Primary 4

Math Term 1

2024 – 2025

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Discovery Education, Inc.

4350 Congress Street, Suite 700

Charlotte, NC 28209

800-323-9084

Education_Info@DiscoveryEd.com

ISBN 13: 978-1-61 708-649-6

1 2 3 4 5 6 7 8 9 10 CJK 25 24 23 22 21 A

Revised by

Dr. Mohamed Mohyeldin Abdelsalam Eman Sayed Ramadan Mohamed George Yuhanna Meikheil Gerges

Supervision

Dr. Akram Hassan Mohamed

Head of the Central Administration

### Table of Contents

Foreword and Words from the Minister of Education and Technical Education .

Letter to the Parent/Guardian

Thème ’. | hlrlri ber 4eh se and Oge!’‹ctio s

VÏÏÏ

. x

Unit 1 Place Value

Concept 1.1 Reinforcing Place Value

Lesson 1 Big Numbers 3

Lesson 2 Changing Place Values 5

Lesson 3 Many Forms to Write Numbers. 7

Lesson 4 Composing and Decomposing 9

Concept 1.2 Using Place Value

Lesson S Comparing Big Numbers. 12

Lesson 6 Comparing Numbers in Multiple Forms. 14

Lesson 7 Descending and Ascending Numbers 17

Lesson 8 Rounding Rules 20

Unit 3 Addition and Subtraction Strategies

Concept 2.1 Using Addition and Subtraction Strategies

Lesson 1 Properties of Addition 24

Lesson 2 Addition with Regrouping .. . 27

Lesson 3 Subtraction with Regrouping 29

Concept 2.2 Solving Multistep Problems

Lesson 4 Bar Models, Variables, and Story Problems 32

Lesson S Solving Multistep Story Problems with Addition

and Subtraction . . . . .. . . . . . . . .. . . . . . . . .. . . . 35

Lesson 2 Measuring Mass 43

Lesson 3 Units of Capacity 45

Concept 3.2 Measuring Time

Lesson 4Lesson S | Units of Measuring Time . . . . . . . . . . . . . . . . . . . . . . . . . . . .Elapsed Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 485O |

Lesson 6 | Applications of measurement 1 . . . . . . . . . . . . . . . . . . . . . . | 53 |

Lesson 7 | Applications of measurement 2 . . . . . . . . . . . . . . . . . . . . . . | 56 |

Unit 4 Area and Perimeter

Concept 4.1 Explore Area and Perimeter

Lesson 1 | Finding perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 59 |

Lesson 2 | Finding area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 62 |

Lesson 3 | Unknown Dimensions . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . | 64 |

Lesson 4 | Complex Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 66 |

Unit S Multiplication as a Relationship

Concept 5.1 Multiplicative Comparisons

Lesson 4 | Commutative Property of Multiplicatio | 77 |

Lesson S | Identity Property and the Zero Prop | 79 |

Lesson 6 | Associative Property of Multiplicatio | 81 |

Lesson 7 | Applying Patterns in Multiplicatio | 83 |

Unit 7 Multiplication and Division: Computation and Relationships

Concept 7.1 Multiplying by 1-Digit and 2-Digit Numbers

Lesson 1 The Area Model Strategy 100

Lesson 2 The Distributive Property 102

Lesson 3 The Partial Products Algorithm 104

Lesson 4 multiply by a one-digit number. 107

Lesson 5 multiply a two-digit number by a multiple of 10 109

Concept 7.2 Dividing by 1-Digit Divisors

Lesson 6 Exploring Remainders 111

Lesson 7 Patterns in Division 113

Lesson 8 The Area Model and Division 116

Lesson 9 The Partial Quotients Algorithm. 117

Lesson 10 The Standard Division Algorithm . . . . . . . . . . . . . . . . . . . . | 119 | ”.•’ |

Lesson 11 Division and Multiplication. . . . . . . . . . . . . . . . . . . . . . . . . . | 121 | ” |

Unit 8 Order of Operations _{}

Concept 8.1 Order of Operations

This is a pivotal time in the history of the Ministry of Education and Technical Education (MOETE) in Egypt. We are embarking on the transformation of Egypt’s K-12 education system. We started in September 2018 with the rollout of KG1, KG2 and Primary 1. In 2021 we have rolled out Primary 4, and we will continue with the rollout until 2030. We are transforming the way in which students learn to prepare Egypt’s youth to succeed in a future world that we cannot entirely imagine.

MOETE is very proud to present this new series of textbooks, with the accompanying digital learning materials that captures its vision of the transformation journey. This is the result of much consultation, much thought and a lot of work. We have drawn on the best expertise and experience

from national and international organizations and education professionals to support us in translating our vision into an innovative national curriculum framework and exciting and inspiring print and digital learning materials.

The MOETE extends its deep appreciation to its own “Central Administration for Curriculum Development” (CACD) and “Disco\/ery Education,”

This transformation of Egypt’s education system would not have been possible without the significant support of Egypt’s current president, His Excellency President Abdel Fattah eI-Sisi. Overhauling the education system is part of the president’s vision of “rebuilding the Egyptian citizen” and it

is closely coordinated with the ministries of Higher Education & Scientific Research, Culture, and Youth & Sports. Education 2.0 is only a part in a bigger national effort to propel Egypt to the ranks of developed countries and to

WORDS FROM THE MINISTER OF EDUCATION & TECHNICAL EDUCATION

Dear students and fellow teachers,

It gives me great pleasure to celebrate this crucial stage of comprehensive and sustainable development, an epic in which all Egyptian people are

ta king part. This pivotal stage necessitates paving a foundation for a strong educational system which yields a generation that is not only ca pable of facing the major challenges the world is witnessing today, but one that also has complete possession of the skills of the future.

At a time when our world is witnessing successive industrial revolutions, the Egyptian state is keen on empowering its citizens by establishing a top-notch educational system that invests in its children the expertise required to get them to compete at both a regional and global level. This dictates that our educational system has at its core an emphasis on skills development, deep understanding, and knowledge production. This can only be done through modern curricula that keep up with the changes taking place globally– curricula which prioritize the development of skills and values, and the integration of knowledge. They are also curricula that focus on the provision of multiple learning sources, and integration of technology to enrich the educational process and to improve its outcomes, while addressing the most important contemporary issues.

To achieve this, we must all join hands to continue to revolutionize our education, and to support it with all that is required to transform it into a globally pioneering educational system.

My wa rmest regards to you, dear students, and my deepest gratitude to my fellow teachers.

Professor Reda Hegazy

Minister of Education & Technical Education

students to make sense of the world around them and to think and act like mathematicians. Throughout the digital and print program, students learn to reason mathematically, communicate using mathematical language, ask meaningful questions, solve complex problems, and work collaboratively with peers.

Prima ry 4 Mathematics Techbook was designed *and *written to teach to the Ministry of Education Prima ry 4 mathematics standards. The structure of Primary 4 Mathematics Techbook represents the Ministry’s shifts in the Framework for Education 2.0, specifically focusing on accessing new and prior knowledge, building contextual understanding and procedural fluency, and making connections across mathematics to support application of skills and concepts. To help students make sense of mathematical content, the program also integrates a thematic approach and a \/ariety of real-world scenarios.

Primary 4 Mathematics Techbook challenges students to build on what they learned in previous grades, applying concepts and skills in new ways. Students also learn new and complex concepts and skills that prepare them for the challenges of Primary 5 and beyond. Primary 4 students assume greater responsibility for their own learning and are encouraged to seek opportunities to apply the mathematics they are learning in the world around them.

The major work of Primary 4 includes multiplication, division, fractions, decimals, and plane figures such as lines, line segments, rays, and angles. Although these may seem like separate topics, students investigate and apply patterns and relationships among the topics to build a deeper understanding of each. They solve fraction multiplication problems, connect angle measurement to fractions, explore the inverse relationship between multiplication and division, and draw parallels among decimal numbers, fractions, and place value. Students learn to think like mathematicians as they notice patterns and rules,

persevere to solve challenging problems, represent and explain their thinking, model their solutions, and strive for accuracy.

To inspire and motivate learning and curiosity, Primary 4 Mathematics Techbook features clear and engaging text, videos, digital tools, and Hands-On Activities. Hands-On Activities require students to investigate patterns and rules in mathematics and challenge them to communicate using mathematical language and models. The program also engages students in many kinds of writing and asks them to explain their reasoning and support their thinking using words, numbers, pictures, and symbols. When studente engage in rich tasks that access prior knowledge and build reasoning, it is easier for them to make connections to the real world and to other mathematical learning.

Primary 4 Mathematics Techbook is divided into units. Each unit is di\/ided into concepts, and each concept is di\/ided into lessons. Each lesson has three main sections: ACCESS, BUILD, and CONNECT.

ACCESS Students activate their prior knowledge and begin to develop and express mathematical language.

BUILD Students focus on communicating their understanding, reasoning, evidence, and mathematical strategies.

CONNECT Students build deep conceptual understanding and a strong foundation for accessing knowledge in future lessons.

In addition, WRAP UP, PRACTICE, and CHECK YOUR UNDERSTANDING features allow students to demonstrate their learning either verbally or in writing.

Within this Student Edition, you will find QR codes and quick codes that take you and your student to a corresponding section of Primary 4 Mathematics Techbook online.

We encourage you to support your student in using the print and online interactive materials on any device. Together, may you and your student enjoy a fantastic year of mathematics.

Sincerely,

The Discovery Education Math Team

UNIT

ace

ACCESS

Exploring Place Value Talk with your Shoulder Pa rtner. Record what you remem ber about the place value system from earlier grades. Be prepared to share your thinking with the class.

BUILD

Reading the Place Value Chart Use the place value chart to help you read the number aloud with your teacher. Write numbers in the place value chart with your teacher. The first one is done for you.

billiards

period

.

period

.

Thousands

period

Ones **

OHTOHTOHTO

3 9 1 4

Practice creating, reading, and **comparing **really big numbers.

- Place all digit cards face down in the middle and mix them up.
- One person in the group turns over a digit card. Each player independently decides which place value to put the digit in and records the digit in their own place value chart.
- The next student turns over a card. Each player independently decides which place value to put the digit in and records the digit in their own place value chart.
- Repeat until all spaces in the row have been filled. Then, players compare their numerals. The player with the greatest numeral wins a point. There is room to play 5 rounds.

**period**

**period**

**period**

**Milliards**

0

**Track ****your ****points.**

CONNECT

**Writing ****About ****Math **Amir says that in the number 222, all of the digits have the same value. Do you agree or disagree? Use words and numbers to explain your thinking.

**Check Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

**ACCESS**

**Multiplying ****by ****Ten **Use your Tens rods to explore patterns in multiplying by 10.

- What quantity is represented by your Tens rods? Draw a picture, write an equation, or write a number to show the quantity.
- What quantity is represented by your group’s Tens rods? Draw a picture, write an equation, or write a number to show the quantity.

BUILD

What Is My Value? Follow the steps to explore how a digit’s value changes when its location changes.

- Choose one digit and enter it in the Ones place.
- Record the value of the digit.
- Continue moving the digit card to the left on the place value chart, recording its new value each time.

My digit is

Value of my digit in the Ones place Value of my digit in the Tens place Value of my digit in the Hundreds place

Value of my digit in the Thousands place Value of my digit in the Ten Thousands place

Value of my digit in the Hundred Thousands place Value of my digit in the Millions place .

