my homework lesson 3 multiplication as comparison

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McGraw Hill My Math Grade 4 Chapter 3 Lesson 3 Answer Key Multiplication as Comparison

All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 3 Lesson 3 Multiplication as Comparison  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 4 Answer Key Chapter 3 Lesson 3 Multiplication as Comparison

Math in My World

A type of model drawing is the bar diagram. A bar diagram can help you understand a problem and plan to solve it.

Talk Math One way to interpret 24 = 8 × 3 is to say that 24 is 8 times as many as 3. What is another way you can interpret this equation?

Answer: Given that the equation is. 24 = 8 × 3. The another way to represent the equation is 8 + 8 + 8 = 24.

Guided Practice

McGraw Hill My Math Grade 4 Chapter 3 Lesson 3 My Homework Answer Key

Write a multiplication equation to describe each model.

Mathematical PRACTICE 4 Model Math Complete each bar diagram. Then complete the multiplication equation.

Problem Solving

Question 9. Henry has 3 gerbils. Hannah has 3 times as many. How many gerbils does Hannah have? Answer: Given that, Henry has 3 gerbils. Hannah has 3 times as many. So, Multiplication of 3 with 3 then you get 9. 3 x 3 = 9. Therefore there are 9 gerbils near Hannah have.

Question 10. Dani needs 6 times as many red beads as gold beads. She needs 7 gold beads. How many red beads does Dani need? Answer: Given that, Dani needs 6 times as many red beads as gold beads. She needs 7 gold beads. So, Multiplication of 6 with 7 then you get 42. 6 x 7 = 42. Therefore there are 42 red beads.

Test Practice

Question 12. Amelia swam four times as many laps as Wesley. Wesley swam 7 laps. How many laps did Amelia swim? A. 11 laps B. 28 laps C. 35 laps D. 21 laps Answer: Given that, Amelia swam four times as many laps as Wesley. Wesley swam 7 laps So, Multiplication of 4 with 7 then you get 28. 4 x 7 = 28. Therefore there are 28 laps. Option B is the correct answer.

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Multiplicative Comparison (Grade 4)

Related Pages More Lessons for Grade 4 Common Core for Grade 4 Common Core Worksheets for Grade 4 Common Core Worksheets for all Grades

These lessons, with videos, examples, and solutions, help Grade 4 students learn to interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Common Core: 4.OA.1

Suggested Learning Targets

• I can explain how a multiple equation can be interpreted as a comparison such as Jason is 4 times as old as Ben.
• I can write an equation for a situation involving multiplicative comparison.

The following diagrams give examples of Multiplicative Comparison: Phrases used, Model Diagram, Multiplication Equation for a Word Problem. Scroll down the page for more examples and solutions.

Printable Worksheets involving Multiplicative Comparison Measurement Word Problems

Multiplicative Comparison using writing How to use models, illustrations and writing to solve multiplicative comparison questions? Things to remember:

• Multiplicative comparison means you are comparing two things together that need to be multiplied.
• Multiplicative comparison questions are usually written in word problems that have this format: Statement, Statement, Question.
• We use the two statements to determine the number sentence or equation.
• An equation is just like a number sentence but it includes letters.
• Darlene picked 7 apples. Juan picked 4 times as many as Darlene. How many apples did Juan pick?
• Joelle read 9 books in the fall. George read 7 times as many books. How many books did George read?
• Sarah is 12 years old. George is g years old. Sarah is 3 times as old as George. How old is George?

Writing Equations with Multiplicative Comparison Problems Things to remember:

• The letter is called a variable.
• Suzie is 4 feet tall. There is a tree in her yard that is 9 times taller than she is. How tall is the tree in Suzie’s yard?
• The tree in Suzie’s yard is 36 feet tall. The tree is 9 times as tall as Suzie. How tall is Suzie?
• Suzie is 4 feet tall. The tree in her yard is 36 feet tall. How much taller is the tree than Suzie?

Multiplicative Comparison Multiplicative comparison problems compare a characteristic of two objects using multiplication. Sometimes we know the value of the object that is bigger/older/faster, sometime we know the value of the object that is smaller/younger/slower and sometimes we know how many times bigger/older/faster one object is over the other? Use a variable for the value you don’t know and fill in the rest of the equation.

Examples: Write an equation and solve for the variable.

• Mrs. K is five times as old as her son. If she is 35, how old is her son?
• Mrs. L has two dogs. Scruffy is 12 inches high at the shoulder and Tuffy is 24 inches high at the shoulders. How much bigger than Scruffy is Tuffy?

