LHM - Level E - Practice Book by lighthousecurriculum

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Lighthouse Math Practice book level E • ISBN 978-1-955773-18-8

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Review 1

In Review 1, we will review

Place Value and the Four Operations

In Level E, students will practice working with large numbers, gain ﬂuency in addition, subtraction, multiplication, and division, and solve word problems to prepare for higher-level math skills.

• Place value

In Level E, students will practice working with large numbers, gain ﬂuency in addition, subtraction, multiplication, and division, and solve word problems to prepare for higher-level math skills.

• Addition and subtraction with large numbers

• Place value

• Double-digit multiplication

• Addition and subtraction with large numbers

• Long division

• Double-digit multiplication

• Long division

We can understand the value of digits based on their place value, including decimals.

We can add and subtract any large number.

We can understand the value of digits based on their place value, including decimals.

We can ﬂuently multiply a number by a single or double digit.

We can add and subtract any large number.

We can ﬂuently multiply a number by a single or double digit.

We can use long division to solve division problems with two or three-digit dividends.

We can use the four operations to solve word problems.

We can use long division to solve division problems with two or three-digit dividends.

We can use the four operations to solve word problems.

56,932.349

Identify the place value of the underlined digit in each number. Write each number in word form.

1 12,738.056

9.34 5,720,008.736 72,493,201.034 8,921,342.725 6,932,671.385 Understand place value to write numbers in multiple ways. For example:

Complete the charts by filling in the value of each digit.

Patrick thought of a number with a 7 in the hundreds place, a 5 in the ones place, 2 more tens than hundreds, and 3 fewer thousands than ones. What number did he think of?

Terry saw that 9,307,194 people lived in his city. Which number is in the ten thousands place?

The school fundraiser raised 34,295.18 for new playground equipment. What is the value of the 8?

Steven has $109.43 in his bank account. What number is in the tenths place?

Subtract numbers with regrouping.

Round numbers to nearest hundred to estimate. 3523 - 1285 2543 - 223 2500 - 200 2300

In order to solve, first we need to regroup and subtract the digits in the ones place. Go to the tens place and borow 10 to bring it over to the ones place. 10+3=13, 13-5=8: 13 – 5 = 8

regroup and subtract the digits in the tens place:

Round numbers to the nearest hundred and then solve.

An airplane flew at 30,000 feet. A helicopter flew at 1,728 feet. How much higher did the airplane fly?

There are 206 people in the pool and another 173 people in line for the water slides. About how many people are there together?

Noah’s family is flying to visit his grandparents. They took one route there and it was 4,379 miles. On the way home, they took a different route and it was 3,918 miles. How much longer was the trip there?

On Tuesday, 6,704 people visited the museum and 2,199 people visited the nearby park. How many people visited altogether on Tuesday?

Subtract across zeros.

Round numbers to the nearest hundred to estimate. 400 - 287 3214 - 375 3200 - 400 2800

To solve, first we need to subtract the digits in the ones place. However, there are not enough tens to regroup a ten.

Instead, regroup using “40” instead of 0. Remove 1 ten to make 10 ones and 39 tens remaining.

Estimate to the greatest common place value. Then solve.

the remaining tens and hundreds.

A factory was making 800 chairs an hour. One of their machines broke, and now they are only making 457 chairs an hour. How many chairs less is this?

The car goes 5,000 miles between oil changes. If it has gone 2,390 miles already, how much further can it drive before it needs an oil change?

The concession stand sold 1,375 glasses of lemonade and 726 glasses of ice water. About how many did it sell in all? Round to the greatest common place value and solve.

A truck weighs 8,950 pounds and is carrying 3,450 pounds of rocks. How much do the truck and rocks weigh together?

Lesson instructions 4

Multiply. Find the missing factor.

To solve this number sentence, think of the multiples of 5. Write out the next eight multiples of 5 below.

Find the missing factor or product.

James has 48 cookies. He places 6 on each plate. How many plates does he fill?

Edward has 3 rows of rosebushes. Each row has 7 rosebushes. How many rosebushes does he have in all?

There are 5,280 feet in a mile. If Harold ran 3 miles, how many feet did he run?

Jack needs 550 grams of fruit for a recipe. If he is making 4 times the recipe, how many grams of fruit will he need?

There are 67 raisins in a box. If a shelf has 24 boxes, how many raisins are there in all?

Mr. Sanders bought 58 packages of pencils for school. There are 28 pencils in each box. How many pencils did he buy?

Each bag of chips weighs 86 grams. If there are 99 bags of chips, how much would they all weigh?

Carl needs 27 nails for each birdhouse he builds. If he wants to build 34 birdhouses, how many nails will he need?

Use your understanding of

Jeffrey lined up 18 toy cars in 3 rows. How many cars were in each row?

Ethan has 5 blueberry bushes. He plants 1 in each row. How many rows does he have?

There are 6 seats on a roller coaster car. How many roller coaster cars would be needed to seat 42 people?

Bryan walks 28 miles a week. If he walks the same amount each day, how many miles does he walk?

Lesson instructions 7 Solve and circle the remainder.

You can only make 1 group of 6 with 8. Therefore, 8 ÷ 6 = 1 - 6 2 1 6)85

Solve and circle the remainder.

Subtract to find the remainder. Then, bring down the ones and divide again. You can make 4 groups of 6 with 25. Therefore, 25 ÷ 6 = 4

Subtract to find the remainder. 14 6)85 - 60 25 - 24 1

On a field day, 135 students are divided up among 5 activities. How many students are at each activity?

Matthew is packing glasses in boxes. Each box holds 8 glasses. If he has 500 glasses to pack, how many boxes will he fill? How many will be left over?

Patrick has 203 cards. He is trying to divide them into 3 decks evenly. How many cards will be left over when he is done making the decks?

Russell completed 186 math problems in 6 hours. If he completed the same amount each hour, how many math problems did he complete each hour?

Solve and circle the remainder.

If there is a zero in the dividend, treat it the same as any other number. Bring it down and make new groups. You can make 3 groups of 3 with 10.

Solve and circle the remainder if there is one.

However, if you cannot make any groups, place a zero in the quotient and bring down the next place value. Now you can make 2 groups of 3 with 6. - 60 10

There are 9 pieces of chocolate in each bag. How many bags would 954 pieces of chocolate make?

Noah biked 108 miles in 4 days. How many miles did he bike each day?

Tyler collected 327 insects this summer. If there are 3 summer months, how many insects did he collect each month?

Daniel has 500 invitations to an event. He puts them in packets of 6 to give to each student. How many students can he give invitation packets to? How many invitations will be left over?

Review 2

In Review 2, we will review

Fraction, Decimals, and Geometry

Students will deepen their understanding of fractions and decimals, which will prepare them for using operations with fractions and decimals in Level E.

• Find area and perimeter

• Deﬁne geometry vocabulary

• Find equivalent fractions

• Simplify fractions

• Compare, order, and locate fractions on a number line

• Add and subtract fractions with like denominators

• Place value with decimals

• Compare, order, and locate decimals on a number line

We can ﬁnd the perimeter of any shape and the area of a rectangle.

We can draw geometric ﬁgures and name them.

We can use a model, multiplication, or division to ﬁnd equivalent fractions.

We can use a common factor to simplify fractions. We can compare fractions with models, number lines, or benchmark fractions.

We can write fractions as decimals and write the word form of decimals.

We can compare decimals by using a model or place value.

Lesson instructions 1

Find the area of each figure.

To find the area, multiply the length by the width. Area is measured in squared units. 3 inches × 5 inches = 15 in2

To find the perimeter, add all of the sides together. 3 + 3 + 5 + 5 = 16 inches

Find the area of each figure.

Find the perimeter of each figure.

Larry notices that all four sides of the field on the playground measure 45 feet. What is the perimeter of the field?

A shape has a perimeter of 134 inches. If three of the sides measure 32, 54, and 19 inches, what is the length of the last side?

A square has a side that is 8 inches long. What is the area of the square?

A driveway measures 35 feet by 24 feet. What is the area of the driveway?

Type of figures, lines and angles.

Types of lines

plane - a flat surface that extends to infinity

point - a geometric element that has zero dimensions

line segment - part of a line that contains every point on the line between its endpoints

endpoints - points that end a line segment

line - a collection of points along a straight path with no endpoints

ray - a line with a single endpoint that goes on and on in one direction

Points E, F, and G are in plane T.

Line relationships

intersecting - lines that cross, but don’t make a right angle

perpendicular - lines that intersect and create a 900 angle

parallel - lines that continue on indefinitely, are equidistant, and never touch

Types of angles

right - measures exactly 900

acute - measures less than 900

obtuse - measures more than 900

straight - measures exactly 1800

Ray AB AC intersecting BD Obtuse angle

Thomas opens his math book all the way up so that both the front and back covers are on his desk. What angle did Thomas make with his book?

Elijah likes to watch the trains pass by the park. He sees the tracks and tries to remember if they are perpendicular or parallel lines. What type of lines are they?

To draw an angle, Dylan draws a point and has a straight path come out of it in two places. He puts an arrow at the end of each path. What type of line did Dylan draw?

Adam notices that when he uses his scissors, they make a set of lines that cross, but not ever at a right angle. What are these lines called?

Lesson instructions 3 Make equivalent fractions.

To make an equivalent fraction, divide or multiply the numerator and denominator by the same number.

For example, multiply the numerator and denominator × 3 to get 3 9 . 3 9 is an equivalent fraction to 1 3 . numerator → 1 × 3 = 3 denominator → 3 × 3 = 9

Write two equivalent fractions that can represent the shaded part of the figure. Find an equivalent fraction. Sample answer provided.

Robert has 2 3 of a pizza left. Is this equivalent to 3 5 or 4 6 ?

To make an equivalent fraction, Phillip multiplies 2 5 by 3 3 . What equivalent fraction does he get?

Walter has 1 3 of a container of ice cream. If he wants to make an equivalent fraction with a denominator of 12, what would the numerator be?

Vincent needs 3 4 pound of strawberries to make jam. He wants to convert it to ounces by making an equivalent fraction with the denominator 16. What will the numerator be?

Lesson instructions 4

Simplify the fractions.

List factors of the numerator and denominator and divide each by the largest factor they have in common. This simplifies the fraction to its lowest terms.

For example, to simplify 6 10 , list the factors, then divide by the largest factor on both lists.

Factors of 6: 1, 2, 3, 6

Factors of 10: 1, 2, 5, 10

Simplify each fraction using the given models. Fill in the factor the numerator and denominator will be divided by to reach simplest terms.

Divide the numerator and denominator by:

Of the 28 guests that were invited to the party, 24 came. What fraction of the invited guests came to the party? Write the answer in simplest form.

Tom ate 6 16 pieces of a chocolate bar. Write this fraction in simplest form.

If 9 27 balloons were red, what fraction of the balloons were not red? Write the answer in simplest terms.

After dinner, 3 8 of a pizza remained. Write this fraction in simplest form.

Lesson instructions 5

Compare fractions using benchmark numbers and visual models. When we compare fractions, we can shade in two pictures of the fractions or use a benchmark to estimate fraction size.

Write the benchmarks for each fraction, then determine if the fraction is closer to the benchmark for 0, 1 2 , or 1. The first one has been done for you.

Use benchmark numbers to determine if the fraction is closer to 0, 1 2 , or 1.

Compare fractions by shading in the figures or plotting the number line. Use <, >, or =.

Eli has cut a cake into eight pieces. How many pieces of cake would be in one whole? How many would be half the cake?

Frank has 8 12 of his paper done. Which benchmark is the best estimate for how much of the paper Frank has completed: 0, 1 2 , or 1?

Eli ran 2 3 of a mile, and Chad ran 3 5 of a mile. Plot these fractions on the number lines below to find out who ran longer.

Create your own model below to prove that 3 6 is the same as 1 2 .

Lesson instructions 6

Add fractions with the same denominator : Add the numerators and keep the denominator the same.

Subtract fractions with the same denominator: Subtract the numerators and keep the denominator the same.

Add and simplify if necessary.

Subtract and simplify if necessary.

Estimate whether the fractions are closer to 0, 1 2 , or 1. Then, place them on the number line.

There are 14 patches on a quilt. 5 of the patches have stripes, and 4 of the patches are solid print. What fraction of the patches have either stripes or are solid print? Write your answer in simplest form.

Larry used 1 2 3 cups of sugar to make cookies and 2 1 3 cups of sugar to make lemonade. How much sugar did Larry use in all? Write your answer in simplest form.

Daniel's father had 7 3 4 gallons of gas in his car. He used 1 1 4 gallons. How many gallons of gas were left in the car? Simplify your answer if possible.

There were 8 3 5 pounds of watermelon in a fruit salad and 3 1 5 pounds of grapes. How many more pounds of watermelon were there than grapes? Simplify your answer if possible.

Lesson instructions 7

Write the decimal.

Use a place value chart to read the decimal and know a number’s value. The decimal point is said as the word “and.” End by saying the number with the last place value name.

In the number 47.35, the 3 is in the tenths place, and the 5 is in the hundredths place. The number is said as “forty-seven and thirty-five hundredths.”

- eight and five tenths seven and forty-two hundredths

Write the decimal in words.

Write the following decimals in written form.

two hundred thirty and six hundredths

Twenty - six and twenty-six hundredths

Order the decimals above from least to greatest.

Abe's mom wrote a check for their groceries. She wrote it for “fifty-seven dollars and twelve hundredths.” Write the cost of the groceries in standard form.

Gas currently costs $4.179 a gallon. Write this number in word form.

The first coin contains 0.57 ounces of gold. A second coin contains fortyseven hundredths ounces of gold. Which coin contains a larger amount of gold?

Jack’s dad bought 5.47 liters of juice for the week. Together, Jack and his brother drink five and seventy-five hundredths liters of juice in 1 week. Do they have enough juice for the week? Why or why not?

Lesson instructions 8

Compare, order and plot the decimals.

Write <, >, or = to compare.

When comparing decimals:

1. Line up the decimal points.

2. Compare each number starting from the largest place value and move to the right one place at a time.

When comparing 8.05 and 8.5, start with the ones place. Since they are the same, move right to the tenths place. 5>0

To plot a decimal on a number line, find the two whole numbers it falls between. Remember that 1 tenth = 10 hundredths.

Order the numbers from smallest to largest.

Plot the decimals on the number line.

Thomas has $13.70, and Victor has $13.07. Who has more money?

James needs 0.15 grams of salt for an experiment. He has 0.51 grams. Does he have enough? Explain.

Nathan has 5 bean plants that are 2.75, 3, 2.5, 2.8, and 3.3 inches tall. Put them in order from tallest to shortest.

Scott bought three items that cost $2.58, $2.80, and $2.08. Put these in order from least expensive to most expensive.

Chapter 1

In Chapter 1, we will learn about

Place Value, Multiplication, and Exponents

Large numbers can be used to describe enormous quantities such as of money, weight, or distance.

• Place value to billions

• Compare and order whole numbers

• Write whole numbers in expanded form and expanded notation

• Estimate products

• Multiply two-digit numbers by three-digit numbers

• Multiply with zeros

• Multiply two-digit numbers by three-digit numbers

• Multiply with zeros

• Evaluate exponents with powers of 10

We can label the place value of whole numbers up to the billions place.

We can use place value to compare and order whole numbers and write them in expanded form.

We can use rounding to estimate products of whole numbers.

