Add and Subtract to Three Digits: a week of ready-to-teach maths
Five days of lessons for Year 3 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus a place-value mat, strategy cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Print one place-value mat per pair and cut out the strategy cards once.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- 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. The week rests on place value: split a number into hundreds, tens and ones, work one place at a time, and when ten of a place gather they bundle into one of the next place (for subtraction, one of a place opens into ten of the next place down). The written vertical algorithm is not needed yet; children show their thinking with parts, jumps and words.
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. No calculators this week.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Split, add, put back | Partition both numbers into hundreds, tens and ones, add each place, then put the parts back together | Partition and add |
| 2 | Ten of a place makes one of the next | Bundle ten ones into a ten and ten tens into a hundred, and predict where a sum regroups | The regroup bundle; Which column regroups? |
| 3 | Split and take away | Subtract place by place, opening a ten or a hundred when a place runs short | Partition and subtract |
| 4 | Count up the gap | Find a difference by jumping up an empty number line from the smaller number | Count up the line |
| 5 | Make it easy first | Round a number to a friendly one and adjust; choose a strategy for each calculation | Rearrange to make it easy |
How the week builds
Day 1 adds by splitting both numbers into their places; Day 2 bundles ten of a place into the next and predicts where that will happen; Day 3 subtracts place by place, opening a ten or a hundred when needed; Day 4 sees subtraction as the gap between two numbers on a line; and Day 5 rearranges a calculation to make it easy, then chooses the best strategy. It builds on Add and Subtract Two-Digit Numbers from Year 2 and on Numbers Beyond 10 000.
Materials for the week (one trip)
- From the classroom: scissors, pencils, this pack printed.
- Base-ten blocks if your school has them. If not, bundles of ten paddle-pop sticks with elastic bands, plus loose sticks, do the same job.
- Printed once: the place-value mat (one per pair) and the strategy cards (one set per group).
Words for the word wall
hundreds, tens, ones, partition, regroup, bundle, carry, open a ten, difference, count up, round, adjust, strategy, estimate
Dear families
This week in maths, Year 3 adds and subtracts two- and three-digit numbers in their heads and on paper, without a calculator. We split numbers into hundreds, tens and ones, regroup when a place reaches ten, and look for easy ways in.
Try this at home
- Add two prices or two scores out loud: hundreds first, then tens, then ones. Did any place make ten or more?
- Find a difference by counting up: from 167 to 523, jump to 170, then 200, then 500, then 523. Add the jumps.
- Use friendly numbers: to add 199, add 200 and take 1 away.
- Ask your child to explain their way. There is often more than one good way.
My sums this week
Fill one row a day. Write a sum or a difference you worked out together, and how.
| Day | The calculation | Answer | How we did it |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Add and Subtract to Three Digits teaching pack · seegongsik.com/au/y3/number/AC9M3N03/pack
Split, add, put back
To add three-digit numbers, split both into hundreds, tens and ones, add like places, then put the parts back together. Place value does the adding; no new rule is needed.
We are learning to
- partition two- and three-digit numbers into hundreds, tens and ones,
- add the hundreds, the tens and the ones, then put the parts back together,
- notice when a place adds to ten or more.
Success criteria
- I can split both numbers and add each place.
- I can put the parts back together to find the total.
You need
The place-value mat (cut-out sheet 1), one per pair, with base-ten blocks or bundled sticks. The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Split it Call out three-digit numbers; children say them split: 342 is 300 and 40 and 2. Then build 342 and 215 on the mat, one number above the other. Ask: “Which parts can go together? Why do hundreds only join hundreds?” |
| 30 min | Add each place Add 342 + 215 place by place (500, 50, 7, so 557). Then the board pair (see the box), where the tens make 13 tens. Children do the worksheet tables. Ask: “The tens made 13 tens. How much is that? Where does it go in the total?” |
| 10 min | Check it Pairs swap sheets and check one sum by building it on the mat. Ask: “Did your partner put every part back? How do you know?” |
Two half-sessions instead? Split after 342 + 215; start Session B with the board pair.
