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 Target You will interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically. Arrays!

Fluency Lesson 4 Rename Units 4 min. Rename the Unit 8 tens = _______ 9 tens = ________ 11 tens = ________ 14 tens = ________

Fluency Lesson 4 Rename Units 4 min. Rename the Unit 14 hundreds = _______ 14 thousands = ________ 18 tens = ________ 28 tens = ________ 1,400 14,

Fluency Lesson 4 Rename Units 4 min. Rename the Unit 28 hundreds = _______ 28 thousands = ________ 12 tens = ________ 267 tens = ________ 2,800 28, ,670

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 Fluency Group Count by Multiples of 10 and 100 Lesson 4 Fluency Count by threes to Now count by 3 tens. When I raise my hand, stop counting. 3 tens 6 tens9 tens Say the number. 90 Continue! 12 tens15 tens 18 tens tens 24 tens27 tens 270

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 Fluency Group Count by Multiples of 10 and 100 Lesson 4 Fluency Count by 400 to 4, ,2001,6002,000 2,400 2,800 3,200 3,6004,000 Now count by 4 hundreds. When I raise my hand, stop counting. 4 hundreds 8 hundreds12 hundreds Say the number. 1,200 Continue! 16 hundreds20 hundreds 24 hundreds 2, hundreds 32 hundreds36 hundreds 3,600

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 Fluency Group Count by Multiples of 10 and 100 Lesson 4 Fluency Count by 600s to 6, ,2001,8002,4003,000 3,600 4,200 4,800 5,4006,000 Now count by 6 hundreds. When I raise my hand, stop counting. 6 hundreds 12 hundreds18 hundreds Say the number. 1,800 Continue! 24 hundreds30 hundreds 36 hundreds 3, hundreds 48 hundreds54 hundreds 5,400

Fluency Lesson 4 2 cm 9 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?

Fluency Lesson 4 5 cm 7 cm On your boards, write a multiplication sentence to find 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?

Fluency Lesson 4 3 cm 8 cm On your boards, write a multiplication sentence to find the area. Did you write 3 cm x 8 cm = 24 square cm? Write the formula for perimeter and solve. Did you write 2 x (3 cm + 8 cm) = 22 cm?

Fluency Lesson 4 7 cm On your boards, write a multiplication sentence to find the area. Did you write 7 cm x 7 cm = 49 square cm? Write the formula for perimeter and solve. Did you write 2 x (7 cm + 7 cm) = 28 cm?

Fluency Lesson 4 8 cm On your boards, write a multiplication sentence to find the area. Did you write 8 cm x 8 cm = 64 square cm? Write the formula for perimeter and solve. Did you write 2 x (8 cm + 8 cm) = 32 cm?

Fluency Lesson 4 2 cm 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? Write the formula for perimeter and solve. Did you write 2 x (2 cm + 5 cm) = 20 cm?

Fluency Lesson 4 5 cm X cm = 7 cm On your boards, draw a rectangle with: A given area of 35 square cm A length of 5 cm A width of X. 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?

Fluency Lesson 4 6 cm X cm = 9 cm On your boards, draw a rectangle with: A given area of 54 square cm A length of 6 cm A width of X. Write the formula for the area. Did you write 9 cm x 6 cm = 54 square cm? Write the formula for perimeter and solve. Did you write 2 x (9 cm + 6 cm) = 30 cm?

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 Development Problem 1 Lesson 4 Problem 1 ThousandsHundredsTensOnes 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.

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? Lesson 4 Problem 1 ThousandsHundredsTensOnes We can shorten this to 3 x ones x 1 X ones x 100 = 3 hundreds Concept Development Problem 1

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? Lesson 4 Problem 1 ThousandsHundredsTensOnes Work with your partner to figure out how to do 3 x 1, ones x 1 3 ones x 10 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? X 10 3 ones x 10 x 10 x 10 = 3 thousands Concept Development Problem 1

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? Lesson 4 Problem 1 ThousandsHundredsTensOnes We can shorten this to 3 x 1, ones x 1 X 1,000 3 ones x 1,000 = 3 thousands Concept Development Problem 1

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? Lesson 4 Problem 1b ThousandsHundredsTensOnes 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 10 4 ones x 1 What if I wanted to multiply that by 10? 4 ones x 10 X 10 Concept Development Problem 1B

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? Lesson 4 Problem 1b ThousandsHundredsTensOnes X 10 4 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 ones x 10 x 10 = 4 hundreds4 ones x 10 X 10 Concept Development Problem 1B

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? Lesson 4 Problem 1b ThousandsHundredsTensOnes We can shorten this to 4 x ones x 1 X ones x 100 = 4 hundreds Concept Development Problem 1b

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? Lesson 4 Problem 1b ThousandsHundredsTensOnes Work with your partner to figure out how to do 4 x 1,000. X 10 4 ones x 1 4 ones x 10 X 10 4 ones x 10 x 10 = 4 hundreds X 10 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 Concept Development Problem 1b

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? Lesson 4 Problem 1b ThousandsHundredsTensOnes We can shorten this to 4 x 1, ones x 1 X 1,000 4 ones x 1,000 = 4 thousands Concept Development Problem 1b

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? Lesson 4 Problem 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? Concept Development Problem 2

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? Lesson 4 Problem 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? Concept Development Problem 2

Lesson 4 Problem 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 × × 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. Concept Development Problem 3

Lesson 4 Problem 3 4 x 20 When 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 Problem 3

Concept Development Decomposing multiples of 10 before multiplying. Problem 3b Lesson 4 Problem 3b 6 x 400 With your partner, solve 6 x 400. Use a simplifying strategy so that you are multiplying by 10, 100, or 1, x 4 hundreds  (6 x 4) x 100  24 x 100 Using the expression of your choice, solve for 6 x x 400 is 24 hundreds or 2,400.

Concept Development Decomposing multiples of 10 before multiplying. Problem 3b Lesson 4 Problem 3b 4 x 500 With your partner, solve 4 x 500. Use a simplifying strategy so that you are multiplying by 10, 100, or 1, x 5 hundreds  (4 x 5) x 100  20 x 100 Using the expression of your choice, solve for 4 x x 500 is 2 thousands or 20 hundreds or 2,000.

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? 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

Debrief Lesson 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