Value of my digit in the Ten Millions place Value of my digit in the Hundred Millions place Value of my digit in the One Milliards place

**Exploring ****Place **Value **Relationships **Work with your teacher to explore place value relationships.

Choose the value from the word bank that completes the sentence.

1 10 1D0 1000

As a digit moves one space to the left on the place value chart, its value — times.

**CONNECT**

Omar and Mariam are (scientists who specialize in studying ants). They found a colony with 10 anthills. Remarkably, each anthill had the same number of ants.

**Multiplying ****Ants **Look at each problem in the table. If Omar and Mariam found the given number of ants in each anthill, how many ants were there all together? Show your work for each problem.

7 ants in 1 anthill.

ants in 10 anthills.

12 ants in 1 anthill.

ants in 10 anthills.

28 ants in 1 anthill.

ants in 10 anthills.

92 ants in 1 anthill.

ants in 10 anthills.

156 ants in 1 anthill.

ants in 10 anthills.

1,786 ants in 1 anthill.

ants in 10 anthills.

**Check ****Your Understanding**

Follow your teacher’s instructions to complete this activity.

counted as follows:

**1,467,303,221**

Mariam recorded her count in this way:

BUILD

Numeral Form Exploration Compare the different forms of the same numeral. Use the information as a guide and reference.

9,231,043,204

9,000,000,000 + 200,000,000 + 30,000,000 + 1,000,000

+ 40,000 + 3,000 + 200 + 4

_{} nine milliard, two-hundred thirty-one million, forty-three thousand, two hundred four

Be prepared to share your thinking about these questions:

- What do you remember about these forms of writing numerals?
- Which do you prefer, the standard form, word form, or expanded form?

Play Creating the Greatest with a partner to practice creating numbers and writing them in multiple forms.

- Combine decks of digit cards with your partner. Place the cards face down in a pile and mix them up.
- Turn over 10 digit ca rds and record the numbers in the order in which you turned them over.
- Rearrange the 10 cards to create the greatest numeral.
- Record the numeral in standa rd form, word form, and expanded form.

Standard Form Expanded Form Word Form

2.

Standard Form Expanded Form Word Form

3.

Standard Form Expanded Form Word Form

CONNECT

Writing About Math Highlight or circle the greatest numeral you created. How

do you know that the numeral you chose was the greatest num ber of all of the numerals you created? Explain the strategy you used to ma ke your determination. Be prepared to share your thinking with the class.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

We Have/Who Has? Sit with your small group. Then, play the game We Have/Who Has to practice reading large numbers in multiple forms.

Directions

- One group starts by reading their ca rd aloud together.
- The group who has the “Who Has?” num ber raises their hands and then reads their card aloud.
- Play until every group has used its card.

BUILD

Terminology Review Complete the activity to check your current understanding of the terms standard, word, and expanded form. For each term, write a definition and give an example.

Vocabulary

Standard Form

Word Form

Expanded Form

Definition Example

Composing and Decomposing Do you remember the terms composing and decomposing from Primary 3? Look at the two images. What do you think the terms mean?

Composing 145 What are some different ways we can compose 145? Use the web to record your ideas. One idea is given to get you sta rted.

100 -r 45

Composed and Decomposed Numbers Several composed and decomposed numbers follow. Fill in the missing numbers. Use the place value chart to help you. The first one has been done for you as an example.

Composed 345,532

Decomposed

(3 x 100,000) * (4 x 10,000) + (5 x 1,000) + (5 x 100) * (3 x 10) + (2 x 1)

‘*Milliards | Mitlians | Thousands | Ones | “] | ||

O | H T | O H | T | O H | T 0 | |

3 | 4 | 5 5 | 3 2 |

1. Composed 6,124,030,420 Decomposed

Milliards | Mi\tians | Thousands | Ones | |||

O | H T | O H | T | O | H T | O |

Decomposed

- Composed

Decomposed (7 x 1,000,000,000) + (5 x 10,000,000) + (4 x 10,000) + (3 x 1,000)

+ (5 x 100) + (9 x 1)

For the next problem, choose your own number and show it composed and decomposed.

- Composed

Decomposed

CONNECT

Writing About Math Reflect on today’s Learning Target and your learning progress. Respond to the questions.

Check Your Understanding

Follow your teacher’s instructions to corriplete this activity.

LESSON 5

## Comparing Big Numbers

Learning Target

- I can use symbols and place value to compare large numerals.

ACCESS

Error Analysis Analyze the student’s work and their answer. Identify what the student did correctly and incorrectly, and then try to solve the problem correctly.

Ouestion: Record the following numeral in standa rd form:

(6 x 100,000) + (5 x 10,000) + (4 x 1,000) + (3 x 100).

Student’s answer: 6,543

What did the student

What did the do incorrectly? Why do student do correctly? you think they made

this error?

Try to solve the **’ problem correctly.

Explain your thinking.

BUILD

Com paring Anthills Highlight or circle the digits that are the sa me in both numbers.

When comparing two numerals, if the first digit is the same in both numerals, how do we determine which numeral is greater?

Anthill 1

14,108

Anthill 2

15,108

Write an Explanation

- Go back to one of the anthill problems and write an explanation for how you knew which symbol to use.
- Create numbers that make the comparison true. Use all the lines.

< 890,789,000

2,456,800,900 >

- In the space provided, write each numeral that you created in the previous problem. Then, write a comparison symbol between the two numerals to express their relationship.

##### CONNECT

Writing About Math When comparing large numbers, what strategies do

you use to determine the greater number? Use words and numbers to explain your thinking.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****6**

# Comparing Numbers in Multiple Forms

**Learning ****Targets**

- I can compare numbers in m ultiple forms.
- I can describe the strategies I use to compare numbers.

ACCESS

**Comparing ****Anthill ****Populations **Work with a partner to compare the populations of the anthills by writing (< , > , or —) in the center column.

**Anthill**

1 40,000 + 3,000 + 100 + 10

**Anthill**

40,000+3,000+100+20

five milliard, two hundred twenty million, five hundred forty thousand, six

1,000,000 + 900,000 + 70,000 +

6,000 + 800 + 80 + 8

BUILD

14,780,064 | 14,790,064 |

5,193,492,500 | five milliard, three hundred million, seven hundred fifteen thousand, |

forty-three |

group A

(7 x 100,000,000) +

3 (4 x 10,000,000) + (9 x 10,000) +

(8 x 10) + (1 x 10)

Seventeen million, four

4 hundred twenty-five thousand,

, six hundred five

8,040,761,903

Four hundred twenty-three thousand, twelve

70,000 + 9,000 + 600 + 40 + 3

17,420,605

8,000,000,000 + 400,000,000 +

700,000 + 60,000 + 1,000 +

900+3

**400,000+30,000+20,000+20+1**

- Put a star next to the set that was the easiest for you to compare. Put an x next to the set that was the hardest for you to compa re.

This game requires 3 players. 2 players are “builders,” and 1 player is the

“ reader.”

Each player needs a set of digit cards 0—9. Players will combine the three decks (30 cards), shuffle the cards, and place them face down in the middle.

- Each builder draws 11 cards.
- Each builder uses 10 of their cards to create the greatest number possible and discards the 11* card.
- The reader will read each builder’s number aloud.
- The builders write their number and their partner’s number in their Student Edition. Be sure to pay attention to how the numbers should be recorded for each round.
- The builders compare their numbers and record the appropriate sign

- The builders discuss: Which place value did you use to determine which number was greater?
- Rotate roles and play again.

CONNECT

Writing About Math What are the most effective strategies for you when comparing numbers in multiple forms? Which forms a re easiest for you to compare? Which are ha rdest? Why? Use words and numbers to explain your thinking.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****7**

Descending and Ascending Numbers

**Learning ****Targets**

- I can numbers in multiple forms.
- I can describe the strategies I use to order numbers.

ACCESS

**Error ****Analysis **Analyze the student’s work and their answer. Identify what the student did correctly and incorrectly, and then try to solve the problem correctly.

**Question: **Compare the numbers below using (< , > , or —) 89,906 100,513

Student’s Answer: I think 89,906 > 100,513 because 8 is larger than 1.

What did the student do

^ !*“

**What ****did ****the ****student ****do incorrectly7 ****Why **do you think they ma:deflhise vT

**Try ****to ****solve ****the ****problem ****correctly. ****Explain ****your ****thinking.**

BUILD

**Ascending ****and ****Descending ****Numbers **Omar and Mariam have been reading about ants in different regions. Omar found the total number of ants that go in and out of an anthill each day. Mariam found the total number each week. The first data set shows the numbers that Omar found for his region each day for 5 days.

**List****Omar’s****data****in****ascending****order:**

Ants Ascending and Desc ending an AntlnilI

78,090 79,010 78,091 79,100 78,999

_{} 3. List the numbers in ascending order. Use the form in which they are piven.

- four milliard, six hundred thousand, four
- 461,014
- four milliard six hundred thousand forty
- (4 x 1,000,000,000) + (4 x 100,000) + (6 x 10)
- 6,400,042

- 6,025,060,990

CONNECT

Writing About Math In the boxes, draw and label anthill images to help you remember the terms *ascending *and *descending.*

_{} Ascending Descending _{}

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

LESSON 8

Rounding Rules

Learning Targets

- I can use multiple strategies to round numbers.
- I can identify which estimation strategy provides more accurate estimates.

ACCESS

Remember Rounding? Record what you and your partner remember about rounding. After the class discussion, add the class notes to your notes.

BUILD

Rounding Using the Midpoint Strategy For each problem that follows, record the midpoint of the number line. Then, identify where each num ber would go on the number line. Finally, round each number to the nearest thousand.

1. 6,700

2. 9,340 .

3. 16,401 =

17,000

16,OOO

4) 19,654 =

20,000

19,000

For each number, draw a number line, label the midpoint, and then round to the hundred thousands place.

5. 250,000= 6. 700,500 =

to the given place value. Remember to circle the digit in the place value you are rounding and draw an arrow to show “looking next door.” The first one is done for you.

Round the numbers to the nearest Thousand. 1. 234,432 =

2. 7,578 =

Round the numbers to the nearest Ten Thousand. 3. 290,290 =

4. 7,435,026,353 =

Round the numbers to the nearest Million. 5. 5,367,544 =

6. 2,453,000,601 =

Round the numbers to the nearest Milliard. 7. 5,266,747,023 =

8. 10,944,352,543 =

**CONNECT**

**Which ****Strategy ****is ****Best?**** **numbers can help you determine whether or

not your answer is

47 40

+ 31 + 30

Look at the two rounding examples that follow.

47 TO

+ 31 30

70 80

**Actual ****Answer: ****47 **-r 31 = 78

Explain Which rounding strategy is more accurate. How do you know?

**Check ****Your Understanding**

Follow your teacher’s instructions to complete this activity.

Unit Video Questions

Omar and Mariam are investigating Quick Code ant movement in and out of the ant egm4050 mound. Soon they may need a faster

way to add and subtract.

How can you use patterns to determine strategies?

What are some patterns you have observed

this week?

LESSON 1

## Properties of Addition

Learning Target

- I can identify the properties of addition.
- I can explain the properties of addition.
- I can investigate to determine if addition properties apply to subtraction.

###### ACCESS

Expanded Form Review Listen as your teacher reads numerals in expanded form. Write the numbers in standard form.