Watch for these ideas
- Adding digits from different places (the 5 tens of 354 with the 3 ones of 283). Line places up first.
- Writing 13 tens as 13 in the tens place. 13 tens is 130: a hundred and three tens.
- Treating 76 as 7 hundreds and 6 tens. A two-digit number has no hundreds.
Answers
- No regrouping: 342 + 215 = 500 + 50 + 7 = 557; 431 + 256 = 600 + 80 + 7 = 687; 523 + 175 = 600 + 90 + 8 = 698.
- One place makes ten or more: 354 + 283 = 500 + 130 + 7 = 637; 408 + 235 = 600 + 30 + 13 = 643; 529 + 346 = 800 + 60 + 15 = 875.
- Two- and three-digit: 465 + 32 = 400 + 90 + 7 = 497; 76 + 218 = 200 + 80 + 14 = 294.
Split, add, put back
Split both numbers. Add the hundreds, the tens and the ones. Then put the parts together for the total.
Every place stays under ten
| Sum | Hundreds | Tens | Ones | Total |
|---|---|---|---|---|
| 342 + 215 | ||||
| 431 + 256 | ||||
| 523 + 175 |
One place makes ten or more
Example: 263 + 452. Hundreds 600, tens 110, ones 5. Total 715.
| Sum | Hundreds | Tens | Ones | Total |
|---|---|---|---|---|
| 354 + 283 | ||||
| 408 + 235 | ||||
| 529 + 346 |
A two-digit and a three-digit number
| Sum | Hundreds | Tens | Ones | Total |
|---|---|---|---|---|
| 465 + 32 | ||||
| 76 + 218 |
Your own sum
Choose two three-digit numbers whose total is less than 1000. Split them and add.
________ + ________ = ________ + ________ + ________ = ________
Ten of a place makes one of the next
Regrouping is just bundling: ten ones make one ten, ten tens make one hundred. Children bundle with blocks or sticks, predict where a sum will regroup, then add.
We are learning to
- bundle ten ones into a ten and ten tens into a hundred,
- predict which place of a sum will regroup before we calculate,
- add two- and three-digit numbers that regroup in the ones, the tens or both.
Success criteria
- I can say which place will regroup, and why.
- I can add numbers that need regrouping.
You need
The place-value mat with base-ten blocks or bundled sticks, one per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Bundle up Count 14 loose ones onto the mat; stop at ten and swap them for a ten. Do the same with 17 tens and a hundred. Ask: “Is 1 ten and 4 ones the same amount as 14 ones? How can you check?” |
| 30 min | Predict, then add Use the two board pictures (see the box). Children predict the regrouping place for each worksheet sum before they add it, then add and check the prediction. Ask: “Before you add 245 + 90, which place will make ten or more? How did you know without adding everything?” |
| 10 min | Double bundle Build 176 + 247 on the mat: the ones make 13, so a ten joins the tens, and now the tens make 12, so a hundred joins the hundreds. Ask: “Why did the tens need regrouping only after the ones did?” |
Two half-sessions instead? Split after the bundle picture; start Session B with predict, then add.
Watch for these ideas
- Writing 15 in the ones place of a total. Fifteen ones must become 1 ten and 5 ones.
- Forgetting the bundled ten when adding the tens. Say “and one more ten” aloud.
- Predicting from the biggest digit. Only the sum of a place decides: 8 + 7 regroups, 9 + 0 does not.
Answers
- Bundle: 1 ten and 4 ones; 2 tens and 3 ones; 1 hundred and 7 tens; 1 hundred and 2 tens = 120.
- Which column: 158 + 37 ones; 245 + 90 tens; 176 + 247 both; 312 + 145 none; 480 + 60 tens; 269 + 25 ones.
- Add: 158 + 37 = 195; 245 + 90 = 335; 176 + 247 = 423; 389 + 46 = 435.
- Own sum: the tens add to ten or more and the ones do not (for example 152 + 64 = 216).
