Estimation and Rounding: a week of ready-to-teach maths

Five days of lessons for Year 4 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out number cards and shop price tags, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the two card sheets once; the cards are reused across the week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week is that an estimate is a check. Children round numbers to an easy ten or hundred, use the rounded numbers to say roughly what an answer should be, and compare. An exact answer close to the estimate is reasonable; one far away means look again. The same check works at the shops.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

Halfway numbers round up

A number exactly halfway, such as 45 or 250, rounds up in this pack (45 to 50, 250 to 300), as it does in the interactive unit. Money follows the same rule: to the nearest dollar, $8.50 rounds to $9.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 is the skill: rounding. Day 2 uses it to estimate before calculating, and Day 3 turns the estimate into a check on finished work. Day 4 sharpens the check by knowing whether an estimate is a little high or a little low, and Day 5 takes all of it to the shops. It builds on the mental strategies from the unit before (AC9M4N06), which children use for the exact answers.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• For Day 5 (optional): a few real shop dockets or a supermarket catalogue, and play money.
• Cut out once, use all week: the number cards and the shop price tags in this pack.

Words for the word wall

round, nearest ten, nearest hundred, halfway, estimate, about, exact, reasonable, rounded up, rounded down, total, change, docket

Dear families

This week in maths, Year 4 learns to round numbers and to estimate before calculating, so they can tell whether an answer makes sense. We finish at the shops, estimating a total and the change before any money is counted.

Try this at home

• At the shops, round each price to the nearest dollar and keep a running total in your heads. Compare it with the docket.
• Before paying, estimate the change. $20 for something costing $13.90 is about $6 change.
• Round the numbers you pass: house number 47 is about 50, and 268 is about 300.
• When someone uses a calculator, ask: is that about right? How do you know?

My estimates this week

Fill one row a day. Write what you estimated, your estimate, and the exact answer.

Printed from the free seegongsik Estimation and Rounding teaching pack · seegongsik.com/au/y4/number/AC9M4N07/pack

Round to the nearest ten or hundred

Children round numbers on a number line. 47 sits between 40 and 50 and is nearer 50, so 47 rounded to the nearest ten is 50. For the nearest hundred the line runs from one hundred to the next: 268 is between 200 and 300 and nearer 300. A number exactly halfway rounds up.

We are learning to

• find the tens (or hundreds) either side of a number,
• use the halfway point to see which one is nearer,
• round a number to the nearest ten or the nearest hundred.

Success criteria

• I can round a two- or three-digit number to the nearest ten.
• I can round a three-digit number to the nearest hundred and say which end it is nearer to.

You need

The number cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 268 on a line from 200 to 300.

Watch for these ideas

• Cutting off the ones: 47 becomes 40. Ask how far 47 is from each end.
• Looking at the wrong digit: 268 to the nearest hundred is 300, not 270. The tens digit decides.
• Halfway numbers: 55 is as near 50 as 60, and rounds up to 60 by the rule.

Answers

• Part A: 36 is between 30 and 40, so 40; 74 is between 70 and 80, so 70; 55 is between 50 and 60, so 60; 91 is between 90 and 100, so 90.
• Part B: 238 to 200; 461 to 500; 750 to 800; 319 to 300. Part C: ring 46, 49, 53 (44 rounds to 40, 55 rounds to 60, 57 rounds to 60). Part D: any number from 255 to 264.

Round to the nearest ten or hundred

A. Round to the nearest ten

Write the tens at the ends of the line. Mark the number, then ring the nearer end.

B. Round to the nearest hundred

C. Ring every number that rounds to 50 (nearest ten)

D. Challenge: write a number that rounds to 260 (nearest ten) and to 300 (nearest hundred)

Estimate first

Before adding or subtracting, children round each number and work out an estimate: 39 + 42 is about 40 + 40, so about 80. Then they calculate exactly and compare. The exact answer, 81, lands close to the estimate, and that is the point: the estimate says roughly what to expect before any working is done.

We are learning to

• round each number in a sum or a difference before calculating,
• work out an estimate from the rounded numbers,
• compare the exact answer with the estimate.

Success criteria

• I can estimate a sum or a difference by rounding each number.
• I can say whether my exact answer is close to my estimate.

You need

The number cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 82 − 39.

