you have learned how to multiply one-digit numbers by

©Curriculum Associates, LLC Copying is not permitted.L11: Multiply Whole Numbers96

Multiply Whole NumbersLesson 11 Part 1: Introduction

Develop Skills and Strategies

You have learned how to multiply one-digit numbers by multiples of 10. Take a look at this problem.

There are 100 stickers on each roll, and a box of stickers has 3 rolls.

How many stickers are there in 4 boxes?

Explore It

Use the math you already know to solve the problem.

How many boxes are there?

How many rolls of stickers are in each box?

What multiplication expression shows how many rolls of stickers there are in all the boxes?

How many stickers are on each roll?

What multiplication expression shows how many stickers there are in all?

How can you show 100 using tens as factors? Write an expression that is equal to the one above using tens as factors.

Explain how to use what you know about multiplying by 10 to solve the problem.

CCSS4.NBT.B.5

©Curriculum Associates, LLC Copying is not permitted.97L11: Multiply Whole Numbers

Lesson 11Part 1: Introduction

Find Out More

To multiply with 3-digit and 4-digit numbers, you need to understand how to multiply by multiples of 10, 100, and 1,000. Take a look at the chart below.

Expression Think of it as... Think of it as... Product4 3 3 4 3 3 ones 12 ones 12

4 3 30 4 3 3 tens 12 tens 120

4 3 300 4 3 3 hundreds 12 hundreds 1,200

4 3 3,000 4 3 3 thousands 12 thousands 12,000

In each expression, the factor 4 is the same. The other factor increases by one place value each time.

Look at the products. The digits 1 and 2 from the basic fact 4 3 3 5 12 appear in each product. In the second expression, 4 is multiplied by 30, which is the same as 3 tens. That’s 4 times 3 tens which is 12 tens or 120. The factor 30 is 10 times as great as 3 and the product 120 is 10 times as great as 12.

Reflect

1 Choose a basic multiplication fact that you know. Show how to multiply the product of the fact by 10, 100, and 1,000. Explain how you know your answer is correct.

Lesson 11

©Curriculum Associates, LLC Copying is not permitted.

L11: Multiply Whole Numbers98

Part 2: Modeled Instruction

Read the problem below. Then explore different ways to multiply a 4-digit number by a 1-digit number.

Ezekiel has 3 building sets. Each set includes 1,125 pieces. How many pieces

are in all 3 sets?

Picture It

You can use an area model to help understand the problem.

3

1,000 100 20 51 1 1

3 3 1,000 3 3 100 3 3 20 3 3 5

3 3 1,125 5 (3 3 1,000) 1 (3 3 100) 1 (3 3 20) 1 (3 3 5) 5 3,000 1 300 1 60 1 15 5 3,375

Model It

You can also use partial products to multiply the numbers.

1,125 3 3

15 60

300 1 3,000

3,375

3 3 5 ones 3 3 2 tens 3 3 1 hundred 3 3 1 thousand

Lesson 11


Part 2: Guided Instruction

Connect It

Now you will explore the problem from the previous page further.

2 What is the expanded form of 1,125? 1 1 1

3 Where do you see the expanded form in the area model?

4 How is the expanded form used in the partial products equation?

5 The partial products equation shows the 3 being multiplied by the ones column first. Would the product change if you multiplied the 3 by the thousands column first, followed by the hundreds, tens, and ones? Explain.

6 Describe how the factor 3 is used with the factor 1,125 to find the product.

7 Explain how you multiply a 4-digit number by a 1-digit number.

Try It

Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

8 2,041 3 6 5

9 5,342 3 4 5

Lesson 11



Read the problem below. Then explore different ways to multiply a 2-digit number by a 2-digit number.

Folding chairs are set up in a school auditorium for a play. There are 16 rows of

chairs, each with 28 chairs. How many folding chairs are there?

Picture It

You can use an area model to multiply 2-digit numbers.

To solve this problem, multiply 16 3 28.

20

8

10 6

1

1

20 3 102 tens 3 1 ten 5 2 hundreds200

8 3 108 3 1 ten 5 8 tens80

20 3 62 tens 3 6 5 12 tens120

8 3 6 5 48

200 1 80 1 120 1 48 5 448

Model It

You can also use partial products to multiply 2-digit numbers.

