Estimation and Reasonableness
Round to the Nearest 10 (A)
Match each number to its rounded value.
Round to the Nearest 10 (B)
Match each number to its rounded value.
Round to the Nearest 100 (A)
Circle the correct answer.
349 rounds to?
672 rounds to?
450 rounds to?
218 rounds to?
Round to the Nearest 100 (B)
Circle the correct answer.
551 rounds to?
149 rounds to?
850 rounds to?
775 rounds to?
Round to the Nearest 1,000
Circle the correct answer.
3,478 rounds to?
6,250 rounds to?
1,890 rounds to?
9,501 rounds to?
Round These Numbers
Round each number as directed.
Round 367 to the nearest 10: ___
Round 367 to the nearest 100: ___
Round 4,832 to the nearest 100: ___
Round 4,832 to the nearest 1,000: ___
Sort by Rounding Result
When rounded to the nearest 100, sort these numbers.
Round and Add
Round each number to the nearest 10 first, then add the rounded numbers.
Front-End Estimation
Use the leading digits to estimate. Circle the best estimate.
312 + 487 ≈ ?
625 − 298 ≈ ?
1,250 + 3,680 ≈ ?
7,900 − 2,100 ≈ ?
Estimate the Answer (A)
Use rounding to estimate. Circle the best estimate.
398 + 205 ≈ ?
812 − 395 ≈ ?
49 × 6 ≈ ?
297 ÷ 3 ≈ ?
Estimate the Answer (B)
Use rounding to estimate.
482 + 319 ≈ ?
753 − 248 ≈ ?
62 × 8 ≈ ?
395 ÷ 4 ≈ ?
Estimate the Answer (C)
Estimate each answer by rounding.
1,234 + 2,567 ≈ ?
5,280 − 1,910 ≈ ?
198 × 5 ≈ ?
603 ÷ 6 ≈ ?
Reasonable or Unreasonable? (A)
Sort each calculation into the correct column.
Reasonable or Unreasonable? (B)
Sort each calculation.
Estimate Before You Calculate (A)
First estimate, then find the exact answer.
Estimate: 387 + 214 ≈ ___ Exact: ___
Estimate: 903 − 456 ≈ ___ Exact: ___
Estimate: 48 × 7 ≈ ___ Exact: ___
Estimate: 246 ÷ 6 ≈ ___ Exact: ___
Estimate Before You Calculate (B)
Estimate first, then calculate exactly.
Estimate: 1,295 + 706 ≈ ___ Exact: ___
Estimate: 3,001 − 1,485 ≈ ___ Exact: ___
Estimate: 73 × 9 ≈ ___ Exact: ___
Estimate: 832 ÷ 8 ≈ ___ Exact: ___
Match Estimates to Calculations
Draw a line from each calculation to its best estimate.
Is This Estimate Reasonable?
Someone estimated these. Circle the reasonable estimates.
42 × 19 ≈ 800. Is this reasonable?
305 + 198 ≈ 500. Is this reasonable?
756 ÷ 8 ≈ 200. Is this reasonable?
4,120 − 2,890 ≈ 1,200. Is this reasonable?
Estimate Then Calculate (A)
First write an estimate by rounding, then calculate the exact answer.
Estimate: 397 × 5 ≈ ___ Exact: 397 × 5 = ___
Estimate: 612 ÷ 3 ≈ ___ Exact: 612 ÷ 3 = ___
Estimate: 248 + 553 ≈ ___ Exact: 248 + 553 = ___
Estimate Then Calculate (B)
Estimate first, then find the exact answer.
Estimate: 583 × 4 ≈ ___ Exact: 583 × 4 = ___
Estimate: 945 ÷ 9 ≈ ___ Exact: 945 ÷ 9 = ___
Estimate: 1,789 − 892 ≈ ___ Exact: 1,789 − 892 = ___
Spot the Error Using Estimation
Use estimation to find which calculation has an error. Explain how you know.
A student says 47 × 8 = 576. Estimate to check: 50 × 8 = ___. Is the answer reasonable?
A student says 315 ÷ 5 = 83. Estimate to check: 300 ÷ 5 = ___. Is the answer reasonable?
A student says 2,489 + 1,515 = 3,004. Estimate to check: 2,500 + 1,500 = ___. Is the answer reasonable?
Real-World Estimation (A)
Estimate the answer to each problem. You do NOT need to calculate exactly.
A school has 487 students. Each student needs 3 exercise books. About how many books are needed?
A pool holds about 12,500 litres. About how many 8-litre buckets would fill it?
Real-World Estimation (B)
Estimate each answer.
Your family spends about $87 per week on groceries. Estimate the cost for 4 weeks.
A train travels at about 95 km/h. Estimate how far it travels in 6 hours.
Which Calculation Is Wrong?
