Grade 6 › U03 Decimal Operations

Grade 6 › U03 Decimal Operations › L5
NUMBER · GRADE 6 · ALBERTAOUTCOME AB-MAT6-N4

L5 · Estimation: checking if an answer is reasonable

Learning goal

“I can estimate a product or a quotient before I calculate, put benchmark bounds around the answer on a number line, and use those bounds to tell whether a finished answer is reasonable - or impossible.”

Estimate — a close-enough answer found with rounded numbers, used to predict or to check.
Benchmark bounds — a low number and a high number the true answer must sit between, found by rounding both numbers down (low) and both numbers up (high).
Compatible numbers — numbers close to the real ones that divide or multiply easily (for 258 / 6, use 240 / 6).
Reasonable — an answer that fits inside the benchmark bounds. Outside the bounds = impossible.
Worked example

A class buys 36 notebooks at $4.80 each. About how much will they cost? Step 1: Look at the place-value chart for 4.80: 4 ones, 8 tenths, 0 hundredths. The 8 tenths push 4.80 up, so 4.80 rounds to 5. Step 2: Round the other number too: 36 rounds to 40. Estimate: 40 x 5 = about $200. Step 3: Set benchmark bounds. Round both numbers DOWN: 30 x 4 = 120. Round both numbers UP: 40 x 5 = 200. On the estimation number line (0 to 250, marked every 50), shade the stretch from 120 to 200 and say it plainly: the true cost must be between $120 and $200. Step 4: Check later against the exact product: 36 x 4.80 = $172.80 - inside the bounds, so it is reasonable. An answer like $1,728 or $17.28 would fall outside and would be impossible.

Check yourself — explain it

Why do we round BOTH numbers down for the low bound and BOTH numbers up for the high bound?

Paired problem — example still visible

Estimate 28 x 6.2, and give the benchmark bounds. -> 28 -> 30 and 6.2 -> 6, so about 180. Bounds: 20 x 6 = 120 and 30 x 7 = 210 - the answer must be between 120 and 210. (Exact: 173.6, inside.)

Faded completion — last step is yours

"Estimate 52 x 3.7. 52 rounds to 50. 3.7 rounds to ___. So the estimate is 50 x ___ = ___." -> 4; 4; 200 (Exact: 192.4, inside the bounds 50 x 3 = 150 and 60 x 4 = 240.)

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