The following activities are from Howard County Public School System

Activity 1: Write a multiplication equation to match each comparison statement.

Activity 2: Hannah was doing a report on animals’ sleep habits. She made the charts below to show the number of hours certain animals usually sleep each day.

Fill in the blanks to make the statements true.

A possum sleeps ______ times as many hours a day as a guinea pig.

A bat sleeps ______ times as many hours per day as a cow.

Write a multiplication equation to show the relationship between the length of time a gray seal sleeps and the length of time a possum sleeps. ________ x ________ = ________

When Hannah was reading about donkeys, she said, “I can’t believe that goats sleep 5 times as many hours per day as donkeys.” Find the number of hours per day a donkey sleeps. Show your thinking below using words, numbers, and/or pictures.

A donkey sleeps _______ hours per day.

Activity 3: Last weekend, Cassidy, Jefferson, and Braden played three basketball games against their cousins, Sammy, Kara, and Mitchell. The chart below shows how many baskets each were able to make during their three games.

Fill in each blank with a player’s name or a number to make each comparison statement true. Below each comparison statement, write a multiplication equation to show that the statement is true.

statement : ________________ made three times as many baskets as Sammy. multiplication equation : _______________________

statement : Cassidy made ______ times as many baskets as Mitchell. multiplication equation : _______________________

statement : Jefferson made _____ times as many baskets as _______________. multiplication equation : _______________________

statement : Sammy made double the number of baskets _____________ made. multiplication equation : _______________________

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Multipli. comparison

Multiplicative comparison

Here you will learn about what multiplicative comparisons are and how to use them to solve word problems.

Students will first learn about multiplicative comparisons in 4th grade and expand that knowledge through 5th grade when working with comparison statements and in 6th grade when learning about ratios.

What is multiplicative comparison?

A multiplicative comparison is a way of comparing two quantities by asking how many times larger or smaller one quantity is than the other quantity. Multiplicative comparisons involve the operations of multiplication and division to solve problems.

A model can help solve multiplicative comparison problems because it helps you to visualize the amounts that need to be compared and to find the unknown quantity.

Let’s look at a few examples.

Lucas and Ryan are working on a construction project for school. Lucas’s wood board is 5 times the length of Ryan’s board. If Ryan’s wooden board is 3 feet, how long is Lucas’s wooden board?

Draw a bar model to help visualize the situation.

Ryan has a 3 foot board.

From the model, you can see that Lucas’s board is 5 times the length of Ryan’s board. There are 5 groups of 3 feet.

So the equation is 5 \times 3=\text{ length of Lucas's board}

5 \times 3=15

Lucas’s board is 15 feet.

Mike has 3 lollipops. Michelle has 4 times as many lollipops as Mike. How many lollipops does Michelle have?

Draw a picture to model this situation.

Michelle has four times as many lollipops as Mike. So she has 4 groups of 3 lollipops.

The equation is 4 \times 3=\text { amount of lollipops}

4 \times 3=12

Michelle has 12 lollipops.

Jillian has 12 inches of hair ribbon. Suzanne has half that length. How long is Suzanne’s hair ribbon?

Draw a bar model.

The equation is, \cfrac{1}{2} \, \times 12=\text { length of Suzanne's ribbon}

12 \div 2 = \text { length of Suzanne's ribbon}

12 \div 2=6

Suzanne’s ribbon is 6 inches long.

Common Core State Standards

How does this apply to 4th grade math and 5th grade math?

• Grade 4 – Operations and Algebraic Thinking (4.OA.A.1) Interpret a multiplication equation as a comparison, for example, interpret 35 = 5 \times 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
• Grade 4 – Operations and Algebraic Thinking (4.OA.A.2) Multiply or divide to solve word problems involving multiplicative comparison, for example, by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
• Grade 5 – Number and Operations Base Ten – (5.NBT.B.7) Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

[FREE] Multiplicative Comparison Worksheet (Grade 4 to 5)

Use this worksheet to check your grade 4 to 5 students’ understanding of multiplicative comparisons. 15 questions with answers to identify areas of strength and support!

How to solve multiplicative comparison problems

In order to solve multiplicative comparison problems:

Draw a model.

Use multiplication or division to write an equation.

Solve the equation.

Multiplicative comparison examples

Example 1: multiplicative comparison using a bar model with whole numbers.

Maddie has collected 21 stickers. Her friend, Anna, has collected 3 times that amount. How many stickers does Anna have in her collection?

• Draw a model. 