BUILD

Additive Identity Property Solve the following problems. 1. 2,345 + 0 2. 0 + 12,567,109

- What did you notice about the problems?

- Write a definition of the Additive Identity Property in your own words.

Commutative Property Solve the following problems.

5. *5 **+ **2 **+ *8 *+ *3 6. 8 *+ *7 + 3 *+ *5 7. *2 **+ **5 **+ *8 *+ *3 8. 3 + 7 *+ *8 *+ *5

- What did you notice about the problems?

- Write a definition of the Commutative Property in your own words.

Associative Property Solve the following problems. Remember to solve what is in the parentheses first.

11. (10 + 4) -r 20 + 17 12. 10 + (4 + 20) + 17 13. 10 + 4 + (20 + 17)

- What did you notice about the problems?

- Write a definition of the Associative Property in your own words.

**Do ****the ****Properties ****Apply? **With your Shoulder Partner, answer the questions that

fo

Circle the property you and your partner have been assigned.

What is your prediction? Will your assigned property also be true for subtraction? Circle Yes or No.

Create two problems to investigate whether your property applies to subtraction. You may use the number line to help you subtract.

Does your property apply to subtraction?

Explain why or why not.

CONNECT

**Writing ****About ****Math **Describe what you discovered about the properties of addition and whether they apply to subtraction. Be sure to explain your findings. Use words and example equations to explain your thinking.

Check Your Understandlng

Föllow your teacherl instructions to complète this aoivïty.

LESSON 2

Addition with Regrouping

Learning Targets

- I can add multidigit whole numbers.
- I can to check the reasonableness of my answer.

ACCESS

Error Analysis Analyze the student’s work. Identify what the student did correctly and incorrectly, and then try to solve the problem correctly.

BUILD

**Estimate ****and ****Solve **Work with your partner to estimate the sums and then solve the problems.

579 | 8,049 | ||

+ 62 | + | 199 | + |

**CONNECT**

**Bridging ****Ants ****and ****Addition **There are many different types, or *genera, *of ants. Army ants are known for being aggressive and are good hunters. One of the more interesting things that army ants do is create living bridges to help them span an elevated distance. Most of the bridges are made with around 50 ants. Once these bridges are complete, all the ants are able to safely move to the other side.

A colony of ants is on a march through the jungle looking for food. On this march they made 2 bridges. The first bridge is composed of 142 ants. The second bridge is composed of 165 ants. How many ants were needed for both bridges? Show your work. Then, explain how you know your answer is reasonable.

Estimate

Exact

**Check ****Your ****Understanding**

Föllow your teacherl instructions to complete this aoivity.

LESSON 3

Subtraction with Regrouping

Learning Target

- I can use place value to help me subtract with regrouping.
- I can estimate to check the reasonableness of my answers.

ACCESS

Error Analysis Analyze the student’s work and answer in the space provided. Identify what the student did correctly and what they did incorrectly, and then try to solve the problem correctly.

What did the student What did the student do incorrectly? Why do

do correctly? you think they made

this error?

Tty to éoIve the

problem corremly.

Explaln your thinking.

BUILD

Subtraction with Regroup Follow your teacher’s directions to complete this learning activity.

**3,328**

— 2,164

Use drawings to model 3,328 on the place value chart

Ant Facts and Algorithms Read the short article. Then, follow your teacher’s directions to complete the activity.

Can Ants Swim?

Some ailts can swim, and some drown. lt depends on the species. Some researc)iers took 3S species of tropical ants and dropped them into the water. Some of them were ainazing sWimmers, especially trap jaw ants. One species could swim art amazing 16—17 cin per second. That ineans in a minute the ant could swim 1,020 cm or approximatefy 10 meters!

rire ants cannot swim, but tliey cv join their legs to form a circular raft to survive floods, Sometimes, the entire ant colony will join legs to survive.

A trap jaw ant wanted to cross a river that was 3,548 cm across. The ant had already swum 1,672 cm. How much farther does the ant have to go?

- Two colonies of fire ants were stuck in

a flood and made floating rafts to survive. The first colony had approximately

1,267 ants and the second had

3,452 ants. How many more ants were in the second colony?

- A fire ant colony 255,000 ants. A
*Gigontiops**destructor*ant colony has 6,200. What is the difference between the size of the two colonies?

**CONNECT**

**Four ****Corners **Follow your teacher*s directions to participate in the Four Corners activity. Record your chosen strategy.

**Check ****Your ****Understanding**

Follow your teechers instructions to corriplete this **ectivity.**

**LESSON ****4**

Bar Models, Variables, and Story Problems

**Learning ****Targets**

- I can use letters to represent unknown quantities in equations.
- I can use to represent and solve story problems.
- I can solve equations that include

ACCESS

**Introducing ****Variables **What does it mean to be balanced? Look at the image of the triangle. What do you notice about Discuss your observations with your Shoulder Partner.

BUILD

**Bar ****Models **Read the following problems. Create a bar model and an equation for each problem, and then solve.

- There are 5,328 ants in the colony. In the colony, 2,164 ants are females and the rest are males. How many male ants a re in the colony?

**Bar ****Model:**

Equation: 2,164 -r a — 5,398

a — 5,398 – 2,164 a — ………….

- In colony A there a re 1,200 ants. Some ants are out foraging for food and supplies, and 700 ants are taking out the colony’s trash. How many ants are foraging for food and supplies?

Bar Model:

Equation:

Solution:

- There are 12,000 species of ants. Of these 12,000 species, 2,500 species live in Africa and the rest live in other parts of the world. How many species ao not live in Africa?

Bar Model:

Equation:

Solution:

Solving Equations with Variables Create a bar model to solve the following

problems.

1. 14,000 — n — 6,000

Bar Model:

Solution:

3. 725,625 * c — 935,075

Bar Model:

Solution:

4. 13,280 — o = 5,420

Bar Model:

Solution:

5. / + 205,925 — 810,775

Bar Model:

Solution:

CONNECT

Writing About Math Write a story problem involving addition or subtraction, where

you need to find the unknown. Then write the equation and draw a bar model of the equation. Lastly, solve for the variable and check.

Word Problem:

Equation: Bar Model (drawn): Solve and Check:

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****5**

Solving **Multistep **Story **Problems**

# with Addition and Subtraction

**Learning ****Targets**

- I can solve multistep story problems.
- I can explain how I solved multistep story problems.

**ACCESS**

**Hidden ****Ouestion **Answer the following questions:

Omar found a website created to study ant colonies. He saw that there were 1,025 ants in Colony A on Wednesday. On Friday, 101 ants leave the colony. How many ants are left in Colony A?

2. Mariam found the sa me website and saw that there were 1,555 ants in Colony B. How many more ants are in Colony B than in Colony A?

BUILD

Putting h **Together **Combine the two given story problems to create one story problem.

- Mariam saw on the website that several smaller Pharaoh ant colonies were joining together to form a larger colony. On Monday, 1,725 ants joined together with 22,750 ants. Then, another 6,075 ants joined. How many ants were in the larger colony on Monday?

Omar checked the website on Friday and learned that there were now 50,750 ants in the colony. How many ants had joined the colony since Monday?

New m ultistep story problem:

Highlight or circle the hidden question in the multistep story problem you wrote.

**Solving ****Multistep ****Story ****Problems **Read the Steps to Solving Story Problems. Then, read the story problem. Next, read the steps a student took to solve the problem and number the steps from a to f to put them in the correct order.

**Steps ****to ****Solving ****Story ****Problems**

- Circle important numbers and labels.

- Underline questions.

- Draw a box around operation clues.

Examine the information:

- What is known?
- What is unknown?
- What is the hidden question?

- Use what is known to answer the hidden question.

Use the new information to solve the problem and find the unknown.

- Ahmed had a pie with 340 calories for breakfast. Then, Ahmed had a glass of milk, an apple, and a chicken sandwich for lunch. The milk had 190 calories, the apple had 85 calories, and the chicken sandwich had 255 calories. If the average adult can eat 2,000 calories per day, how many more calories can Ahmed eat today?

Arrange the following steps to solve the story problem:

I subtracted 870 from 2,000. The answer is 1130, so Ahmed can eat 1,130 more calories today.

I drew a box around “how many more.”

I added the calories of the foods Ahmed has eaten to answer the hidden question (how many calories Ahmed has already eaten). The answer is 870 calories.

I circled 340 calories, 190 calories, 85 calories, 255 calories, and

2,000 calories.

I identified the known information (what Ahmed ate and how many calories each item had; the average adult is supposed to eat 2,000 calories per day). I identified the unknown information (how many calories Ahmed has already eaten; how many more calories Ahmed can eat).

I underlined “how many more calories should Ahmed eat today?”

Use the problem-solving steps to solve the story problems. Remember, you will have to answer the hidden question first and then answer the main question. Be sure to show your work.

- The ant colony website hopes that a new colony with up to 173,500 will form. If

- The Great Pyramid had 59,000 visitors in January, 27,525 visitors in February, and 32,975 visitors in March. They expect to have 150,000 visitors by the end of April. How many visitors need to show up in April to reach this count?

- New Valley has a population of 256,088. If Matrouh has a population of 429,999 and South Sinai has a population of 108,951, how many more people do Matrouh and South Sinai have combined than New Valley?

**CONNECT**

**Writing ****About ****Math **If you had to teach a friend how to solve multistep story problems, what would you tell them? What strategies would you recommend? What helpful hints would you share?

**Check ****Your ****Understandlng**

Föllow your teacherl instructions to complète this aoivïty.

**Unit ****Video ****Ouestions**

The video It’s an Ant*s Life uses

measurement to describe the life and Quick Code work of different types of ants. Omar egm4027 and Mariam are fascinated by ants

and are exploring different types of anthills. They want to use measurement to compare. Because anthills vary greatly in size, they may need help converting measurements between units of length.

@ How big was the biggest ant or anthill you

have ever seen?

Why would Omar and Mariam need to change units of measure to compare anthills?

**LESSON ****1**

**Measuring ****length**

Learning Targets

- I can bthe relationship between metric units of
- I can between metric units of length.

**ACCESS**

**Measurement ****Review **Circle the best unit to measure each length.

1. Height of a student | Kilometer | Meter | Centimeter | Millimeter |

2. Distance between home and school | Kilometer | Meter | Centimeter | Millimeter |

3. Length of the Nile River | Kilometer | Meter | Centimeter | Millimeter |

4. Length of an ant | Kilometer | Meter | Centimeter | Millimeter |

5. Distance from Cairo to Alexandria | Kilometer | Meter | Centimeter | Millimeter |

Fill in the blanks to answer the following questions. Think of things that could be measured in each unit.

6.

7.

8.

9.

BUILD

is best measured in kilometers because is best measured in meters because

is best measured in centimeters because is best measured in millimeters because .

**Metric ****Units **View and discuss the Conversion chart with your Shoulder Partner.

Work with your Shoulder Partner to fill in the blanks that follow to help you remem ber the relationship.

1 km = m 1 m = cm

Decomposing and Rena ming Unit Conversions.

FiII in the table with proper conversions.

Kilometer | Meter | *”‘, | Meter | Centimeter | ||

1 | 1,000 | 4 | 1 | |||

2 | 3 | 300 | ||||

3 | 40,000 | 6 | 10 |

Look at the following exa mple:

l4Ocm

1 m

40 cm

Convert the following lengths into the given units in the bar models. Use the previous example to help you.