16 3 28

48 80

120 1 200

448

8 ones 3 6 ones 8 ones 3 1 ten 2 tens 3 6 ones 2 tens 3 1 ten

Part 3: Modeled Instruction

Lesson 11


Connect It

Now you will explore the problem from the previous page further.

10 Why is the area model divided into four sections?

11 How do the four steps in the partial products equation relate to the four sections in the area model?

12 Would the product change if 20 1 8 on the left side of the area model were changed to 10 1 10 1 8? Explain.

13 List two different ways that you could break up the numbers in 34 3 12 to find the product. Explain why both ways would have the same product.

Try It

Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

14 27 3 21 5

15 37 3 23 5

Part 3: Guided Instruction

Student Model

Part 4: Guided Practice Lesson 11



How did you decide which model to use to help you solve the problem?

Pair/Share

Should you multiply 15 3 24 or 24 3 15?

How else could you solve this problem?

Pair/Share

The student multiplied 6 by the value of the digit in each place in 1,785.

Study the model below. Then solve problems 16–18.

An aquarium has 6 female sea turtles. Each turtle lays up to

1,785 eggs a year. If each turtle lays 1,785 eggs this year, how

many eggs will there be in all?

Look at how you could show your work using an area model.

6 3 1,000 6 3 700 6 3 80 6 3 5

1,000 700 80 5

6

1 1 1

6 3 1,785 5 (6 3 1,000) 1 (6 3 700) 1 (6 3 80) 1 (6 3 5) 5 6,000 1 4,200 1 480 1 30 5 10,710

Solution:

16 A deli is preparing trays of sandwiches. There are 15 trays, each with 24 sandwiches. How many sandwiches are there?

Show your work.

Solution:

10,710 eggs

Part 4: Guided Practice Lesson 11


Could you use an area model to help solve the problem?

How is this problem different than the one modeled on page 102?

Pair/Share

Multiply 5 by the value of the digit in each place in 147.

Does Dale’s answer make sense?

Pair/Share

17 The owner of 12 bookstores is buying 32 copies of a new book for each of the stores. How many books is the owner buying in all?

Show your work.

Solution:

18 A hardware store has 147 containers of paint. If each container holds 5 gallons of paint, how many gallons of paint are at the store? Circle the letter of the correct answer.

A 235

B 505

C 735

D 905

Dale chose A as the correct answer. How did he get that answer?

Part 5: Common Core Practice Lesson 11



Solve the problems.

1 A person blinks about 16 times per minute. About how many times does a person blink in 3 hours? [Hint: 1 hour 5 60 minutes]

A 48

B 96

C 960

D 2,880

2 Mr. Larson is planning a pizza party for 273 people. He plans on 3 slices of pizza for each person. How many slices of pizza is this in all?

A 276

B 546

C 619

D 819

3 Tell whether each expression can be used to solve 29 3 14.

a. (9 3 4) 1 (20 3 4) 1 (9 3 1) 1 (20 3 1) Yes No

b. (14 3 9) 1 (14 3 20) Yes No

c. (9 3 4) 1 (20 3 4) 1 (9 3 10) 1 (20 3 10) Yes No

d. (29 3 4) 1 (29 3 10) Yes No

Part 5: Common Core Practice Lesson 11


4 Which model(s) below could represent the solution to the problem 45 3 15? Circle the letter for all that apply.

A

40 5

5

10

B 0 15 30 45

C (4 3 1) 1 (4 3 5) 1 (5 3 1) 1 (5 3 5)

D (4 3 1) 1 (5 3 5)

E 0 45 90 135 180 225 270 315 360 405 450 495 540 585 630 675

5 Mo attended 14 tutoring sessions. Each session was 45 minutes long. How many minutes long were all 14 sessions?

Show your work.

Answer Mo was tutored for minutes.

6 Fourth grade students held a recycling drive. During one week they collected an average of 1,238 water bottles each day. How many water bottles did the fourth graders collect? [Hint: There are 7 days in one week.]

Show your work.

Answer The fourth grade students collected water bottles.

Go back and see what you can check off on the Self Check on page 95.Self Check

Multiply Whole NumbersLesson 11

L11: Multiply Whole Numbers 105©Curriculum Associates, LLC Copying is not permitted.

