Lesson 7: I can connect area diagrams and the distributive property to partial products of the standard algorithm with renaming. Time to Sprint!. Your teacher will give you today’s sprint. Let’s Review Multiplying Using the Area Model & Algorithm (solve in your notebook). 24 x 15 = _____.
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Lesson 7: I can connect area diagrams and the distributive property to partial products of the standard algorithm with renaming.
5th Grade Module 1 – Lesson 7
Your teacher will give you today’s sprint.
5th Grade Module 1 – Lesson 7
24 x 15 = _____
Solve each using an area model
Solve each using the standard algorithm
824 x 15 = _____
Solutions on next slide.
5th Grade Module 1 – Lesson 7
2 4
x 1 5
1 2 0
+ 2 4 0
3 6 0
20
40
8 24
x 1 5
4 1 2 0
+ 82 4 0
1 236 0
800 20 4
20 4
20
100
5
5
4,000
100
40
200
200
8,000
10
10
5th Grade Module 1 – Lesson 7
The length of a school bus is 12.6 meters. If 9 school buses park end to end with 2 meters between each one, what’s the total length from the front of the first bus to the end of the last bus?
5th Grade Module 1 – Lesson 7
5th Grade Module 1 – Lesson 7
524 x 136
Let’s name
524
as our unit.
We will have
3 columns & 3 rows
What do you notice about this problem compared to the problems we did yesterday?
Turn & Talk
Which factor should we use as our unit?
524 or 136?
Think which way would be easier to count.
How will our area model be different than the ones we made in yesterday’s lesson?
Let’s work together to solve using the area model & standard algorithm
5th Grade Module 1 – Lesson 7
Problem 1
Let’s label the top unit (524)
Draw a rectangle with 3 columns & 3 rows
Let’s build the area model. Record in your notebook with me.
Let’s label the rows using the other factor
Work with your partner to to solve the partial products.
Then solve for the final product.
500 20 4
6
30
100
Solution on next slide…
5th Grade Module 1 – Lesson 7
Solution Using Area Model
500 20 4
6
30
100
3,144
+
15,720
+
52,400
= 71,264
Notice how the partial products match up to the partial products in the standard algorithm.
Now try to solve this problem using the standard algorithm. Remember that you are multiplying with 3 different place values so you will have 3 addends!
Compare the solutions
5th Grade Module 1 – Lesson 7
Problem 2
4,519 x 326
5,000 x 300 = 1,500,000
What is different about this problem?
Before we solve,
let’s ESTIMATE our product.
Round the factors & make an estimate.
Which factor will be our unit?
Is one more efficient to use?
Turn & Talk
Will the fourth digit change anything about how we multiply?
Why or why not?
Let’s Solve the Actual Product
Partner A
Solve using the
Area Model
Partner B
Solve using the
Standard Algorithm
Volunteers will share their solutions!
Is your actual product reasonable given the estimate?
5th Grade Module 1 – Lesson 7
Problem 3
5,000 x 300 = 1,500,000
4,509 x 326
Let’s estimate the product first. Round each factor to multiply.
The first factor has a zero in the tens place.
Let’s write 4,509 in expanded form.
4,000 + 500 + 9
How many columns will we need to represent the top length of our area model?
We need 3 columns!
Why only three columns if we have a 4-digit number?
Work with your partner to solve in your notebook.
Partner B solve using the area model. Partner A solve using the standard algorithm.
Compare your solutions!
5th Grade Module 1 – Lesson 7
Is our product reasonable compared to our estimate of 1,500,000?
5th Grade Module 1 – Lesson 7
Problem 4
4,509 x 306
5,000 x 300 = 1,500,000
Estimate the Product
How is the problem different from 4,509 x 326?
Thinking about the expanded forms of the factors, imagine the area model.
How will you decompose the
length & width?
Why don’t we need three rows this time?
5th Grade Module 1 – Lesson 7
Problem 4
4,509 x 306
Solve the area model in your notebook.
Record the partial products for each row.
Let’s record what we drew with the algorithm.
4 5 0 9
x 3 0 6
24,000
3,000
54
2 7 0 5 4
+ 1 3 5 2 7 0 0
Now let’s record
300 x 4,509
When we multiply a number by 100, what happens to the value and position of each digit?
Begin with the first partial product 6 x 4,509
27,054
So, if we multiply 4,509 x 300 what needs to be recorded in the ones and tens place after the digit shift?
1,200,000
150,000
2,700
1, 3 7 9, 7 5 4
1,352,700
5th Grade Module 1 – Lesson 7
Complete Pages 2.B.63 - 2.B.65
You will have 10-15 minutes to work.
Try your Best!
5th Grade Module 1 – Lesson 7
LET’S Debrief
5th Grade Module 1 – Lesson 7
EXIT
TICKET
Page 2.B.66
5th Grade Module 1 – Lesson 7