Use estimation to identify the wrong answer. Circle it.
Which is WRONG?
Which is WRONG?
Which is WRONG?
Estimation Strategies
Explain what estimation strategy you would use.
To estimate 498 × 6, I would round 498 to ___ and multiply by 6 to get ___.
To estimate 2,345 + 1,678, I would round each to the nearest ___ and add to get ___.
To check if 432 ÷ 8 = 54 is correct, I would multiply ___ × ___ = ___ and compare.
Create Your Own Estimation Problems
Write your own estimation challenges.
Write a multiplication where estimation helps check the answer. Then solve it.
Write a word problem where an exact answer is not needed — just an estimate.
Round to the Nearest 10 (A)
Circle the best estimate.
47 rounds to...
83 rounds to...
125 rounds to...
556 rounds to...
Round to the Nearest 100 (A)
Circle the best estimate.
347 rounds to...
851 rounds to...
1,249 rounds to...
4,550 rounds to...
Round and Estimate Addition (A)
Round each number to the nearest 100, then estimate the sum.
348 + 251 ≈ ___ + ___ = ___
789 + 412 ≈ ___ + ___ = ___
1,234 + 2,567 ≈ ___ + ___ = ___
3,890 + 1,120 ≈ ___ + ___ = ___
Round and Estimate Addition (B)
Estimate each sum.
672 + 318 ≈ ___
4,567 + 3,421 ≈ ___
899 + 1,050 ≈ ___
12,345 + 6,789 ≈ ___
Round and Estimate Subtraction
Round then estimate each difference.
803 − 397 ≈ ___ − ___ = ___
5,621 − 2,890 ≈ ___ − ___ = ___
9,999 − 4,501 ≈ ___ − ___ = ___
Match Estimates to Calculations
Draw a line from each calculation to its best estimate.
Rounding Bonds
Round each number to the nearest 100.
Round and Estimate Multiplication (A)
Round each factor then estimate the product.
48 × 22 ≈ ___ × ___ = ___. Actual = 1,056. How close?
73 × 31 ≈ ___ × ___ = ___
199 × 5 ≈ ___ × ___ = ___
312 × 9 ≈ ___ × ___ = ___
Round and Estimate Multiplication (B)
Estimate each product.
67 × 42 ≈ ___
88 × 11 ≈ ___
249 × 4 ≈ ___
501 × 8 ≈ ___
Is the Answer Reasonable? (A)
Circle REASONABLE or NOT.
45 × 12 = 540
89 × 7 = 6,230
256 + 744 = 1,000
8,000 ÷ 4 = 200
Is the Answer Reasonable? (B)
Circle REASONABLE or NOT.
3,456 − 1,234 = 2,222
125 × 8 = 10,000
999 + 1 = 1,000
600 ÷ 12 = 500
Sort: Good or Bad Estimate?
For 48 × 52, sort each estimate.
Estimation Word Problems (A)
Use estimation to solve.
A school has 312 students. Each student needs 4 exercise books. About how many books are needed?
A factory makes 489 toys per day. About how many in 5 days?
Estimation Word Problems (B)
Estimate to solve.
Movie tickets cost $14.95 each. You buy 6 tickets. Estimate the total.
A road is 8,750 m long. About how many kilometres is that?
Spot the Wrong Answer (B)
Circle the WRONG answer.
Which is WRONG?
Which is WRONG?
Which is WRONG?
Check with Estimation
A student got these answers. Use estimation to check.
347 × 6 = 2,082. Estimate: ___ × ___ = ___. Is the answer reasonable? ___
4,896 ÷ 8 = 512. Estimate: ___ ÷ ___ = ___. Is the answer reasonable? ___
2,345 + 6,789 = 9,134. Estimate: ___ + ___ = ___. Is it reasonable? ___
Over-Estimate or Under-Estimate?
Explain whether rounding gives an over- or under-estimate.
48 × 52: if we round to 50 × 50, is the estimate too high or too low? Explain.
If both numbers round up, will the estimate be too high, too low, or just right?
When is it better to over-estimate? Give an example.
Front-End Estimation
Use front-end estimation (use just the leading digits).
4,567 + 3,210: front-end estimate = 4,000 + 3,000 = ___
7,891 − 2,345: front-end estimate = ___
Is front-end estimation more or less accurate than rounding? Why?
Match Estimate Strategy to Example
Draw a line.
Estimation Bonds (B)
Round each number to the nearest 10 and find the sum.
Best Estimate (C)
Circle the most reasonable estimate.
312 × 5
7,890 ÷ 9
4,523 + 2,977
9.8 × 4.1
Sort: Over or Under Estimate?
Rounding up gives over-estimate, rounding down gives under-estimate.
Estimation Strategies Comparison
Compare strategies.