Develop Skills and Strategies

(Student Book pages 96–105)

Lesson objectives

• Multiply whole numbers of up to four digits by one-digit whole numbers.

• Multiply a two-digit number by a two-digit number.

• Use equations, rectangular arrays, and area models to illustrate and explain calculations.

Prerequisite skiLLs

In order to be proficient with the concepts/skills in this lesson, students should:

• Recall basic multiplication facts.

• Know properties of operations.

• Understand place value.

• Understand and use rectangular arrays and area models.

vocabuLary

There is no new vocabulary. Review the following key terms.

multiplication: an operation used to find the total number of items in equal-sized groups

product: the answer to a multiplication problem

factor: numbers that are multiplied together to get a product

multiple: the product of the number and any other whole number (0, 4, 8, 12, etc. are multiples of 4)

the Learning Progression

In Grade 3, students used equations, rectangular arrays, and the properties of operations to develop an understanding of multiplication. They multiplied one-digit whole numbers by multiples of 10, within 100. In Grade 4, students should continue to utilize equations, rectangular arrays, and the properties of operations as they multiply a whole number up to four digits by a one-digit number, and as they multiply two-digit numbers. This foundation will prepare them for Grade 5, when they become fluent with the standard multiplication algorithm with multi-digit whole numbers.

Teacher Toolbox Teacher-Toolbox.com

✓ ✓

✓

✓

✓ ✓

Prerequisite Skills 4.NBT.B.5

Ready Lessons

Tools for Instruction

Interactive Tutorials ✓

ccss Focus

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.

aDDitionaL stanDarDs: 4.OA.A.2, 4.OA.A.3, 4.NBT.A.1 (See page A42 for full text.)

stanDarDs For MatheMaticaL Practice: SMP 1, 2, 3, 4, 5, 7 (See page A9 for full text.)

L11: Multiply Whole Numbers106©Curriculum Associates, LLC Copying is not permitted.

Part 1: Introduction Lesson 11

at a gLance

Students read a word problem and answer a series of questions designed to explore a method for multiplying a 3-digit number by a 1-digit number.

steP by steP

• Tell students that this page models how to multiply two numbers by a factor of 10.

• Have students read the problem at the top of the page.

• Work through Explore It as a class.

• Ask students to explain how they found the total number of rolls of stickers in all of the boxes. Point out that they may find it helpful to write “100” under each roll of stickers.

• Explain to students that putting a zero at the end of a number is a shortcut for multiplying by 10. Make sure they understand what is happening to the value of the number when it is multiplied by a factor of 10.

sMP tip: Point out to students that when multiplying by multiples of 10, there is a pattern of putting zeros at the end of the number you are multiplying. In other words, when multiplying by 10, add 1 place value or 1 zero; when multiplying by 100, add 2 places or 2 zeros; when multiplying by 1,000, add 3 place values, or 3 zeros, and so on. (SMP 1) • If you have a multiplication problem such as

100 3 12, will it change your answer if you write it as 12 3 100?

Students’ responses should be that both problems have the same answer. This is an example of the Commutative Property of Multiplication, of which students understand the concept, but may not necessarily know the name. It states that regardless of the order in which you multiply two numbers, the product is the same.

Mathematical Discourse

©Curriculum Associates, LLC Copying is not permitted.L11: Multiply Whole Numbers96

Multiply Whole numbersLesson 11 Part 1: introduction

Develop skills and strategies

you have learned how to multiply one-digit numbers by multiples of 10. take a look at this problem.

There are 100 stickers on each roll, and a box of stickers has 3 rolls.

How many stickers are there in 4 boxes?

explore it

use the math you already know to solve the problem.

How many boxes are there?

How many rolls of stickers are in each box?

What multiplication expression shows how many rolls of stickers there are in all the boxes?

How many stickers are on each roll?

What multiplication expression shows how many stickers there are in all?

How can you show 100 using tens as factors? Write an expression that is equal to the one above using tens as factors.

Explain how to use what you know about multiplying by 10 to solve the problem.

ccss4.nbt.b.5

Possible explanation: When you multiply by 10, the digits in the other

factor move one place to the left and a 0 goes in the ones place.