Watch for these ideas

• Working out the exact answer first, then rounding it. The estimate comes first, from rounded numbers.
• Thinking an estimate that is not exact is wrong. 90 for 85 is a good estimate.
• Rounding only one number. In 617 − 298, both numbers round.

Answers

• Part A: 40 + 40 = 80, exactly 81; 60 + 30 = 90, exactly 85; 200 + 400 = 600, exactly 601; 60 + 20 = 80, exactly 79.
• Part B: 80 − 40 = 40, exactly 43; 600 − 300 = 300, exactly 319. Rounding to the nearest ten gives a closer estimate for 617 − 298: 620 − 300 = 320. Part C: it tells you roughly what to expect, so a very different answer shows a mistake.

Estimate first

A. Estimate the sum, then work it out

B. Estimate the difference, then work it out

C. Why is it useful to estimate before you calculate?

Card sums: two number cards, estimate first

Is it reasonable?

Children judge calculations someone else has finished. They estimate first, then compare: an answer close to the estimate is reasonable, and one far away is a sign of a mistake. 46 + 38 = 714 cannot be right, because 46 + 38 is about 50 + 40 = 90. Then they find the right answer and, where they can, the slip that caused the wrong one.

We are learning to

• estimate a calculation before judging the answer,
• decide whether an answer is close to the estimate or far from it,
• explain why an answer is reasonable or not, using the estimate.

Success criteria

• I can say whether an answer is reasonable by comparing it with an estimate.
• I can explain my decision in a sentence that uses the estimate.

You need

The worksheet, one per child. Mini whiteboards are handy for the opening votes.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the first three rows of Part A; start Session B with 5 × 42.

Watch for these ideas

• Trusting an answer because it is written down. The estimate decides, not the neat working.
• Checking only the last digit: 714 ends in 4, as 6 + 8 does, but it is far bigger than 90.
• Thinking a close answer must be right. An estimate catches big slips, not small ones.

Answers

• Part A: 29 + 38 is about 70, so 67 is reasonable; 46 + 38 is about 90, so 714 is not reasonable (it is 84); 8 × 19 is about 160, so 152 is reasonable; 5 × 42 is about 200, so 2010 is not reasonable (it is 210); 304 − 98 is about 200, so 206 is reasonable; 512 − 189 is about 300, so 701 is not reasonable (it is 323). The slips: 6 + 8 written as 14 with no ten carried; 5 × 4 and 5 × 2 written side by side; adding instead of subtracting.
• Part B: (a) yes, 72 is close to 80. (b) 38 + 35 = 73. An estimate catches big mistakes but not a small slip.

Is it reasonable?

A. Estimate, then decide

Estimate each calculation. Is the answer reasonable? If not, write the right answer.

B. Mia worked out 38 + 35 = 72. Her estimate was 40 + 40 = 80.

(a) Does 72 pass the estimate check? (b) Work out 38 + 35 exactly. What does this tell you about estimates?

C. Write a calculation of your own with an answer that is not reasonable. Swap with a partner.

Up or down

Rounding moves a number a little. 47 rounded to the nearest ten moves up 3 to 50; 42 moves down 2 to 40. Children track the moves and use them: if both numbers in a sum were rounded up, the estimate is a little high, and the exact answer will be a little below it.

We are learning to

• say whether rounding moved a number up or down, and by how much,
• decide whether an estimate is a little high, a little low or spot on,
• use that to predict the exact answer before working it out.

Success criteria

• I can say how far rounding moved a number, and which way.
• I can say whether my estimate is high or low, and why.

You need

The number cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 48 + 49.

Watch for these ideas

• Counting the move from the wrong end: 67 to 70 is 3, not 7.
• Thinking moves always cancel. They do only when one number goes up as far as the other goes down.
• Forgetting that a move is repeated when you multiply: 6 lots of 2 is 12.

Answers

• Part A: 34 to 30, down 4; 67 to 70, up 3; 85 to 90, up 5; 52 to 50, down 2.
• Part B: 50 + 50 = 100, a little high (exactly 97); 30 + 40 = 70, a little low (exactly 73); 50 + 30 = 80, spot on (exactly 80). Part C: high; 6 × 48 = 288, which is 6 lots of 2 = 12 below 300.