We can use area models, partial products, and the standard algorithm to multiply two-digit numbers by three-digit numbers.

We can use rounding to estimate products of whole numbers.

We can use area models, partial products, and the standard algorithm to multiply two-digit numbers by three-digit numbers.

We can understand, write, and evaluate exponents with powers of 10.

Identify place value to the billions and write numbers in word form and standard form. For example, 5,123,459,400 in word form is five billion, one hundred twenty-three million, four hundred fifty-nine thousand, four hundred.

Fill in the place value chart below.

Word bank: trilions, billions, milions, thousands, ones, tens, hundreds

Write the place value of each bolded digit.

1,254,125,234

Write the standard form of each number.

Eight billion, two hundred fifty-four million, six hundred fifty thousand ,one hundred thirty-two

One hundred two million, eight hundred fifty-four thousand, six hundred ninety-five

Two hundred fifty-four billion, six hundred ninety-seven million, fifty-five thousand, four hundred sixty-five 1,235,658 25,235,002,125 5,281,008 13,158,256,002 21,341,245,245 52,235,456 235,255, 235,124 923,285,359,392 4,301,098,091

Alan’s teacher challenged the students to write the biggest number they could think of. Alan wrote 758,939,382,006. What is this number in word form?

Alan’s teacher challenged the students to write the biggest number they could think of. Alan wrote 758,939,382,006. What is the place value of the 5?

Alan’s teacher challenged the students to write the biggest number they could think of. Alan wrote 758,939,382,006. What is the place value of the 2?

Alan’s teacher challenged the students to write the biggest number they could think of. Alan’s friend George wrote four million, six hundred ninety-eight thousand, twenty-one. What is this number in standard form?

Write numbers in standard form, word form, and expanded form.

Complete the chart below.

10,000,000,000 + 2,000,000,000 + 200,000,000 + 50,000,000 + 3,000,000 + 200,000 + 10,000 + 400 + 50 + 2

52,364,110,035

twenty-five billion, three hundred sixty-four million, two hundred thirty-five thousand, two

Compare the following numbers using <, >, or =.

1,235,025 1,250,758 5,021,204 72,235,245 12,235,236 236,235 546,785,236 21,758,009 21,356,580 124,536,205,458 1,275,025 982,078 5,235,265 90,245 12,235,236 236,245 96,785,236 21,758,002 21,356,580 452,526,235,458

A city in the mountains has a population of 5,598,129, and a city near the shore has a population of 5,610,787. Which city has less people?

Canada has an area of 9,984,670 square kilometers, and China has an area of 9,706,961 square kilometers. Which country has more area?

Order the population of the listed continents from most to least.

Order the size of the listed continents from smallest to biggest. Population

Round and estimate the products.

Round to the nearest hundred, or ten. Then, estimate the product.

A panda weighs 270 pounds. About how much would 19 pandas weigh? Round to estimate the product.

A factory can make 675 cars a day. About how many cars can they make in 220 days? Round to estimate the product.

Douglas can bounce a ball 93 times in one minute. At this rate, about how many times can he bounce the ball in 14 minutes? Round to estimate the product.

Samuel’s heart beats 62 times a minute. If there are 1,440 minutes in a day, about how many times does Samuel’s heart beat in a day? Round to estimate the product.

Find the product of a two-digit by three-digit multiplication problem.

Solve using area models.

231 × 24 = 1.

First write the expanded form of each of the factors. Then, multiply the digits that are on opposite sides to fill in the box.

× 14 = 2.

536 × 65 = 3.

124 × 54 = 4.

928 × 19 = 5.

182 × 35 = 6.

Thomas is stacking boxes of screws at the hardware store. One size screw has 274 screws in each box. Thomas stacks 48 boxes. How many screws are there in all?

Jack is painting a house. One can of paint will cover 175 square feet. How many square feet will 25 cans of paint cover?

There are 186 cars on a train. If each car carried 69 boxes, how many boxes would be on the train?

A gas station gets 995 gallons of gas delivered each day. How many gallons of gas would it have delivered in 31 days?

Lesson instructions

Multiply three-digit numbers by two-digit numbers. 862 × 59 7,758 + 43,100 50,858 685 × 25 3,425 + 13,700

Rebecca is planning a garden in her backyard. She wants to plant rows of flowers, with each row consisting of 134 flowers. If she plans to have 27 rows in total, how many flowers will Rebecca plant in her garden?

Rose is organizing a bake sale to raise money for charity. She wants to make batches of cookies, with each batch containing 256 cookies. If she plans to make 15 batches in total, how many cookies will Rose bake for the bake sale?

Jake is organizing a book drive for his school. He plans to collect boxes of books, with each box containing 387 books. If he aims to collect 42 boxes in total, how many books will Jake collect for the book drive?

Donna is organizing a fundraiser for her school’s music club. She plans to sell boxes of chocolates, with each box containing 178 chocolates. If she intends to sell 63 boxes in total, how many chocolates will Donna sell for the fundraiser?

Solve using the standard algorithm.

Solve using the area model.

There are 450 sheets of paper in each package. A store gets 85 packages of paper. How many sheets did the store get?

Samuel rode his bike for 208 days this year. Each day he rode his bike, he went 17 miles. How many miles did Samuel bike this year?

Andrew saw that a box of building toys has 107 pieces. If there are 49 boxes of building toys on the store's shelf, how many pieces are there in all?

A package contains 24 plates. The school ordered 509 packages this month. How many plates did the school order?

Lesson instructions 7

Write the powers of 10 in standard form and multiply by the powers of ten.

Write the powers of 10 in standard form.

Write the missing exponent.

Multiply by the powers of

A bacteria culture doubles in size every hour. If the initial population of the bacteria culture is 1,000 bacteria, how many bacteria will there be after 5 hours?

John is a birdwatcher. He observes a pair of birds building a nest. Each day, the number of twigs they collect doubles. If on the first day they collect 5 twigs, how many twigs will they have collected by the end of the 6th day?

A population of rabbits doubles every month in a certain forest. If there are initially 50 rabbits in the forest, how many rabbits will there be after 6 months?

The number of students attending a tutoring session triples every week. If there are initially 20 students attending the session, how many students will be there after 5 weeks?

Compare. Use <, >, or =.

Standard form: 854,123

Expanded Form: 800,000 + 50,000 + 4,000 + 100 + 20 + 3

Word Form: eight hundred fifty-four thousand, one hundred twenty-three

95,542,625 one million, six hundred thousand, nine hundred seventy-two

900,000,000 + 30 + 5 nine hundred million, three hundred five

30,542,983 (3 × 10,000,000) + (5 × 5,000) + (9 × 100) + (3)

Solve using estimation.

Estimate.

Solve using the standard algorithm or an area model.

Algorithm

James plays outside for 45 minutes after school. If he had 183 days of school, about how long did he play outside afterwards? Round to estimate the answer.

There are 34 students in a class. Each student brings in 32 pencils. How many pencils are there in all?

A farmer plants 392 corn seeds in each row. If there are 54 rows, how many corn seeds are planted in all?

There are 305 students in the school. Each student was given a 16 ounce bottle of water. How many ounces of water were given out?

Chapter 2

In Chapter 2, we will delve into

Order of Operations and Division

In Chapter 2, we will delve into

Order of Operations and Division

Learning how to interpret a remainder or divide by a two-digit number helps increase division number sense.

• Use order of operations

• Multiply and divide multiples of 10

• Use order of operations

• Estimate quotients

• Multiply and divide multiples of 10

• Interpret quotients

• Estimate quotients

• Divide by two digits

• Interpret quotients

• Divide by two digits

We can use PEMDAS to solve multi-step problems.

We can use patterns to multiply and divide multiples of 10, 100, 1,000….

We can use PEMDAS to solve multi-step problems.

We can ﬁnd compatible numbers to estimate quotients.

We can use patterns to multiply and divide multiples of 10, 100, 1,000….

We can decide whether to round, drop, use, or split the remainder in a division word problem.

We can ﬁnd compatible numbers to estimate quotients.

We can decide whether to round, drop, use, or split the remainder in a division word problem.

We can see how many times the divisor goes into the dividend to divide a number by two digits.

Lesson instructions 1

Use the order of operation to solve the expressions.

Use the order of operations to solve each expression.

First, solve for all of the operations that are in parentheses or brackets, if there are any. Next, solve the exponents, if there are any included.

Then, solve all of the multiplication and division from left to right. →

Lastly, solve all of the addition and subtraction from left to right. →

× 3 + 7 × 2 = (8 + 7) + 6 × 3 = 1. 2.

÷ 3 × 7 + 4 = 3.

+ 3) ÷ 5 + 2 =

− 3 × 3 + 4 =

− 28) × (45 − 40) =

(15 − 5) × (2 + 8) = (100 − 52) × 3 − 25 = 7. 8. 2 × (12 + 16 ÷ 2) = 190 − (42 + 20 ÷ 5) = 9. 10.

Benjamin had 13 stones. He lost 6, and then he found 3 more. How many does he have now?

Edward thought of a number. He told Arthur that the number was 3 more than 48 divided by 6. What was Edward’s number?

Dennis made 24 chocolate chip cookies and 16 mint chocolate cookies. He ate 4 cookies. How many cookies does he have?

Albert picked 75 carrots, dug up 34 potatoes, and picked 3 rows of cabbage with 8 heads in each row. How many vegetables did he gather in all?

Lesson instructions 2 Find patterns of zero when multiplying and dividing. For example, use the basic fact to multiply and divide with zeros.

Fill in the blank to complete each multiplication or division number sentence.

Complete the table.

Matthew rides his horse 8 miles a day. If he rides his horse for 200 days, how many miles will they go?

The cafeteria manager has $2,800 to buy milk. Each gallon of milk costs $4. How many gallons can the cafeteria manager buy?

The aquarium has 24,000 pounds of fish food to feed all the fish. Kane uses 4 pounds of fish food for each tank. How many tanks does Kane give fish food to?

William hikes 5 miles a week. How many miles will he have hiked in 40 weeks?

Lesson instructions 3

Find compatible numbers to create an estimate equation that’s as close as possible to the accurate answer.

For example, compatible numbers to create an estimate equation for 247 ÷ 5.

Use compatible numbers to estimate the quotient.

A gallon holds 128 ounces. If Stephen was pouring glasses that were 12 ounces each into it, about how many glasses could he fill? Use compatible numbers to estimate the quotient.

Alan wants to divide 124 marbles evenly among 3 people. About how many should he give to each person? Use compatible numbers to estimate the quotient.

James is setting tables for a school picnic. If there are 478 students coming, and 8 can sit at a table, about how many tables should be set up? Use compatible numbers to estimate the quotient.

Gabriel has 83 quarters. If he wants to divide them into two groups, about how many will be in each group? Use compatible numbers to estimate the quotient.

Lesson instructions 4 Write an estimate equation with compatible numbers and solve for the accurate answer.

For example, create an estimate equation, then divide for the accurate answer.

Use compatible numbers to write an estimated equation for each problem and solve for an accurate answer.

Solve. Use the chart from the Learn and Connect section to help you.

Mr. Smith has 97 pencils. He wants to give the same number of pencils to each of his 8 students. How many pencils will each of his students get?

Solve using compatible numbers.

96 ÷ 8 = 12

Solve for the exact answer. 97 ÷ 8 = 12 R1

What does the remainder represent?

What do you with the remainder?

What is the answer?

Eli baked 404 cookies. He sells the cookies in boxes of 8. After he boxes all of the cookies, he will give the leftovers to his brother. How many cookies will he give his brother?

Solve using compatible numbers.

400 ÷ 8 = 50

Solve for the exact answer. 404 ÷ 8 = 50 R4

What does the remainder represent?

What do you with the remainder?

What is the answer?

Eitan has 294 tulip bulbs he needs to plant. He puts 5 bulbs in each row. How many rows will he make?

Solve using compatible numbers.

300 ÷ 5 = 60

Solve for the exact answer. 294 ÷ 5 = 58 R4

What does the remainder represent?

What do you with the remainder?

What is the answer?

Mannie’s grandmother gave him $89 to share with him and his brother. How much money did each of them get?

Solve using compatible numbers.

$90 ÷ 2 = $45

Solve for the exact answer. $89 ÷ 2 = $44 R1

What does the remainder represent?

What do you with the remainder?

What is the answer?

Lesson instructions 5

Divide. Then, multiply to check your answer. Remember to add back in your remainder.

For example, divide a two-digit dividend by a two-digit divisor, then use multiplication to check the answer.

Find the remainder for each of the following.

There are 89 boxes of cereal. 14 boxes of cereal can be placed on a shelf. How many shelves can be filled? How many boxes will be on the partial shelf?

At the apple orchard, Roy’s family picked 45 apples. They put 12 apples in a bag. How many full bags did they have? How many apples were in the partial bag?

A store bought 65 fans. If they can fit 13 fans on a shelf, how many shelves will be needed?

Thomas is getting silverware ready for a class picnic. He has 38 spoons. He puts 11 spoons in each bag. How many bags can he make? How many are left over?

Lesson instructions

Divide two-digit dividends by twodigit divisors and use multiplication to check the answers.

To Solve: Divide Multiply Subtract Bring Down Check

Divide and use multiplication to check your answers.

To Check: 1. Multiply the quotient by the divisor. 2. Add the remainder.

The school store has 88 folders and 12 erasers. Mr. Williams has 18 students. Does the school store have enough folders for each of his students to get 4 folders? How do you know? If each student needs 5 folders, how many more folders does the school store need?

Jack and Leo solved 82 ÷ 18. Below is the work each boy showed to check their answers:

Jack (3 R28) Leo (4 R10)

Leo has $96 to spend on model airplane kits. Each kit costs $15. How many kits can he buy? How much money will he have left over?

Who had the correct quotient? Why was the other one wrong?

Mr. Smith sells apple juice to stores in gallons. He has 98 gallons of juice and 12 containers. He uses the leftover gallons of juice to make punch. How many gallons will he use in each container? How many gallons will he use to make punch?

Lesson instructions 7

Divide three or four-digit dividends by two-digit divisors and use multiplication to check the answers. To Solve: Divide Multiply Subtract Bring Down Check

Divide and use multiplication to check your answers.

To Check:

1. Multiply the quotient by the divisor. 2. Add the remainder.

Mr. Anderson has 2,412 tiles for his art class. Each student needs 45 tiles to make their projects. He has 55 students. How many more tiles does he need for each of his students to get 45 tiles?

Eli printed 789 workbooks to sell. Each shipping box holds 35 workbooks. How many boxes does he need to order to ship the workbooks?

There are 598 passengers at the airport. Each shuttle holds 42 passengers. How many shuttles will the airport use to transport all of the passengers?

There are 1,260 guests at the resort. The cafeteria tables seat 12 guests. How many tables do they need to seat all of the guests?

Solve using what you have learned about dividing by multiples of ten.

Use compatible numbers to estimate the quotient.

Divide: 7 ÷ 6 = 1

Multiply: 1 x 6 = 6

Subtract: 7 - 6 = 1

Bring down: 4

Divide 14 ÷ 6 = 2

Multiply: 2 x 6 = 12

Subtract: 14 - 12 = 2

Bring down: 8

Divide 28 ÷ 6 = 4

Multiply: 4 x 6 = 24

Subtract: 28 - 24 = 4

Remainder: 4

A school is buying chairs for the library. If each chair costs $35, and they have $2,000 to spend, how many chairs can the school buy?