4 3 3 3 10 3 10

4

3

4 3 3

100

4 3 3 3 100


Part 1: Introduction Lesson 11

at a gLance

Students find a pattern for multiplying by multiples of 10, such as 10, 100, and 1,000. They learn that when multiplying basic facts by a multiple of 10, the product increases by the same place value as the multiple of 10.

steP by steP

• Read Find Out More as a class.

• Using base-ten blocks, emphasize to students that 120 is 10 times greater than 12.

• Use the chart to show how the product increases by one place-value position as the multiple of 10 increases.

• Make sure students know how many zeros are associated with each place value name. [ones 5 no zeros, tens 5 1 zero, hundreds 5 2 zeros, thousands 5 3 zeros]

use a bingo game to understand multiplying numbers (multiples of ten).

Materials: Bingo game cards that have squares filled with various types of answers to multiplication problems involving multiples of ten.

• Distribute a bingo card and some markers to each student or pair of students.

• Choose a multiplication problem (from a set you have) and read it aloud (e.g., 5 times 60).

• Students will then look for any way that this problem may be represented on their bingo card.

• Repeat the steps of reading problems and covering spaces until a student has covered all the spaces in a column or in a row on his or her card.

hands-on activityEncourage students to think of any everyday situation where they may encounter the need to multiply.

Examples: calculating the number of minutes in a given number of hours, calculating the number of pennies, nickels, or dimes in a given number of dollars, calculating the number of rows of items

real-World connection


Lesson 11Part 1: introduction

Find out More

To multiply with 3-digit and 4-digit numbers, you need to understand how to multiply by multiples of 10, 100, and 1,000. Take a look at the chart below.

expression think of it as... think of it as... Product4 3 3 4 3 3 ones 12 ones 12

4 3 30 4 3 3 tens 12 tens 120

4 3 300 4 3 3 hundreds 12 hundreds 1,200

4 3 3,000 4 3 3 thousands 12 thousands 12,000

In each expression, the factor 4 is the same. The other factor increases by one place value each time.

Look at the products. The digits 1 and 2 from the basic fact 4 3 3 5 12 appear in each product. In the second expression, 4 is multiplied by 30, which is the same as 3 tens. That’s 4 times 3 tens which is 12 tens or 120. The factor 30 is 10 times as great as 3 and the product 120 is 10 times as great as 12.

reflect

1 Choose a basic multiplication fact that you know. Show how to multiply the product of the fact by 10, 100, and 1,000. Explain how you know your answer is correct.

answers may vary. Look for explanations that include following a pattern

of shifting the product one place to the left or adding a place value to each

product.

108 L11: Multiply Whole Numbers


Lesson 11Part 2: Modeled instruction

at a gLance

Students use partial products and an area model to find the product of a 4-digit number and a 1-digit number.

steP by steP

• Read the problem at the top of the page as a class.

• Read Picture It. Have a volunteer explain how the number is written in the area model and why it is written this way. [The number 1,125 is written in expanded form to multiply 3 by a multiple of 10 and make calculations easier.]

• Ask students how they could use addition to check the answer. [1,125 1 1,125 1 1,125 5 3,375]

• Read Model It.

• Make sure students understand that the digits in the tens, hundreds, and thousands places represent 20, 100, and 1,000.

sMP tip: Discuss with students the benefits of using an area model. An area model is a tool they can use to help visualize the multiplication problem, which can sometimes seem abstract. Models also break down the problem into smaller, simpler pieces that can be easier to multiply. (SMP 5)

To help students understand the concept of multiplication, let them know that multiplication is the same as repeated addition. Show a few simple examples, such as:

3 3 7 5 3 1 3 1 3 1 3 1 3 1 3 1 3

eLL support • How can you determine if your answer to the

problem is reasonable?

Students should explain that 1,125 is close to 1,000. Replacing 1,125 with 1,000 in the problem, you get an estimate of 3,000. The actual product should be close to 3,000.

Mathematical Discourse

Lesson 11



Part 2: Modeled instruction

read the problem below. then explore different ways to multiply a 4-digit number by a 1-digit number.

Ezekiel has 3 building sets. Each set includes 1,125 pieces. How many pieces

are in all 3 sets?

Picture it

you can use an area model to help understand the problem.

