1. Engage NY Math Module 5
Lesson 5: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.

2. Estimate Products by Rounding
Estimate and then multiply.
29 x 11 ≈ ____
43 x 21 ≈ ____
703 x 11 ≈ ____
29 x 21 ≈ ____
403 x 21 ≈ ____
43 x 34 ≈ ____
29 x 31 ≈ ____
303 x 21 ≈ ____
53 x 34 ≈ ____
23 x 12 ≈ ____
203 x 21 ≈ ____
53 x 31 ≈ ____
23 x 22 ≈ ____
41 x 11 ≈ ____
53 x 51 ≈ ____
23 x 32 ≈ ____
41 x 21 ≈ ____
93 x 31 ≈ ____
23 x 42 ≈ ____
41 x 31 ≈ ____
913 x 31 ≈ ____
37 x 13 ≈ ____
401 x 31 ≈ ____
73 x 31 ≈ ____
37 x 23 ≈ ____
501 x 31 ≈ ____
723 x 31 ≈ ____
36 x 24 ≈ ____
601 x 31 ≈ ____
78 x 34 ≈ ____
24 x 36 ≈ ____
801 x 31 ≈ ____
798 x 34 ≈ ____
43 x 11 ≈ ____
803 x 31 ≈ ____

3. MULTIPLY MENTALLY 9 x 10 = ____ 9 x 10 = 90
9 x 9 = 90 - ____ Write the number sentence, filling in the blank.
9 x 9 =
9 x 9? 81
9 x 100 = ____
9 x 100 = 900
9 x 99 = ____ Write the number sentence, filling in the blank.
9 x 99 =
9 x 99?
891

4. MULTIPLY MENTALLY 15 x 10 = ____ 15 x 10 = 150
15 x 9 = ____ Write the number sentence, filling in the blank.
15 x 9 =
15 x 9?
135
29 x 100 = ____
29 x 100 = 2,900
29 x 99 = 2,900 - ____ Write the number sentence, filling in the blank.
29 x 99 = 2,
29 x 99?
2,871

5. MULTIPLY BY MULTIPLES OF 100
31 x 100 = ____
31 x 100 = 3,100
3,100 x 2 = ____
3,100 x 2 = 6,200
31 x 200 = ____
= 31 x 100 x 2 =
31 x 200 = 6,200
Solve these two problems using the same method.
24 x 300 = ____
34 x 200 = ____

6. Application Problem:
Aneisha is setting up a play space for her new puppy. She will be building a fence around part of her yard that measures 29 feet by 12 feet. How many square feet of play space will her new puppy have? Try to solve this problem in more than one way.
30 twelves – 1 twelve = 29 twelves
(30 x 12) – (1 x 12) = 360 – 12 = 348
20 twelves + 9 twelve = 29 twelves
(20 x 12) + (9 x 12) = = 348
Aneisha’s puppy will have 348 square feet of play space.

7. Concept Development – Problem 1: Represent units using first the tape diagram, then the area model.
21 x 5
Can you solve this mentally using the unit form strategy?
(20 x 5) plus 5 more. This is twenty 5’s and 1 more 5. The product is 105.
Represent that thinking with a tape diagram. 5 5 5 5
21 fives
So you chose the factor 5 to be the unit. Can you imagine the area in each unit?
Draw the first image.

8. Concept Development – Problem 1: Represent units using first the tape diagram, then the area model.
Imagine that all 21 boxes are stacked vertically. Draw the second image.
1 five
20 fives
There are so many units in the above drawing. Let’s represent all the boxes using an area model like the type you used in fourth grade.
Draw the image.

9. Concept Development – Problem 1: Represent units using first the tape diagram, then the area model.
Draw the area model. 5 1 20
What values could you put in the area model? How many units are in each part of the rectangle?
1 x 5 = 5 and 20 x 5.
1 five and 20 fives
100 and 5
105

10. Concept Development – Problem 1: Represent units using first the tape diagram, then the area model.5 1
1 x 5 = 5
How are the area model and the tape diagram similar? How are they different?
They both show the same number of units.
The tape diagram helped us think 21 x 5 as (20 x 5) plus 5 more.
The area model helped us show all the boxes in the tape diagram without having to draw every single one.
It made it easier to see (20 x 5) + (1 x 5).
Can we turn this area model so that we count 5 groups of 21? What effect will turning the rectangle have on our area (product)? Draw it. 20
20 x 5 = 100 21 5

11. Concept Development – Problem 2: Products of two-digit and two-digit numbers, the area model and standard algorithm.
Now that we have discussed how the area model can show multiplication, let’s connect it to a written method – the standard algorithm.
23 x 31
Let’s think about which factor we want to name as our unit. Which do you think is easier to count, 31 twenty-three’s or 23 thirty-ones? Turn and talk to those at your table.
It’s easier to count units of twenty-three because we can find 30 of them and then just add 1 more.
Let’s label the top with our unit of 23.
We showed units of five before. How can we show units of twenty-three now?
Does it matter how we split the rectangle? Does it change the area (product)?
No it doesn’t matter. The area will be the same.
What’s the product of 1 and 23?
What’s the product of 30 and 23?
Now add your partial products to find the total area of our rectangle.
= 713
What is 23 x 31?
713 23 1 23
690 30

12. Concept Development – Problem 2: Products of two-digit and two-digit numbers, the area model and standard algorithm.
Now, let’s solve 23 x 31 using the standard algorithm. Show your neighbor how to set up this problem using the standard algorithm.
Work with your neighbor to solve using the standard algorithm.
2 3
x 3 1
Take a look at the area model and the standard algorithm. Compare them. What do you notice?
We added 1 unit of 23 to 30 units of 23.
In the area model we added two parts just like in the algorithm.
First we wrote the value of 1 twenty-three. Then we wrote the value of 30 twenty-threes.
Explain the connections between (30 x 23) + (1 x 23), the area model and the algorithm.

13. Concept Development – Problem 3: Products of two-digit and three-digit numbers.
343 x 21
What should we designate as the unit?
343
Let’s label the top with our unit of 343.
Let’s split our 21 into 1 and 20.
What’s the product of 1 and 343?
What’s the product of 20 and 343?
6,860
Now add your partial products to find the total area of our rectangle.
,860 = 7,203
What is 343 x 21?
7,203
343 1
343 20
6860

14. Concept Development – Problem 3: Products of two-digit and three-digit numbers.
Now, let’s solve 343 x 21 using the standard algorithm. Show your neighbor how to set up this problem using the standard algorithm.
Work with your neighbor to solve using the standard algorithm.
3 4 3 x
Did your area model match your standard algorithm?
Explain the connections between (20 x 343) + (1 x 343), the area model and the algorithm.

15. Concept Development – Problem 4: Products of two-digit and three-digit numbers.
In your math journal, solve the following problem using an area model and the standard algorithm.
2 3 1 x
Did your area model match your standard algorithm?

16. Exit Ticket

17. Problem Set
Display Problem Set on the board. Allow time for the students to complete the problems with tablemates.

18. HOMEWORK TASK Assign Lessons 4 and 5 Homework Tasks.
Due Date: Tuesday, January 21.