There are 419 students in a school. If the principal wants them to be in classes of 20 students, about how many classes will there be?

Matthew made 66 ounces of lemonade. If he puts it in 16 ounce jars, how many jars can he fill?

Ryan has a book that is 259 pages long. If he wants to read it in 7 days, about how many pages should he read each day? Use compatible numbers to help you estimate.

Chapter 3

In Chapter 3, we will learn about

Decimal Place Value

In Chapter 3, we will learn about

Decimal Place Value

Decimal numbers are important because they can describe a situation more accurately than whole numbers.

• Place value of decimals to thousandths

• Write decimals in expanded form

• Place value of decimals to thousandths

• Write mixed numbers as decimals

• Write decimals in expanded form

• Identify decimals

• Write mixed numbers as decimals

• Compare and order decimals

• Identify decimals

• Round decimals

• Compare and order decimals

• Problem solve

• Round decimals

• Problem solve

We can write the place value of digits up to the thousandths place.

We can write decimals in decimal and fractional expanded form.

We can write a decimal from a model or mixed number.

We can use place value to compare and order decimals.

We can write a decimal from a model or mixed number.

We can round decimals to a given place value.

We can solve word problems with decimals.

We can use place value to compare and order decimals. We can round decimals to a given place value. We can solve word problems with decimals.

Lesson instructions 1 Write numbers less than one. We can write numbers less than one in different forms.

Fraction Form: 1 10

Decimal Form: 0.1 Word Form: One-tenth

Fraction Form: 1 100

Decimal Form: 0.01 Word Form: One-hundredth

7 10 of Eugene's cars are red. Write this number as a decimal and in word form.

Adam spent three tenths of his money on a new ball. Write this number as a fraction and in decimal form.

Gerald received $0.05 back in change when he bought some candy. Write this number as a fraction and in word form.

Robert saw that 76 100 of an inch of rain fell yesterday. Write this number as a decimal and in word form.

Write the expanded form.

Expanded form shows the value of each individual digit.

For example, in the decimal 3.45, there are three ones, four tenths, and five hundredths.

Write the value of the bold digit in each number.

3.256

Write the expanded form of each number.

Write the standard form of each of these numbers.

300 + 70 + 5 + 0.2 + 0.005

James bought 3.26 pounds of bananas. Write the expanded form of this number.

Noah took 17.541 seconds to swim across the pool. Write the expanded form of this number.

Paul weighed a rock and found that it was 75.46 kg. What is the value of the 6 in this number?

Ralph found that a door was 2.13 meters tall. What is the value of the 1 in this number?

Lesson instructions 3 Read mixed numbers.

When reading mixed numbers, start with the largest place value to the left. Read the decimal point as “and.” Then add the value of the last digit.

One Tenths Hundredths

For example, 7.08 is read as “seven and eight hundredths” and 7 8 100 in fraction form. 7. 0 8

Michael ran a race in 9 75 1,000 seconds. Write this number in decimal and word forms.

Randy spent $8.12 on a hat. Write this number in word and fraction forms.

Patrick saw that two and three tenths inches of snow fell last night. Write this number in both decimal and fraction forms.

Alan walked 8.050 km in a fundraiser. Write this number in both fraction and word forms.

Identify each number.

Complete the chart.

There are 5 boxes shaded out 1,000. We can write this number in different ways: Fraction: 5 1,000

Decimal: 0.005

Word Form: five thousandths

Helen’s bead collection of 1,000 beads has 120 red beads, 515 blue beads, and 365 green beads. Write each of these values as a fraction, decimal, and word form.

Tim spent seventy-five hundredths of his money on a candy bar. Write this number as a fraction and as a decimal.

Mr. Ross filled his car with 12.048 gallons of gas. Write this number as a fraction and in word form.

It took Rose 45.123 seconds to drink her milk. Write this number in expanded form.

Red Blue Green

Lesson instructions 5

Compare and order decimals.

To compare and order decimals using <,>, and =, line up the decimals and compare starting with the largest place value to the left. If numbers are equal, move to the next number on the right. Compare the following numbers using <, >, or

For example, the numbers in the tens and ones are the same. Move to the right of the decimal point and compare. 8>7, so 15.8 > 15.7

Write the numbers in order on the lines below.

Richard ran a race in 17.015 seconds, and Nathan ran the race in 17.1 seconds. Who ran the race faster?

Jason's backpack weighs 3.05 kg, and Raymond's backpack weighs 3.009 kg. Whose backpack weighs more?

Jeremy swam four laps. His times for each lap were 18.41, 18.3, 18.1, and 18.05. Put his times in order from least to greatest.

Bruce measured three sunflowers and found the heights were 3.09 m, 2.76 m, and 2.9 m. What is the height of the shortest sunflower? What is the height of the tallest sunflower?

Lesson instructions 6

Round decimals.

To round decimals:

1. Identify the digit in the place value you are rounding to. 2. Look the number to the right. If it is lower than 5 ( 0,1,2,3, or 4), it should be rounded down. If it is 5 or higher (5,6,7,8, or 9), round up to the next number.

. 3 8 7

For example, to round 6.387 to the nearest hundredths, find the digit in the hundredths place, 8, then use the digit to the right. 7. 7 is higher than 5, so round the 8 up one number → 6 . 3 9

Round the following decimals to the nearest whole numbers.

Round the following decimals to the nearest tenths.

Round the following decimals to the nearest hundredths.

Billy jumped 120.4 inches. About how many inches is this? Round to the nearest whole number.

Andrew ate 0.45 pounds of grapes. About how many pounds did he eat? Round to the nearest tenth of a pound.

Matthew ran 142.95 meters in ten seconds. About how far is this? Round to the nearest tenth of a meter.

Walter saw that the gas price was $3.449. About how much did the gas cost? Round to the nearest hundredth.

Appy decimal skills to different situations and problems.

Recipe A uses 4.25 cups flour

Recipe B uses 4 30 100 cups flour

Which recipe uses more flour? Write both as decimals and compare, 4.25 < 4.30; recipe B uses more flour.

Write in the decimal and put the boxes in order from smallest to largest value shaded.

Write the word form of each decimal.

Mr. Smith drove 15.262 miles to work, and Mrs. Smith drove 15.226 miles to work. Who drove farther to work?

Donald takes nineteen and forty-five hundredths seconds to put on his shoes. Harry takes nineteen and fiftyfour hundredths seconds to put on his shoes. Who is quicker at putting on his shoes?

Sam spent $35.67 on school supplies, and Jake spent $36.76. Who spent more money?

Donna is comparing two boxes of cereal. One box contains 5.5 grams of fiber, and the second box contains 5 1 2 grams of fiber. Which box of cereal has more fiber?

Eli has to carry two piles of books to the library. The first pile weighs 5.376 pounds, and the second pile weighs 5.367 pounds. Which pile should Eli give his friend so Eli can carry the lighter pile?

A writer has written 658 words of a 1,000 word story. Write the value as a decimal and its expanded form.

Complete the chart.

+ 0.02

Word Form: twelve hundredths

Line up place values. 54.92 <- greater

Round the numbers to the place value indicated.

Round 5.32 to the nearest tenths.

5.32 → 5.3

The digit on the right is less than 5, so we round down.

A jar of applesauce has 10.1 ounces. Write this number in both fraction and word forms.

A container of yogurt had 5.3 ounces. Write this number in both fraction and word forms.

Brandon's sculpture weighed 4.729 kg. Round the weight of his sculpture to the nearest hundredth.

Rick’s container of pennies weighed 2.482kg. Round the weight of his penny jar to the nearest tenth.

Chapter 4

In Chapter 4, we will delve into

Addition and Subtraction of Decimals

Decimals are used in everyday life, especially with money.

• Add decimals

Decimals are used in everyday life, especially with money.

• Subtract decimals

• Add decimals

• Check subtraction with addition

• Subtract decimals

• Find missing addends and continue patterns

• Check subtraction with addition

• Problem solve

• Find missing addends and continue patterns

• Problem solve

We can use models and place value to add and subtract decimals.

We can use inverse operations to check our work.

We can use models and place value to add and subtract decimals.

We can ﬁnd a rule for a pattern and use it to ﬁnd missing numbers.

We can use inverse operations to check our work.

We can solve decimal word problems with money.

We can ﬁnd a rule for a pattern and use it to ﬁnd missing numbers.

We can solve decimal word problems with money.

Add and subtract decimals using models. For example, color in each decimal number in the models to find the answer.

Fill in the grid to show decimals, then add.

Add the decimals using the standard algorithm.

Eli has 0.3 of a yard of cloth. He bought 0.65 of a yard. He needs 1 yard of cloth. Does he now have enough cloth? How much cloth does he have?

Richard read for 1.47 hours on Monday. On Wednesday, he read for 2.34 hours. How many hours did he read altogether on Monday and Wednesday?

During the first week of training camp, Moses swam 4.64 miles. For the next 2 weeks, he swam 5.78 miles per week. How many miles did he swim during training camp?

Solomon ran the 40 yard dash during practice. The first day, he ran for 4.22 seconds. The next day, he ran for 4.41 seconds. The final day, he ran for 4.01 seconds. How many seconds did Solomon run the 40 yard dash during his fastest and slowest times?

Lesson instructions 2 Add decimals by stacking the numbers and lining up the place values. 2.73 + 1.20 3.93 651.0 + 23.6 674.6

Add by stacking the numbers on top of each other and lining up the place values.

17.2 + 13.65 = 5.63 + 7.365 =

6. 0.56 + 2.785 = 32.1 + 15.32 =

1. 2. 15 + 13.2 = 225 + 13.2 =

7. 8. 7.002 + 5.6 = 0.306 + 2.01 =

9. 10. 12.56 + 25 = 57 + 5.362 =

Max ran his first race in 13.247 seconds and his second race in 13.095 seconds. How long did it take him to run both races?.

2.7 inches of snow fell on Monday, 1.3 inches fell on Tuesday, and 4.8 inches fell on Thursday. How much snow fell in all?

Jack walked 0.3 miles to school and then another 0.18 miles to his friend. How far did he walk in all?

George bought 2.3 pounds of pears, 7.2 pounds of bananas, and 5 pounds of apples. How much did the fruit he bought weigh altogether?

Lesson instructions 3

Subtract decimals using models and the standard algorithm.

For example, show the minuend on the model and cross out the subtrahend to get the answer.

Subtract by coloring in the model. Start by coloring in the minuend and crossing out the subtrahend to find the answer.

Solve using the standard algorithm.

David ran a mile in 8.25 minutes. Eli ran a mile in 7.69 minutes. How many minutes faster was Eli than David?

Richard has $20.00. He spent $18.09. How much change did he get back?

Leo has $35.98, and Chad has $48.12. How much more money does Chad have than Leo?

Moses needs to run 84.8 miles per month. So far this month, he has run 47.9 miles. How many more miles does he have left to run?

Lesson instructions 4

Subtract decimals by stacking the numbers and lining up the place values.

- 1.20

- 1.200 2.454

Subtract by stacking the numbers on top of each other and lining up the place values.

6. 0.82 � 0.005 = 21.36 � 20 =

1. 2. 22 � 14.2 = 57 � 18.603 =

7. 8. 82.2 � 7.43 = 362 � 19.36 = 9. 10. 85.36 � 35 = 6.35 � 5.321 =

Jack ran the race in 14.037 seconds. Gary ran the race in 11.985 seconds. How many seconds faster was Gary than Jack?

Jeffrey found that a bunch of bananas weighed 3.86 pounds. After eating two, he found that it weighed 2.19 pounds. How many pounds of bananas were eaten?

A bag of chips weighed 5.3 ounces.

Frank ate 1.45 ounces. How many ounces of chips are left?

Daniel's backpack weighed 16 pounds, which was too much. He took out a book that weighed 5.2 pounds. How much does his backpack weigh now?

instructions 5

Subtract decimal numbers and use addition to check your answer.

Subtract by stacking the numbers on top of each other and lining up the place values. Then use addition to check your answers.

Leo has $15.49. He needs $23.45 to buy a toy he wants. How much more money does he need?

When David measured his plant, it was 38.78 cm. He measured it 3 weeks later, and it was 45.34 cm. How many centimeters did his plant grow?

Kane drinks 32.10 ounces of water every day. By lunchtime, he drank 29.44 ounces of water. How many more ounces of water does he need to reach his goal?

Leo swims 5.75 miles per week. By Thursday, he swam 3.99 miles. How many more miles does he have to swim to reach his weekly goal?

Find the missing decimal number and identify the rule.

Identify the rule and fill in the missing numbers in the sequences.

Finding the missing addends.

Fill in the missing numbers in Input/Output tables.

Leo reads the same amount of time every day. He adds up his reading time per week. His time for Monday and Tuesday was 3.3 hours. When he added in Wednesday, his reading time for the 3 days was 4.95. What will his reading time be when adds Thursday? How much time does he spend reading each night?

David’s bakery orders butter every month. In March, he ordered 12.5 pounds of butter. In April, he ordered 14 pounds of butter. In May, he ordered 15.5 pounds of butter. If this pattern continues, how many pounds of butter will he order in June?

Mr. Levine gave his David 4.1 points. He gave Leo 8.2 points. He gave Moses 12.3 points. Following the same pattern, how many points will he give Kane?

In science class, Mr. Andersen had 1.8 mL of liquid in the first beaker. There was 3.6 mL in the second beaker. The third beaker had 5.4 mL of liquid. How many mL of liquid will be in the fourth beaker?

$2.56 + $1.34

Rewrite vertically. Line up the decimals, then solve. $21.70 + $1.25 $22.95 $21.70 + $1.25 = $22.95

+ $1.75 $11.25 + $6.43

$3.82 + $0.46 = $15.75 + $6.19 = $21.45 + $13.74 =

+ $0.91

+ $3.15 $12.09 + $10.99 $4.05 + $1.86 $15.75 + $4.22 $22.74 + $18.56

+ $2.11 =

+ $3.71 =

Carl went swimming at the pool. It cost him $5.50 for admission to get in and $1.65 to rent a tube. How much did he spend in all?

Henry bought a new backpack for $12.99 and a package of pencils for $2.74. How much did he spend altogether?

Gerald went to the store and bought meat and bread for his mother. The meat cost $10.74, and the bread was $2.97. How much did he pay in all?

Jeffrey has saved $52.19. He earned $4.65 more this week. How much does he have now?

Use models to solve.

0.24 + 0.24 = 0.48

Fill in the missing zeros and solve.

Subtract. Then check with addition.

Fill in the missing numbers in the sequences.

Use subtraction to find the missing addends.

Mr. Levine has $325.50 to buy supplies for his class. His total comes to $321.84. How much money does he have left over?

Eli bought a box of cereal that had 22.83 oz of cereal. His brothers ate 19.75 ounces of cereal. How many ounces are left for Eli to eat?

David fed his dog 5.8 ounces of food on Monday. He fed his dog 7.2 ounces of food on Tuesday. How much more food did his dog get on Tuesday?

Mr. Smith wrote the following sequence of numbers on the board:

5.2, 4, 2.8, ?

What is the next number in the sequence?

What is the rule of the pattern?

Chapter 5

In Chapter 5, we will learn about

Multiplying Decimals

We will begin to recognize the role of the decimal point in multiplication and use estimation to see if our answers are reasonable.