3

1,000 100 20 51 1 1

3 3 1,000 3 3 100 3 3 20 3 3 5

3 3 1,125 5 (3 3 1,000) 1 (3 3 100) 1 (3 3 20) 1 (3 3 5)5 3,000 1 300 1 60 1 155 3,375

Model it

you can also use partial products to multiply the numbers.

1,1253 3

1560

3001 3,000

3,375

3 3 5 ones 3 3 2 tens 3 3 1 hundred 3 3 1 thousand


Lesson 11Part 2: guided instruction

at a gLance

Students revisit the problem on page 98.

steP by steP

• Read Connect It as a class. Be sure to point out that the questions refer to the problem on page 98.

• Make sure that students see the connection between the expanded form and base-ten blocks: 5 is 5 ones blocks, 20 is 2 tens rods, 100 is 1 hundreds flat, 1,000 is 1 thousands cube.

• Have students explain their answer to problem 4. Have them use colored pencils to connect the partial products in the Model It to the area model in the Picture It.

• Have students explain their answer to problem 5. Make sure they understand that multiplication can be performed in any order and the product remains the same.

try it soLutions

8 Solution: 12,246; Multiply 6 by each digit in 2,041: (2,000 3 6) 1 (0 3 6) 1 (40 3 6) 1 (1 3 6). Find the partial products: 12,000 1 240 1 6. Add to find the product: 12,246

9 Solution: 21,368; Multiply 4 by each digit in 5,342: (5,000 3 4) 1 (300 3 4) 1 (40 3 4) 1 (2 3 4). Find the partial products: 20,000 1 1,200 1 160 1 8. Add to find the product: 21,368.

relate the partial products method to the Distributive Property.

The partial products method is an example of the Distributive Property.

The Distributive Property states that you can multiply a number and a sum by multiplying the number by each part of the sum and then adding these products.

• Explain that when breaking down the numbers into expanded form, you get 1,000 1 100 1 20 1 5.

• You can write the problem like this: 3 3 1,125 5 3(1,000 1 100 1 20 1 5)

• Using the Distributive Property, this simplifies to 3,000 1 300 1 60 1 15, which matches the partial products shown.

concept extension

ERROR ALERT: Students who wrote 1,446 multiplied 6 by 241 instead of 2,041. Those students added partial products of 1,200, 240, and 6.

Lesson 11


Part 2: guided instruction

connect it

now you will explore the problem from the previous page further.

2 What is the expanded form of 1,125? 1 1 1

3 Where do you see the expanded form in the area model?

4 How is the expanded form used in the partial products equation?

5 The partial products equation shows the 3 being multiplied by the ones column fi rst. Would the product change if you multiplied the 3 by the thousands column fi rst, followed by the hundreds, tens, and ones? Explain.

6 Describe how the factor 3 is used with the factor 1,125 to fi nd the product.

7 Explain how you multiply a 4-digit number by a 1-digit number.

try it

use what you just learned to solve these problems. show your work on a separate sheet of paper.

8 2,041 3 6 5

9 5,342 3 4 5

one side of the area model is separated into the expanded form.

the 3 is multiplied by the number in each place-value position in 1,125.

then all the partial products are added.

Multiply the

numbers in each place-value position of the 4-digit number by the 1-digit

number. Find the partial products and then add to find the final product.

each number in the expanded form is multiplied by the other factor, 3.

no, the product

would be the same. you would add the partial sums in a different order,

but the sum doesn’t change when you add in a different order.

12,246

21,368

1,000 100 20 5



Lesson 11Part 3: Modeled instruction

at a gLance

Students use an area model and partial products to multiply a 2-digit number by a 2-digit number.

steP by steP

• Read the problem at the top of the page as a class.

• Read Picture It.

• Relate one side of the area model to the number of rows and one side of the area model to the number of chairs in each row.

• Have students identify the multiplication expression for each section of the area model. [10 3 20, 10 3 8, 6 3 20, 6 3 8]

• Encourage students to circle the partial products within each section to help them distinguish the addends for the final step.

• Read Model It.

• Be sure students use placeholder zeros as they multiply by the multiples of ten.

Present the lattice multiplication method for multiplying two 2-digit numbers. The following is an example of how to use this method to find 53 3 41.

1 Draw a 2-by-2 table. Draw diagonal lines through all four squares. Write the digits in 53 above the columns and the digits in 41 next to the rows.