230cm

478 cm

’ s

cm

Answer the story problems. Use your conversion ta bles to help you.

- Carpenter ants can be up to 3 centimeters long. A mature colony can have up to 100,000 ants. If the ants lined up end to end and each ant is 1 centimeter long, how many meters long would a line of 100,000 ants be?
- Using the information from the first item, how many kilometers long would the line of 100,000 ants be?

**CONNECT**

The Nest When scientists studied the anthill, they found that it was 8 meters deep.

- How many centimeters would that be? Show your work.

- The colony had to move tons of soil to construct their nest. The worker ants had to carry loads of soil 1 kilometer to the surface. If one ant carried 10 loads of soil in a week, how many kilometers did it travel while moving soil? How many meters? How many centimeters?

**CfTl**

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

LESSON 2

Measuring Mass

Learning Targets

- I can explain the relationship between metric units of mass.
- I can convert between metric units of mass.

ACCESS

Error Analysis Analyze the student’s work and answer. Identify what the student did correctly and incorrectly, and then try to solve the problem correctly.

Convert 7 meters 45 centimeters to centimeters.

Student’s answer: 7 m 45 cm = 7,045 cm

What did the student What did the student do incorrectly? Why do

do correctly? you think they made this error?

Try to solve the problem correctly. **Explain ****your ****thinking.**

BUILD

Mass Review Sha re what you remember about mass. Take turns sha ring ideas of objects that would be weighed in grams. Talk to your Shoulder Pa rtner about the similarities between the relationship between mass measurements and the relationship between length measurements from the last lesson.

FiII in the blank to help you remember the relationship and then complete the conversions.

1 ton = kg 1 kg = g Conversion and Application Look at the following Conversion Exa mple:

2,300 g

1,000 g = 1 kg

2,000 g = 2 kg

+ 300 g

Work with a partner to complete the conversions. Use the previous example to help you.

- 3 kg =

3.

s.

kg — 5,000 g kg — 30,000 g

- 8 kg =

4. 4 kg —

- 5 tons — kg

Convert the masses into the units on the bar models.

” 7. 4,590 g 8. 8,400 g

9. 10. kg

7 414 g 2 tons 30 kg

Answer each question. Use words, pictures, or numbers to explain your thinking.

- A colony of black ants is estimated to weigh 3,493 grams. Rewrite that number using kilograms and grams.

- A different ant colony is estimated to weigh 14 kilograms and 89 grams. Rewrite that weight in grams.

**CONNECT**

**Writing ****About ****Math **When might you need to convert grams to kilograms or kilograms to grams in your daily life? How do the mental math strategies you have learned help you convert units of measurement? Work independently to respond to the prompt.

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

**LESSON ****3**

Units of Capacity

Learning Targets

- I can explain the relationship between metric units of
- I can convert between metric units of capacity.

**ACCESS**

**Number ****Talk **Listen to each problem your teacher reads aloud. Use benchmark numbers and the mental math strategies you have lea rned to solve each one. Be prepared to discuss how you solved each problem.

BUILD

**Decomposing ****and ****Renaming **Fill in the blanks using the cylinder to show how many milliliters it takes to make 1 liter. Then, answer the question.

1 L — mL

Work with a partner to solve the problems.

1. 6 L m L 2. 9 L = mL

3. L — 6,000 mL 4. 3 L = mL

5. L — 10,000 mL

Look at the following Conversion Example:

5,403 mL

1,000 m L — 1 L

5,000 m L — 5 L

+ 403 mL

Using the conversion examples above, convert the following weights into the given units on the bar models.

6. 9,425 mL 7. 6,360 m L

- mL

8 L 910 m L *’,

Solve each problem.

- A car is filled with 45 liters of petrol. How many milliliters would that be?
- Use the recipe that follows to answer the questions. Sobia Ingredients:
- 100 g raw short grain rice
- 500 mL of water
- 750 mL cold milk
- 100 g caster sugar
- 5 mL vanilla
- 500 mL coconut milk

Which ingredients are measured by mass?

Which ingredients are measured by capacity?

_{} What is the total amount of liquid ingredients in the drink in milliliters? In liters?

Multistep Conversions Solve the problems.

1. A fam ily drank 1 liter 500 m illiliters of orange juice at breakfast. If there were 3 liters of orange juice before breakfast, how m uch orange juice is left?

t 2. A car was filled with 20 liters 500 m illiliters of petrol. At the end of the day, there were 15 liters 250 milliliters left in the tank. How much petrol was used?

3. Doha’s fish tank contains

5 liters 245 milliliters of water. If the tank can hold 10 liters of water, how much more water ooes she need to fill the tank?

CONNECT

Math Language Review Work with your Shoulder Partner to fill in the chart with the measurement units for each form of measurement. Use what you remember from previous grades to complete the time colum n.

Length Mass Volume/Capacity Time

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

LESSON 4

Units of Measuring Time

Learning Targets

- I can tell time to the minute.
- I can explain relationships between units of time.

ACCESS

Take out a red and blue crayon to indicate the hour and minute hands.

Analog and Digital Clocks Think about three events that ha ppen in your day and

- the times at which each occurs. Record the event and the time on the analog clock and digital clocks that follow. Use red for the hour hand and blue for the minute hand.

Event 1:

Event 2:

_{} Event 3:

BUILD

Brainstorm and name as many units of time as you can. Work with your Shoulder Partner to create a rule for converting units of time.

Ratio Tables Part 1 Work with your teacher and your classmates to fill in Table 1.

Minutes 1 2 3 4 5 6 7 s 9 10”’

^{Table }^{1}^{ }Seconds 60

Work with your teacher to solve the first three conversions for Tables 2, 3, and 4. Discuss rules for converting. Once answers are reviewed, do a Hands up, Pair Up to find a partner to work with to solve the remaining conversion problems in Tables 2, 3, and 4.

**Ratio ****Tables ****Part **2 Complete Tables 2, 3, and 4.

HOUF3. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||||

^{Table }^{2}^{ }Minutes | 60 | |||||||||||||

DayS | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||||

Table 3 _{Hours} | 24 | |||||||||||||

Weeks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||||

Solve the conversion problems using the ratio tables above.

- 10 hours 30 minutes — minutes
- 6 minutes 15 seconds — seconds
- 4 days 20 hours = hours

**CONNECT**

How Hard Do Ants Work? Answer the questions and show your work.

The average worker ant works about 19 hours per day. Worker ants can lift over 100 times their own body weight and they do that hundreds of times every day. They can move pretty quickly at about 3 centimeters per second, so they cover a lot of ground each day. If we were to translate that data to a human adult, that

person would have to carry a 22-kilogram weight 60 kilometers every day. Could you do that on only 5 hours of sleep a night?

- An average ant works for 19 hours a day. How many hours does an ant work in 3 days?
- A worker ant takes 240 naps a day. Each nap lasts 1 minute. About how many hours did the nap ant?

**Check ****Your ****Understanding**

Follow your teacher’s instructions to corriplete this activity.

LESSON 5

Elapsed Time

Learning Targets

- I can explain
- I can solve elapsed time problems.
- I can explain the strategies I use to solve elapsed time problems.

ACCESS

Error Analysis Analyze the student’s work and answer. Identify what the student did correctly and incorrectly, and then try to solve the problem correctly.

It takes Dalia 2 hours and 15 minutes to drive to her grandmother’s house.

How many minutes doea the drive take?

Student*s work: 2 x 6 = 1Z 12 + 15 = 27 it took Z7 minutes.

What did the student

do incorrect! ? Wh

you think they made

Ttyto solve the probtern correctly.

Explain your thinking.

BUILD _{}

Passage of Time Read the problem in the box silently. How is this problem different from the time problems you solved in the last math lesson? Be prepared to discuss.

F-arah was training for a marathon. Her goal was to run for 1 hour and 30 minutes. If she started running at 8:35 a.In., what time did she finish running?

After sharing your thinking with the class, work with a partner to solve the story problem.

**Solving ****Elapsed ****Time ****Problems **Solve the problems and write the new time. Based on the examples shown to you by your teacher, try a few different strategies to solve the problems. Show your work.

1. 3:25 + 1:26 =

2. 3:25 + 45 minutes —

3. 5:43 — 1:25 minutes —

4. Jana and Maha have 5 hours to watch three movies that last 1 hour and 22 minutes; 2 hours and 12 minutes; and 1 hour and 57 minutes.

Do the girls have enough time to watch all three movies? How do you know?

The girls decide to just watch the two shortest movies. If they start watching them at 5:30 p.m., what time will their movies end?

* 5. A worker ant went out to find food for the colony. It left at 6:30 a.m. and returned at 7:42 a.m. How long was that ant looking for food?

CONNECT

Origins of Telling Time Read the following article about why time is measured in groups of 12 and 60. Be prepared to share your thoughts about what you read.

w are there 12 hours In the morning and 12 hours in the afternoon ana 6o

minutes In an hour and 6O aetonds tn a minute? Why not use a aase 10 system7

The answer lies in those ancient civl1izatinns.The

Sumerians used a system nf 12 and 6O starting .in 3,500 _

B.C. However, why Base 12 and Base 60? The .reason – “

actually £OTffRS fTom the Structure of our Dngers. ” -.

The ilUiTib£ir ßf Joints OH each hand, minus the thumb,

makes it possihle to count to 12 liy using the thumb.

The division of an hour into 60 minutes and 60

seEonds was determined by astronomers using the i

Base 60 system of the Babyloniani. So our units ‹sf time, whlEh Can seem so confusing, are linked to the first clvtlizafions anil our own hands.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****6**

**Applications ****of ****measurement ****1**

**Learning Targets**

- I can add and subtract to solve measurement problems.
- I can solve story problems involving measurement.
- I can apply a variety of strategies to solve story problems.

**ACCESS**

**Take ****Steps ****to ****solve ****Problems **Use the Steps for Solving Story Problems to solve the problem.

In Colony A, the ants collect 950 grams of food. If they consume 25 grams of food on Monday and 37 grams of food on Tuesday, how many grams of food are left?

BUILD

**So ****Many ****Strategies **Record your favorite and least favorite problem-solving strategy.

The problem-solving strategy that works best for me is

because

The problem-solving strategy I use the least is

because

Solve as many problems as you can. Use at least three different problem-solving strategies (you may not finish them all, so choose the ones you want to try first). Use the Steps for Solving Story Problems, if that is helpful. Be sure to label your answers.

- The potatoes Aya bought weighed 2 kilograms 920 grams. Her onions weighed 1,075 grams less than the potatoes. How much did the potatoes and onions weigh together?

- A pharaoh ant grows from egg to adult in 45 days. A carpenter ant grows from egg to adult in 12 weeks. Which species takes longer to grow from egg to adult? How m uch longer?

- A fish tank with a capacity of 100 liters is filled with 20,000 milliliters of water. How many more liters of water are needed to fill it up completely?

- Zeina purchased 8 kilograms of sugar, 10 kilograms of flour, 500 grams of cocoa, 225 grams of pecans, and 275 grams of coconut. What is the total mass of her groceries in kilograms?

s. Taher grew 10 centimeters in 1 year. He is now 1 meter 6 centimeters tall. How many centimeters tall was Taher 1 year ago?

- An ant from Colony A walked 2 kilometers in a day. An ant from Colony B walked 3,000 meters in a day. Which ant walked the farthest and how much farther in kilometers did it walk?