• Estimate decimal products

• Multiply decimals by whole numbers and decimals

• Multiply decimals by 10, 100, or 1,000

• Multiply decimals by whole numbers and decimals

• Find area and perimeter with decimals

• Multiply decimals by 10, 100, or 1,000

• Find area and perimeter with decimals

We can use rounding or compatible numbers to estimate decimal products.

We can use models and an algorithm to multiply decimals.

We can use patterns of 10 to move the decimal point over when multiplying by 10, 100, or 1,000. We can ﬁnd area and perimeter with decimals.

Lesson instructions 1

Estimate the product using rounding. 4.2 + 3.8 = 4 + 4 = 8

Estimate the answers to the following problems.

A car can drive 17.3 miles for every gallon of gas. Approximately how far can it drive with 2.8 gallons of gas? Estimate to solve.

James's watering can holds 3.96 liters. If he fills it 5 times, about how much water did he use? Estimate to solve.

A kilometer is 0.6 miles. If Matthew's dad drove 14.2 kilometers, about how many miles did he drive? Estimate to solve.

Andrew bought 5 packages of rolls which cost $2.79 each. About how much did he pay for the rolls? Estimate to solve.

Lesson instructions 2

Multiply a whole number by a decimal.

Multiply a decimal by a decimal.

1. Show one factor vertically.

2. Show the other factor horizontally.

3. The place they overlap is the product.

Match the model to the equation. Write the sum.

One side of a square box is 0.89 feet. What is the perimeter of the box? Draw a model to show your work.

Find the area of a field that is 0.6 miles long and 0.4 miles wide. Use the hundreds chart to show your work.

John tasted 3 different cakes. He ate 0.25 of each cake. How many cakes did he eat in total?

A pound of onions costs about $0.80 per pound. If you buy 0.6 pounds of onions, how much will you spend?

Lesson instructions 3 Multiply decimals by one-digit whole numbers.

Set up the problem. Multiply. Count the digits behind the decimal in the problem. Put that many in the answer. 3.65 × 2 7.30

Michael bought 2 backpacks that cost $14.99 each. How much did he pay in all?

Bruce's uncle pays $4.50 each time he uses the car wash. If his uncle used the car wash 3 times this month, how much has he paid?

Mr. Jackson buys 8 pounds of deli meat that cost $5.99 a pound. How much does he pay in all?

Mrs. Branson needs 3 gallons of milk. Each gallon costs $2.67. How much does she pay for milk?

Lesson instructions 4 Multiply decimals by two-digit whole numbers.

Set up the problem. Multiply. Count the digits behind the decimal in the problem. Put that many in the answer.

A school ordered 42 books for $36.95 each. How much did they pay in total for the books?

Sarah bought a dozen donuts. Each donut was 3.99. How much did Sarah spend on donuts?

A box of cereal weighs 17.64 ounces. How much do 63 cereal boxes weigh?

A large window is 12 feet wide and 5.8 feet tall. What is the area of the window?

Multiply a decimal by a decimal.

1. Set up the multiplication problem by putting the number with the most digits at the top. 2. Solve the multiplication problem as you would normally do.

3. Count the number of digits to the right of the decimal in each factor. Put the same number of digits to the right of the decimal point in the product.

2 digits after decimals + 1 digits after decimals = 3 digits after decimals

Bananas cost $0.69 per pound. If Samuel bought 7.4 pounds, how much did he pay for the bananas? Round to the nearest hundredth for dollar amounts.

Gas costs $3.79 per gallon. 8.3 gallons were bought. How much did the gas cost in all? Round to the nearest hundredth for dollar amounts.

David bought 13.5 pounds of peaches at the orchard and paid $0.40 a pound. How much did he pay in all? Round to the nearest hundredth for dollar amounts.

Timothy can walk 4.3 miles in an hour. How far can he walk in 1.25 hours?

Lesson instructions 6 Multiply decimals by multiples of ten.

Find the missing numbers.

1. Multiply the non-zero numbers.

2. Move the decimal point to right for each zero. 3.22 × 10 = 3.22 = 32.2 3.22 × 100 = 3.22 = 322 3.22 × 1000 = 3.22 = 3220

8. 0.11 × 10 = 4.33 × = 43.3 9. 10. 9.40 × 1,000 = × 1 = 1.2

70.0 × 10 = × 100 = 850

Jeremy bought a package of 100 plates for $26. How much did each plate cost?

It costs $0.58 to drive a mile. How much does it cost to drive 1,000 miles?

One ticket cost $13.85. How much would 10 tickets cost?

There are 5.4 grams of mustard in a serving. The bottle says it contains 100 servings. How much does the mustard in the bottle weigh?

Lesson instructions 7

Find area and perimeter with decimal measurements. Area = Length × Width

Perimeter = Sum of side lengths

Find the area and perimeter of each figure.

Stephen's living room is in the shape of a rectangle. It measures 17.6 feet in one direction and 12.2 feet in the other direction. What is the perimeter of his living room?

The Smith family wants to build a fence around their backyard. Their backyard is rectangle that is 32.65 feet wide and 24.51 feet long. Will 117 feet of fencing be enough? Explain.

Mark's room measures 12 feet by 9.8 feet. What is the area of Mark's room?

How many square feet of tile are needed to tile a bathroom that is 6.8 feet by 5.8 feet?

Estimate the answers to the following problems.

2 digits after decimals + 0 digits after decimals = 2 digits after decimals 1.35 × 3 4.05

Find the area and perimeter of each figure. Round to the nearest tenths.

Area = Length × Width

6.2 × 3.4 = 21.08 cm2

Perimeter = Sum of side lengths

6.2 + 6.2 + 3.4 + 3.4 = 19.2 cm

Helen is planting a flower garden that is 12.8 feet by 3.6 feet. What is the area of the flower garden?

Hannah is fencing her rectangular garden, which measures 9.5 feet by 7.2 feet. What is the total length of fencing Hannah needs to enclose her garden?

Grapes cost $1.62 a pound. Tyler bought 3.5 pounds. How much did he pay?

Each day, Gabriel's dad drives 67.4 miles for work. If Gabriel's dad worked 5 days this week, how many miles did he drive?

Chapter 6

In Chapter 6, we will expand on

Multiplying and Dividing Decimals

We can use multiplication and division of decimals to ﬁnd the price of a unit item or the price when we buy a few of the same item.

• Estimate decimal quotients

• Multiply decimals by whole numbers and decimals

• Multiply and divide money

• Use multiplication to check division with decimals

• Problem solve with decimals

We can use compatible numbers to estimate decimal quotients.

We can use models and an algorithm to divide decimals by whole numbers and decimals.

We can use what we know about decimals to multiply and divide money.

We can check our work by using inverse operations. We can solve word problems with decimals using all four operations.

Lesson instructions 1 Use compatible numbers to estimate quotients. For example, use the multiples of a divisor to find the closest compatible dividend.

Use compatible numbers. Circle the better estimate.

Rewrite each equation to show the best estimate for each problem below.

Moses traveled 23.2 miles to and from work over 3 days. About how many miles did he travel per day?

Eli bought 39.1 pounds of fruit salad for his class. There are 10 kids in his class. About how many pounds of fruit salad will each student get?

Mannie uses 145.1 chocolate chips to bake 11 cookies. About how many chocolate chips does each cookie have?

Solomon poured 29.6 liters of juice into cups for his 15 friends. About how many liters of juice did each friend get?

instructions

Use models to divide decimals.

Draw a model for each problem. Write the equation. Then, solve.

Solomon has 5.25 gallons of water. He needs to transfer the water into 5 containers. How many gallons of water will go into each container?

Richard uses 3.6 ounces of chocolate to make 6 chocolate bars. How many ounces of chocolate were put into each chocolate bar?

Eli has 1.25 feet of cloth. He needs to use the cloth to make 5 art projects. How many feet of cloth will he use for each project?

David has 2.4 gallons of paint. He has 3 rooms to paint. How many gallons will he use in each room?

Divide decimals by whole numbers.

First, set up the division problem and solve the same way you divide whole numbers. Then, place a decimal in the quotient by moving the decimal point directly above the decimal in the dividend.

example, 5.35 divided by 5 = 1.07

Nathan bought 6 books for $8.10. If each book cost the same amount, how much did one book cost?

Patrick bought 8 bananas, which weighed 4.16 pounds total. If each banana weighed the same amount, how much did each banana weigh?

Samuel has 7 bags of salt that weigh 249.2 pounds. If each bag of salt weighs the same amount, how much does one bag of salt weigh?

Phillip mowed lawns for 4.25 hours this week. If he mowed the same amount every day for 5 days, how long did he mow each day?

Divide decimals by decimals.

1. First set up the division problem. Move both decimal points to the right until the divisor is a whole number.

2. Move the decimal point to be used in the quotient.

Solve. Round answers to the nearest hundredths when necessary.

3. Then, divide normally.

A bag of chips weighs 7.8 ounces. If a serving of chips is 1.2 ounces, how many servings are in the bag?

Richard bought 2.8 pounds of strawberries for $5.32. How much did one pound of strawberries cost?

A box of cereal weighs 15.6 ounces and costs $2.34. How much does it cost per ounce ($/oz)?

The race is 12.6 miles long. If Vincent can run 4.5 miles an hour, how long will it take him to run the whole race?

Multiply and divide money amounts.

Make sure to add back in the dollar sign and decimal point.

Solve. Round answers to the nearest hundredths when necessary.

Jamie spent $48.24 for 3 dozen cookies. How much was each cookie?

The school cafeteria bought 65 cans of corn. Each can cost $1.37. How much did they cost in all?

Harry spent $12.48 for 12 bracelets. How much was each bracelet?

The school cafeteria bought 9 cases of milk. Each case cost $33.95. How much did they cost in all?

Lesson instructions 6 Divide decimals and use multiplication to check your answers. For example, divide 3.57 by 3.

Solve each division problem. Then, check your answer using multiplication.

Solve. Use multiplication to check your answers.

Harry bought 3 bags of potato chips for $9.75. How much did each bag cost?

David’s mom gave him $16.50 to pay for his and his brother’s carnival tickets. How much did each carnival ticket cost?

Eli spent $25.75 on 5 snack packs. How much did each snack pack cost?

Kane spent $40.48 on books. He bought 8 books. How much money did each book cost? × 3 × 5 × 2 × 8 3 $9.75

instructions

Decide which operation is needed to solve.

For example, if the problem requires multiplication, choose the expression that shows multiplication with the correct factors.

Circle the expression that will help solve the problem correctly.

Moses has $23. He spent $12.95. How much change did he get back?

Bags of cookies cost $3.99. How much does it cost to buy 3 bags? $3.99 × 3

Kane bought 5 donuts. Each donut cost $1.55. How much money did he spend?

Richard bought a hot dog for $3.05 and a drink for $1.75. How much money did he spend?

Match the expression to the correct answer.

Harry paid $5.75 for 3 cupcakes. How much did each cupcake cost?

Eli makes $15 per hour. He worked 7.5 hours. How much money did he make?

David bought a pizza for $15.90 and a bag of cookies for $7.65. How much money did he spend?

Solomon bought 5 packs of cards for $12.25. How much did each pack cost?

Kane has $45. He spent $34.88. How much money did he have left?

Use a model to help you divide, then use multiplication to check.

Mannie bought a 6-pack of juice for $6.90. How much did each bottle of juice cost?

Richard bought 8 cookies. He paid $21.60. How much did each cookie cost?

Eli bought 3 pairs of shoes for $88.20. How much did each pair of shoes cost?

Mr. Levine spent $231.75 on tickets for his students to go to the aquarium. He has 9 students. How much did each ticket cost?

Chapter 7

In Chapter 7, we will practice

Addition and Subtraction with Fractions

This chapter involves fractions that have diﬀerent denominators since many fractions we need to work with in the real world do not have the same denominator.

• Compare, order, and locate fractions on a number line

• Estimate sums and diﬀerences with mixed numbers

• Compare, order, and locate fractions on a number line

• Add and subtract fractions with unlike denominators

• Estimate sums and diﬀerences with mixed numbers

• Add and subtract mixed numbers with unlike denominators

• Add and subtract fractions with unlike denominators

• Problem solve

• Add and subtract mixed numbers with unlike denominators

• Problem solve

We can ﬁnd equivalent fractions in order to compare them. We can use benchmark numbers to estimate sums and diﬀerences of mixed numbers.

We can ﬁnd a common multiple to make equivalent fractions or mixed numbers so we can add or subtract them. We can solve word problems with addition and subtraction of fractions and mixed numbers.

Lesson instructions 1

Rewrite each fraction with a common denominator. Then, compare using <, >, or =.

The common denominator is 30

Equivalent fractions with a common denominator are:

and

Rewrite each fraction with a common denominator. Then, compare using <, >, or =.

The common denominator is:

Equivalent fractions are: Equivalent

The common denominator is:

Helen and Judy each have a collection of marbles. Helen has 3 5 of her marbles in blue, while Judy has 2 3 of her marbles in blue. Who has more blue marbles?

John and Leo are both saving money for a trip. John saved 3 4 of his monthly allowance, while Leo saved 5 6 of his. Who saved a larger portion of money?

Ben and David are both preparing for a big test. Ben completed 2 3 of the test material, while David completed 3 4 of the same test material. Who completed the most?

Ann and Lisa are participating in a baking competition. Ann baked 2 5 of her recipes using chocolate, while Lisa baked 3 8 of her recipes using chocolate. Who used less chocolate?

Determine if each fraction is closer to 0, ½, or 1.

Estimate the solution to each problem using benchmark numbers.

7 15 of the players were wearing white shirts. Is this closer to 0, 1 2 , or 1?

At the farmer's market, Jack bought 5 1 3 pounds of green beans and 1 5 6 pounds of tomatoes. About how much did the vegetables weigh in all?

Estimate using benchmark numbers.

Kevin drank 7 1 2 cups of water today and 8 7 8 cups of water yesterday. About how much more water did he drink yesterday?

Estimate using benchmark numbers.

Vincent spent 7 20 of an hour doing chores. Is this closer to 0, 1 2 , or 1 hour?

4, 8, 12, 16, 20, 24, 28 5, 10, 15, 20, 25, 30

1. Find the lowest common multiple for both denominators.

2. Write equivalent fractions.

Solve and reduce the fractions to simplest form. If the answers are improper fractions, turn them into mixed numbers.

Jason needs 1 3 a cup of butter for muffins and 1 4 cup of butter for the muffin topping. How much butter does he need in all?

Peter studied math for 1 2 of an hour and history for 3 10 of an hour. How long did he study in all?

Vincent ate 1 3 of a cup of raisins and 2 5 of a cup of dried cranberries. How much dried fruit did he eat in all?

Tyler ate 3 8 of his candy bar. He gave 1 4 of his candy bar to his brother. How much of the candy bar is gone now?

Add mixed numbers with unlike denominators.

Simply if necessary.

1. Find the lowest common multiple for both denominators.

2. Write equivalent fractions by multiplying the numerator and denominator by the same factor.

3. Add the numerators and then the whole numbers. Simplify if necessary.

At the deli, Mrs. Thomas orders 2 1 4 pounds of sliced turkey and 1 2 3 pounds of sliced roast beef. How much meat does Mrs. Thomas order in all?

Alexander is making a wood door stop in the shape of an L. One side of the door stop will be 2 1 8 inches. The other side of the door stop will be 4 3 4 inches. How much wood will Alexander need to make the whole door stop?