2 Multiply 3 times 4, and record the product, 12, in the corresponding box (keeping the digit in the tens place above the diagonal and the digit in the ones place below the diagonal).

3 Repeat Step 2 for the other numbers.

4 Add the numbers you recorded in the diagonals, writing their sums outside the lattice boxes. (In the sample shown, the answers are underlined.)

5 Read the answer from top left to bottom right, so the final product is 2,173.

visual Model

Lesson 11



read the problem below. then explore different ways to multiply a 2-digit number by a 2-digit number.

Folding chairs are set up in a school auditorium for a play. There are 16 rows of

chairs, each with 28 chairs. How many folding chairs are there?

Picture it

you can use an area model to multiply 2-digit numbers.

To solve this problem, multiply 16 3 28.

20

8

10 6

1

1


8 3 108 3 1 ten 5 8 tens80

20 3 62 tens 3 6 5 12 tens120

8 3 6 5 48

200 1 80 1 120 1 48 5 448

Model it

you can also use partial products to multiply 2-digit numbers.

163 28

4880

1201 200

448


Part 3: Modeled instruction

5

2

17 3

2

05

0

0

12

3

4

1

3


Lesson 11Part 3: guided instruction

at a gLance

Students revisit the problem on page 100.

steP by steP

• Read Connect It as a class. Be sure to point out that the questions refer to the problem on page 100.

• Have students explain their answer to problem 10. Ask, When you multiply the ones in 28 and the tens in 16, why is the product 80 and not 8? [There are 8 groups of 10, which is 80.]

• Have students explain their answer to problem 11. Students should understand how the partial products and the area model are related. [The partial products are the same numbers as the areas in each section of the area model.]

try it soLutions

14 Solution: 567; Students can use any method shown to find the product. The partial products are (20 3 20) 1 (20 3 7) 1 (1 3 20) 1 (1 3 7) 5 400 1 140 1 20 1 7.

15 Solution: 851; Students can use any method shown to find the product. The partial products are (20 3 30) 1 (20 3 7) 1 (3 3 30) 1 (3 3 7) 5 600 1 140 1 90 1 21.

sMP tip: Discuss the importance of being able to use mathematical language accurately. Review the meanings of the terms digit, factor, and product, showing examples of each. Encourage students to practice using these terms in the right context at the appropriate time. (SMP 1)

use base-ten blocks to multiply a 2-digit number by a 2-digit number.

Materials: base-ten blocks

• Group students in pairs. Distribute base-ten blocks to each pair. Use the steps below to model 43 3 14 (similar to using an area model).

• Model 43 on a flat surface by displaying 4 tens rods and 3 unit cubes in a single row.

• Model 14 by displaying 1 tens rod and 4 unit cubes in a single column to the left and below the row showing 43.

• Fill the inside with the largest blocks that match the area of each row and column. For this example, use 4 flats, 19 rods, and 12 unit cubes.

• The product is the value of the inside blocks. [400 1 190 1 12 5 602]

• Model other products as time allows.

concept extension

Lesson 11


connect it

now you will explore the problem from the previous page further.

10 Why is the area model divided into four sections?

11 How do the four steps in the partial products equation relate to the four sections in the area model?

12 Would the product change if 20 1 8 on the left side of the area model were changed to 10 1 10 1 8? Explain.

13 List two diff erent ways that you could break up the numbers in 34 3 12 to fi nd the product. Explain why both ways would have the same product.

try it

use what you just learned to solve these problems. show your work on a separate sheet of paper.

14 27 3 21 5

15 37 3 23 5

Part 3: guided instruction

567

851

each step shows the product in one section of the

area model.

no, the product would be the same.

instead of a partial product of 200, you would have two partial products of

100. instead of a partial product of 120, you would have two partial

products of 60. the total of all the partial products would still be the same.

each number in the

expanded form of one factor is multiplied by each number in the

expanded form of the other factor. each section shows a product.

Possible answer: 30 1 4 and 10 1 2 or 20 1 10 1 4 and 5 1 5 1 2. as long

as the sum of the numbers equals the factor, the partial products will add

up to the same product.