Anna has 3 times the amount of stickers as Maddie. So she has 3 groups of 21.

2 Use multiplication or division to write an equation.

The equation is 3 \times 21= \; ?

3 State the answer.

3 \times 21=63

Anna has 63 stickers.

Example 2: multiplicative comparison using a bar model with whole numbers

Aderonke owns an animal shelter. She has 24 dogs in her shelter and twice as many cats. How many cats are in the shelter?

There are twice as many cats as dogs which means there are two groups of 24.

The equation is 2 \times 24= \; ?

2 \times 24=48

Aderonke has 48 cats in her animal shelter.

Example 3: multiplicative comparison using a bar model

Amani has 18 yards of wire. Austin has a third of that length of wire. How much wire does Austin have?

Austin’s wire is a third of the length of Amani’s wire. So, 18 yards is divided into three equal groups.

The equation is 18 \div 3=\text{ length of Austin's wire}

\cfrac{1}{3} \times 18=\text { length of Austin's wire}

\begin{aligned} & 18 \div 3=6 \\\\ & \cfrac{1}{3} \, \times 18=\cfrac{18}{3} \, =6 \end{aligned}

Austin’s wire is 6 yards long.

Example 4: multiplicative comparison using a bar model

Billy saved \$122 dollars. His sister, Nikki, has saved 4 times that amount. How much money has Nikki saved?

Nikki has 4 times the amount of money saved than Billy, which means she has 4 groups of \$122.

The equation is 4 \times 122=\text{ amount of money Nikki saved}

4 \times 122=488

Nikki saved \$488.

Example 5: multiplicative comparison with decimals

Jerome’s neighbor has 92 yards of fencing. Jerome has a fourth of that amount of fencing. How much fencing does Jerome have?

Jerome’s neighbor has 92.4 feet of fencing. He has a fourth of that amount, which means 92.4 is divided into 4 equal groups.

The equation is 92.4 \div 4=\text { length of Jerome's fence}

92.4 \div 4=23.1

Jerome has 23.1 yards of fencing.

Example 6: multiplicative comparison with fractions

Carl has 5 \, \cfrac{1}{2} \, gallons of paint. Lucy has three times that amount.

How many gallons of paint does Lucy have?

Lucy has three times the amount of gallons of paint than Carl which means there are 3 groups of 5 \, \cfrac{1}{2} .

The equation is 3 \times 5 \cfrac{1}{2}=\text { gallons of paint for Lucy}

\begin{aligned} & 3 \times 5 \, \cfrac{1}{2} \, =3 \times \cfrac{11}{2} \\\\ & 3 \times \cfrac{11}{2} \, =\cfrac{33}{2} \, =16 \cfrac{1}{2} \end{aligned}

Lucy has 16 \, \cfrac{1}{2} \, gallons of paint.

Teaching tips for multiplicative comparison

• Connect visual models to the equations so students can see the visual representation of the abstract equation.
• Math worksheets have their place in a math lesson, but providing students with alternative opportunities to practice such as math games or digital platforms are more engaging.
• Another visual representation that can be used when doing multiplicative comparison word problems is the number line.
• Incorporate projects such as having students create their own multiplicative comparison word problems with answer keys and share them on the Google Classroom.

Easy mistakes to make

• Confusing when to use multiplication versus when to use division For example, when you are given an amount such as 18 and are asked to find 3 times that amount, use multiplication. However, if you are given the amount of 18 and are asked to find a third of that amount, use division.

Related multiplication and division lessons

• Multiplication and division
• Multiplying and dividing integers
• Multiplying and dividing rational numbers
• Multiplication and division within 100
• Multiplying multi digit numbers
• Dividing multi digit numbers
• Understanding multiplication
• Long division
• Understanding division

Practice multiplicative comparison problems

1. Doug has 16 pieces of candy. Dhalia has 3 times that amount. How many pieces of candy does Dhalia have?

Dhalia has 3 times the amount of candy as Doug which means she has 3 groups of 16.

3 \times 16=48

Dhalia has 48 pieces of candy.

2. Danni has 35 pens in her classroom. Jo has 5 times that amount. How many pens does Jo have in her classroom?

Jo has 5 times as many pens as Danni which means she has 5 groups of 35.

5\times 35=175

Jo has 175 pens in her classroom.

3. Coach Tony has 82 students trying out for his volleyball team. Coach Luke has half that amount trying out for his soccer team. Which equation represents the amount of students trying out for Coach Luke’s soccer team?

Coach Luke has half the number of students trying out for his soccer team than Coach Tony which means 82 is divided into 2 equal groups.