Christopher is bringing fruit to a picnic. He buys a watermelon that weighs 10 2 5 pounds and a cantaloupe that weighs 5 1 2 pounds. How many pounds of fruit did he buy in all?

Ethan is making some scarves. He buys 4 5 6 yards of one type of fabric and 1 7 8 yards of a different type of fabric. How many yards of fabric did he buy in all?

instructions

Subtract fractions with unlike denominators.

1. Find the lowest common multiple for both denominators.

2. Write equivalent fractions by multiplying the numerator and denominator by the same factor.

3. Subtract the numerators and simplify if necessary.

David had 2 3 of a cup of milk and needed 1 2 of a cup for a recipe. How much milk will he have left?

Gary had 4 5 pound of peanuts and ate 1 3 of a pound. How many pounds of peanuts does he have left now?

Larry had 3 4 of a book left to read. He read 2 5 of the book this weekend. How much does he have left to read?

Scott had 1 2 of a chocolate bar and ate 1 4 of it. What fraction of the bar is left now?

Lesson instructions 6 Subtract mixed numbers with unlike denominators. 1. Find the lowest common multiple for both denominators. 2. Write equivalent fractions and subtract. If the top numerator is smaller than the bottom numerator, borrow a whole in fraction form.

There were 9 2 5 gallons of water left in a bucket. After filling the water bowls for his cats and dogs, Roy found that there were only 6 1 4 gallons left. How much water did Roy put in the water bowls? Simplify your answer if possible.

7 1 2 pounds of apples were on the kitchen table. Stephen used 2 4 5 pounds for making apple tarts. How many pounds of apples are left? Simplify your answer if possible.

Wayne had 4 3 4 pounds of strawberries. He used 2 1 2 pounds for a strawberry pie. How many pounds of strawberries does he have left? Simplify your answer if possible.

Thomas made 3 2 9 quarts of lemonade. After serving his family, there was 1 3 8 quarts left. How much lemonade did he serve?

Use the following steps to solve word problems:

1. Read the problem and think about what is being asked.

2. Make a plan to add or subtract to solve.

3. Solve and check by estimating.

Fred studied 8 10 of an hour on Monday. On Tuesday, he studied 4 5 of an hour. How many total hours did Fred study on Monday and Tuesday combined?

Solve using the problem solving strategy.

Ken’s rose is 3 8 of an inch long. How much does his rose have to grow to reach 19 20 of an inch? 1.

» Read and Understand

Read the problem and consider what is being asked.

» » Plan

Make a plan to solve the problem.

» » » Solve

Work out the problem and check that your answer is reasonable by estimating the answer.

John’s shoes are 1 1 9 feet long, and Tim’s shoes are 16 18 feet long. What is the difference between the lengths of John’s and Tim's shoes? 2.

Kevin has a table that is 6 1 12 feet long. He can extend the table to be even longer by adding a piece that is 1 3 8 feet long. What is the total length of the table when the extra piece is added? 3.

At the first visit to the vet, a panda at the zoo weighed 16 6 15 pounds. A month later, the panda weighed 42 2 45 pounds. How much weight did the panda gain between visits?

Jordan lives 1 7 8 miles from the shopping center. Nathan lives 2 1 2 miles from the shopping center. How much further is Nathan than Jordan from the shopping center?

Gary's bed is 7 1 3 feet long, and his dresser is 3 1 8 feet long. If he put them next to each other, how much of the room will they take up?

Harold had a bag of candy that weighed 3 1 8 ounces. His brother had a bag that weighed 2 1 4 ounces. How many ounces did their bags weigh together?

Raymond played outside for 1 1 3 hours and played board games with his family for 2 3 4 hours. How long did he play in all?

Solve and reduce the fractions to simplest form. If the answers are improper fractions, turn them into mixed numbers.

1. Make sure both fractions have the same denominator 2. Add 3. Simplify

Jerry has 8 5 8 ounces of juice. Noah has 7 3 4 ounces of juice. How much more juice does Jerry have than Noah?

Matthew combined 2 3 of a cup of yogurt with 1 2 a cup of blueberries to make a smoothie. How much smoothie does he have altogether?

Timothy's room was 10 7 12 feet long and 8 1 3 feet wide. How much longer is it than wide?

Anthony had a board that was 25 5 8 inches long. He cut a smaller board that was 14 3 4 inches long to make a shelf. How long is the original board now?

Chapter 8

In Chapter 8, we will learn about

Multiplying Fractions

In Chapter 8, we will learn about

Multiplying Fractions

Multiplying fractions comes up often in real life, especially in statements that use the word “of.”

• Multiply fractions and wholes

Multiplying fractions comes up often in real life, especially in statements that use the word “of.”

• Multiply fractions and fractions

• Multiply fractions and wholes

• Multiply fractions and mixed numbers

• Multiply fractions and fractions

• Use factoring to multiply fractions

• Multiply fractions and mixed numbers

• Understand size when multiplying fractions

• Use factoring to multiply fractions

• Problem solve

• Understand size when multiplying fractions

• Problem solve

We can use models and the standard algorithm to multiply fractions by fractions, wholes, or mixed numbers.

We can use factoring to get a simpliﬁed product. We can accurately predict if the product will be greater or less than each factor and one.

We can solve word problems with multiplication of fractions.

We can use factoring to get a simpliﬁed product. We can accurately predict if the product will be greater or less than each factor and one.

We can solve word problems with multiplication of fractions.

Lesson instructions 1

Multiply fractions and wholes.

You can use a number line or the standard algorithm.

Turn the whole number into a fraction by placing the whole over 1.

Multiply the numerators and denominators

Solve and reduce the fractions to simplest form. If the answers are improper fractions, turn them into mixed numbers.

Samuel poured 3 4 of a cup of orange juice for every person at the table. There were 5 people at the table. How many cups of orange juice did he need? Simplify your answer and write it as a mixed number, if possible.

Eric is making trail mix. If he wants to fill 7 bags with 1 2 cup of trail mix, how much trail mix will he need? Simplify your answer and write it as a mixed number, if possible.

Charles feeds his dog 7 8 cup of dog food every day. How much food will he feed his dog in 5 days? Simplify your answer and write it as a mixed number, if possible.

Thomas needs 2 3 a cup of milk for each batch of cookies. If he makes 4 batches of cookies, how much milk will he need? Simplify your answer and write it as a mixed number, if possible.

Multiply fractions using a model and the standard algorithm.

= pounds

Model - divide the grid to match the first fraction. Then, find the amount of the second fraction in the divided part.

Standard algorithm - multiply the numerators and denominators across. Simplify as needed.

Solve and reduce the fractions to simplest form. If the answers are improper fractions, turn them into mixed numbers.

Jack has 1 2 a pizza remaining. He eats 1 4 of the remaining pizza. What fraction of the original pizza did Jack eat?

Mark is walking 5 6 of a mile to his friend’s house. He stops at a stoplight when he is 1 2 way there. What fraction of a mile had Mark walked when he stopped?

William has 3 4 of a cup of almonds. He uses 2 3 of them for a recipe. How many cups of almonds did he use in the recipe?

2 7 of Justin's school day is working on reading and writing. Because of an assembly, his teacher announced that they would only have 1 2 the amount of time they normally do to work on reading and writing. What fraction of the school day will they work on reading and writing today?

Solve and reduce the fractions to simplest form. If the answers are improper fractions, turn them into mixed numbers.

Larry's pizza dough recipe calls for 3 1 2 cups of flour. He only wants to make 1 2 the recipe. How many cups of flour will he need?

Frank spent 6 3 4 hours at school today. If he worked on his science project for 1 9 of the time, how many hours did he spend on his science project?

A room is 4 1 2 yards long and 3 1 3 yards wide. What is the area of the room?

A trail is 1 1 4 miles long. If Gregory walked it 2 1 2 times today, how many miles did he walk?

Solve using factoring if possible. Solve and simplify if necessary.

There is 3 8 gallon of milk in the fridge. At breakfast, Henry's family uses 1 3 of the milk. How much milk did they use? If possible, use factoring to solve.

Mrs. Johnson bought 1 2 pound of carrots. If she uses 2 5 of them when making salads, what fraction of a pound did she use? If possible, use factoring to solve.

During free time in art class, 1 2 of the students chose to paint. If 4 5 of those painting chose to mix paints to create new colors, what fraction of the whole class was mixing paints? If possible, use factoring to solve.

Jeffrey read 3 4 of a book this weekend. If he read 2 3 of that on Sunday, what fraction of the book did he read on Sunday? If possible, use factoring to solve.

Lesson instructions 5 Shade in two out of three boxes in each of the two shapes. Then, answer the more or less questions.

Will your answer be more or less than 2? less of 2 2 3 Shade in the models to represent each multiplication equation and answer the questions.

Will your answer be more/less than 2 3 ? more

Will your answer be more or less than 2 5 ?

Will your answer be more or less than 2?

Will your answer be more or less than 1 2 ?

Will your answer be more or less than 4?

Will your answer be more or less than 2 5 ?

Will your answer be more or less than 2?

Will your answer be more or less than 1 2 ?

Will your answer be more or less than 4?

your answer be more or less than 1 3 ? Will your answer be more or less than 3? Will your answer be more or less than 1 3 ? Will your answer be more or less than 3?

The Empire State Building in New York City is about 1 1 2 times as tall as the Eiffel Tower in Paris. The Tokyo Skytree in Japan is about 3 4 as tall as the Empire State Building.

List the buildings in order from tallest to shortest.

Andy and Ben are siblings. Andy is 3 5 as tall as their father, while Ben is 4 7 as tall as their father.

If their father is 180 centimeters tall, how tall are Andy and Ben?

Father’s height = 180 centimeters

Eli and Jake are baking cookies. Eli’s recipe calls for 2 3 cup of sugar, while Jake’s recipe calls for 3 4 cup of sugar.

If they both want to make the same amount of cookies, who needs more sugar, Eli or Jake?

Sam and Max are training for a marathon. Sam runs 3 5 of the distance every day, while Max runs 2 3 of the distance every day.

If the marathon is 30 kilometers long, who runs a greater distance each day, Sam or Max?

Lesson instructions

Multiply fractions with a model.

1. Color in the first fraction vertically. 2. Color in the second fraction horizontally. 3. The overlapping fraction is the product.

Solve. Then, create a model to represent each multiplication equation.

Harry is remodeling his bathroom. He plans to cover the bathroom floor with tiles that are 1 square foot. His bathroom floor is 6 1 2 feet wide by 4 1 4 feet long. How many tiles will he need to cover the floor?

John has 20 tiles that are each 1 4 square foot. Does he have enough tiles to cover a space that is 25 square feet? Does he have enough cover a space that is 7 square feet?

There was 2 3 of leftover cake. Kelly ate half of that. Did she eat more or less than half the cake? Explain.

Lisa jogged 1 3 of a 1 2 mile loop around the park. How much did she jog?

Lesson instructions 7 Multiply fractions and mixed numbers.

1. Convert the mixed number into an improper fraction (5 × 2 + 1).

2. Multiply the numerators (1 × 11).

3. Multiply the denominators (2 × 5).

4. Simplify/convert back to a mixed number ( 11 10 = 1 R1).

On Monday, Emma baked for 3 4 of an hour. On Tuesday, she baked for 5 12 of an hour. Did she bake for a longer or shorter amount of timeon Tuesday than she did on Monday?

Sara and her two friends, Judy and Helen, are sharing pizzas equally. They each want to have 3 4 of a pizza. How much pizza do they need to order so they can all have the same amount?

A farmer has two sacks of apples on the scale with a combined weight of 18 kilograms. If the weight of sack A is 1 4 of the total weight, how much does sack A weigh?

Steven has a rectangular swimming pool that is 8 1 2 meters long. If he has a pool cover that covers 2 3 the length of his pool, how many meters does the cover span?

Solve and reduce the fractions to simplest form. If the answers are improper fractions, turn them into mixed numbers.

1. Change mixed numbers to improper fractions

2. Multiply the numerators and denominators across.

3. Change the improper fraction back to a mixed number and simplify as needed.

Analyze each question, then circle MORE or LESS to answer each question.

Multiplying Fraction rules:

Fraction × fraction→ answer is less than smaller factor

Fraction or mixed number × mixed number → answer is greater than smallest factor

Create models to represent each multiplication equation and solve.

Ava needs 1 2 gallon of paint to cover a small wall. She has 3 walls that are the same size. How many gallons of paint will she need to paint all the walls?

Liam needs 1 3 of a yard of fabric to make a small flag. He wants to make 5 flags for his classroom. How much fabric does he need in total?

David is building a bird feeder out of wood. He needs 2 1 2 feet of wood to make each side of the feeder. He wants to build the feeder with 3 4 sides. How much wood will David need in total?

Lisa paints pictures. She uses 1 1 4 cups of paint per picture. If she paints 2 1 2 pictures, what fraction of a cup of paint will she use in total?

In Chapter 9, we will expand on

Dividing Fractions

In Chapter 9, we will expand on

Dividing Fractions

Dividing fractions helps us ﬁgure out how much we get when we share a portion of a fraction.

• Write fractions as division equations

• Find reciprocals of fractions

• Write fractions as division equations

• Divide whole numbers and fractions

• Find reciprocals of fractions

• Use patterns that follow rules

• Divide whole numbers and fractions

• Use the order of operations with fractions

• Use patterns that follow rules

• Problem solve

• Use the order of operations with fractions

• Estimate products and quotients with fractions

• Problem solve

• Estimate products and quotients with fractions

We can rewrite fractions as division problems and solve them.

We can ﬂip the numerator and denominator to ﬁnd the reciprocal of a fraction.

We can multiply by the reciprocal to divide fractions.

We can ﬂip the numerator and denominator to ﬁnd the reciprocal of a fraction.

We can ﬁll in an input/output table using a rule and ﬁnd missing values in patterns with fractions.

We can multiply by the reciprocal to divide fractions.

We can use the order of operations to solve problems with fractions.

We can ﬁll in an input/output table using a rule and ﬁnd missing values in patterns with fractions.

We can solve word problems with division of fractions.

We can use the order of operations to solve problems with fractions.

We can use compatible numbers to estimate products and quotients with fractions.

We can solve word problems with division of fractions. We can use compatible numbers to estimate products and quotients with fractions.

Lesson instructions 1 Write the mixed number as a division problem. Then, solve and write as a decimal.

Write the mixed number as a division problem.

Fill in the missing numbers.

Mrs. Alpine’s class is baking cookies for a charity event. They need to know how much sugar to add to the recipe. The recipe calls for 3 4 cups of sugar. What is 3 4 cup as a decimal?

Emma is planning a road trip, and she wants to calculate the distance she’ll travel each day. She estimates that she’ll drive 150.6 miles per day. To better understand her daily distance in terms of fractions, she wants to convert this decimal into a fraction. Can you help her?

Bob and Abe were asked to calculate the ratio of water to vinegar in a solution. Bob wrote the ratio as 9÷6, while Abe wrote it as 9 6 . Which student is correct in representing the ratio of water to vinegar?

John is planning a bike trip and wants to calculate the distance he’ll travel each day. He estimates that he’ll ride 8.7 miles per day. To better understand his daily distance in terms of fractions, he wants to convert this decimal into a mixed number. Can you help him?

Fill in the missing factor.

Justin wants to share a chocolate bar among 9 friends. What fraction of the bar would each friend get? Use the reciprocal to help you find the answer.