Lesson 11Part 4: guided Practice

at a gLance

Students solve problems involving multiplication of a whole number of up to 4 digits by a 1-digit number and a 2-digit number by a 2-digit number.

steP by steP

• Ask students to solve the problems individually and label units in their calculations.

• When students have completed each problem, have them Pair/Share to discuss their solutions with a partner or in a group.

soLutions

Ex Multiplying using partial products in an area model is shown as one way to solve the problem. Students need to multiply 6 by each digit in 1,785. Then add the partial products.

16 Solution: 360 sandwiches; Multiply 10 by each digit in 24, and multiply 5 by each digit in 24 to find the partial products: 200 1 40 1 100 1 20. Then add. (DOK 1)

17 Solution: 384 books; Multiply 10 by each digit in 32 and multiply 2 by each digit in 32 to find the partial products: 300 1 20 1 60 1 4. Then add. (DOK 1)

18 Solution: C; Multiply 5 by each digit in 147, and then add the partial products.

Explain to students why the other two answer choices are not correct:

B is not correct because 5 3 100 5 500 and 47 3 5 is more than 5.

D is not correct because 5 should be multiplied by (100 1 40 1 7), not (1 1 40 1 700) (DOK 3)

Part 4: guided Practice Lesson 11


Could you use an area model to help solve the problem?

How is this problem different than the one modeled on page 102?

Pair/share

Multiply 5 by the value of the digit in each place in 147.

Does Dale’s answer make sense?

Pair/share

17 The owner of 12 bookstores is buying 32 copies of a new book for each of the stores. How many books is the owner buying in all?

Show your work.

Solution:

18 A hardware store has 147 containers of paint. If each container holds 5 gallons of paint, how many gallons of paint are at the store? Circle the letter of the correct answer.

a 235

b 505

c 735

D 905

Dale chose a as the correct answer. How did he get that answer?

384 books

Dale multiplied 5 by the tens and 5 by the ones. he did not

multiply 5 by the hundreds.


2 3 102 3 1 ten 5 2 tens20

30 3 23 tens 3 2 5 6 tens60

2 3 2 5 4

10 2

30

2

1

1

Student Model

Part 4: guided Practice Lesson 11



How did you decide which model to use to help you solve the problem?

Pair/share

Should you multiply 15 3 24 or 24 3 15?

How else could you solve this problem?

Pair/share

The student multiplied 6 by the value of the digit in each place in 1,785.

study the model below. then solve problems 16–18.

An aquarium has 6 female sea turtles. Each turtle lays up to

1,785 eggs a year. If each turtle lays 1,785 eggs this year, how

many eggs will there be in all?

Look at how you could show your work using an area model.

6 3 1,000 6 3 700 6 3 80 6 3 5

1,000 700 80 5

6

1 1 1

6 3 1,785 5 (6 3 1,000) 1 (6 3 700) 1 (6 3 80) 1 (6 3 5)5 6,000 1 4,200 1 480 1 305 10,710

Solution:

16 A deli is preparing trays of sandwiches. There are 15 trays, each with 24 sandwiches. How many sandwiches are there?

Show your work.

Solution:

10,710 eggs

360 sandwiches

153 24

2040

1001 200

360



Lesson 11Part 5: common core Practice

at a gLance

Students solve multiplication problems that might appear on a mathematics test.

soLutions

1 Solution: D; Multiply 3 by each digit in 16: (10 3 3) 1 (6 3 3). Add the partial products: 30 1 18 5 48. Multiply 60 by each digit in 48: (60 3 40) 1 (60 3 8). Add the partial products: 2,400 1 480 5 2,880. (DOK 1)

2 Solution: D; Multiply 3 by each digit in 273. Find the partial products. Add to find the product. (DOK 1)

3 Solution: a. No; b. Yes; c. Yes; d. Yes (DOK 2)

4 Solution: A; The area model can be split into four sections: 40 3 10, 40 3 5, 5 3 10, and 5 3 5. Those partial products can be added together to equal the product of 45 3 15. E; The number line shows 45 added 15 times, which is the same as multiplying 45 3 15. (DOK 2)

5 630; Multiply 10 by each digit in 45 and multiply 4 by each digit in 45. Add the partial products: 400 1 50 1 160 1 20 5 630 (DOK 1)

6 8,666; Multiply 7 by each digit in 1,238. Add the partial products: 7,000 1 1,400 1 210 1 56 5 8,666 (DOK 1)

Part 5: common core Practice Lesson 11



Solve the problems.

