Can you draw something? What can you draw? The projection screen in the school auditorium is 5...

Can you draw something? What can you draw? The projection screen in the school auditorium is 5 times as long and 5 times as wide as the screen in the library. The screen in the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium? The projection screen in the school auditorium is 5 times as long and 5 times as wide as the screen in the library. The screen in the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium? What conclusions can you make from your drawing?

Math Module 3 Multi-Digit Multiplication and Division

Topic B: Multiplication by 10, 100, and 1,000

Lesson 4:Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically

4.OA.1 4.OA.2 4.NBT.5 4.NBT.1

Lesson 4

TargetYou will interpret and

represent patterns when multiplying by 10, 100, and 1,000 in

arrays and numerically.

Arrays!

FluencyLesson 4Rename Units 4 min.

Rename the Unit

• 8 tens = _______

• 9 tens = ________

• 11 tens = ________

• 14 tens = ________

Rename the Unit

• 14 hundreds = _______

• 14 thousands = ________

• 18 tens = ________

• 28 tens = ________

14,000

Rename the Unit

• 28 hundreds = _______

• 28 thousands = ________

• 12 tens = ________

• 267 tens = ________

28,000

Can you draw something? What can you draw? The projection screen in the school auditorium is 5 times as long and 5 times as wide as the screen in the library. The screen in the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium? The projection screen in the school auditorium is 5 times as long and 5 times as wide as the screen in the library. The screen in the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium? What conclusions can you make from your drawing? Sat

FluencyGroup Count by Multiples of

10 and 100

Lesson 4Fluency

• Count by threes to 30.

3 6 9 12 15 18 21 24 27 30• Now count by 3 tens. When I raise my hand,

stop counting.

3 tens 6 tens 9 tens

Say the number.

Continue!12 tens 15 tens 18 tens 180

21 tens 24 tens 27 tens

10 and 100

Lesson 4Fluency

• Count by 400 to 4,000.

400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600 4,000

• Now count by 4 hundreds. When I raise my hand, stop counting.

4 hundreds 8 hundreds 12 hundreds

Say the number.

Continue!16 hundreds 20 hundreds 24 hundreds

10 and 100

Lesson 4Fluency

• Count by 600s to 6,000.

600 1,200 1,800 2,400 3,000 3,600 4,200 4,800 5,400 6,000

• Now count by 6 hundreds. When I raise my hand, stop counting.

Say the number.

Continue!24 hundreds 30 hundreds 36 hundreds

FluencyLesson 4

Lesson 42 cm

• On your boards, write a multiplication sentence to find the area.

• Did you write 2 cm x 9 cm = 18 square cm?

• Write the formula for perimeter and solve.

• Did you write 2 x (2 cm + 9 cm) = 22 cm?

FluencyLesson 4

Lesson 4

• Write the formula for perimeter and solve.• Did you write 2 x (5 cm + 7 cm) = 24 cm?

FluencyLesson 4

Lesson 4

FluencyLesson 4

Lesson 4

• Write the formula for perimeter and solve.• Did you write 2 x (7 cm + 7 cm) = 28

FluencyLesson 4

Lesson 4

FluencyLesson 4

Lesson 4

X cm = 5 cm

• On your boards, draw a rectangle with:• A given area of 10 square cm• A length of 2 cm• A width of X.

• Write the formula for the area.• Did you write 2 cm x 5 cm = 10 square cm?

FluencyLesson 4

Lesson 4

X cm = 7 cm

• Write the formula for the area.• Did you write 5 cm x 7 cm = 35 square cm?• Write the formula for perimeter and solve.• Did you write 2 x (5 cm + 7 cm) = 24 cm?

FluencyLesson 4

Lesson 46 cm

X cm = 9 cm

• Write the formula for the area.• Did you write 9 cm x 6 cm = 54 square cm?• Write the formula for perimeter and solve.

Can you draw something? What can you draw? The in four weeks combining her allowance and her babysitting? the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium? The projection screen in the school auditorium is 5 times as long and 5 times as wide as the screen in the library. The screen in the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium? What conclusions can you make from your drawing?

Application Problem Lesson 4

Samantha received an allowance of $3 every week. By babysitting, she earned $30 every week. How much money did Samantha have in four weeks combining her allowance and her babysitting?

of 14 feet. What is the perimeter of the screen in the auditorium? The projection screen in the school auditorium is 5 times as long and 5 times as wide as the screen in the library. The screen in the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium? What conclusions can you make from your drawing?

Concept DevelopmentProblem 1

Lesson 4Problem 1

Thousands Hundreds Tens Ones

• How many groups of 3 do you see?

3 ones x 1

• Suppose I wanted to multiply 3 ones by ten instead. How would I do that?

3 ones x 10

• We can just move each disk over to the tens place and get 3 tens. X 10

• What if I wanted to multiply that by 10? X 10

3 ones x 10 x 10 = 3 hundreds

• Look at my equation. I started with 3 ones. What did I multiply 3 ones by to get 3 hundreds? Turn and talk.

• We multiplied by 10 and then multiplied by 10 again.

• 10 x 10 is really 100.• I can group the 10 x 10, so this is

really 3 x (10 x 10). That’s just 300.

Lesson 4Problem 1

• We can shorten this to 3 x 100.3 ones x 1

3 ones x 100 = 3 hundreds

Lesson 4Problem 1

Thousands Hundreds Tens Ones• Work with your partner to figure out how to do 3 x 1,000.

3 ones x 1

3 ones x 10

3 ones x 10 x 10 = 3 hundreds• I showed 3 times 1,000 by

showing 3 ones x 10 to get 3 tens. Then I did times 10 again to get 3 hundreds and times 10 again to show 3 thousands.

