Breaking numbers apart to multiply

Mathematics · Multiplication & Division · ages 8-9

Name ______________________ Date ____________

What is 8 x 5 + 8 x 2?
- 40
- 26
- 56
- 48
Which pair shows that order does not matter in multiplication?
- 6 x 4 and 4 - 6
- 6 x 4 and 4 x 6
- 6 x 4 and 6 + 4
- 6 x 4 and 6 - 4
Which equation breaks 8 × 7 into two easier parts?
- 8 × 5 + 8 × 2
- 8 × 4 + 8 × 4
- 8 × 5 + 8 × 3
To multiply 2 × 3 × 5, which is a good first step?
- Multiply any two of them first, like 2 × 3
- Add all three numbers together
- Only multiply the first two and stop
Leo says 8 x 7 = 8 x 5 + 8 x 2 because 7 is 5 + 2. Is Leo right?
Circle one: True False
Sam breaks 6 × 9 into 6 × 5 + 6 × 4. What is the total?
- 45
- 60
- 54
Which split equals 8 x 7?
- 8 + 5 + 8 + 2
- 8 x 5 x 8 x 2
- 8 + 7
- 8 x 5 + 8 x 2
What is 3 x 12?
Answer: ______________
Nina solves 8 × 9 by writing 8 × 9 = 8 × 6 + 8 × 4. What mistake did she make?
- Multiplication cannot be broken apart this way
- 6 + 4 does not equal 9, so the parts are wrong
- 8 × 6 is calculated incorrectly
Ana says (4 x 2) x 3 gives a different answer from 4 x (2 x 3). Is Ana right?
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

56 · 56 is right because 40 + 16 = 56.
6 x 4 and 4 x 6 · 6 x 4 and 4 x 6 is the commutativity pair: both equal 24, while the rest give 10, 2 and -2.
8 × 5 + 8 × 2 · 7 splits into 5 and 2, so 8×7 = 8×5 + 8×2 = 40 + 16 = 56.
Multiply any two of them first, like 2 × 3 · You can group any two numbers first: 2×3=6, then 6×5=30.
True · Leo is right: 40 + 16 = 56, which equals 8 x 7.
54 · 6×5=30 and 6×4=24. 30+24=54, which matches 6×9=54.
8 x 5 + 8 x 2 · 8 x 5 + 8 x 2 is right because 7 is 5 + 2. The rest give 23, 640 and 15.
36 · 3 x 12 = 36, same as 12 x 3.
6 + 4 does not equal 9, so the parts are wrong · 6+4=10, not 9. She needs parts that add up to 9, like 5 and 4: 8×5 + 8×4 = 40+32 = 72 = 8×9.
False · Ana is wrong: both groupings equal 24, which is what associativity guarantees.