Kevin is working on reciprocals in class. The original fraction is 5 3 8 . He is stuck and can't decide if the reciprocal is 8 23 or 8 43 . Which one is correct?

John is explaining that there are two steps to finding the reciprocal of a mixed number. Fill in the blanks to finish his explanation: “First, you change the mixed number to an fraction. Then, you the position of the numerator and denominator.”

A glass holds 2 3 of a cup. How many times should Bruce fill it to get one cup?

1. Flip the fraction to find its reciprocal.

2. Turn the whole into a fraction by placing a 1 as the denominator.

3. Multiply the numerators and denominators across. If the answer has a 1 as the denominator, it is a whole number.

Solve and reduce the fractions to simplest form. If the answers are improper fractions, turn them into mixed numbers.

Richard ordered 3 pizzas for the party. If he estimates that each person will eat 1 3 of a pizza, how many people will the pizzas feed?

Timothy has 2 3 of a pound of chocolate candy. If he splits it into 4 equal groups to share with friends, how much will each person get?

Anthony bought a large, 5 pound bag of peanuts. He divides it up into 1 2 pound bags to have for snacks. How many snack bags can he make?

Mrs. Thomas spreads 1 4 cup of salad dressing over 5 salads. How much salad dressing does each salad get?

A bean plant grew 5 6 inch each week for 4 weeks. If it started out 2 1 6 inches tall, how tall is it now?

A sunflower grew 3 4 inch each week for 6 weeks. If it started out 1 1 2 inches tall, how tall is it now?

At the age of 10, Emma was 52 3 8 inches tall. She grew 1 5 8 inches each year. How tall was she when she was 15?

At the age of 9, Sara was 45 7 10 inches tall. She grew 1 3 5 inches each year. How tall was she when she was 12?

Lesson instructions

( ) Parentheses A2 Exponents × Multiplication ÷ Division + Addition - Subtraction or or

Use the order of operations to solve. 5 + 3 × (8 - 2)2 ÷ 4

1. Parentheses: 8 - 2 = 6

2. Exponents: 62 = 36

3. Multiplication and Division: 3 × 36 = 108, 108 ÷ 4 = 27

4. Addition: 5 + 27 = 32

Amy went to the store to buy some fruits. She bought 3 apples for $1 each, 2 bananas for $0.50 each, and 1 pineapple for $3. She also bought a bag of grapes that cost $2. If she gave the cashier a $10 bill, how much change did she receive?

Tom is planting roses around the perimeter of his rectangular garden with a length of 7 meters and a width that is 3 meters less than twice the length. He wants to plant 10 roses per meter and needs to buy enough rose bushes before he starts planting. How many rose bushes does Tom need to purchase?

Helen is planning a party for her friend. She needs to decorate the party room with balloons. Each balloon bouquet consists of 3 small balloons and 2 large balloons. Helen has ordered 5 bouquets for the party. Additionally, she wants to add 10 extra large balloons scattered around the room. If each small balloon costs $0.50, each large balloon costs $1.00, and each extra large balloon costs $2.00, how much will Helen spend on balloons?

Judy wants to bake cupcakes for her friends. She needs to buy cupcake liners, each pack containing 12 liners, and frosting, each tub containing enough for 24 cupcakes. If Judy wants to make 36 cupcakes, how many packs of cupcake liners and tubs of frosting should she buy?

Lesson instructions 6 Use reciprocal fractions to solve.

To divide fractions:

1. Multiply by the reciprocal.

2. Simplify.

The cafeteria has 6 bags of chips for snack time. There are 24 students in the class. What fraction of a bag of chips can each student have? 24 1 ÷ 6 1 = 24 1 × 1 6 = 24 6 = 1 4

A serving of trail mix contains 1 4 cup of raisins. A box of trail mix contains 3 cups of raisins. How many servings of raisins are in the box?

The teacher has 4 boxes of crackers for snack. There are 20 students in the class. What fraction of a box of crackers can each student have?

There is 1 2 of a pan of brownies left on the counter. If Sarah wants to divide the brownies between 6 people, how much of the pan does each person get?

The bag of rice holds 4 cups. If a serving size is 1 2 cup, how many servings are in the bag?

A baby bathtub needs 10 gallons of water. If Sarah uses a cup that holds 1 4 of a gallon to fill the bathtub, how many cups will she pour into the bathtub?

There are 4 bags of candies to share among 16 children. What fraction of a bag does each child get?

A bottle of juice is 6 cups. If a serving size is 1 2 of a cup, how many servings are in the bottle?

Sarah has 3 4 of a bag of sugar. If she bakes 8 batches of muffins with the sugar, how much of the bag does each batch use?

A blow up pool can hold 12 gallons of water. If Tim uses a bucket that holds 1 3 of a gallon, how many buckets will he need to fill the pool?

A serving of almonds is 1 4 cup. A bag contains 3 cups of almonds. How many servings are in the bag?

Thomas walks 1 1 8 miles to school every day. About how far does he walk in 5 days? Estimate the answer using benchmark numbers. Show your work.

Samuel is dividing 2 5 8 cups of sunflower seeds into 1 3 cup servings. About how many servings does he have? Estimate the answer using benchmark numbers. Show your work.

Vincent has 16 1 4 pounds of potatoes. A recipe takes 3 4 5 pounds of potatoes. About how many batches of the recipe can he make? Estimate using benchmark numbers. Show your work.

A room measures 9 7 8 feet by 13 1 12 feet. What is the approximate area of the room? Estimate the answer using benchmark numbers. Show your work.

Write each improper fraction as a division problem. Then, solve.

Find the reciprocal to make the equation true.

Michael wants to give 3 4 of a candy bar to each of his 8 friends. How many candy bars does he need?

Frank had 8 cups of corn. He gave 1 2 of a cup to each chicken. How many chickens did he feed?

Each juice carton has 3 4 cup of juice. If there are 11 juice cartons, how many cups of juice are there? Simplify and write your answer as a mixed number, if possible.

Edward walks 9 10 of a mile around the block. If he stops at the park 1 2 of the way around the block, how far has he walked?

Chapter 10

In Chapter 10, we will explore

Geometry

In Chapter 10, we will explore

Geometry

The world is composed of three-dimensional shapes that are each composed of two-dimensional shapes.

• Classify polygons, triangles, and quadrilaterals

The world is composed of three-dimensional shapes that are each composed of two-dimensional shapes.

• Classify 2-D ﬁgures in a hierarchy

• Classify polygons, triangles, and quadrilaterals

• Find area and perimeter with fractional side lengths

• Classify 2-D ﬁgures in a hierarchy

• Classify solid ﬁgures

• Find area and perimeter with fractional side lengths

• Classify solid ﬁgures

We can name 2-D ﬁgures and describe them by their side lengths and angles.

We can classify a shape in more than one category. We can solve word problems with area and perimeter with and without fractions.

We can name 2-D ﬁgures and describe them by their side lengths and angles.

We can classify a shape in more than one category. We can solve word problems with area and perimeter with and without fractions.

We can name 3-D ﬁgures and describe them based on the number of faces, edges, and vertices.

Name the polygons.

Name each polygon and write regular or irregular.

Complete the chart.

Number

Edward notices that a STOP sign has 8 equal sides and angles. What shape is the STOP sign?

Edward then notices that the YIELD sign he passes has three sides, but not all of the same length. What shape is the YIELD sign?

As Edward's family continues on their drive, he notices a rectangular sign telling the speed limit. Is this sign regular or irregular?

Finally, Edward's family passes by a school sign that has five sides and looks like a house. What shape is this sign?

Lesson instructions 2 Classify triangles by the sides and angles. Equilateral (allall sides equal; is also isoceles)

Isosceles (two sides equal)

Scalene (all sides different)

Right angle (may be isosceles or scalene, but one angle must be a right angle)

For each triangle, specify if it is equilateral, isosceles, or scalene. If it is a right triangle, put a checkmark by it.

An architect is designing a new park and wants to include a triangular fountain as a centerpiece. The architect sketches out her design on paper, with one side of the triangle measuring 8 meters, one side 11 meters, and one side 5 meters. Identify the type of triangle.

A group of friends is planning a camping trip and needs to set up a triangular canopy over their tent to provide shade during the day. The friends have a roll of fabric that is 10 meters wide. They decide that the two equal sides of the triangular canopy should each measure 8 meters in length. Identify the type of triangle.

Sara is designing a flower bed in her garden with each side of the triangle measuring 6 feet.

Identify the triangle.

A carpenter is constructing a triangular roof frame for a small shed. The base of the frame measures 12 feet, and each of the two equal sides measures 8 feet. Identify the type of triangle.

Name the polygons.

Decide if each polygon below is an example of the five types of quadrilaterals. Write Y for yes or N for no on the line next to each quadrilateral name.

1. 3. 2. 4. square rectangle rhombus parallelogram trapezoid square rectangle rhombus parallelogram trapezoid

Write true or false for each statement.

5. All squares are rectangles.

6. Some parallelograms are also squares.

7. Every rectangle is a square.

8. A rhombus must have four congruent sides.

9. Parallelograms cannot be rectangles.

10. Some rectangles are also rhombuses.

11. A parallelogram may have just one pair of parallel sides.

12. All squares are rhombuses. square rectangle rhombus parallelogram trapezoid square rectangle rhombus parallelogram trapezoid

Arthur drew a quadrilateral. What could be another name for this shape?

Is a rhombus always a square or a square always a rhombus? Explain.

What is the name for a quadrilateral that only has one pair of parallel sides?

A farmer wants to enclose a rectangular field with a fence. However, due to the uneven terrain, the sides of the field are not all the same length. After measuring, the farmer finds that the longer side of the field measures 60 meters, while the shorter side measures 40 meters. What rectangular shape is the field?

Lesson instructions 4 Use the images to help answer the questions.

Are the following statements true or false? Put an X in the appropriate box.

All quadrilaterals are parallelograms.

All parallelograms are quadrilaterals.

A square is a parallelogram.

A parallelogram with a right angle is a square.

All rectangles are parallelograms.

All rhombuses are squares.

All squares are rectangles.

A parallelogram with four congruent sides is a square.

A trapezoid cannot be a parallelogram.

All parallelograms with perpendicular angles are kites.

A parallelogram with four congruent sides is a rhombus.

All rectangles are squares.

I am a quadrilateral with four right angles. What shape am I?

I am a quadrilateral with at least one pair of parallel sides. What shape am I?

I am a quadrilateral containing two pairs of parallel sides. What shape am I?

I am a quadrilateral with four equallength sides. What shape am I?

the area by the measurement provided.

Find the length of the missing side, x.

Emma is planning to put a fence around her rectangular garden, which measures 30.2 meters by 18 meters. The fencing costs $15 per meter. How much will Emma spend on fencing for her garden?

Leo goes for a jog around a park on a beautiful morning. The track around the park is rectangular, measuring 3.5 kilometers by 2 kilometers. If he completes three laps around the park, how far will he have jogged in total?

Mrs. Williams is renovating her bathroom and wants to tile the floor. If the bathroom floor measures 8.7 feet in length and 6.5 feet in width, how many one square foot tiles will she need to cover the entire floor?

Amy goes for a walk around a neighborhood park on a sunny afternoon. The track around the park is rectangular, measuring 4.2 kilometers by 2.8 kilometers. If she completes five laps around the park, how far will she have walked in total?

Multiply the fractions by each other to find the area.

Label each square as a unit fraction.

Mark 1 4 and 3 4 on the sides of the rectangle. Shade the area of the rectangle with sides of 1 4 unit and 3 4 unit. Area of the shaded rectangle = square units

Multiply the numerators. Multiply the denominators.

Simplify the fraction by dividing the numerator and denominator by their largest common factor.

Label each square as a unit fraction.

Mark 3 8 and 5 8 on the sides of the rectangle. Shade the area of the rectangle with sides of 3 8 unit and 5 8 unit. Area of the shaded rectangle = square units

A tailor is crafting a patchwork blanket using fabric scraps. She has a piece of fabric that measures 7 8 of a meter by 3 4 of a meter. How many square meters is the fabric scrap?

The section of the garden with tomato plants measures 2 5 yard by 6 7 yard. How many square yards do the tomato plants take up?

The bookshelf against the wall measures 2 1 2 feet by 1 3 4 feet. How much wall space does the bookshelf occupy?

The bathroom floor is being renovated with new tiles. The floor measures 2 3 4 feet by 5 1 3 feet. How many square feet of tiles are needed for the bathroom floor?

Name the solid figures and then determine how many vertices, edges, and faces they have.

Vertices: Edges: Faces:

Rudy walks down the cereal aisle at the store. What shape is a box of cereal?

Jordan is outside shooting free throws. What shape is his ball?

How many faces and how many edges does a cylinder have?

Does a square pyramid have more vertices or edges? Explain.

Complete the chart. Polygon quadrilateral hexagon octagon nonagon

Triangle: 3 sides 3 vertices

Number of sides

Number of vertices

Drawing

Name the solid figures and then determine how many vertices, edges, and faces they have.

Vertices: Edges: Faces:

Name: Name: Name: Name:

Vertices: Edges: Faces:

Alice has a mirror that has 8 equal sides and angles. What shape is her mirror?

Jacob cut a slice of pie for himself. The slice had 3 sides that were different lengths. What shape is the slice?

A baker is decorating a cake using fondant. She has a piece of fondant that measures 5 6 of a meter by 2 3 of a meter. How many square meters is the fondant sheet?

A gardener is planning to install a rectangular flower bed in her backyard. She has a piece of land that measures 3 4 of a meter by 5 6 of a meter. What is the area of the flower bed in square meters?

Chapter 11

In Chapter 11, we will learn about

Volume and Data

In Chapter 11, we will learn about

Volume and Data

Volume helps us understand how much space is inside diﬀerent shapes.

• Find volume

• Use volume to ﬁnd a missing side

• Find volume of composite ﬁgures

• Use volume to ﬁnd a missing side

• Find elapsed time

• Find volume of composite ﬁgures

• Find elapsed time

• Create and interpret line plots

We can use cubes and side lengths to ﬁnd the volume of a rectangular prism.

We can ﬁnd the length of a missing side when we are given the volume.

We can divide composite ﬁgures into two smaller prisms to ﬁnd the total volume.

We can use a number line or subtraction to ﬁnd elapsed time.

We can create and interpret a dot plot with whole numbers and fractions given a list or frequency chart.

Lesson instructions 1 Use the number of cubes along the length, width, and height to find the volume of the prism. 3 cubes 4 cubes 3 cubes 3 × 4 × 3 = 36 36 cubes will fill this prism V=36u3

Find the volume of a prism that has a length of 5cm, a height of 6cm, and a width of 8cm. Find the volume of a prism that has a length of 7m, a height of 12m, and a width of 3m.

Find the volume of a prism that has a length of 3in, a height of 9in, and a width of 5in.

Find the volume of a prism that has a length of 15yd, a height of 6yd, and a width of 12yd.

Lesson instructions 2

Find the volume of rectangular prisms using the length, width, and height provided.

To find the volume, multiply the height, width, and length.

Height is 3

Width is 4

Length is 7.

Volume is 3 × 4 × 7 = 84

Label correctly: 84 units3

Find the volume of the rectangular prisms below. Be sure to show your work and check your units!

A drawer is 5 feet wide, 4 feet deep, and 2 feet tall. What is the volume of the drawer?