82 \div 2=41

4. Devin has \$243.30 in her savings account. Debra has a third of that amount in her savings account. How much money does Debra have?

Debra has a third of the amount of money as Devin. So \$243.30 has to be divided into 3 equal groups.

243.30 \div 3=81.10

Debra has \$81.10 .

5. Julie has 4 \, \cfrac{2}{3} \, feet of yarn. Dylan has 6 times that amount. How much yarn does Dylan have?

Dylan has 6 times the amount of yarn as Julie, which means 6 groups of 4 \, \cfrac{2}{3} \, .

\begin{aligned} & 6 \times 4 \, \cfrac{2}{3} \, = \\\\ & 6 \times \cfrac{14}{3} \, = \cfrac{84}{3}=28 \end{aligned}

Dylan has 28 feet of yarn.

6. Rory planted a vegetable garden. He planted 51 tomato plants and a third the amount of zucchini plants. How many zucchini plants did he plant?

16 zucchini plants

17 zucchini plants

18 zucchini plants

19 zucchini plants

Rory planted a third of the number of tomato plants which means 51 is divided into 3 equal groups.

51 \div 3=17

\cfrac{1}{3} \, \times 51=17

Multiplicative comparison FAQs

No, you do not always have to write an equation. However, writing equations is a skill necessary for secondary mathematics.

The next lessons are

• Types of numbers
• Rounding numbers
• Factors and multiples

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Multiplicative Comparisons Lesson

• Donna Ventura
• Categories : Lesson plans for middle school math
• Tags : Teaching middle school grades 6 8

Lesson Objective

The lesson is aligned to the Common Core State Standards for Mathematics – 4.OA.1 Operations and Algebraic Thinking - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Materials Required

Interpreting a multiplication equation as a comparison.

Look at the multiplication equation below.

This multiplication equation compares the numbers 14, 2 and 7.

The symbol “=” means “is” and the symbol “x” means “times as many as.”

The equation means 14 is 2 times as many as seven.

The equation can also mean 14 are 7 times as many as two.

Look at the multiplication equations below. Explain in words what each equation means. Write the two statements.

• 36 = 12 x 3
• 81 = 3 x 27
• 117 = 9 x 13
• 344 = 4 x 86
• 36 is 12 times as many as 3 and 36 is 3 times as many as 12.
• 56 is 8 times as many as 7 and 56 is 7 times as many as 8.
• 81 is 3 times as many as 27 and 81 is 27 times as many as 3.
• 117 is 9 times as many as 13 and 117 is 13 times as many as 9.
• 344 is 4 times as many as 86 and 344 is 86 times as many as 4.

Representing Verbal Statements of Multiplicative Comparisons as Multiplication Equations

Look at the verbal statement below.

18 is 2 times as many as 9

This verbal statement compares the numbers 18, 2 and 9.

The word “is” means equal. We use the symbol “=” to represent the word “is.”

The words “times as many as” means multiply. We use the symbol “x” to represent the words “times as many as.”

The verbal statement can be represented by the multiplication equation 18 = 2 x 9.

Look at the word statements below. Write the equation that represents each word statement.

• 48 is 4 times as many as 12
• 72 is 9 times as many as 8
• 90 is 5 times as many as 18
• 136 is 4 times as many as 34
• 520 is 8 times as many as 65
• 48 = 4 x 12
• 90 = 5 x 18
• 136 = 4 x 34
• 520 = 8 x 65

Individual or Group Work

Explain in words what each equation means. Write the two statements.

• 24 = 2 x 12
• 30 = 10 x 3
• 92 = 4 x 23
• 144 = 12 x 12

Write the equation that represents each word statement.

• 27 is 3 times as many as 9
• 48 is 6 times as many as 8
• 50 is 5 times as many as 10
• 64 is 8 times as many as 8
• 93 is 3 times as many as 31
• 16 is 2 times as many as 8 and 16 is 8 times as many as 2
• 24 is 2 times as many as 12 and 24 is 12 times as many as 2
• 30 is 10 times as many as 3 and 30 is 3 times as many as 10
• 92 is 4 times as many as 23 and 92 is 23 times as many as 4
• 144 is 12 times as many as 12 and 144 is 12 times as many as 12
• 50 = 5 x 10
• 93 = 3 x 31

This post is part of the series: Mathematics Lesson Plan

This lesson plan covers Common Core math lessons for multiplicative comparisons, mutlistep word problems, factors, multiples and patterns.