Estimate 289 + 412 using rounding to nearest 100: ___
Estimate using front-end: ___
Which is closer to the actual answer (701)? ___
When would you use each strategy?
Estimation in Science
Scientists use estimation.
A sample of 12 leaves has an average mass of 3.2 g. Estimate the total mass of 100 leaves: ___
A beaker holds 480 mL. Estimate how many beakers needed for 3 litres: ___
Why do scientists estimate before they measure?
Estimation Sequences
Continue the pattern (estimated values acceptable).
Estimation Accuracy
Students estimated 6 × 78. Results shown.
| Said 400 | |
| Said 480 (best) | |
| Said 500 | |
| Said 600 |
How many students total?
Most common estimate?
Actual answer is 468. Who was closest?
How many were within 50 of 468?
Estimation Errors Tally
Students estimated 347 × 8 = 2,776. The class estimates were tallied.
| Item | Tally | Total |
|---|---|---|
Within 100 | ||
Within 200 | ||
Within 500 | ||
Off by more than 500 |
Compare Estimate Accuracy
Compare how close each estimate is to the exact answer.
Estimating 48: 50 vs 45 — which is closer to 48?
Estimating 124: 100 vs 150 — which is closer?
Estimation Poster Plan
Plan a classroom poster about estimation.
Write 3 key rules for good estimation:
Give one example of estimation in sport:
Give one example of estimation in cooking:
What is the most important reason to be able to estimate?
Estimation in News Reports
News reporters use approximate numbers.
A crowd of 37,842 people is often reported as 'about 38,000.' Why?
Round 37,842 to the nearest thousand: ___ to the nearest hundred: ___
When is an exact number needed instead of an estimate?
Reasonableness of Calculator Answers
Check whether a calculator answer is reasonable.
A student typed 45 × 18 and got 81. Is this reasonable? Estimate: ___
Another student got 4,500 for 45 + 18. Is this reasonable? Why?
How do you know when a calculator answer is probably wrong?
Estimation in Engineering
Engineers use estimation regularly.
A bridge needs 450 steel beams, each weighing about 850 kg. Estimate total weight: ___
A pipeline is 35 km long. Pipes come in 6 m sections. Estimate number of pipes: ___
Why must engineers be careful not to under-estimate? Give an example:
Rounding Strategies (B)
Choose the best rounding strategy.
Which rounding gives a better estimate for 4.7 × 12.3: (5 × 12) or (5 × 12.5)? ___
Round 78 × 52 to the nearest 10 and estimate: ___
Actual answer is 4,056. How close is your estimate?
Estimate or Calculate Exactly? (B)
Circle whether you need to estimate or calculate exactly.
Finding the exact change from a $50 note
Deciding if $30 is enough to buy 4 items at about $7 each
Working out a tax return
Judging if a shelf will fit in a space
Benchmarks for Estimation
Use benchmark numbers to estimate.
Benchmark: 1,000 m = 1 km. If you walk 1,500 steps ≈ 1 km, about how many km in 6,000 steps? ___
Benchmark: a healthy adult heart beats about 60 times/min. Beats in 24 hours ≈ ___
Benchmark: a litre of water weighs 1 kg. Estimate the mass of a 600 mL bottle of water: ___
Mental Estimation Strategies (B)
Use mental maths to estimate.
Estimate 198 × 5 by adjusting: 200 × 5 − 2 × 5 = ___
Estimate 303 × 6: ___. Show method.
Estimate 499 ÷ 5: ___. Show method.
Estimation Strategy to Description (B)
Match each strategy to its description.
Estimation Bonds: Complete the Estimate (B)
Fill in the missing estimated value.
Which Estimate is Closer?
Circle the estimate that is closer to the actual answer.
Actual: 489. Which estimate is closer?
Actual: 7,250. Which estimate is closer?
Actual: 3.8. Which estimate is closer?
Actual: 142. Which estimate is closer?
Sort by Estimation Accuracy
Sort from closest estimate to furthest from actual.
Estimation in Science (B)
Scientists estimate before measuring.
A scientist estimates 400 bacteria per mL in a sample of 250 mL. Estimate total bacteria: ___
A forest sample shows about 12 trees per 100 m². Estimate trees in a 3 km × 2 km forest: ___
Why do scientists estimate before doing exact calculations?
Estimation and Probability
Use estimation in probability contexts.
In 200 coin flips, estimate how many heads: ___. Why is this an estimate?
A survey of 50 people shows 32 prefer coffee. In a city of 2 million, estimate coffee drinkers: ___
Estimation Sequences (B)
Round each number to the nearest 100 and continue the pattern.
Estimation in Project Planning
Estimate costs and quantities.