- Ali’s cat weighs 7 kilograms and his dog weighs 17 kilograms. When Ali took them to the vet, he learned that his cat gained 450 grams and his dog gained 120 grams. How much do his two pets weigh in all now?

- Mr. Emad bought four 2-liter bottles of soda for the Primary 4 picnic. If there were 2 liters and 829 milliliters of soda remaining at the end of the party, how many milliliters of soda did the students drink?

- Worker ants take power naps totaling up to 250 m inutes a day. A queen ant may sleep up to 9 hours a day. Which ant sleeps longer and by how many minutes?

- Rania is measuring two ant lines. Colony A’s ant line is 30 centimeters lonp, and Colony B’s ant line is 500 millimeters long. How many centimeters long are the two ant lines together?

CONNECT

Writing About Math Choose one of the BUILD problems. Explain how you solved the problem, why you chose the strategy you used, and how you know your answer is correct.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****7**

**Applications ****of ****measurement ****2**

Learning Targets

- I can multiply and divide to solve measurement problems.
- I can solve story problems involving measurement.
- I can apply a variety of strategies to solve story problems.

**ACCESS**

Ant Math Solve the problem and explain your solution with words, numbers, a drawing, or a table.

An ant is at the bottom of a 20-meter deep well and is trying to get to the top. Each day he climbs 4 meters up, but each night he slides back 2 meters. How many days does it take for him to get out of the well?

BUILD

**Multistep ****Measurement **Work with a partner to solve the problem using the “Draw a picture or model” strategy. Be prepared to discuss your thinking.

Ahmed has a 12-meter-long piece of wood. He wants to cut it into 3 equal lengths. How long should each cut piece be in meters? How long will each of these pieces be in centimeters?

**Jigsaw **Work with your Home Team small group to solve the problem assigned to you by your teacher. Be ready to share your strategy with others.

Circle your assigned team number. _{}

- Ayman is a runner. While Ayman is in training, he needs to drink 500 milliliters of water 4 times per day. How many liters of water will that be for 1 week?

- Ehab is a weightlifter. He has a mass of 100 kilograms. His aim is to gain

500 grams per week. If he does that for 5 weeks, what will his mass be at the end?

- Amany is a swimmer. She spends half an hour every day swimming. How many minutes in total does she swim for during a 5-day period?

- Sara practices walking. She travels 9 days continuously. She travelled 5,000 meters each day. How many kilometers did she walk in all?

**CONNECT**

**Ants ****Are ****Amazing **solve the problem. Show your work.

Mariam was having a picnic with her family and counted 10 ants walking by. If each ant weighed 1 gram and each ant carried 50 times its body weight, how much weight was being carried in all?

**Check ****Your ****Understanding**

Follow your teechers instructions to corriplete this **ectivity.**

**Unit **Video **Ouestions**

Omar and Mariam are observing a group of worker ants in the park. When ants leave the colony, they can travel long distances. To study the ants, Omar and Mariam decide to only observe the ants while they are in a certain space.

They may need some help creating boundaries for this space.

Ouick Code egm4083

@ What shape should Omar and Mariam make their observation space?

Why do worker ants travel long distances away from their colony?

@ Can the ants be contained in the space Omar and Mariam create?

LESSON 1

Finding perimeter

Learning Targets

- I can define perimeter.
- I can use formulas to calculate the perimeter of rectangles.
- I can explain how to calculate perimeter.

ACCESS

Rectangle Review Compa re the shapes in the boxes. Highlight or circle all of the rectangles and place a star on the squares.

303 cm

545cm

545cm

9 cm

303 cm 4 cm

17 cm

17 cm

8 m

_{4 }_{cm}_{ }30 30 mm

30 mm

13 cm

9 cm

9 cm

23 mm

9 cm

8 m 8 m 25 cm

8 m

20cm

25cm

45 mm 45 mm

23 mm

BUILD

Marching Ant Addition Solve the problems. Show your work.

- Work with your partner to write a rule or formula to help mathematicians efficiently solve perimeter problems.
- Use
*P**——**I**w**+**I**P**——*(/ + w) x 2 to calculate the perimeter of the shapes. Show your work.

4cm

17 cm

17 c m

4 cm

- Use
*P**——**I*+ w + / + w or*P**——**(I*+ w) x 2 to calculate the perimeter of the shapes. Show your work.

9 c m

9 c m 9 c m

9 cm

Foraging for Formulas Calculate the perimeter of the shapes that follow. Use two different form ulas to solve each problem. Show your work.

). 27 cm

27 cm 27 cm

27 cm

Formula 1:

Formula 2:

2

21 m

Formula 1:

Formula 2:

67 m

67 m

21 m

- 30 mm

50 mm 50 mm

30 mm

Formula 1:

Formula 2:

Solve the following perimeter problems. For each problem, sketch a rectangle and record the length and width according to the problem.

- Sarah is putting a border around the edge of a squa re cake. One side of the cake is 30 centimeters long. How long will the border of Sarah ’s ca ke be?

- A soccer team is roping off part of a field to play soccer. To have enough room for a large crowd, they need a space that is 105 meters long by 68 meters wide. How much rope will they need for this part of the field?

CONNECT

Carpenter March Solve the perimeter problem. Show your work.

A carpenter ant walked a perimeter of 100 centimeters. Draw two different rectangles that could represent its walk.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

LESSON 2

Finding area

Learning Targets

- I can define area.
- I can use formulas to calculate the area of rectangles.
- I can explain how to calculate area.

ACCESS

Num ber Talk Describe the strategy (or strategies) you used to solve the addition problems mentally.

BUILD

Area Review Determine the a rea of the rectangles. Show your work.

12 cm

Area — Area

- Create a formula for finding the area of a rectangle.

- Could you use your formula to find the area of a square? Sketch a square and show your thinking.

Area Practice Solve the problems. By using: A = L x W.

- Find the area.

10 m 10 m

18 m

- Find the area.

6 mm

6 mm

- A glass company is cutting a piece of glass to cover the top of a banquet table. The table measures 8 meters by 6 meters. What is the a rea of the glass needed for the ta ble?

- A small rectangular ant farm measures 20 centimeters by 8 centimeters. What is the area of the ant farm?

What is the measurement of the glass? Should you calculate area or perimeter to find that measurement?

CONNECT

Carpet Tile Solve the problem. Show your work.

You have 36 squa re carpet tiles to arrange on the floor in the shape of a rectangle. Draw two possible arrangements and label the length and width. What is the perimeter of each arrangement? What is the area?

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

LESSON 3

Unknown Dimensions

Learning Target

- I can use formulas to calculate unknowns when given some dimensions of rectangles.

ACCESS

Error Analysis Analyze the student’s work and answer that follow. Identify

what the student did correctly and incorrectly, and then try to solve the problem correctly.

Amir is a myrmecologist who found a large fire ant mound. He placed string around the outside of the mound in a rectangular shape so that he could study the mound safely. The width of the rectangle was 8 meters and the length of the rectangle

was 12 meters. How many square meters are roped off to study?

Student’s Solution:

There are 40 meters of ground to study. 8 + 8 + 12 + 12 = 40.

’’ What did the student

What did the student do incorrectly? Why do do correctly? you think they made

this error?

Try to solve the problem correctly and explain your thinking.

BUILD

Mystery Dimension Work with a partner to answer the questions about the rectangles.

x units

5 units Perimeter 26 units

- What is known about this rectangle?
- What is unknown about this rectangle?

- How can we use the perimeter to help find the missing dimension? What is the missing dimension?
- What is known about this rectangle?
- What is unknown about this rectangle?
- How can we use the a rea to help find the missing dimension? What is the missing dimension?

10 units

SCOOT Your task is to solve as many perimeter and area problems as you can with your partner. Show your work in the box that matches the card num ber. When you finish a ca rd, solve another one.

**SCOOT ****Recording Sheet**

**CONNECT**

**Compound ****Shape ****Challenge **Read the problem and solve to find the perimeter. Then, take the challenge and find the area.

Some fire ants left the mound to go look for food. They went 8 meters east from the mound

and then turned and walked 4 meters north. _{}_{ }They came to a big tree so they walked around ” ^{e}^{t}^{e}’^{s }i

it. When they passed the tree, they turned _{}_{ }_{ }west for 3 more meters and then headed south

8 meters back home. See their path in the diagram. Label the missing measurements. How many meters in total did they walk?

Perimeter —

3 meters

I

| 4 m eters

I I

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

LESSON 4

Complex Shapes

**Learning ****Targets**

- I can find the area and perimeter of shapes.
- I can explain my strategy for finding the area and perimeter of complex shapes.

ACCESS

BUILD

Calculating Crazy Shapes Solve each problem.

- Divide this sha pe into smaller rectangles or squares. Then, calculate its area and perimeter. Show your work.

24 m

6 m

_{13 }_{m}_{ }18 m

Area =

Perimeter —

- Divide the shape in a different way and calculate its area and perimeter. Show your work.

24 m

6 m

_{13 }_{m}_{ }18 m

Area — .

Perimeter —

- What do you notice?

Calculate the area and perimeter of the complex shapes. Show your work.

4.

6 cm

Area —

Perimeter =

8cm

3 cm

1 cm

2 cm

2 cm

5 cm

3cm

’2 cm

’2 cm

Area —

Perimeter =

4 m

10 m

Area =

Perimeter —

7. Calculate the area and perimeter of the complex sha pe you created in ACCESS. Area

Perimeter —

Challenge: Design your own complex shape and calculate its area and perimeter.

CONNECT

Writing About Math Read and solve the problem.

What do you think is the easiest part of calculating the a rea and perimeter of complex shapes? What do you think is the most challenging part of calculating the area and perimeter of complex shapes?

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

Unit Video Questions ñl D•

of multiplication tocslculate the Quick.Code number of people who 1rsveI by egm4061 different modes of transportation.

Omar and Mariam are investigating and comparing numbers of people

who travel on different types of transportation.

D How can they use multiplication inStesd of addition to calculate large quantities?

**LESSON ****1**

## Multiplicative Comparison

Learning Targets

- I can define
- I can explain how multiplication can be used to compare numbers.
- I can create models to show multiplicative comparisons.

**ACCESS**

Seat Belt Safety Have you ever wondered how much safer you are in a car when you wear a seat belt? Your teacher will give you a strip of paper. Compare your strip of paper to your teacher’s strip of paper. Then estimate:

- How many times could your strip fit on your teacher’s strip?
- How many times could you and your partner’s strip laid end-to-end fit on your teacher’s strip?
- How many times could four or five strips laid end-to-end fit on your teacher’s strip?

Multiplicative Comparison with Numbers Use tape diagrams or m ultiplication facts to compare the numbers. Be sure to show your work for each problem.

- Compa re 15 and 3. 15 is

- Compa re 28 and 7. 28 is

- Compa re 27 and 9. 27 is

CONNECT

times greater than 3. times greater than 7. times greater than 9.

Writing About Math Respond to the questions. Use numbers and words to explain your thinking.

- How do multiplicative comparisons help us understand how much safer it is to wear a seatbelt?
- How can we use multiplicative comparisons to help us understand and describe the world around us?

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

LESSON 2

Creating Multiplicative Comparison Equations

Learning Targets

- I can create multiplication equations to represent comparisons.
- I can use a letter to represent a missing number in a multiplication problem.

ACCESS

Comparing Transportation Speeds Read the infographic. Highlight or circle phrases that show multiplicative comparison.