• Multiplicative Comparisons
• Word Problems Involving Multiplicative Comparisons
• Multistep Word Problems
• Factors and Multiples
• Teaching About Patterns
• Assessment on Math Series

Multiplication Comparison Word Problems

With our Multiplication Comparison Word Problems lesson plan, students learn how to interpret and solve multiplicative comparison problems.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to create a quiz or test using the story problems students create for the lesson activity.

Description

Additional information, what our multiplication comparison word problems lesson plan includes.

Multiplication Comparison Word Problems teaches students strategies for solving multiplicative comparison problems.  At the end of the lesson, students will be able to solve multiplicative comparison problems, write multiplication and division equations for those problems, and use models. This lesson is for students in 4th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. To prepare for this lesson ahead of time, you can copy the handouts and pair students for the activity.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. If you want to add another activity to this lesson, you can create a quiz or test using the story problems students create for the lesson activity. You can also have your students create multiplication comparison word problems for them to exchange with another student to solve. You can have students count items in the classroom, like desks or chairs, to use for their own word problems. Finally, your students could discuss when they might use multiplication comparison in the real world.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.

MULTIPLICATION COMPARISON WORD PROBLEMS LESSON PLAN CONTENT PAGES

Comparing using multiplication.

The Multiplication Comparison Word Problems lesson plan includes two content pages. The lesson begins by stating that you might compare how many of something you have with your friends. You might have more money, read fewer books, or score more points in a game. You can compare numbers using addition or subtraction. And you can use multiplication when you compare two or more numbers! For example, if you had two pieces of pizza and your friend had six, your friend ate three times as much pizza (3 x 2 = 6).

To solve multiplicative comparisons, you can write an equation with symbols or use drawings. The lesson includes an example problem that you can solve using either a model or an equation. In the example, Noah earned $200, which was four times as much as Haley earned. To figure out how much Haley earned, we can use a model that illustrates the amounts. We can also use the equation 4a = 200. 200 / 4 = 50, so Haley earned $50. We know this is the right answer because 4 x 50 = 200.

The lesson closes with two more examples that students can read to learn how to solve multiplication comparison problems. Both of these examples show how to solve problems using a model and an equation, and how to check to make sure the answer is correct.

MULTIPLICATION COMPARISON WORD PROBLEMS LESSON PLAN WORKSHEETS

The Multiplication Comparison Word Problems lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

CREATING PROBLEMS ACTIVITY WORKSHEET

Students will work with a partner to complete the activity. Each pair with use the provided equations or drawings to create multiplication word problems. They can add to the drawings if needed. They will then solve their problems.

Students can work either alone or in larger groups if you’d prefer.

TRUE OR FALSE PRACTICE WORKSHEET

The practice worksheet asks students to complete two short exercises. For the first, they will tell whether various statements are true or false using the information given in a chart. For the second, they will use multiplication statements to compare pairs.

MULTIPLICATION COMPARISON WORD PROBLEMS HOMEWORK ASSIGNMENT

For the homework assignment, students will complete the chart using the information given. They will also solve word problems using both equations and models or drawings.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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Course: 4th grade   >   Unit 3

• Multiply by 1-digit numbers: FAQ
• Comparing with multiplication
• Comparing with multiplication and addition: giraffe
• Comparing with multiplication and addition: money
• Comparing with multiplication: magic
• Compare with multiplication

Compare with multiplication word problems

• (Choice A)   ◻ × 24 = 8 ‍   A ◻ × 24 = 8 ‍  
• (Choice B)   ◻ × 8 = 24 ‍   B ◻ × 8 = 24 ‍  
• (Choice C)   24 × ◻ = 8 ‍   C 24 × ◻ = 8 ‍  

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Multiplicative Comparison Involving Fractions

Description.

Objective:  Solve multiplicative comparison word problems involving fractions.

In Lesson 39, students build their problem-solving skills by solving multiplicative comparison word problems involving mixed numbers, e.g., “Jennifer bought 3 times as much meat on Saturday as she did on Monday. If she bought 1 1/2 pounds on Monday, what is the total amount of meat bought for the two days?” They create and use tape diagrams to represent these problems before using various strategies to solve them numerically.

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• Grade 4 Mathematics Module 5, Topic G, Lesson 39

Prerequisites

• CCSS Standard:

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Curriculum  /  Math  /  4th Grade  /  Unit 2: Multi-Digit Multiplication  /  Lesson 4

Multi-Digit Multiplication

Lesson 4 of 18

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Multiply 10, 100, and 1,000 by one- and two-digit numbers.

