Arrays
1. Elena arranged her pencils in an array.
Look at the array below:
🟦🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦🟦
Which two expressions can be used to find the total number of pencils?
A. 3 × 6 and 2 × 6
B. 6 × 5 and 5 × 6
C. 5 × 5 and 1 × 6
D. 2 × 5 and 3 × 6
✅ Correct Answer: B. 6 × 5 and 5 × 6
(Commutative Property: Same total, different order)
2. Choose Yes or No to tell if the Commutative Property of Multiplication is being used.
2a. 3 × 7 = 3 × (3 + 4)
☐ Yes ☐ No
2a. 3 × 7 = 3 × (3 + 4) → ❌ No (This is distributive, not commutative)
3. Carlos says a 10s fact can be broken into two 5s facts.
Write an equation to test his generalization.
✅ Sample Equation:
10 × 4 = (5 × 4) + (5 × 4)
10 × 4 = 20 + 20 = 40 ✔️
6. A toy store displays 5 toys on each shelf.
There are 3 shelves on each of the store’s 5 walls.
How many toys are displayed? Show your work.
6. A toy store displays 5 toys per shelf, 3 shelves on 5 walls.
Shelves: 3 shelves × 5 walls = 15 shelves
Toys: 15 × 5 = 75 toys
✅ Answer: 75 toys
8. Sarah has 4 boxes of marbles.
There are 10 marbles in each box.
How many marbles does Sarah have? Show your work.
__________ marbles
8. Sarah has 4 boxes of 10 marbles.
4 × 10 = 40 marbles
✅ Answer: 40 marbles
4. Nadia broke up a large array into a 2 × 9 array and a 5 × 9 array.
What was the large array? Show your work.
✅ Total array: (2 × 9) + (5 × 9) = 18 + 45 = 63
So, large array is 7 × 9
2. Choose Yes or No to tell if the Commutative Property of Multiplication is being used.
2b. 5 × 9 = 9 × 5
☐ Yes ☐ No
2b. 5 × 9 = 9 × 5 → ✅ Yes
5. Which facts can you use to find 7 × 9?
Select all that apply.
☐ 7 × 4 and 7 × 5
☐ 7 × 1 and 7 × 8
☐ 2 × 9 and 5 × 9
☐ 3 × 3 and 4 × 9
☐ 6 × 9 and 1 × 9
5. Which facts can you use to find 7 × 9?
✅ Correct Answers:
☑ 7 × 4 and 7 × 5 → 28 + 35 = 63
☑ 2 × 9 and 5 × 9 → 18 + 45 = 63
☑ 6 × 9 and 1 × 9 → 54 + 9 = 63
❌ 7 × 1 and 7 × 8 = 7 + 56 = 63 (correct sum, but not a common strategy)
❌ 3 × 3 and 4 × 9 = 9 + 36 = 45 ✖️
10. A farmer has 3 barns.
Each barn has 4 stalls.
Each stall holds 6 cows.
How many cows are there in total?
Write an expression: ____________________________
Answer: __________ cows
10. Farmer has 3 barns, 4 stalls per barn, 6 cows per stall
Expression: 3 × 4 × 6
Step 1: 3 × 4 = 12
Step 2: 12 × 6 = 72 cows
✅ Answer:
Expression: 3 × 4 × 6
Total: 72 cows
7x8
56
11. Chase arranged his counters into this array:
🔴🔴🔴🔴🔴🔴🔴🔴
🔴🔴🔴🔴🔴🔴🔴🔴
🔴🔴🔴🔴🔴🔴🔴🔴
A. What two multiplication facts could Chase use to write an equation for the array?
11. Chase’s array: 3 rows of 8 counters
2x8 plus 1x8
2. Choose Yes or No to tell if the Commutative Property of Multiplication is being used.
2c. (2 × 5) × 3 = (5 × 2) × 3
☐ Yes ☐ No
2c. (2 × 5) × 3 = (5 × 2) × 3 → ✅ Yes
7. Find the number that makes the equation correct.
(2 × 6) + (5 × 6) = _______
Explain your reasoning:
7. (2 × 6) + (5 × 6) =
12 + 30 = 42
✅ Answer: 42
Reasoning: Add the two products that share the same factor (6):
(2 + 5) × 6 = 7 × 6 = 42 ✔️
Priya bought 3 adult tickets and 5 child tickets for a concert.
Ticket Prices:
Child: $3
Adult: $8
How much did she spend? Show your equations.
✅ Answer:
Equations:
3 × 8 = 24
5 × 3 = 15
24 + 15 = $39
9x9
81
11. Chase arranged his counters into this array:
🔴🔴🔴🔴🔴🔴🔴🔴
🔴🔴🔴🔴🔴🔴🔴🔴
🔴🔴🔴🔴🔴🔴🔴🔴
B. If Chase adds one more row of 8 counters,what equations can he use?
2x8 plus 2x8
2. Choose Yes or No to tell if the Commutative Property of Multiplication is being used.
2d. (3 × 2) × 5 = 5 × (3 × 2)
☐ Yes ☐ No
2d. (3 × 2) × 5 = 5 × (3 × 2) → ✅ Yes
9. Ben organizes his trading cards into a 4 × 5 array.
How can he break apart his arrays?
4 × 5
☐ 2 × 5 and 2 × 5
☐ 1 × 5 and 3 × 5
☐ 4 × 3 and 4 × 2
4 × 5
☑ 2 × 5 and 2 × 5
☑ 1 × 5 and 3 × 5
❌ 4 × 3 and 4 × 2 → These break the columns, not rows.
A classroom has 2 bookshelves.
Each bookshelf has 3 rows.
Each row holds 4 books.
How many books are there in total?
Show your work.
2x3 is 6
6x4 is 24
7x 6
42
Maya organizes hers into a 6 × 7 array.
How can they break apart their arrays?
6 × 7
☐ 3 × 7 and 3 × 7
☐ 2 × 7 and 4 × 7
☐ 6 × 3 and 6 × 4
6 × 7
☑ 3 × 7 and 3 × 7
☑ 2 × 7 and 4 × 7
❌ 6 × 3 and 6 × 4 → Doesn’t break up 7 correctly