You need to paint 4 walls. Each wall is about 3 m × 2.5 m. Estimate total area: ___ m²
Paint covers about 12 m² per litre. Estimate litres needed: ___
Paint costs $18 per litre. Estimate total cost: ___
Compare Estimation Methods (B)
Which estimation is more accurate?
Rounding 348 to 350 vs rounding to 300 — which is more accurate for 348 × 3?
Estimating 4.8 × 9.1 as 5 × 9 = 45 vs 4.8 × 9 = 43.2 — which is closer?
Estimation Accuracy in Class Test
How close were student estimates to the actual answer?
| Item | Tally | Total |
|---|---|---|
Within 10 | ||
Within 50 | ||
Within 100 | ||
More than 100 off |
Defending Your Estimate
Explain and justify your estimation.
Estimate the number of words on this worksheet page: ___. Explain your method:
Would you feel confident using this estimate to plan printing costs? Why or why not?
Estimation: Round Up or Round Down?
When is it safer to round up? Round down?
Buying enough food for a party — safer to:
Estimating how long a trip takes — safer to:
Estimating change you'll receive — safer to:
Buying materials for a project — safer to:
Home Activity: Estimate at the Shops
Use estimation when shopping!
- 1Before paying at the shops, estimate the total cost by rounding each item to the nearest dollar.
- 2Estimate how many minutes you spend on different activities in a day. Then time yourself and compare!
- 3Pick three items from a catalogue. Estimate the total cost, then use a calculator to check.
- 4Estimate how many steps it takes to walk around your house, then count to check.
Trace Rounding Benchmarks (A)
Trace these benchmark numbers used in estimation.
Match Numbers to Nearest 10 (A)
Draw a line from each number to its rounding to the nearest 10.
Match Numbers to Nearest 100 (A)
Match each number to its rounding to the nearest 100.
Round to Nearest 10,000 (A)
Circle the correct rounding to the nearest 10,000.
34,567 rounds to?
75,000 rounds to?
99,001 rounds to?
15,499 rounds to?
Round to Nearest 100,000 (A)
Circle the correct rounding.
349,000 rounds to?
750,001 rounds to?
1,450,000 rounds to?
Rounding Bonds (B)
Round each number to the nearest 1,000.
Sort by Rounding Error
Sort each estimate by how far it is from the actual answer.
Estimate for Large Numbers (A)
Estimate each calculation involving large numbers.
234,567 + 456,789 ≈ ___
987,654 − 345,678 ≈ ___
1,234,567 + 2,345,678 ≈ ___
Estimate for Large Numbers (B)
Use estimation to solve.
Australia's population is about 26,500,000. Round to the nearest million: ___
The distance from Earth to the Moon is about 384,400 km. Round to the nearest 10,000: ___
Is the Estimate Useful? (A)
Circle YES or NO — is this a useful estimate?
Estimating $4.95 × 6 as $30
Estimating 1,234 + 876 as 2,000 (rounding each up)
Estimating 999 × 8 as 800 × 8 = 6,400
Estimating 3.2 + 4.1 as 10
Estimation Word Problems (C)
Use estimation to solve.
A stadium holds 48,750 spectators. Round to the nearest 10,000. About how many watched a sellout?
A marathon runner's pace is 5:48 per km. Estimate her time for 42 km to the nearest 10 minutes.
Estimation Word Problems (D)
Estimate and explain.
A spacecraft travels 28,000 km/h. Estimate how far it travels in 24 hours.
A library has 12,456 books. They receive 378 more. About how many books do they have now?
Mental Estimation Strategies (A)
Explain the strategy.
To estimate 499 × 9, I would: ___
To estimate 3,215 ÷ 4, I would: ___
Why is estimation useful even when you have a calculator?
Estimation Accuracy Graph
Students estimated a calculation. Each icon = 1 student in accuracy range.
| Within 10 | |
| Within 50 | |
| Within 100 | |
| More than 100 away |
How many were within 50?
Which group was largest?
What fraction were within 100?
What does this tell us about estimation?
Estimation Methods Tally
Students chose a strategy. Count each.
| Item | Tally | Total |
|---|---|---|
Round to nearest 10 | ||
Round to nearest 100 | ||
Front-end | ||
Compatible numbers |
Compare Estimates (A)
Which estimate is closer to the actual answer?
Actual 548: estimate 500 vs estimate 600 — which is closer?
Actual 370: round to 400 vs round to 300 — which is closer?
Round Numbers in Sequence (A)
Fill in the rounded values.
Estimation Reflection (A)
Think about estimation.
When would you choose to round to the nearest 10? Give an example.
When would you choose to round to the nearest 1,000? Give an example.
Describe a situation where over-estimating is safer than under-estimating.
Create Your Own Estimation Problems (B)
Write and solve estimation problems.
Write a real-life problem where estimating to the nearest 10 is most useful. Solve it.
Write a problem involving millions where estimation is essential. Solve it.