Common Core Standards

Core standards.

The core standards covered in this lesson

Number and Operations in Base Ten

4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Foundational Standards

The foundational standards covered in this lesson

3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Operations and Algebraic Thinking

3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Multiply 10, 100, and 1,000 by one-digit numbers.
• Multiply 10, 100, and 1,000 by two-digit numbers.
• Identify patterns in multiplication of 10, 100, and 1,000 by one- and two-digit numbers (MP.8).

Suggestions for teachers to help them teach this lesson

• Throughout this topic and then next one, students rely on many math practices in their work with multiplication. For example, “when students decompose numbers into sums of multiples of base-ten units to multiply them, they are seeing and making use of structure (MP.7). As they illustrate and explain the calculation by using physical or drawn models, they are using appropriate drawn tools strategically (MP.5) and attending to precision (MP.6) as they use base-ten units in the appropriate places” ( PARCC Model Content Frameworks, Mathematics, Grades 3–11 ). Further, “by reasoning repeatedly (MP.8) about the connection between math drawings and written numerical work, students can come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities” (NBT Progression, p. 14).
• It is important to preserve place value when talking about products of multi-digit numbers. For example, when discussing the computation 1,768 × 4, the partial product of the 6 digit and the 4 digit should be referenced as “six tens times four” or “sixty times four” rather than “six times four.” 

Lesson Materials

• Optional : Base ten blocks (3 ones, 3 tens, 3 hundreds, and 3 thousands per student or small group) — Students might not need these depending on their reliance on concrete materials.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

a.   Solve. 

• $$3\times1=$$  ________
• $$3\times10=$$  ________
• $$3\times100=$$  ________
• $$3\times1,000=$$  _______

b.   What do you notice about Part (a)? What do you wonder? 

Guiding Questions

Grade 4 Mathematics > Module 3 > Topic B > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds . © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US  license. Accessed Dec. 2, 2016, 5:15 p.m..

a.   4 × 1,000 = _____

b.   _____ = 8 × 100

Grade 3 Mathematics > Module 3 > Topic B > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds . © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US  license. Accessed Dec. 2, 2016, 5:15 p.m..

a.   15 × 10 = _______

b.   ______ = 28 × 100

c.   1,000 × 30 = ______

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

• What is the difference between saying “10 more” and “10 times as many”?
• What is another expression that has the same value as 10 x 800 and 1,000 x 8?

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve. 

a.   7 × 10 = _______

b.   100 × 7 = _______ 

c.   _______ = 7 × 1,000

d.   10 × 3 = _______

e.   1,000 × 30 = _______

f.   _______ = 10 × 30

g.   100 × 14 = _______

h.   _______ = 10 × 25

i.   54 × 1,000 = _______

Student Response

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

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Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Topic A: Multiplicative Comparison

Solve multiplicative comparison problems with a larger unknown. Distinguish multiplicative comparison from additive comparison.

4.OA.A.1 4.OA.A.2

Solve multiplicative comparison problems with a smaller unknown.

Solve multiplicative comparison problems with an unknown multiplier. Interpret a multiplication equation as a comparison. 

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Topic B: Multiplication of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Multiply multiples of 10, 100, and 1,000 by one-digit numbers. Estimate multi-digit products by rounding numbers to their largest place value.

Multiply two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies.

Multiply two-digit numbers by one-digit numbers.

Multiply three-digit numbers by one-digit numbers.

Multiply four-digit numbers by one-digit numbers.

Multiply two-, three-, and four-digit numbers by one-digit numbers and assess the reasonableness of the product. 

Topic C: Multiplication of Two-Digit Whole Numbers by Two-Digit Whole Numbers

Multiply two-digit multiples of 10 by two-digit multiples of 10. Estimate multi-digit products by rounding numbers to their largest place value.

Multiply two-digit multiples of 10 by two-digit numbers.

Multiply two-digit numbers by two-digit numbers using a variety of mental strategies.

Multiply two-digit by two-digit numbers using four partial products.

Multiply two-digit by two-digit numbers using two partial products and assess the reasonableness of the product.

Topic D: Multi-Step Word Problems

Abstract the formulas for the area and perimeter of a rectangle and apply those formulas in real-world and mathematical problems involving multiplication, addition, and subtraction.

4.MD.A.3 4.OA.A.3

Solve two-step word problems involving multiplication, addition, and subtraction.

4.OA.A.2 4.OA.A.3

Solve multi-step word problems involving multiplication, addition, and subtraction.

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