A carton of juice is 16 cm long, 5 cm wide, and 20 cm tall. What is the volume of the carton?

A paper bag is 16 cm long, 5 cm wide, and 20 cm tall. What is the volume of 5 bags?

The closet is 6 feet wide, 5 feet deep, and 8 feet tall. In the closet, there is a suitcase that is 2 feet wide, 3 feet long, and 4 feet tall. How much room is left in the closet?

Lesson instructions 3

Find the missing side lengths when given the volume and two side lengths.

You can use V = l × w × h to find h.

If volume is 32 and the length and width is 4 × 4, we can solve for the missing height, h. 32 = 4 × 4 × h 32

Find the missing side length using the volume. Show your work.

Volume = 840 mm3

Volume = 2,448 cm3

Volume = 2,280 m3

Volume = 405 m3

Volume = 3,080 mm3

Volume = 108 cm3

A shipping container is 10 yd long and 3 yd wide and has a volume 120 yd3. What is the length?

A box of cereal is shaped like a rectangular prism. The box is 20 cm long and 30 cm high. Its volume is 3,600 cubic cm. Find the width of the box.

The area of the base of a rectangular juice box is 4.5 square inches. If the volume of the juice box is 18 cubic inches, how tall is the juice box?

A large storage bin has a volume of 24 ft3. The length is 3 ft, and the width is 4 ft. Find the height.

How many small containers with dimensions 1 × 1 × 2 can fit into the large bin?

Lesson instructions 4

Find the volume of more than one prism. V = 15 × 6 × 9 V = 810m3

Divide the shape into multiple rectangular prisms. Find the volume of each. Add the volumes together. 810 + 216 = 1,026

Find the volume of the prisms below:

Ben has a raised garden bed. The diagram shows its measurements. All of the corners are right angles. If he fills the bed to the top with soil, how many cubic feet of soil will Ben need?

The rec center has a pool that is L shaped. One part is 8 meters by 6 meters, and the other is 12 meters by 6 meters. The whole pool is 4ft deep. Find the total volume of the pool.

A new sidewalk needs to be poured. How much concrete will be needed for the project?

A candy store is building a display with two rectangular prisms. The base of each prism is a square with an edge length of 5 inches. One prism is 12 inches tall, and the other is twice as tall. What is the total volume of the display?

A) 180in3 B) 300in3 C) 600in3 D) 900in3

Abe chose B as the answer. How did he get that answer? Is he correct? If not, what is the correct answer?

Lesson instructions 5

Determine the elapsed time or how much time has passed.

Look at the start and end times. Count up using a number line to find elapsed time. Count by hours first, then groups of minutes. 10:30 am - 3:25 pm 10:30 11:30 12:30 1:30 2:30 +30 minutes: 3:00 + 25 min 3:25 4 hours 55 minutes is the elapsed time.

Determine the elapsed time.

hours and minutes.

3:45 a.m. - 5:00 p.m.

hours and minutes.

8:36 a.m. - 12:00 p.m.

hours and minutes.

7:40 a.m. - 3:15 p.m.

hours and minutes.

6:52 p.m. - 2:00 a.m.

hours and minutes. 7:15 p.m. - 9:52 p.m.

hours and minutes.

6:45 a.m. - 11:30 a.m.

hours and minutes. 4:25 p.m. - 5:22 p.m.

hours and minutes. 9:00 a.m. - 7:22 p.m.

Identify the time on each clock and find the elapsed time.

Jeremy walked to school. He left at 7:55 a.m. and got there at 8:13 a.m. How long did it take him to get to school?

Jeremy's school started at 8:15 a.m. and got out at 3:30 p.m. How long was his school day?

Jeremy went to his friend’s house when he got out of school at 3:30 p.m. He got home at 5:15 p.m. How much time had passed since school got out?

Jeremy had piano practice at 6:45 p.m. and got out at 7:38 p.m, a little earlier than usual. How long was piano practice today?

Lesson instructions 6 Interpret and create dot plots using whole numbers.

This dot plot corresponds to the given set of numbers. Books read in one week: 1, 1, 1, 1, 1, 2, 2, 2, 3, 4

Books read in 1 week Number of books

1 2 3 4

A teacher calculated the number of minutes it took students to finish the test. The results were: 23, 18, 15, 22, 20, 17, 25, 19, 24, 15, 21, 21, 18, 18, 20, 22, 18, 20, 21, 19. Make a dot plot to display the data and use it to answer the questions that follow.

How many students took at least 22 minutes to finish the test?

How many minutes passed between the first and last student who finished the test?

How many students took less than 18 minutes to finish the test?

Which was more common, taking longer than 20 minutes, or taking less than 20 minutes?

What was the most common length of time the test took?

What was the median (middle) time it took to take the test?

Look at the tally chart and dot plot below. What error was made?

List at least two things every dot plot needs.

How are a dot plot and a frequency table the same? How are they different?

What is the range for the dot plot below?

Lesson instructions 7

Create dot plots using the data provided. A dot plot corresponds to a given set of numbers. Here one dot is put above the number line for each fraction listed.

homework:

Make a dot plot from the data below. Use it to answer the questions that follow.

Age of young children in a daycare center (in years):

What are the most common ages of students in the daycare?

How many students are in the daycare center?

What is the range of ages in the daycare center?

The oldest ten students will be in the same room. What is the range of ages for the oldest ten students?

How many students are at least 2 years old?

How many students are younger than 1 year?

What is different about using fractions in dot plots compared to whole numbers? What is the same?

A tailor has the following lengths of ribbon (in inches): 4, 4 1 2 , 4 1 2 , 5 1 2 , 6, 6, 6 1 2 , 8. Does a dot plot need to include the numbers 5, 7, and 7 1 2 ? Why or why not?

A grocery store owner is keeping track of the weights of bunches of bananas. What would be an appropriate title for the dot plot?

What mistake was made in the dot plot below?

Length of shoes in inches: 8, 8, 8 1 2 , 8 3 4 , 9, 9 1 4 , 9 1 4 , 9 3 4 , 10, 10, 10, 10 1 2 , 11

L = 3, w = 2, h = 4

V = l × w × h

V = 3 × 2 × 4 V =

Find the volume of a box with measures: 5in × 7in × 10in.

How much dirt fits in a planter box that is a cube with sides of 5 cm.?

How much water fits in a pool that is 8 meters × 4 meters and is 6 meters deep?

The volume of a prism is 140ft3. If the length is 5ft, and the height is 7ft, what is the width?

A cereal box has a volume of 1,540cm3. What is the height if the area of the base is 110cm?

You are building a wooden chest. The length is 5ft, and the width is 3ft. If the volume is 45 ft3, what is the height?

Create a dot plot for the number of cars sold each day last week using the data below. Create a frequency table if it’s helpful. Use the data to answer the question.

M, W, F, M, SU, F, W, T SU, F, M, ST, W, SU, F

Complete the table with the missing information.

On which day were the most cars sold? The least?

Create a dot plot for the number of bushels of hay used each day to feed the animals on the farm. The data is below. Create a frequency table if it’s helpful. Use the data to answer the question.

Which train has a longer route?

How many total bushels of hay were used in total?

Train B: Departure Time Arrival Time 8:36 a.m. 11:33 a.m.

Chapter 12

In Chapter 12, we will delve into

Measurement

The customary system of measurement is the most commonly used system in the U.S., while the metric system is easier to use and is used all over the world.

• Convert length

• Convert weight

• Convert length

• Convert capacity

• Convert weight

• Problem solve

• Convert capacity

• Problem solve

We can convert between units of length, weight, and capacity within the U.S. customary system.

We can move the decimal point over to convert between units of length, weight, and capacity within the metric system.

We can solve problems with conversions in everyday life.

We can move the decimal point over to convert between units of length, weight, and capacity within the metric system.

We can solve problems with conversions in everyday life.

Measure and convert the lengths.

Remember:

• When converting greater to lesser units, multiply.

• When converting from lesser to greater units, divide.

Use the chart to help convert the measurements.

To convert 3 feet, 8 inches to inches, first convert the feet to inches by multiplying: 3 ft × 12 in = 36 inches

Add the remaining inches: 36 in + 8 in = 44 inches

Customary Units of Length

1 mile (mi) = 1,760 yards (y) 1 mile (mil) = 5,290 feet (ft) � �

1 yard (y) = 3 feet (ft)

1 foot (ft) = 12 inches (in)

228 in ft

Jason is 4 feet, 11 inches tall. How many inches is this?

Carl can jump 90 inches in the long jump. How far is this in feet and inches?

The playground is 24 yards long. How many feet is this?

Ethan's car is 210 inches long. How long is this in feet and inches?

Convert from one unit to another.

Use the proper operation to convert.

Emma jogged a total of 80 kilometers this week. She jogged the same distance each day for 5 days. How many meters did she jog each day?

Amy is building a fence around her garden. Each wooden post she uses is 40 centimeters wide. If she needs 18 posts to enclose the entire garden, how many meters long is the fence?

In a craft store, there was a spool of ribbon containing 120 meters of ribbon. Twenty-five customers each purchased 80 centimeters of ribbon for their projects. How many meters of ribbon are left on the spool?

Kayla swam 1.5 kilometers on Tuesday, 2.1 kilometers on Thursday, and 1.8 kilometers on Saturday. How many meters did she swim this week?

Measure and convert weight.

• When converting a larger unit to smaller unit, multiply

• When converting a smaller unit to a larger unit, divide

Compare the units of measure using <, >, or =. Complete the conversion tables.

To convert 3 tons into pounds, multiply 2,000 × 3 = 6,000 pounds To convert 64 ounces in pounds, divide 64 by 16 = 4 pounds

Benjamin buys 80 oz of flour to make cookies. How many pounds is this?

An elephant weighs 6 tons. How many pounds does it weigh?

A small airplane weighs about 8,000 pounds. How many tons is this?

Dylan bought 2 pounds of strawberries for a recipe. He needs 30 ounces. Does he have enough?

Convert from one unit to another.

Use the proper operation to convert.

1. 2.

Sara is preparing a batch of cookies. She combined 300 grams of sugar, 400 grams of flour, 50 grams of chocolate chips, and 30 grams of baking soda. How many kilograms do all of the dry ingredients weigh?

Each book weighs 750 grams. If there are 6 books in a box, how many kilograms does the box of books weigh?

The weight limit for a luggage carousel at the airport is 300 kilograms. If 6 suitcases are placed on the carousel, each weighing the same amount, what is the maximum number of grams each suitcase can weigh?

A jar contains 1 kilogram of jelly beans. If 16 children each took 50 grams of jelly beans from the jar, how many grams of jelly beans are left in the jar? answer 200 grams

Convert liquid capacity.

Capacity is the measurement of how much a container can hold.

• When converting a larger unit to smaller unit, multiply.

• When converting a smaller unit to a larger unit, divide.

Use the chart to help convert the liquid measurements.

6 gallons c

14 cups pt

4 pints

To convert 1 gallon into pints, first convert 1 gallon into quarts. Then, convert the quarts into pints.

1 gallon × 4 = 4 quarts

4 quarts × 2 = 8 pints

1 pint (pt) = 2 cup 1 quart (qt) = 2 pt 1 gallon(gal) = 4 q � �

15 gal pt Capacity

1 cup (c) = 8 fluid ounces (fl oz)

20 quarts pt

Samuel needs 7 cups of juice for a special family brunch he is making tomorrow. He has 2 quarts of juice. Does he have enough?

Timothy's water bottle says it holds 16 ounces. How many cups is this?

Kevin drinks a pint of milk a day. How many quarts would he drink in 2 weeks (14 days)?

Anthony has a five-gallon bucket he filled with water. How many quarts of water is this?

Convert from one unit to another.

Use the proper operation to convert.

Judy takes 10 mL of cough syrup three times a day. She takes the syrup every day for six months (180 days). How many liters of syrup does she take in six months?

A farm has 4 separate animal pens. The total amount of feed in all the pens is 200 kilograms. If each pen contains the same amount of feed, how many kilograms of feed are in each pen?

Leo poured 3,500 milliliters of juice into a pitcher. Then, he added 1,200 milliliters of soda. He used 2 liters of the mixture to fill glasses for his guests. How many liters of the liquid are left in the pitcher?

A juice bar poured drinks for 4 people. Each persons juice filled a 300-milliliter glass. What is the total liters of juice in the four glasses?

centimeters = meters

kilograms = grams 2. 2.3 centimeters = milimeters

92 milimeters = centimeters

0.043 kilometers = meters

liters = 30,000 mililiters

mililiters = 18 liters

days = hours Convert from one unit to another.

mililiters = 22 liters

grams = kilograms

minutes = hours and minutes

= 2 hours and 38 minutes

Mrs. Madison is weaving a rug. The rug requires 500 meters of yarn in total. If she uses 30 centimeters of yarn per minute, how many hours will it take her to weave the rug?

Amy is a baker. She uses 2,500 grams of sugar each day. A 20 kg bag of sugar costs $30. How much does the sugar for 1 day cost?

Four members of the Stark family have set a goal of spending at least 800 hours reading books this year. If they each read for 45 minutes a day, will they meet their goal?

The Smith family is filling their new fish tank with water. The tank is 80 centimeters deep. They have used 2,000 liters of water and have only filled the tank 5 centimeters. How many kiloliters (kL) of water will it take to fill the whole tank?

12 inches = 1 foot

3 feet = 1 yard

36 inches = 1 yard

5,280 feet = 1 mile

1,760 yards = 1 mile inches = in

8 ounces = 1 cup

2 cups = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

At recess, Nic found that he could jump 3 1 3 yards. How many feet is this?

Ric and Abe measured their classroom and found that it was 396 inches long. How many yards is this?

Kane notices that a container says that it holds 100 ounces of liquid. How much is this in cups and ounces?

Jamie had one squash grow to be 3 lb 14 oz and another squash grow to be 3 lbs 12 oz. How much did the two squash weigh together?

Chapter 13

In Chapter 13, we will explore

Coordinate Planes and Graphing

In Chapter 13, we will explore

Coordinate Planes and Graphing

A coordinate plane can be used to describe a speciﬁc place in a space. It can also be used to show patterns.

• Deﬁne lines, points, and planes

A coordinate plane can be used to describe a speciﬁc place in a space. It can also be used to show patterns.

• Find and plot points on a coordinate plane

• Deﬁne lines, points, and planes

• Graph points in a line to represent real-world scenarios

• Find and plot points on a coordinate plane

• Generate patterns

• Graph points in a line to represent real-world scenarios

• Problem solve with dot plots

• Generate patterns

• Problem solve with dot plots

We can draw diﬀerent types of lines and points.

We can write the coordinates for a point on a coordinate plane and use an ordered pair to plot a point on a coordinate plane.

We can interpret a coordinate plane with points that represent a real-world situation.

We can write the coordinates for a point on a coordinate plane and use an ordered pair to plot a point on a coordinate plane.

We can generate a pattern to ﬁnd ordered pairs and graph them on the coordinate plane.

We can interpret a coordinate plane with points that represent a real-world situation.

We can interpret and problem solve with dot plots.

We can generate a pattern to ﬁnd ordered pairs and graph them on the coordinate plane.

We can interpret and problem solve with dot plots.

Lesson instructions 1

Study and understand the terms used in plane geometry. Plane geometry is about flat shapes that can be drawn on a piece of paper like lines, circles, and triangles. A plane is a two-dimensional surface. This means that it does not have height, only length and width that extend indefinitely in all directions.