BUILD

**Multiplying ****to ****Show ****Comparisons **Write an equation based on the comparison statement. Use a letter to represent the unknown number. You do not have to solve the equations.

- 4 times greater than 3 is
- 18 is 6 times as many as
- 2 times greater than 7 is
- 24 is 4 times as great as
- 25 is 5 times as many as

**Creating ****Equations ****for ****Multiplicative ****Comparisons **Work with a partner to complete this activity. Read the story problems. Think about the comparisons being expressed in the story. Then, write a multiplication equation based on the story problem. Use a letter to represent the unknown number. You do not have to solve the equations.

- Nadia collected 5 marbles in March. By May she had 4 times as many marbles. How many marbles does Nadia have in May?

- Hamed had 12 cookies, which was 3 times as many cookies as his brother, Ahmed. How many cookies did Ahmed have?

- It took Aida 21 minutes to walk to school on Monday. On Tuesday, it took her

7 minutes to ride her bike to school. How many times faster was riding her bike than walking?

**CONNECT**

**Exit ****Ticket **Imagine a car is 3 times faster than a bicycle. It takes Salma 24 minutes to get to school by bicycle. Write a multiplication equation that shows how long it would take Salma to get to school by car. Use a letter to represent the unknown number. Use words, numbers, or pictures to explain your thinking. You do not have to solve the equation.

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

**LESSON ****3**

**Solving ****Multiplicative ****Comparison ****Equations**

**Learning Target**

- I can solve a multiplication equation that represents a comparison.

ACCESS

**Different ****Ways ****of ****Solving **Read the problem and decide whether you agree or disagree with Moustafa.

Moustafa is solving the equation 6 x a = 18. He says that he can solve the problem by doing 18 + 6 = o. Do you agree or disagree with Moustafa? Why? Use words, numbers, and pictures to explain your thinking.

BUILD

How Many Seats? Use the information in the table to compare numbers of seats

in different modes of transportation. Then, enter and solve an equation for each *- comparison. ‘

**Mode ****of ****Transportation**** **

Bicycle 1

Motorbike 2

Car 4

Truck 6

8us 36

Metro Train 48

- How many times as many seats are on a bus than in a truck?

Equation:

Answer:

- How many times as many seats are on the metro train than in a car?

Equation:

Answer:

- A metro train can fit how many times more people than a truck?

Equation:

Answer:

- A bus has how many times more seats than a car?

Equation: .

Answer:

CONNECT

More Seats to Sail A boat has 12 seats. Write your own problem comparing the number of seats on a boat to another mode of transportation in the table in BUILD. Write and solve an equation for your comparison.

Check Your Understandlng

Föllow your teacherl instructions to complète this aoivïty.

Learning Targets

- I can explain the .
- I can apply the Commutative Property of Multiplication to solve problems

with and without an unknown number.

ACCESS

Toy Car Number Talk Solve the problem. Give the teacher a Thumbs-Up when ” you are finished.

Ahmed has 48 toy cars and wants to display them in his room. He wants to arrange them in equal rows and equal columns. How can he display his cars? Draw your solution.

BUILD

Exploring the Commutative Property of Multiplication Turn and talk about what you remember about the Commutative Property of Multiplication.

- Repeat the activity until time is up. There is space for you to write 5 array equations.

Array Equation 1:

Array Equation 2:

Array Equation 3:

Array Equation 4:

Array Equation

CONNECT

Writing About Math Read and solve the problem.

There are 42 people who want to play football. Badr says that you can make 6 teams with 7 people on each tea m. Salma says you can make 7 teams with 6 people on each team. Who is correct? Use numbers, words, and pictures to explain your thinking.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

- I can explain the Identity Property and the Zero Property of Multiplication.
- I can apply the Identity and Zero Properties of Multiplication to

solve problems.

- I can identify patterns I observe when multiplying by JO, 100, and 1,000.

ACCESS

Mental Math Number Talk Look at the problems below. Solve them mentally (without writing anything down).

1 5 x 4 | 2. J2 x | 3. 672 x 4 |

4. 8×0 | 5. J6xO | 6. 758xO |

Write a definition for the properties in your own words. Write an example of each using numbers and symbols.

BUILD

Mental Math Multiplication Read the problem. What do you notice about the problem? What numbers do you think belong in the blanks? Why do you think so?

The metro can get people around the city

as walking. If the average person walks fast does the metro go?

times as fast

kilometers an hour, about how

TOO x 4-

Thousands

1,000 x 4 —

Ones

Ones Hundreds Tens Ones

Describe the patterns you observe in the problems and their solutions.

CONNECT

Writing About Math Tarek says that 9 x 1,000 equals 900. What would you tell Tarek to help correct his mathematical thinking? Use words, numbers, or pictures to explain your thinking.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

- I can explain the Associative Property of Multiplication.
- I can apply the Associative Property of M ultiplication to solve problems.

ACCESS

Dot Card Number Talk Look at the image. How many dots do you see in the image below? How did you come up with your answer?

BUILD

Uncovering the Associative Property of Multiplication Solve the problem assigned by your teacher.

Writing About Math Use what you have learned about the Associative Property of Multiplication to help Farouk solve the problem. Use words and numbers to explain your thinking.

Farouk is trying to solve the problem 2 x 7 x 4.

He starts by solving 2 x 7 and gets 14. Place parentheses to show how Fa rouk started this problem.

2 x 7 x 4

Next, he writes 14 x 4, but he does not know how to solve that multiplication problem. Can you show Farouk another way to soI\ie the problem?

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

Learning Target

- I can use decomposing and the Associative Property of Multiplication to solve equations with multiples of 10, 100, or 1,000.

ACCESS

Review Multiplying by 10 Look at Set 1.

Solve each problem mentally. Think about any connections or patterns you notice in each set of

problems.

BUILD

Decomposing Multiples of 10 Decompose each number into a factor pair with 10. Write the m issing factor in the box.

11. 120 — Tens 12. 110 — Tens

Multiplying by Multiples 10, 100, and 1,000 Use decomposing and the Associative Property of Multiplication to solve each problem.

Example: 7 x 20 =

1. 5 x 50 =

2. 4 x 700 —

3. 3 x 4,000 =

##### CONNECT

Writing About Math Review each student’s work. Then, answer the questions.

How is Heba’s and Ashraf’s work the same? How are they different? Which student’s strategy do you prefer? Why?

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

Unit Video Questi

Omar and Mariam sre helpi their teacher plsn a school .

To determine which type of Ouick Code transportation the school should egm4073 use for the trip, they will use their

understanding of multiplication facts. But they may need help assigning students to seats.

What are the different ways seats can be arranged?

@ How would you arrange the students in your class for a field trip?

LESSON 1

Identifying Factors of Whole Numbers

Learning Targets

- I can define factors of a whole number.
- I can identify factors of a whole number.
- I can explain patterns I observe in numbers that have 2, 5, or 10 as a factor.

ACCESS

Lots of Rectangles There are 24 seats on an airplane a rranged in a rectangle. Each of your counters represents one seat. Use all of your counters to create as many seating arrangements as you can. Draw your rectangles and label the dimensions (width and height).

BUILD

Num bers with Factors of 2, 5, and 10 Count by 2s. Shade the numbers that you say as you count.

71 72

75 76

47

17

99

89

69170

58 59

99

85 89

71 747576 78

Count by 5s. Shade the numbers that you say as you count.

65 67 6970

57

47

37 29

29

17

Count by 10s. Shade the numbers that you say as you count.

93 97

85 86 87

74 75 76 78 79

65 9170

57 58

Determine if the given number has 2 as a factor, 5 as a factor, or 10 as a factor. Circle yes or no.

26 | Yes | No | Yes | No | Yes | No |

70 | Yes | No | Yes | No | ||

15 | Yes | No | Yes | No | ||

17 | Yes | No | Yes | No | Yes | No |

**Finding **Factor Pairs Work with your teacher to create a factor rainbow and T-chart for 40.

- List the factors of 40.

Factor Rainbow **T-Chart**

- List the factors of 36. There are 5 factor pairs. Factor Rainbow T-Chart

- List the factors of 20. There are 3 factor pairs. Factor Rainbow T-Chart

CONNECT

**Writing ****About ****Math **Write three numbers that have 2, 5, and 10 as factors. What do the three numbers you wrote have in common?

**Check ****Your ****Understanding**

Follow your teacher’s instructions to corriplete this activity.

**Prime ****and ****Composite ****Numbers**

Learning Targets

- I can identify factors of a whole number.
- I can explain patterns I observe in numbers that have 3, 6, or 9 as factors.
- I can determine if a number is or

**ACCESS**

**Factor ****Riddles **Listen to the riddles read by your teacher. Solve the riddles and record your answers.

The number is an even number between 20 and 30. Some of its factors include 1, 2, 4, 7, and 14. What number is it?

- The number is an even number greater than 40. It has 10 as a factor. It is less than 60. What num ber is it?

BUILD

**Numbers ****with ****Factors ****of ****3, ****6, ****or **9 Determine if each number has 3, 6, or 9 as a factor. Explore these patterns:

- A number has 3 as a factor if the sum of the digits is a number that is said when skip counting by 3.

Example: 63 has 3 as a factor because 6 + 3 — 9 and 9 is a number we say

- A number has 6 as a factor if it has both a factor of 2 and a factor 3. This means it has to be even and the sum of the digits have to be a number said when skip counting by 3s.

Example: 36 has 6 as a factor because it is even and because 3 + 6 = 9 and 9 is a number we say when we skip count by 3s.

Use these patterns to solve the problems.

- Is 3 a factor of 53? How do you know?

- Is 9 a factor of 63? How do you know?

- Is 6 a factor of 84? How do you know?

Prime or Composite List all of the factors of each num ber. Then, write whether the number is prime or composite.

A prime number has exactly two factors: 1 and the number itself. A composite number has more than two factors.

Prime or Composite?

2. | 21 |

3 | 31 |

4. | 44 |

5. | 23 |

**Prime ****Numbers ****Less ****than ****100 **Identify all of the prime numbers less than 100. Use skip counting and factor patterns to help you eliminate composite numbers.

Circle 2 and cross out all other num bers that you say when you skip count by 2s.

- Circle 3 and cross out all other numbers that you say when you skip count by 3s.

- Circle 5 and cross out all other numbers that you say when you skip count by 5s (some are already crossed out).

Circle 7 and cross out all other numbers that you say when you skip count by 7s.

5. Circle all numbers that remain except for 1.

When you are finished, the circled numbers ^{91 }^{92 }^{93 }^{94195196 }^{97198199 }are prime and the crossed out numbers are

composite.

31 32 33134 35136 37 38139

23 24 25 26 27 28 29130

13 15 16 17 18 19

**CONNECT**

**Writing ****About ****Math **The seats on the new ferry will be arranged in a rectangle. Is it better for the ferry to have 48 seats or 53 seats? How do you know? Would 49 seats be a good idea? Use numbers, words, and pictures to explain your thinking.

1 | 2 83184 85l86l87l88l89l90 | |

71 72 73 74 75 76 | 77 78 79180 | |

61 62 63164 65166 | 67I68I69I 70 | |

51 52 53 54155156 | 57 58159160 | |

42 43 44 45146 | 47 48149150 |

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

**LESSON ****3**

Greatest **Common ****Factor ****G.C.F**

**Learning Targets**

- I can find T b een t o whole numbers.
- I can identify the between two whole numbers.

