Splitting a rectangle to find its area

Mathematics · Measurement · ages 8-9

Name ______________________ Date ____________

Work out 3 x 4 + 3 x 2.
Answer: ______________
A 3 by (4 + 2) rectangle splits into 3 by 4 and 3 by 2. What is its area?
- 12
- 18
- 16
- 20
This 3×6 rectangle is split into two parts: 3×4 and 3×2. What is 3×4 + 3×2?
- 16
- 18
- 24
6×13 can be found by adding 6×10 and 6×3.
Circle one: True False
Split 5 x (7 + 3) as 5 x 7 + 5 x 3. What is the total?
Answer: ______________
An area model splits 5×(7+3) into two rectangles. What is the total area?
Answer: ______________
Which equals 6 x 13?
- 6 x 10 + 6 x 3
- 6 x 10 + 3
- 6 + 10 x 3
- 6 x 13 + 6
Eva draws 5 x (7 + 3) as one 5 by 7 block beside one 5 by 3 block. She says the two blocks prove 5 x 10 = 50. Is Eva right?
Circle one: True False
Leo says 4×(5+3) = 4×5 + 3. What mistake did he make?
- He added 5 and 3 wrong
- He multiplied both parts by 3 instead of 4
- He forgot to multiply the 3 by 4 too
A 3 by 6 wall is the same as 3 x (4 + 2). Use 3 x 4 = 12 and 3 x 2 = 6 to find 3 x 6.
Answer: ______________

Answer key

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

18 · 3 x 4 + 3 x 2 = 18 because 12 + 6 = 18.
18 · 18 is correct because 3 x 4 = 12 and 3 x 2 = 6, and 12 + 6 = 18.
18 · 3×4 = 12 and 3×2 = 6. Together, 12 + 6 = 18, the same as 3×6.
True · 13 splits into 10 and 3, so 6×13 = 6×10 + 6×3 = 60 + 18 = 78.
50 · The total is 50 because 35 + 15 = 50.
50 · 5×7 = 35 and 5×3 = 15. Add them: 35 + 15 = 50, the same as 5×10.
6 x 10 + 6 x 3 · 6 x 10 + 6 x 3 is correct: 60 + 18 = 78. The rest total 63, 36 or 84.
True · Eva is right because 35 + 15 = 50 and 7 + 3 = 10, so 5 x 10 = 50.
He forgot to multiply the 3 by 4 too · Both parts of the split must be multiplied by 4: 4×5 + 4×3, not just add 3 at the end.
18 · 3 x 6 = 18 because 12 + 6 = 18.