Read the definitions of each of the plane geometry vocabulary below and draw a line to the image that best represents the description.

1. Intersecting Lines

Lines that will cross but do not make right angles

2. Point

An undefined dot on the page with no size or shape, just position

3. Ray

A portion of a line that has one endpoint and extends forever in one direction

4. Perpendicular Lines

Lines that will cross to make right angles

5. Line

A straight path of points that has no beginning or end

6. Parallel Lines

Lines that never touch

7. Line segment

A portion of a line that has two endpoints

Donald saw a set of railroad tracks. Were these lines intersecting or parallel?

Christopher saw two roads intersect at a stoplight. Could these be parallel or perpendicular lines?

What is the difference between a ray and a line?

What object has two endpoints?

Lesson instructions

Plot points on a coordinate plane.

Coordinates are written (x,y), where x tells us how far to move horizontally, and y tells us how far to move vertically.

Plot the points below and label them!

A = (7, 5) B = (3, 9)

C = (3, 6) D = (2, 4)

E = (2, 2) F = (1, 2)

G = (9, 6) H = (8, 3)

I = (0, 4) J = (1, 1)

Coordinate (3, 2) 3 units to the right & 2 units up

Write the coordinates for each of the points on the graph.

Define and label on the coordinate grid: X-axis

Define and label on the coordinate grid: Origin

Define and label on the coordinate grid: Y-axis

Define and label on the coordinate grid: Coordinate Point

Plot points on a coordinate plane.

1. Plot the points (find x on horizontal line, y on vertical line.)

2. Connect the points in order.

3. Determine which shape is created.

Plot the points and label them. Write the coordinate of each point.

(3,3) S (1,10)

(2,8) E (6,9)

(5,4) L (7,5)

(3,1) V (9,6)

(7,1) A (4,7)

(0,5) Y (9,0)

Use the points to create a shape. Plot a point and connect it to the next point.

Connect the last point to the first.

(2,2) (3,6), (7,6) (8,2)

Use the points to create a shape. Plot a point and connect it to the next point.

Connect the last point to the first.

(2,3) (4,6), (2,9) (0,6)

Use the points to create a shape. Plot a point and connect it to the next point.

Connect the last point to the first.

(4,6) (5, 3), (8,3) (9,6) (6.5,8)

Use the points to create a shape. Plot a point and connect it to the next point.

Connect the last point to the first.

(2,0) (2,8), (0,8) (0,0)

Identify the points.

1. Identify the point. 2. Use the units on the axes to determine context.

point (1,20) represents that in 1 hour, 20 pages are read.

What does the point (2, 80) mean in this context? What does the point (4, 200) mean in this context? What does the point (2,10) mean in this context? What does the point (6,30) mean in this context?

What does the point (1,300) mean in this context? What does the point (4,150) mean in this context?

The student council has a bake sale and sells packs of cookies each day for 5 days. Use the table to create a graph.

Use the context from scenario 1 to answer the questions below.

What does the point (2,10) mean in this context?

What does the point (4,6) mean in this context? How many packs of cookies were sold total?

Mr. Ross’s class goes to the library to borrow books each week. Use the coordinates below to create a graph.

(1, 4) (2,3) (3,8) (4,6) (5,5)

Use the context from scenario 3 to answer the questions below.

What does the point (2,3) mean in this context?

What does the point (5,5) mean in this context?

On which week did they borrow the most books? How many books were borrowed?

Lesson instructions 5

Complete the tables.

1. Plug the given values into the equation.

2. Solve the equation & record the solution in the table.

3. Continue for all given values.

Use the equation to complete the table.

Use this scenario to complete the table and explain the first set of values given the context.

Sam always scores two points higher than Max on his spelling quiz. If s is Sam’s score, and m is Max’s score, then s = m + 2

Use this scenario to complete the table and explain the first set of values given the context.

Each batch of brownies uses 2 eggs. If b = batches of brownies, and e = eggs used, then e = 2b.

Use this scenario to complete the table and explain the first set of values given the context.

The seventh-grade sewing club always sew 3 more projects a week than the fifth-grade sewing club. If s = the projects the seventh-grade sews, and f = the fifth-grade, then s = f +3.

Use this scenario to complete the table and explain the first set of values given the context.

For each T-shirt the store sells, they earn $6. If t = T-shirts sold, and e = earnings, then e = 6t.

Lesson instructions 6

Complete the tables.

1. Write coordinates from the table.

2. Use these coordinates to create a graph.

Complete the table and then write the coordinates from the table.

Write the coordinates from the graph.

Fill in the table, write the coordinates, and graph.

Each batch of cookies makes 20 cookies, b = batches and c = cookies.

Fill in the table, write the coordinates, and graph.

At a certain intersection, there are always 6 more bikes than scooters, if b = bikes and s = scooters.

Fill in the table, write the coordinates, and graph.

Denny always owns 10 more pairs of socks than he does shoes, p = pairs of socks and s = shoes.

Fill in the table, write the coordinates, and graph.

Every pack of candy costs $2, p = packs of candy and t = total cost.

Lesson instructions

Create dot plots.

Add a dot above the number that corresponds to each data point. There are five ones, so there are 5 dots above one.

Books read in 1 week: 1, 1, 1, 1, 1, 2, 2, 2, 3, 4

Use the data points to create a dot plot. Then, label the dot plot.

These are the resting heart rates of 16 boys sitting in the classroom.

80, 83, 82, 79, 80, 85, 83, 81, 79, 82, 80, 83, 80, 82, 83, 85

The data points show the number of road trips students have taken.

2, 0, 4, 1, 3, 2, 1, 0, 3, 5, 1, 2, 1, 4, 2, 3, 2, 2, 3, 5

The data points represent the amount of milk 9 families use in a week measured in gallons. 1, 1 3 , 1 3 , 1, 2 3 , 1, 1 2 3 , 1, 1 1 3

The data points represent the amount of time students studied for their test. 3, 2 1 2 , 4 1 2 , 3 1 2 , 5, 4 1 2 , 2 1 2 , 3 1 2 , 4, 3, 3 1 2 , 4,

Use the dot plot to answer the following questions.

A) What is the difference between the closest and farthest distance students live from school?

B) How many more students live 6 miles or closer to school than live farther than 6 miles?

A) What is the difference between the tallest and shortest students?

B) One student was absent. Their height was 3 8 of an foot less than the tallest student. What is their height?

Use the dot plot to answer the following questions.

A) What is the difference in height between the tallest bean plant and shortest?

B) How many more plants are 5 1 2 inches or taller than are less than 5 1 2 inches?

A) What is the difference between the most and least snowfall measurements?

B) How many times as much snow fell on the most snowy day as compared to the least snowy day?

For questions 1-6, plot the points and label them. For questions 7-12, write the coordinates for the point.

(3, 2)

Use the points to create a shape. Plot a point and connect it to the next point. Connect the last point to the first.

2) -> (5,2) -> (4,4)

George is a cashier at the farmers market. He tracked how many people bought apples each day this week. Use the table to create a graph.

Use the context from scenario 1 to answer the questions below.

What does the point (3,20) mean in this context?

On which days were the same amount of apples sold?

On which day were the most apples sold?

Each batch of muffins makes 14 muffins, b = batches and m =muffins. Complete the table and graph.

Use the dot plot to answer the following questions. On a field trip, students found animal footprints and measured them in inches. The data is below.

A) Which footprint length was the most frequently observed?

B) How many times longer is the longest footprint than the shortest?

Chapter 14

In Chapter 14, we will conclude with

Review

In Chapter 14, we will conclude with

Review

This chapter includes all concepts covered in this book.

• Understand place value with decimals

• Add and subtract decimals

• Understand place value with decimals

• Add and subtract decimals

• Use the order of operations with decimals and whole numbers

• Add and subtract fractions

• Use the order of operations with decimals and whole numbers

• Add and subtract fractions

• Multiply fractions and mixed numbers

• Divide fractions

• Multiply fractions and mixed numbers

• Solve for volume

• Divide fractions

• Solve for volume

• Use coordinate planes

We can write decimals in expanded notation and order numbers.

We can use place value to add and subtract decimals. We can use the order of operations to solve multistep problems with fractions, decimals, and whole numbers.

We can ﬁnd equivalent fractions to add and subtract fractions.

We can use place value to add and subtract decimals. We can use the order of operations to solve multistep problems with fractions, decimals, and whole numbers.

We can ﬁnd equivalent fractions to add and subtract fractions.

We can multiply fractions and mixed numbers with models and an algorithm.

We can multiply by the reciprocal to divide fractions.

We can multiply fractions and mixed numbers with models and an algorithm.

We can ﬁnd the volume or a missing side given the dimensions of a rectangular prism.

We can ﬁnd and plot points on a coordinate plane.

We can multiply by the reciprocal to divide fractions. We can ﬁnd the volume or a missing side given the dimensions of a rectangular prism.

We can ﬁnd and plot points on a coordinate plane.

Write the place value of the digit in bold.

Write the number in expanded form and word form.

854.123

Expanded Form:

800 + 50 + 4 + 0.1 + 0.02 + 0.003

Word Form: eight hundred fifty-four and one hundred twenty-three thousandths

Compare the following numbers using <, >, or =.

Line up place values

54.92 54.3

854.123 Thousandths place greater

Draw a model to represent 1.023. Then, write the fraction, expanded form, and word form.

Model of 2.4

Danny drank a glass of water in 27.891 seconds, and Larry drank the same amount in 27.981 seconds. Who drank faster?

Richard weighed some fruit. The blueberries weighed 2.719 pounds, and raspberries weighed 2.917 pounds. Compare the decimals using <, >, or =.

A company makes 5,690,250 boxes of cereal each year. Write this number in word form.

Jeffrey's dog weighed 9.71 kg. Write this number in expanded form.

Round to the nearest whole number and estimate the sum or difference. Then solve for the exact answer.

Rewrite vertically to line up the decimal points and estimate the sum or difference. Then, solve for the exact answer.

Albert put 39.8 pounds of sand in a sandbox. Jeremy put 26.9 pounds of sand in the sandbox. About how much sand did the two boys put in the sandbox? Round to the nearest whole number to estimate.

A new couch cost $650.99, but was on sale for $329.99. About how much cheaper is the couch now? Round to the nearest whole number to estimate.

Timothy has $6.83. If he buys a ball for $4.25, about how much money will he have left? Round to the nearest whole number to estimate.

Dennis filled a 12.8 pound wheelbarrow with 51.95 pounds of dirt. How much did the wheelbarrow and dirt weigh together? Round to the nearest whole number to estimate.

Simplify each expression using the order of operations.

P Parentheses & grouping symbols

Addition and Subtraction From left to right + -

Put parentheses in the correct place to make the expression true.

Placement of parentheses affects the answer!

3 + (2 × 6.5) - 8 = 8 (3 + 2) × 6.5 - 8 = 24.5

Harold's mom gave him 8 cookies. He gave 2 to his brother and then divided up the rest among 6 people (including himself). Because he was so kind, his mom gave him 3 more cookies, and he ate all his cookies. How many cookies did Harold eat? Write and solve an expression to represent this problem.

Benjamin's room is a square with each side being 12 feet, but it has a closet in the middle of it that takes up a 3-foot by 6-foot section. What is the area of Benjamin's room minus the space the closet takes up? Write and solve an expression to represent this situation.

David's family is replacing the tile in their dining room and laundry room. The dining room is 11 feet on each side. The laundry room measures 7 feet by 9 feet. What is the area of both rooms together? Write and solve an expression to represent this situation.

Adam had 8 rocks in his pocket, lost 3, and found 6 more. When he showed his friend Dennis, Dennis told him he had twice as many rocks. How many rocks did Dennis have? Write and solve an expression for this situation.

Estimate the solution to each problem using benchmark numbers.

Estimated answer

Add and simplify if necessary.

1. Make sure both fractions have the same denominator.

2. Add 3. Simplify

Subtract and simplify if necessary.

1. Make sure both fractions have the same denominator.

2. Subtract / regroup if needed

3. Simplify if needed.

Willie has 3 4 cup of chocolate chips and 1 3 cup of butterscotch chips. How much does he have in all? Simplify your answer if possible.

There were 7 1 4 gallons of gas in the car, and Vincent's dad put another 3 2 5 gallons in it. How many gallons of gas are in the car now? Simplify your answer if possible.

An aquarium holds 10 gallons. If Terry put in 2 1 3 gallons of water to fill it back up, how many gallons of water were in it to start with?

7 8 of the seats on the bus were empty when the bus came to the bus stop. When it started again, only 3 5 of the seats on the bus were empty. What fraction of the seats were filled at the bus stop? Simplify your answer if possible.

Multiply. 1. Turn to an improper fraction. 2. Factor. 3. Multiply. 4. Change to a mixed number.

Tim has 4 5 of a gallon of paint. If he uses 1 6 of it to paint a bookshelf, how much paint did he use? Simplify your answer if possible.

Michael walked to his friend's house, which was 3 4 of a mile away. He passed by school when he was 1 2 way to his friend's house. How far was school from Michael's house? Simplify your answer if possible.

A sea lion at the zoo eats 3 1 4 pounds of fish each day. If a penguin eats 2 3 of the amount eaten by the sea lion, how many pounds of fish does the penguin eat a day? Multiply, using factoring if possible.

Ryan and his little brother are watering the garden. His brother has 1 1 3 gallons of water in his watering can. Ryan has 2 1 2 times this amount. How many gallons does Ryan have in his watering can?

Write each improper fraction as a division problem. Then, solve.

Write the reciprocal.

Divide. Simplify if necessary.

Use the rule to fill in the table.

Solve using the order of operations.

Donald has 4 1 2 cups of flour. A recipe calls for for 1 1 2 cups of flour. How many batches of the recipe can he make?

Elijah needs 2 1 3 cubic yards of mulch for a flower bed. He orders 10 cubic yards. How many flower beds can he do with this much mulch? Write your answer as a mixed fraction.

David is trying to walk 15 1 2 miles. If he can walk 3 3 4 miles an hour, how long will it take him to walk the whole distance?

Ethan's class brought in 1 1 3 tons of recycling in March. In April, they brought in another 2 3 tons of recycling. How many tons did they bring in total? Write your answer as an addition problem and a whole number.

L = 3, w = 2, h = 4

V = l × w × h

V = 3 × 2 × 4 V = 24in3

V = 840in3 V = 2,280yd3

= 156ft3

Find the volume of a box with measures: 8in × 7in × 10in.

How much dirt fits in a planter box that is a cube with sides of 10cm.?

The volume of a prism is 140ft3. If the length is 4ft and the height is 7ft, what is the width?

A cereal box has a volume of 1,440cm3. What is the height if the area of the base is 120cm2?

For questions 1-6, plot the points and label them. For questions 7-12, write the coordinate for the point.

Use the points to create a shape. Plot a point and connect it to the next point. Connect the last point to the first.

George is a cashier at the farmers market. He tracked how many people bought cabbage each day this week. Use the table to create a graph.

Use the context from scenario 1 to answer the questions below.

What does the point (3,6) mean in this context?

On which days were the same amount of cabbages sold?

On which day were the most cabbages sold?

Each pair of shoes costs $18, s = pairs of shoes and t = total cost. Complete the table and dot plot.

The elementary school always has 10 more students than the middle school, e = elementary & m = middle school. Complete the table and dot plot.