Upload
marion-green
View
213
Download
0
Tags:
Embed Size (px)
Citation preview
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 = ________
80
90
110
140
FluencyLesson 4Rename Units 4 min.
Rename the Unit
• 14 hundreds = _______
• 14 thousands = ________
• 18 tens = ________
• 28 tens = ________
1,400
14,000
180
280
FluencyLesson 4Rename Units 4 min.
Rename the Unit
• 28 hundreds = _______
• 28 thousands = ________
• 12 tens = ________
• 267 tens = ________
2,800
28,000
120
2,670
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
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.
90
Continue!12 tens 15 tens 18 tens 180
21 tens 24 tens 27 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
FluencyGroup Count by Multiples of
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.
1,200
Continue!16 hundreds 20 hundreds 24 hundreds
2,400
28 hundreds 32 hundreds 36 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
FluencyGroup Count by Multiples of
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.
6 hundreds 12 hundreds 18 hundreds
Say the number.
1,800
Continue!24 hundreds 30 hundreds 36 hundreds
3,600
42 hundreds 48 hundreds 54 hundreds
5,400
FluencyLesson 4
Lesson 42 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?
FluencyLesson 4
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?
FluencyLesson 4
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?
FluencyLesson 4
Lesson 4
7 cm
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?
FluencyLesson 4
Lesson 4
8 cm
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?
FluencyLesson 4
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?
FluencyLesson 4
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?
FluencyLesson 4
Lesson 46 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 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.
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 4Problem 1
Thousands Hundreds Tens Ones
• We can shorten this to 3 x 100.3 ones x 1
X 100
3 ones x 100 = 3 hundreds
Concept DevelopmentProblem 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 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
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 DevelopmentProblem 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 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
Concept DevelopmentProblem 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 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
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 4Problem 1b
Thousands Hundreds Tens Ones
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
X 10
Concept DevelopmentProblem 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 4Problem 1b
Thousands Hundreds Tens Ones• We can shorten this to 4 x 100.
4 ones x 1
X 100
4 ones x 100 = 4 hundreds
Concept DevelopmentProblem 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 4Problem 1b
Thousands Hundreds Tens Ones
• 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
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 DevelopmentProblem 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 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
Concept DevelopmentProblem 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 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?
Concept DevelopmentProblem 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 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?
Concept DevelopmentProblem 2
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.
Concept DevelopmentProblem 3
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 DevelopmentProblem 3
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.
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
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