**ACCESS**

**Math ****Fluency ****Sprint **Your teacher will assign you a multiplication facts review activity. Answer as many problems as you can in 60 seconds.

BUILD

**Common ****Factors **List the factors of each number. Highlight or circle the common factors of each pair of numbers.

1. 36 and 42

2. 18 and 4

3. 20 and 30

4. 21 and 35

5. 17 and 22

**Finding ****the ****Greatest ****Common ****Factor **Use what you know about factors and common factors to solve each problem.

- A class is going on a field trip. There a re 36 girls and 27 boys in the class. Students will be divided into groups of girls and groups of boys. What is the greatest number of groups that can be made so that each group has the same number of children? How many children will be in each group of boys? How many children will be in each group of girls?

- Amira and her friends are going on a picnic. Amira wants to make snack packs of apples and candy to take on the picnic. She has 24 apples and 36 small bags of candy. What is the greatest number of snack packs Amira can ma ke if each pack must have exactly the same number of apples and exactly the same number of bags of candy with no snacks left over? How many apples will be in each snack pack? How many bags of candy will be in each snack pack?

- Mohab is ma king flower arrangements. He has 7 roses and 14 daisies. If Mohab wants to make all the arrangements identical and have no flowers left over, what is the greatest number of flower arrangements that he can make? How many roses and how many daisies will be in each flower arrangement?
- Find the greatest common factor (GCF) of 40 and 50.

Find the GCF of 10 and 24.

6. Find the GCF of 33 and 11.

**CONNECT**

**Writing ****About ****Math **Describe how a number and its factors are related. Use numbers, words, and symbols to explain your thinking.

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

LESSON 4

Identifying Multiples of Whole Numbers

Learning Targets

- I can define multiples of whole numbers.
- I can identify multiples of whole numbers.

ACCESS

Skip Counting on a Num ber Line Draw a line connecting each number to show skip counting on the number line. Start at 0 each time.

1. Skip count by 2 on the number line. 0 1 2 3 4 U 6 7 8 9 10 11 12 13 14 1′ | 16 | 17 18 | 19 | 20 | 21 | 22 | 23 | 2< | 25 | 26 | 27 | 28 | 29 | 30 |

2. Skip count by 3 on the num ber line. 0 1 2 3 4 U 6 7 8 9 10 11 1z 13 14 15 | 16 | 17 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

3. Skip count by 4 on the number line. 0 1 2 3 4 U 6 7 8 9 10 11 12 13 14 15 | 16 | 17 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

4. Skip count by 5 on the number line. | ||||||||||||||

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | 16 | 17 18 | 19 | 20 | z1 | zz | zz | z< | 25 | 26 | 27 | 28 | 29 | 30 |

5. Skip count by 10 on the number line. | ||||||||||||||

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | 16 | 17 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

BUILD

Color **the ****Multiples **Use the Hundreds charts provided by your teacher to color the multiples.

Skip count and color the multiples of 2.

- Skip count and color the multiples of 3.
- Skip count and color the multiples of 4.
- Skip count and color the multiples of 5.
- Skip count and color the multiples of 6.
- Skip count and color the multiples of 7.
- Skip count and color the multiples of 8.
- Skip count and color the multiples of 9.

**Find ****the ****Patterns **Use Hundreds Charts to help you identify patterns in the multiples of 2, 3, 4, 5, 6, 7, 8, and 9. Then, share your observations about the patterns with a partner. Record your observations.

**CONNECT**

**Writing ****About ****Math **Tahani takes the bus home from school every day, but it does not take her directly to her house. After the bus drops Tahani off, she must walk the rest of the way home. The bus she takes stops every 4 kilometers as it leaves the school. If Tahani lives 18 km from school, how far does she have to walk home from the bus stop? Draw a picture to represent your thinking.

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

LESSON 5

Common Multiples

Learning Target

- I can identify common multiples of two numbers.

ACCESS

The Bus Stops Here Show where each bus stops on the num ber line.

- Bus 1 stops every 3 kilometers.
- Bus 2 stops every 5 kilometers.
- Bus 3 stops every 9 kilometers.

0 1 2 3 4 U 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

BUILD

Multiple Match Your teacher will assign you to work with a partner. One of you is Partner A and the other is Partner B. Look at your first card and write 10 multiples on it. Then, look at your partner’s first card to see what multiples are in common. Record your answers.

See th i i i aeL st the multiples for each pair nu e until yo find the first two common multiples for each pair.

- 5 and 7:

- 6 and 9:

- 6 and 8

- 4 and 7:

CONNECT

Writing About Math What is the relationship between a number and its multiples? Use examples to support your thinking.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

LESSON 6

Relationships between Factors and Multiples

Learning Targets

- I can explain the relationship between factors and multiples.
- I can determine if a num ber is a factor or a multiple of another number.

ACCESS

Multiples Riddles Read each riddle and solve. There may be more than one answer.

- The num ber is an odd number. It is a multiple of 3 and 5. It is greater than 20. What number is it?

- The num ber is an even number. It is a multiple of 4 and 8. It is between 10 and

20. What number is it?

- The num ber is an even number. It is a multiple of 3, 4, and 6. What num ber is it?

BUILD

Making Connections Think a bout the relationships between the numbers in each group. Write at least two sentences describing what you notice. Be ready to sha re your thinking.

1. 3, 6, and 12

2. 4, 8, 16, and 24

3. How are factors and multiples related?

Factors and Multiples Game Play this game with a partner. Place the factors and multiples cards face down in a pile and shuffle them. Choose one card. One partner writes factors of the number, the other writes m ultiples. Show each other

your work and record your answers in the boxes. Choose another card and switch roles.

Number: Number:

Factors: Factors:

Multiples: Multiples:

Number:

Factors:

Multiples:

CONNECT

Writing About Math Reflect on what you have learned about factors and multiples. How do factors and multiples relate to multiplication facts? Use numbers, words, and sym bols to support your reasoning.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****1**

The Area Model Strategy

_{} **Learning ****Targets**

‘“ ” ‘’ • I can use an to represent two-digit by one-digit multiplication.

- I can explain how I use place value to multiply.

. .” ” **ACCESS**

**Notice ****and ****Wonder **Look at the image that follows. Write down something that you notice and something that you wonder about the image.

I notice

I wonder

BUILD

Ouick Draw Use a quick draw to solve the problems that follow.

‹ ‘—”

_. , –—

- Twenty-two passengers can fit on each river bus at a time. What is the maxim um number of passengers the river bus can carry if it makes 5 trips?

2. 17 x 4 3. 21 x 3 4. 14 x 5

2. 35 x 7 3. 91 x 4 4. 88×6

CONNECT

Error Analysis Exam ine the student work that follows. Identify what the student did correctly and incorrectly, and then try to solve the problem correctly.

A student solved the problem 36 x 8 in the following way:

8

Explain your thinking.

3 6

36 x 8 = 72

48

+ 24

72

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

LESSON 2

**The ****Distributive ****Property**

_{} **Learning ****Targets**

- I can use an area model to m ultiply a one-digit number by a whole number with to four digits.
- I can explain the
- I can apply the Distributive Property of Multiplication to solve

multiplication problems.

ACCESS

**Decomposing ****Numbers **Fill in the missing number for each decomposition.

1. 536 — 500 +

2. 1,275 —

3. 264 = 60 + 4 +

+ 6

+ 200 + 70 + 5

4. 7,625 — 5 + 7,000 + 20 +

5. 357 = 50 + + 7

BUILD

**The ****Distributive ****Property ****and ****Area ****Models **Use the area model to solve each problem.

1. 249 x 5

3. 530 x 7

2. 4,734 x 5

4. 2,391 x 8

Let’s Try It Use numbers and symbols to solve each problem. Draw an a rea model to help you if necessary.

32 x 7

2. 5×483

7 x 723

1,673 x 8

CONNECT

Making Connections Read the problem. Sol\ie using an area model or using numbers and symbols. Be prepared to share your thinking.

A city bus is 1,280 centimeters long. What is the length of 3 city buses?

LESSON 3

The Partial Products Algorithm

Learning Target

- I can use the to multiply a

one-digit number by a whole number with up to four digits.

ACCESS

The Amazing Race Write as many different ways as you can to represent the number 136. Use a separate box for each representation.

BUILD

Partial Products Use the area model to solve the problem. Then, copy the partial products algorithm solution modeled by your teacher.

Example: 731 x 4

7 x 59

624 x 4

6 x3,293

Fill in the Blanks Fill in the blanks with the m issing numbers.

239

1,400 | (. | x ) | |

210 | ( | x ) | |

1,673 | |||

2. | 6,421 |

36,000

(6 x 400)

120

3. 2,523

x 5

10,000 (

(5 x 500)

100 (5 x

(5 x 3)

– ” CONNECT

Error Analysis Examine the student work that follows. Do you agree or disagree with the student’s work and solution?

Solve the problem using the partial products algorithm.

Student’s work:

328

x | 4 | |

32 | (8 x 4) | |

8 | (2 x 4) | |

+ | 12 | (3 x 4) |

What did the student

What did the student do incorrectly7 Why do do correctly? you thihk they made

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

Tty to solve the problem correctly.

Explain your thinMng.

LESSON 4

## Multiply by a one-Digit Number

Learning Targets

- I can estimate roducts.
- I can use the

number with up to four digits.

to multiply a one-digit number by a whole

ACCESS

Similarities in Models Estimate the products of the two problems. Then, solve using the method assigned by your teacher.

64 x 7

Estimate:

Solved Answer:

2. 132 x 8

Estimate:

Solveo Answer:

BUILD

Using the Standard Algorithm Estimate the product for Problems 3—8. Then, solve using the standard algorithm. Multiply using another strategy to help you if necessary.

###### CONNECT

3 32x 3 | 17 | |

Estimate: | Estimate: | |

Answer: | Answer: | |

5. 134 x 2 | 6. | 758 x 3 |

” Estimate: | Estimate: | |

Answer: | Answer: | |

7. 1,349 x 2 | 8. | 2,327 x 4 |

Estimate: | Estimate: | |

Answer: | Answer: |

Writing About Math Three students tried solving 328 x 2 using the standard algorithm. Explain who you think solved the problem correctly, and identify at least one error in another student’s solution.

Student 1 | Student 2 | Student 3 | ||

328 x 2 | 328 x 2 | 328 x 2 | ||

646 | 656 | 746 |

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**Learning Targets**

- I can identify patterns when multiplying two multiples of 10.
- I can multiply a two-digit number by a multiple of 10.
- I can assess the reasonableness of an answer using estimation and mental math.

ACCESS

**Mental ****Math **Read each question. Circle your answer. Be prepared to explain your reasoning.

–

BUILD

1. Is 56 x 4 closer to 200 or closer to 2,000? | 200 | 2,000 |

2. Is 156 x 4 closer to 500 or closer to 5,000? | 500 | 5,000 |

Ten Times Predict what you think will happen when you multiply two multiples of 10 together.

30 x 5 — 150 | 30 | x 50 — |

2 x 80 = 160 | 20 | x 80 — |

70 x 7 — 490 | 70 | x 70 — |

50 x 60 — | 90 | x 70 — |

40 x 40 — | 60 | x 30 — |

40×62

2.

54×30

4O x 78

5. 44×20

6. 15 x 3O

7. 10 x 4O

8. 72 x 40

CONNECT

Error Analysis Exam ine the student’s work. Is their answer reasonable? How do you know? Explain your thinking.

