Checking Multiplication by Estimation

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.