonable to infer from the passage that prior to the transatlantic cable, all underwater telegraph cables were:

A. shorter than 2,000 nautical miles.

B. longer than 1,700 nautical miles.

But perhaps the cable’s greatest legacy is evident in the most basic tasks of 21st century life, from sending an email to receiving a cell phone call. Its success effectively laid the foundation for modern computer science, as businesses on either end quickly recognized the value of condensing frequently repeated terms into code. The resulting data compression gave rise to a whole new field of study that continues to shape the digital world in which we live today.

C. constructed with funding from national governments.

D. off-limits to private enterprises.

2. The passage most strongly implies that the discovery of an undersea plateau between Newfoundland and Ireland affected the cable project by:

F. providing a plausible path to lay the cable across the sea floor.

G. hindering the passage of ships attempting to lay the cable.

H. eliminating the need for submarines to lay the cable at vast depths.

J. complicating the planning of where exactly to lay the cable.

3. The passage indicates that after the 1857 attempt to lay the cable failed, Cyrus Field felt:

A. proud.

B. uneasy.

C undeterred.

D. defeated.

4. The passage most strongly suggests that once the 1858 cable stopped working, the public regarded the project’s future with:

F. weary optimism.

G. mild regret.

H. intense doubt.

J. indifference.

5. The passage most strongly suggests that the transatlantic cable’s effect on modern life is most deeply felt in terms of:

A. its impact on computer science and data technology.

B. London losing prominence as a global financial capital.

C. the importance of stock markets to national economies.

D. its encouragement of other large-scale public works.

Lesson 5 – Drawing Conclusions

Embedded Test-Taking Strategies and Time Management Tips:

Call-outs highlight opportunities to reinforce key test-taking and time management strategies.

Lesson 8 – Identify Purpose

8.3.2 Relevant, Emphasize, Explain

> After students write their paragraphs, present the following sentence. During the second piece that Huberman performed at the recital, Huberman’s valet noticed the Strad was missing, so she hurried on stage during applause and whispered the news to Huberman.

> Teacher Dialogue: Can anyone use this sentence anywhere in their essay? If any student can, ask them to share their paragraph first and then say where they could put the new sentence. Call on a few volunteers to do the same.

> Teacher Dialogue: Can anyone NOT use this sentence anywhere in their essay?

These students can also read or paraphrase their paragraph and explain why the new sentence wouldn’t fit with what they had written.

> Reinforce that even though the students had the same topic, how they used the facts and wrote about the topic determined whether the additional sentence was a good addition or unnecessary. Explain that this is common on the ACT. Questions may offer an extra phrase or sentence that is well-written and accurate, but the real question is: does it fit with the information already given?

Tell students that they can determine whether to add information by thinking REE—relevant, emphasizes, explains. If information is both relevant and explains or emphasizes something, then it makes sense to add it. If it doesn’t do this, it shouldn’t be added!

Mastery for the ACT® Math Teacher Manual

12.3.1 Circumference

> Work these basic circumference problems with the students. Have them attempt the answer on their own, then write the calculations on the board while explaining the answer.

Encourage them to draw out the problems. On the ACT, everyone is an artist! It doesn’t matter how it looks. Draw out the questions to help yourself make sense of them.

When drawings are already given on ACT problems, the figures are usually drawn to scale. That means if something looks about half the size of something else, it probably is. If two angles look equal, they probably are. If it looks like it could be a midpoint, it most likely is. Tell students to use this to their advantage when solving problems involving geometric drawings.

> Try these problems as a class:

> Teacher Dialogue: What is the circumference of a circle with a radius of 5 cm?

Circumference = 2π(5) = 10π, or about 31.4

> Teacher Dialogue: What is the circumference of a circle with a diameter of 20 cm?

That radius is half the diameter. 20 ÷ 2 = 10. Plug 10 in for r in the circumference formula. Circumference = 2π(10) = 20π or about 62.8.

> Teacher Dialogue: What is the radius of a circle with a circumference of 30π?

Students work backward using the same formula. Remember in the formula circumference = 2πr, the circumference on the left of the equal sign is part of the formula. You can plug a value in there if you know it. 30π = 2πr. Divide both sides by 2π, and you’re left with r = 15.

Working Backward: Remind students that items on both sides of the equal sign are part of the formula. This means that in the formula perimeter = 2πr, perimeter is part of the formula. It’s one of the variables. Remind them that if they are given the perimeter but not a radius or diameter, they plug it into the formula the same way and solve for the unknown. (Examples of this will come up during the ACT practice section.)

Lesson 7 – Interpret Words and Phrases Part 1

7.3.1 Vocabulary in Context

Have students try the last three on their own. After each question, let students explain how they arrived at their answers.

3. The correct answer is A. Choice B is too literal. Choice C does not make sense, as the rabbits do not stumble upon disease and famine. Choice D is also incorrect, as the passage makes no reference to the shock or surprise of the rabbits. Choice A most nearly captures the meaning of the phrase, which is meant to show that rabbits suffer from these diseases and famines.

4. The correct answer is G. The famine and disease that the rabbits suffer from is not tangible and cannot be touched or handled, eliminating choices F and J. Choice H is incorrect because the animals and humans are not trying or testing these diseases and famines. Choice G is correct because the sentence is indicating that the impact of famines and diseases extends to both rabbits and humans.

5. The correct answer is D. The pikas are not using the dried grasses and plants to defend or assist themselves until spring and are using them as a food source, eliminating choices A and B. Choice C also does not make sense, as it is too awkward and formal in context. Choice D is correct because the pikas are using the dried grasses and plants to help them survive the winter.

Plug In: When the ACT asks students to determine the meaning of a word or phrase, they should first go back to the passage and determine what they think that word or phrase means in the context. If that fails, they can plug in the answer choices and eliminate any that seem weird, then mark and move.

Lesson 13 – Text and Experiments

13.3.1 Describing an Experiment

> Next have students attempt the question, using the details given in the first paragraph.

2. The correct answer is H. The passage states when gases dissolve in a solvent, they are affected by both temperature and pressure. It also later gives a formula for the effect of pressure on gas and graphs showing the effect of temperature on gas. Choices F, G, and J are all contradicted by this information, making choice H the best answer.

> Teacher Dialogue: The ACT science test is an open book test. If a question doesn’t clearly refer you to information in a figure, go find it in the passage text. If, when you are reading passage text, you find it difficult to concentrate, some students find it helpful to quiz themselves after they read each paragraph. They ask themselves, “What did I just read, here?” They create a one-sentence mental summary of what they read, just like in the exercise we completed today. If you decide to use this technique, be sure to save it only for the passages with

13.3.1 Describing an Experiment

2. Which of the following statements best describes the solubility of hydrogen gas?

F. The solubility of hydrogen gas is not affected by temperature.

G. The solubility of hydrogen gas is not affected by pressure.

H. The solubility of hydrogen gas is affected by temperature and pressure.

J. The solubility of hydrogen gas is affected by temperature only.

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