Up or down

A. Round to the nearest ten. Which way did it move, and how far?

B. Round both numbers and estimate. Is the estimate high, low or spot on?

C. Jo estimates 6 × 48 as 6 × 50 = 300. Is 300 high or low? By how much?

D. Card pairs: predict high or low, then add

Check the change

Children take the week to the shops. They round each price to the nearest dollar to estimate a total, estimate the change from a note, and check a shop docket: a total far from the estimate is worth a second look, as a far-off answer was on Day 3. Then they work out the exact amounts.

We are learning to

• round prices to the nearest dollar,
• estimate a total and the change before paying,
• use an estimate to check whether a docket total is reasonable.

Success criteria

• I can estimate a shop total and the change by rounding to the nearest dollar.
• I can explain whether a total on a docket is reasonable.

You need

The price tags and the docket (cut-out sheet 2), one set per group. Play money if you have it. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the change in Part B.

Watch for these ideas

• Rounding by dropping the cents: $8.50 becomes $8. Halfway rounds up, so $9.
• Adding the money paid and the cost to find the change, as in “about $32”. Change is less than the note.
• Lining up cents as if they were dollars when adding exactly. Keep dollars under dollars and cents under cents.

Answers

• Part A: basket 1 about $8, exactly $8.30; basket 2 about $24, exactly $23.45; basket 3 about $28, exactly $27.85. Part B: basket 1 from $10: about $2, exactly $1.70; basket 2 from $50: about $26, exactly $26.55; basket 3 from $50: about $22, exactly $22.15.
• Part C: about $17 (4 + 2 + 9 + 2), so $26.80 is not reasonable. The exact total is $16.80: the till added $10.00.

Check the change

A. Estimate each basket, then work it out

Use the price tags. Round each price to the nearest dollar first.

B. Estimate the change, then work it out

C. Check the docket (cut-out sheet 2)

Estimate the total. Is the total on the docket reasonable? What would you say at the counter?

Number cards

Cut out the 24 cards, one set per pair. Partners turn a card and round it (Day 1), turn two and estimate the sum before adding (Day 2), or say which way rounding moves it and how far (Day 4).

Teacher note: twelve cards are two-digit and twelve are three-digit. Five are halfway numbers (35 and 65 for the nearest ten; 150, 350 and 650 for the nearest hundred), and they round up.

Shop price tags and a docket

Cut out the eight price tags and the docket (Day 5), one set per group. Lay the tags out as a shop, and keep the docket face down until Part C.

Price tags

The docket

Teacher note: the docket total is wrong on purpose, so cut it out before children see this note. The estimate, the exact total and what went wrong are on the Day 5 plan.

What we know: Estimation and Rounding

Estimate first in every question. Show your rounded numbers.

1. Round to the nearest ten: 63 is about ______, and 85 is about ______.
2. Round 247 to the nearest hundred: ______
3. Estimate 58 + 33: ______ + ______ = about ______. Now work it out: ______
4. Estimate 412 − 189: ______ − ______ = about ______
5. Leo says 7 × 29 = 403. Estimate: 7 × ______ = ______. Is 403 reasonable? ______ If not, what is it? ______
6. 48 + 49 is about 50 + 50 = 100. Is the exact answer more or less than 100? ______ How do you know? ______________________
7. You pay $20 for a book costing $13.90. About how much change? ______
8. A docket says $4.95 + $2.10 + $6.95 = $21.00. Estimate the total: about ______. Is $21.00 reasonable? ______

Answers and marking guide

Answers

1. 60 and 90 (85 is halfway, so it rounds up).
2. 200 (the tens digit is 4, so 247 is nearer 200).
3. 60 + 30 = about 90; exactly 91.
4. 400 − 200 = about 200 (exactly 223).
5. 7 × 30 = 210, so 403 is not reasonable; 7 × 29 = 203.
6. Less: both numbers were rounded up, so the estimate is a little high. Exactly 97.
7. About $6 ($13.90 is about $14, and $20 − $14 = $6). Exactly $6.10.
8. About $14 (5 + 2 + 7), so $21.00 is not reasonable; the exact total is $14.00.

A quick three-level guide

Eight questions, three ideas. A child at standard rounds correctly, estimates before calculating, and can say in a sentence why an answer is or is not reasonable.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: rounding, estimating first, judging reasonableness, high or low, and money.