• I drew an arrow representing times 1,000 from 3 ones to the thousands column.

• What is 3 x 10 x 10 x 10 or 3 x 1,000?

3 ones x 10 x 10 x 10 = 3 thousands

Lesson 4Problem 1

Thousands Hundreds Tens Ones• We can shorten this to 3 x 1,000.

3 ones x 1

X 1,000

3 ones x 1,000 = 3 thousands

Lesson 4Problem 1b

Thousands Hundreds Tens Ones• How many groups of 4 do you see?

• Suppose I wanted to multiply 4 ones by ten instead. How would I do that?

• We can just move each disk over to the tens place and get 4 tens.

X 104 ones x 1• What if I wanted to multiply that

by 10?

4 ones x 10X 10

Concept DevelopmentProblem 1B

Lesson 4Problem 1b

X 104 ones x 1

• Look at my equation. I started with 4 ones. What did I multiply 4 ones by to get 4 hundreds? Turn and talk.

• We multiplied by 10 and then multiplied by 10 again.

• 10 x 10 is really 100.• I can group the 10 x 10, so

this is really 4 x (10 x 10). That’s just 400.

4 ones x 10 x 10 = 4 hundreds4 ones x 10

Concept DevelopmentProblem 1B

Lesson 4Problem 1b

Thousands Hundreds Tens Ones• We can shorten this to 4 x 100.

4 ones x 1

4 ones x 100 = 4 hundreds

Concept DevelopmentProblem 1b

Lesson 4Problem 1b

• Work with your partner to figure out how to do 4 x 1,000. X 10

4 ones x 1

4 ones x 10X 10

4 ones x 10 x 10 =

4 hundreds

• I showed 4 times 1,000 by showing 4 ones x 10 to get 4 tens. Then I did times 10 again to get 4 hundreds and times 10 again to show 4 thousands.

• I drew an arrow representing times 1,000 from 4 ones to the thousands column.

• What is 4 x 10 x 10 x 10 or 4 x 1,000?

4 ones x 10 x 10 x 10 =

4 thousands

Lesson 4Problem 1b

Thousands Hundreds Tens Ones• We can shorten this to 4 x 1,000.

4 ones x 1

X 1,000

4 ones x 1,000 = 4 thousands

Lesson 4Problem 2

15 x 10

• Use number disks to represent 15 and draw 15 x 10.

• Does your chart look like this?• We drew an arrow to show times 10

for the 1 ten and also for the 5 ones.• What is 1 ten x 10?• 15 x 10 equals?

Lesson 4Problem 2

22 x 100• Use number disks to represent 22

and draw 22 x 100.• Does your chart look like this?

• We drew 2 tens and 2 ones and an arrow to show times 10 and then I did times 10 again.

• We also could have shown times 100 by moving two place values to the left.

• How can we express this as multiplication sentences?

• 22 x 10 x 10 becomes 22 x 100.• What is 22 x 100?

Lesson 4Problem 3

4 x 20• Just like 3 × 100 could be expressed as 3 × 10

× 10, there are different ways to show 4 × 20 to help us multiply. What is another way that I could express 4 × 20?

4 × 2 tens is the most helpful for me

because I know 4 × 2.

• 4 × 2 tens OR 4 × 2 × 10 OR 8 × 10. • Discuss with your partner which of these

methods would be most helpful to you to solve 4 × 20.

4 × 2 × 10 is the most helpful because it is similar to 4 × 2 tens. I can do 4 × 2 first, which I know is 8. Then I can do 8 times 10, which I know is 80.

Lesson 4Problem 3

4 x 20When multiplying with multiples of 10, you can decompose a factor to help you solve. In this example, we expressed 4 × 20 as (4 × 2) × 10.

Concept Development

Decomposing multiples of 10 before multiplying.

Problem 3b

Lesson 4Problem 3b6 x 400

• With your partner, solve 6 x 400. Use a simplifying strategy so that you are multiplying by 10, 100, or 1,000.

• 6 x 4 hundreds4(6 x 4) x 100 4 24 x 100

• Using the expression of your choice, solve for 6 x 400.

• 6 x 400 is 24 hundreds or 2,400.

Concept Development

Decomposing multiples of 10 before multiplying.

Problem 3b

Lesson 4Problem 3b4 x 500

• With your partner, solve 4 x 500. Use a simplifying strategy so that you are multiplying by 10, 100, or 1,000.

• 4 x 5 hundreds4(4 x 5) x 100 4 20 x 100

• Using the expression of your choice, solve for 4 x 500.

• 4 x 500 is 2 thousands or 20 hundreds or 2,000.

Lesson 4

Problem Set

10 Minutes

Problem Set

10 Minutes

Lesson 2

Problem Set

10 Minutes

Lesson 4

Problem Set

10 Minutes

Lesson 4

Problem Set

10 Minutes

DebriefLesson Objective:

Interpret and represent patterns when multiplying by 10, 100, and 1,000 both in arrays and numerically.

• What is the difference between saying 10 more and 10 times as many?

• What is another expression that has the same value as 10 × 800 and 1,000 × 8?

• Think about the problems we solved during the lesson and the problems you solved in the Problem Set. When does the number of zeros in the factors not equal the number of zeros in the product?

• For Problem 4, 12 × 10 = 120, discuss with your partner whether or not this equation is true: 12 × 10 = 3 × 40. (Problem 7 features 3 × 40.)

• How did the Application Problem connect to today’s lesson?

Exit Ticket Lesson 4

Can you draw something? What can you draw? The projection screen in the school auditorium is 5...

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