Round whole numbers and decimals, with up to two places, to the nearest whole number, or tenth.
Use rounding to check the answers to multiplication and division problems.
Number Framework Stages 7 and 8
Using Number Properties
Problem: “Marcia and Linda swap books to mark each other’s work. Marcia has written 32 x 78 = 2 574. Linda looks at the 4 in the answer and immediately says the answer is wrong.How does Linda know?”
(Answer: 2 x 8 = 16 so the answer must have a 6 in the ones column.)
“Marcia sees Linda has written 32 x 78 = 2 856. While the ones digit is correct, Marcia says Linda must be wrong. How does Marcia know?”
(Possible answer: 32 x 78 ≈ 30 x 80 = 2 400. So 2 856 is well away from the correct answer.)
Problem: Discuss rounding 25.45 x 34.01.
(Possible answer: Here the problem is that rounding both numbers up to 30 x 40 respectively gives the answer 1 200, which is too large, and rounding down to 20 x 30 = 600 is too low. Somewhere between 600 and 1 200, say 900, is sensible.)
Problem: Discuss why 29.023 x 88.912 is a little less than 2 700.
(Possible answer: 29.023 x 88.912 < 30 x 90 = 2 700. So, 29.023 is a little less than 30 and 88.912 is a little less than 90.)
Examples: Worksheet (Material Master 8–3). Do not use calculators.
Understanding Number Properties:
Make up a four-digit decimal number times a three-digit decimal number problem of your own and explain how you would estimate the answer.