1 A person blinks about 16 times per minute. About how many times does a person blink in 3 hours? [Hint: 1 hour 5 60 minutes]

A 48

B 96

C 960

D 2,880

2 Mr. Larson is planning a pizza party for 273 people. He plans on 3 slices of pizza for each person. How many slices of pizza is this in all?

A 276

B 546

C 619

D 819

3 Tell whether each expression can be used to solve 29 3 14.

a. (9 3 4) 1 (20 3 4) 1 (9 3 1) 1 (20 3 1) Yes No

b. (14 3 9) 1 (14 3 20) Yes No

c. (9 3 4) 1 (20 3 4) 1 (9 3 10) 1 (20 3 10) Yes No

d. (29 3 4) 1 (29 3 10) Yes No

3333

Part 5: common core Practice Lesson 11


4 Which model(s) below could represent the solution to the problem 45 3 15? Circle the letter for all that apply.

A

40 5

5

10

B 0 15 30 45

C (4 3 1) 1 (4 3 5) 1 (5 3 1) 1 (5 3 5)

D (4 3 1) 1 (5 3 5)

E 0 45 90 135 180 225 270 315 360 405 450 495 540 585 630 675

5 Mo attended 14 tutoring sessions. Each session was 45 minutes long. How many minutes long were all 14 sessions?

Show your work.

Answer Mo was tutored for minutes.

6 Fourth grade students held a recycling drive. During one week they collected an average of 1,238 water bottles each day. How many water bottles did the fourth graders collect? [Hint: There are 7 days in one week.]

Show your work.

Answer The fourth grade students collected water bottles.

Go back and see what you can check off on the Self Check on page 95.self check

630

8,666

Differentiated Instruction Lesson 11

L11: Multiply Whole Numbers114©Curriculum Associates, LLC Copying is not permitted.

assessment and remediation

hands-on activity challenge activityPresent the students with the following problems.

Each problem will require two steps to solve, multiplication being one of the steps involved.

• Brandon had 48 collectible cards. He gave 3 cards to each of his 10 friends. How many cards does Brandon have left? [18 cards]

• Amelia earns $12 an hour babysitting. She babysat for 16 hours. She also earned $25 for watering her neighbor’s tomato garden. How much has Amelia earned altogether? [$217]

• Mr. Rutledge is taking inventory of the items on the shelves of his store. He has 9 unopened boxes of soap and 16 bars of soap on the shelf. Each unopened box of soap has 312 bars in it. How many total bars of soap does Mr. Rutledge have? [2,824 bars]

use play money to understand multiplying numbers.

Materials: play money: one-dollar bills (for hundreds); dimes (for tens); pennies (for ones) (You can also use hundred-dollar bills for hundreds, ten-dollar bills for tens, and one-dollar bills for ones.)

• Have students work in pairs.

• Present a multiplication problem to students.

• Have students model the problem with the play money. For example: 154 3 3 would be modeled with 3 sets of 1 one-dollar bill, 5 dimes, and 4 pennies.

• Have students exchange 10 of the pennies for 1 dime and 10 of the dimes for a one-dollar bill.

• The final result would be: 4 one dollar bills, 6 dimes, and 2 pennies, which is 462.

• Ask students to find the product of 36 and 15. [540]

• For students who are still struggling, use the chart below to guide remediation.

• After providing remediation, check students’ understanding. Ask students to explain their thinking while finding the product of 18 and 27. [486]

• If a student is still having difficulty, use Ready Instruction, Level 3, Lesson 2.

if the error is . . . students may . . . to remediate . . .

51 have added. Remind students that “product” means multiplication.

54 have found all partial products as ones times ones.

Demonstrate using base-ten blocks that 36 is 30 1 6 and 15 is 10 1 5. Draw an area model to show students each partial product.

270 have incorrectly found the tens by tens partial product as 3 3 10.

Remind students that when multiplying tens by tens, the result is 30 3 10 5 300, not 3 3 10 5 30.

440 have incorrectly added partial products.

Remind students that they must regroup 14 tens as 1 hundred and 4 tens when adding partial products.

you have learned how to multiply one-digit numbers by

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