PSHS NCE Estimation and Reasonableness Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Estimation and Reasonableness

Estimate quickly, reject impossible answers, and use number sense to check whether a result makes sense.

Grade 6–7 friendlyFast checking strategiesRegular practiceQuick Fire + Mastery

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Estimation and Reasonableness

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You do not always need the exact answer first

Suppose you see:

3,982 + 6,117

You can estimate first:

4,000 + 6,000 ≈ 10,000

So an answer like 10,099 is reasonable. An answer like 1,009 is not.

Estimation is a safety check. It helps you catch wrong operations, misplaced decimal points, and answers that are too big or too small.

DO IT FAST

Use ROUND → PREDICT → CHECK

1. ROUND: Change awkward numbers into friendly numbers.
2. PREDICT: Decide about how large the answer should be.
3. CHECK: Compare your exact answer with the estimate.
4. REJECT: If an option is clearly too large, too small, or has the wrong sign, cross it out immediately.

WORKED EXAMPLES

Six patterns you should recognize

1. Estimate a sum

4,921 + 3,087

5,000 + 3,000 ≈ 8,000

Best estimate: about 8,000.

2. Estimate a difference

9,870 − 4,950

10,000 − 5,000 ≈ 5,000

Best estimate: about 5,000.

3. Estimate a product

49 × 21

50 × 20 ≈ 1,000

The exact answer should be close to 1,000.

4. Estimate a quotient

398 ÷ 8

400 ÷ 8 = 50

The answer should be about 50.

5. Catch a decimal mistake

A student says 3.8 × 2.1 = 79.8.

4 × 2 ≈ 8

79.8 cannot be reasonable. The product should be near 8.

6. Check direction

A student says 15 − 23 = 8.

Impossible. Subtracting a larger number from a smaller number should give a negative result.

TRY WITH ME

Which answer makes sense?

What is a reasonable answer for 62 × 19?

1. Round 62 to 60.
2. Round 19 to 20.
3. 60 × 20 = 1,200.

The exact answer should be close to 1,200. Among choices, pick the one nearest that size.

COMMON TRAPS

Watch out for these

Rounding too roughly.
Use friendly numbers that still stay close to the originals.

Ignoring size.
Multiplying two numbers near 10 should not give 10,000.

Ignoring direction.
Subtraction, negatives, and fractions can tell you whether an answer should go up or down.

Using exact arithmetic when elimination is enough.
On a timed test, a fast estimate may remove three choices instantly.

REGULAR PRACTICE

Build the skill

These mix estimating sums, differences, products, quotients, and checking whether answers are sensible.

QUICK FIRE

Can you reject bad answers fast?

Five short questions. Estimate before calculating exactly.

Question 1 of 5

FRESH MASTERY CHECK

Can you judge an answer without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Not sure how to estimate quickly?

Send Teacher Abi the problem that slowed you down. I can show you which numbers to round and what size answer to expect.

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