Using Mathematical Structure

Mathematics · Mathematical Thinking · ages 8-9

Name ______________________ Date ____________

Work out 7 x 10 + 7 x 3.
Answer: ______________
Which splits 7 x 13 using tens and ones?
- 7 x 10 + 7 x 3
- 7 x 10 + 3
- 7 + 10 x 3
- 13 x 7 + 7
Break apart 8 × 12 using the distributive idea. Which one is the same as 8 × 12?
- 8×10 + 8×2
- 8×10 + 8×12
- 8+10 + 8+2
A square is always a rectangle.
Circle one: True False
Work out 5 x (7 + 3) by splitting: 5 x 7 + 5 x 3.
Answer: ______________
A shape has 4 right angles and all 4 sides the same length. What can you call it?
- Both a square and a rectangle
- Only a square
- Only a rectangle
What is 34 x 10?
- 304
- 3400
- 340
- 34
Lena splits 6 x 13 into 6 x 10 + 6 x 3 and gets 78. She says splitting by place value always works. Is Lena right?
Circle one: True False
Which way of breaking apart 9 × 24 uses the distributive property correctly?
- 9×2 + 9×4
- 9×20 + 9×4
- 9×10 + 9×10
Digits shift one place left when multiplying by 10. What is 56 x 10?
Answer: ______________

Answer key

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

91 · 7 x 10 + 7 x 3 = 91 because 70 + 21 = 91.
7 x 10 + 7 x 3 · 7 x 10 + 7 x 3 is correct: 70 + 21 = 91. The rest total 73, 37 or 98.
8×10 + 8×2 · 12 splits into 10 and 2, so 8×12 = 8×10 + 8×2.
True · A square has 4 right angles and equal opposite sides, so it fits the rule for a rectangle too.
50 · 5 x (7 + 3) = 50 because 35 + 15 = 50.
Both a square and a rectangle · It has every property of a rectangle, plus equal sides, so both names fit.
340 · 340 is correct: digits shift one place left. 304 shuffles wrongly, 3400 shifts twice, 34 never moved.
True · Lena is right because 60 + 18 = 78 and place value splitting is the distributive property, which always holds.
9×20 + 9×4 · 24 splits into 20 and 4, so 9×24 = 9×20 + 9×4.
560 · 56 x 10 = 560 because the digits 5 and 6 shift left and zero fills the ones.