1. 3.OA.3 Multiplication and Division Strategies
Arrays and Drawings

2. Group size unknown - Array
If 18 apples are arranged into 3 equal groups. How many apples will be in each group?
6 apples in each of the 3 equal groups

3. Number of Groups unknown - Array
I have 28 pieces of gum for my friends. Each friend gets 4 pieces. How many friends do I have?
7 friends
It is important here for students to see the array in a table with columns and rows. However, the vocabulary of columns and rows is not important. It is also important to see the array in pictures.
This word problem depicts that the number of groups is unknown.

4. Unknown Product - Array
What multiplication problem is represented by the drawing below?
4 x 5 = 20
And/ or
5 x 4 = 20

5. Product Unknown– Area Model Array
I have 18 packs of markers. Each pack has 4 markers in it. How many markers do I have in total?
total markers 40 32
Since students do not have the traditional algorithm as a strategy yet. An area model array can be used. Students can actually see the area grid of 10 x 4 which is 40 plus 8 x 4 which is 32. From there they can see the total area or 18 x 4 = 72 markers.

6. True or False
My friend multiplied these two numbers. Below is their reasoning. Are they correct? If not, what advice do you have for this student? 18 x 6 = 60 56
Have student analyze and explain the “friend’s” reasoning or thought process. Perhaps have student discuss with a partner, they can use paper or a white board to describe their thinking.
They are not correct. 18 x 6 = 108
10 x 6 = 60
8 x 6 = 48 not 56, that is the mistake.

7. Write a word problem represented by the drawing
We are looking for students to know how to create a word problem based on an array.
A teacher could ask for some student to create a product unknown word problem, a group unknown word problem and the number of groups unknown word problem.
Examples,
Product unknown = I have 4 pairs of socks. How many socks do I have in total? 8 socks
Group Unknown = If 8 socks are shared equally among 4 siblings. How many socks does each sibling get? 2 socks
Number of groups unknown = If 8 socks are paired together then how many people will get a pair of socks? 4 socks

8. Division - Area Model Array Group Size unknown
If you have 48 inches of ribbon cut into 6 pieces, how long will each piece measure? 48 inches of Ribbon 6 pieces
3 X 6 = 18
5 X 6 = 30
8 inches
These are new strategies. Teacher must help facilitate the division problem here.
What is the question asking?
How can we think about this?
If we divide 6 by 48 how long will the pieces be?

9. Division – Array Number of groups unknown
If 56 pieces of fruit are to be packed 4 to a bag. How many bags will be needed? Use a drawing or array to solve. Be prepared to share your answer and explain.
Let students try on their own. They can use a drawing to divide the fruit or a division area model array.

10. Division – Array Number of groups unknown
Same Problem - If 56 pieces of fruit are to be packed 4 to a bag. How many bags will be needed? Can you explain this drawing? Is it correct? Is there anything missing?
The answer is missing. 14 bags needed

11. Division – Array Number of groups unknown
Same Problem - If 56 pieces of fruit are to be packed 4 to a bag. How many bags will be needed? Can you explain this array? Is it correct? Is there anything missing?
The answer is not indicated.
Explain the to get 14 bags needed

12. Given the array write a word problem
72 buttons 8 buttons

13. Given the array write a word problem
How many shirts can I make if a shirt requires 8 buttons and I have a total of 72 buttons? 9 shirts 72 buttons 4 x 8 buttons 5 x 8 buttons 8 buttons
32 buttons
40 buttons