22 x 50

(20 + 2) x 50

(20 x 50) + (2 x 50)

100 * 100

200

**LESSON ****6**

**Exploring ****Remainders**

**Learning ****Targets**

- I can identify the @$ @, and of a division problem.
- I can solve division problems.
- I can explain what a represents in a division problem.

**ACCESS**

Compare and Connect Read each problem with a partner. Answer each problem.

There are 8 teams playing soccer. There are 9 students on each team. How many students are there in all?

- There are 72 students on the field. They want to make teams with 9 students on each team. How many teams will they be able to make?

- There are 72 students on the field. They want to split into 8 teams. How many students will be on each team?

- How are the problems alike? How are they different?

BUILD

What Is Left? Draw a picture to show your thinking.

Saleem brought 15 pies to give to 4 of his friends. How can Saleem share the pies equally?

Equation

**Getting ****to **Zamalek Write equations that show how many of each form of transportation you would need to get the people to their event. Note if there would

be people left out (remainder). Draw a picture to help you if necessary.

Thirty-two people need to travel to a special event in Zamalek. There are many different ways they can travel to the event. They can only choose one of the ways to travel for the whole group of people. Look at all of the forms of transportation they can take on the chart.

Mic rob us Motorbike Car

Which form of transportation should the group ta ke to the event? Explain your answer.

CONNECT

Going to a Swim Meet The swim team is taking a bus to a swim meet. Each bus seats 40 students. Sixty students will attend the meet. How many buses are needed? Use numbers, words, and symbols to explain your thinking.

LESSON 7

# Patterns in Division

Learning Target

- I can use place value, multiplication facts, and patterns with zeros to divide multiples of 10, 100, and 1,000 by one-digit divisors.

ACCESS

**Follow ****the ****instructions **to create arrays to show **division **problems. Materials per two players

Number cards 6—25

One 6-sided number cube One piece of graph paper

Objective of the game

To have the highest total score Directions

Shuffle the number cards. Place the deck with the numbers facing down on the table.

- Player A draws a number card. This number becomes the dividend.
- Player A rolls the number cube. The number on the number cube is the divisor. this many squares per row on the graph paper until you reach the dividend. You may have squares left over that do not fill a whole row. These are remainders.
- Fill in the information in the chart, including if there are any leftover squares.

Division Array Game

- Player A’s score is the number in the “number of rows” column. If all

‹ the squares were used in the array (no remainders), then Player A’s score is double the number of rows.

”” . 6. Keep track of the score in the chart. The player with the highest total score after 5 rounds wins.

Round

Example

1

4

Number of

(Dividend)

23

Squares Number Leftover

per Row of Rows Squares Score

(Divisor) (Quotient) (Rezriainder)

4 3

Total Score

BUILD

Division Patterns Label the parts in the equation using the words divisor, dividend, and quotient. Then, look for patterns to complete the remaining problems. The first problem in the table is an example that is filled in for you.

600 + 3 — Answer 600 is called the 3 is called the

The answer is called the

How did you use facts and patterns you know to help you solve the problems?

600- | 3=2 | 200 |

150 – | ||

1,200 – | ||

200- | ||

700 – | ||

6,400- | ||

4,500- | ||

270 – |

###### CONNECT

Riding the Metro

There are 8,100 people that need to get to work on Monday morning at 7:00 a.m. They all want to take the Metro to work. There are 9 cars on each Metro. If 90 people can fit in each car, can all the people take the same metro to work?

Explain your thinking using numbers, words, and symbols.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****8**

**The ****Area ****Model ****and ****Division**

Learning Target

- I can use area models to represent and solve division problems.

**ACCESS**

**Target ****Number **Your teacher will give you a number card. You will use your number to help create a target number.

BUILD

**Understanding ****the ****Area ****Model **Solve each problem using an area model.

- An organization donated 89 books to a school. The books will be shared among 6 classrooms. How many books will each classroom get?

- Rashida saved 545 LE to buy a toy car. She did this by saving 5 LE every day she worked around her neighborhood. How many days did she have to work to save enough money to buy a toy car?

- Amir bought a book of stickers. There were 92 stickers in the book. He wanted to give them to 4 of his friends. How many stickers will each of his friends get?

**CONNECT**

**Writing ****About ****Math **There are 492 cars that need to park at the stadium. The stadium has 4 parking lots. The stadium wants the same number of cars to park in each lot. How could you use Problem 3 to help you solve 492 + 4? Use words, numbers, and symbols to explain your thinking.

**Check ****Your ****Understanding**

Follow your teacher’s instructions to complete this activity.

LESSON 9

The Partial Ouotients Algorithm

Learning Target

- I can use the partial quotients algorithm to solve division problems.

ACCESS

Model Match Write the division problem that matches each area model. Remember to include the quotient and remainder, if there is one.

300 60

50 JO

2. 4 4,000 1,200 400

1,000 300 100 R3

BUILD

Partial Ouotients Algorithm Solve each problem using the partial quotients algorithm. Decide who will solve each problem with your group. You will each teach each other how to solve your problem.

Example

897

Problem 1

4

Problem 3

3

Problem 2

5

Problem 4

6

##### CONNECT

Writing About Math Look at the two different strategies for solving 812 + 4. Describe how the area model and the partial quotients algorithm are similar and how they are different.

812 – 4 = 203 | ||||

Area Model | Partial Ouotients | |||

4 | 4 x 200= 800 | 4 x 3= 12 | 0 | 4 812800 200_{12}_{ }_{3 }200+3=203120 |

200+3=203 |

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****1O**

**The ****Standard ****Division ****Algorithm**

**Learning Targets**

- I can estimate quotients using place value and patterns in multiplication and division.
- I can use the standard algorithm to solve division problems.

**ACCESS**

Let’s **Estimate **Use estimation to answer the questions. Circle your answer. Be ready to explain your reasoning.

Will 1,836 -: 3 be closer to 60 or 600?

Will 7158 – 3 be closer to 2,000 or 3,000?

Will 736 + 4 be closer to 100 or 200?

Will 491 + 4 be closer to 120 or 150?

BUILD

**Find ****the ****Similarity **Estimate the quotient and then do a Quick Draw of the problem.

68 ‘.

The quotient will be between

Ouick Draw

Standard Algorithm

2. 457 :

The quotient will be between . Ouick Draw

Standard Algorithm

Let’s Try It Solve the problems using the standard algorithm.

2. 778 — 2

3. 368 :— 3

CONNECT

Making Connections

4. 4,858 :—4

A train has 784 seats for passengers. If there are 7 cars on the train and each car has the same number of seats, how many passengers can sit in each car? Solve the problem using at least two different strategies.

784 :—7

First strategy

Second strategy

LESSON 11

## Division and Multiplication

Learning Targets

- I can use properties of place value to accurately record quotients.
- I can use multiplication to check answers to division problems.

ACCESS

Spot the Difference Study the two division problems solved using the standard algorithm. Identify as many differences as you can between the two problems.

BUILD

Place Value and the Ouotient First, circle the problems you think will have a quotient with fewer digits than the dividend. Then, estimate the quotient and solve each problem using the standard algorithm for division. Think about where to place the first digit in the quotient.

346

The quotient is between Solution

2. 1,266

The quotient is between

Solution

3. 834

The quotient is between Solution

4. 1,429 :— 7

The quotient is between Solution

5. 4,590 + 3

The quotient is between Solution

6. 562 — 8

The quotient is between Solution

and

and

and

Checking Your Answer Select three problems from Place Value and the Quotient

to check.

CONNECT

From Cairo to Alexandria Kazem wants to travel from Cairo to Alexandria, which is a distance of 218 kilometers. He plans to stop 3 times along the way. After

how many kilometers should he plan to stop? Do not solve this problem. Instead, explain how you would help a friend solve it. What steps would you tell them to take? How should they check their answer? Record your thinking.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

Unit Vldeo Queséons Ds• ‘Ds

how the factory makes cers. The Quick Code

§uide explains the order of each egm4091 step end why the order matters.

After the school trip, Omar and Mariam want to know what else

has an order and where the order matters.

What has an order in your school or home?

Does the order maber? What happens if the order is changed?

In mathematics, are there any opera’tions in which order matters? What are they? Give examples of what happens if the order is changed.

LESSON 1

Order of Operations

Learning Target

- I can use the order of operations to solve problems with multiple operations.

ACCESS

Which Does Not Belong? Solve the problems. Then, think about which problem does not belong in the set. Highlight or circle the problem you think does not belong and explain your thinking.

6×4-4-

3. 60 + 20 — SO —

2. 100 — 80 x I =

4. 2,356 — 2,336 —

BUILD

Fina the Answer Work with your partner to solve each problem. Locate the correct answer and write the equation under it. If the answer is not listed, rewrite the problem under “Other.”

2 + 4 x 6 48+4+9 | 24 — 8 + 4 + 6 36+9+4 | ||

7 + 7O + 10 — 2 | 99 — 10 x 9 + 7 | ||

49 — 7 x 6 + 4 | 12 — 72 + 12 + 2 80 + 10 + 6 — 3 | 40 | — 7 x 5 + 2 |

11 | 16 | ||

aa | 32 |

Other

CONNECT

Who Is Correct? Saleem and Sarah both solved the problem 74 — 61 + 8 x 5. Saleem says the answer is 105 and Sarah says the answer is 53. Who is correct? How *do *you know? Help the person who is not correct realize their mistake.

Check Your Understanding

Follow your teacher’s instructions to complete this activity.

**LESSON ****2**

## The Order of Operations and Story Problems

**Learning ****Targets**

- I can use the order of operations to solve problems with m ultiple operations.
- I can write and solve an equation to represent what is happening in a multistep story problem.

**ACCESS**

**Number ****Talk **Solve the problems. Then, rewrite each problem more efficiently.

67 + 67 + 67 + 67 + 67 — 15 —

2. 568 + 78 — 4 — 4 — 4 — 4 — 4 — 4 — 4 — 4 — .

BUILD

**The ****Order ****of ****Operations ****and ****Story ****Problems **Use numbers and symbols to represent what is happening in each problem, and then solve. Remember the order of operations.

Abdullah loves collecting stamps. He received 246 stamps for his birthday.

He kept 25 of the stamps and now he wants to give the rest to 6 of his friends. How many stamps will each friend get if they share them equally?

- Maha walked 14 kilometers every day for 2 weeks. The next week she walked 56 kilometers. How many kilometers did she walk over those 3 weeks?

- Ashraf has to take the bus to work. It takes 27 minutes to get to the bus stop near his job. Then, he has to walk for 12 minutes from the bus stop to his place of work. How many minutes does Ashraf spend going to work during a 5-day week?

- A group of tourists are taking a tour of Alexandria. There are 172 tourists and 8 tour guides in the group. They want to travel to the pyramids in microbuses. Each microbus fits 9 people. How many microbuses will they need in order to get everyone to the pyramids?

Sita wants to bake berry muffins. Each muffin will have 6 berries in it. She buys 198 berries from the store. On the way home, she eats 17 of the berries. How many muffins can she make with the berries she has left?

**CONNECT**

**Writing ****My ****Own ****Problem **Write a story problem that can be represented by (50 — 36) + 4.

**Check ****Your ****Understanding**

Follow your teechers instructions to corriplete this **ectivity.**