Bundle and regroup
Bundle it
14 ones = ____ ten and ____ ones
23 ones = ____ tens and ____ ones
17 tens = ____ hundred and ____ tens
12 tens = ____ hundred and ____ tens = ________
Which column regroups?
Before you add, tick the place that will make ten or more. Then add to check.
| Sum | Ones | Tens | Both | None |
|---|---|---|---|---|
| 158 + 37 | □ | □ | □ | □ |
| 245 + 90 | □ | □ | □ | □ |
| 176 + 247 | □ | □ | □ | □ |
| 312 + 145 | □ | □ | □ | □ |
| 480 + 60 | □ | □ | □ | □ |
| 269 + 25 | □ | □ | □ | □ |
Add and regroup
158 + 37 = ____________
245 + 90 = ____________
176 + 247 = ____________
389 + 46 = ____________
Your own sum
Write a sum that regroups in the tens only: ________ + ________ = ________
Split and take away
Subtract place by place. When the top number runs short in a place, open one of the next place up into ten: a ten into ten ones, a hundred into ten tens. The amount does not change.
We are learning to
- subtract two- and three-digit numbers place by place,
- open a ten or a hundred when a place of the top number is too small,
- check a subtraction by adding the answer back on.
Success criteria
- I can say when I need to open a ten or a hundred.
- I can subtract and check my answer by adding.
You need
The place-value mat with base-ten blocks or bundled sticks, one per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Take away on the mat Build 586 and take away 243 place by place (343). Then build 742 and try to take 8 ones from 2 ones. Ask: “We have 2 ones and need to take 8. Where can more ones come from?” |
| 30 min | Open a ten Open a ten on the mat (742 becomes 700, 30 and 12), finish 742 − 318, then step through the board pictures (see the box). Children do the worksheet and check each answer by adding. Ask: “805 has no tens to open. What can we open instead?” |
| 10 min | Check by adding Pairs add each answer to the number taken away: 424 + 318 should give 742. Ask: “If the check does not give the top number, what went wrong?” |
Two half-sessions instead? Split after 742 − 318; start Session B with the board pairs.
Watch for these ideas
- Taking the smaller digit from the bigger one in every place (742 − 318 = 436). The top number is always the one we take from.
- Opening a ten but not crossing it off: the tens place still says 4. Show the 3 tens left.
- Getting stuck on a zero, as in 805. Open a hundred into ten tens first, then a ten into ones.
Answers
- No opening: 586 − 243 = 343; 768 − 351 = 417; 695 − 82 = 613.
- Open one place: 742 − 318 = 424; 651 − 225 = 426; 538 − 172 = 366 (open a hundred).
- Board pairs: 523 − 167 = 356; 805 − 348 = 457; 640 − 275 = 365; 412 − 158 = 254.
- Checks: 356 + 167 = 523; 457 + 348 = 805; 365 + 275 = 640; 254 + 158 = 412.
Split and take away
Subtract place by place. If a place is too small, open one of the next place up. Then check by adding.
Every place is big enough
586 − 243 = ________
768 − 351 = ________
695 − 82 = ________
Open one place
Example: 361 − 145. Open a ten: 361 is 300 + 50 + 11. Take away 100 + 40 + 5. Answer 216.
742 − 318 = ________ Check: ________ + ________ = ________
651 − 225 = ________ Check: ________ + ________ = ________
538 − 172 = ________ Check: ________ + ________ = ________
Two places to open
523 − 167 = ________ Check: ________ + ________ = ________
805 − 348 = ________ Check: ________ + ________ = ________
640 − 275 = ________ Check: ________ + ________ = ________
412 − 158 = ________ Check: ________ + ________ = ________
Explain it
Kai worked out 742 − 318 = 436. What did Kai do? What is the right answer?
Count up the gap
Subtraction is also the distance between two numbers. Jump up an empty line from the smaller number to a friendly ten, then a friendly hundred, then the larger number, and add the jumps.
We are learning to
- see a subtraction as the gap between two numbers,
- count up an empty number line in friendly jumps,
- add the jumps to find the difference, and choose this way when the numbers are close to a hundred.
Success criteria
- I can draw jumps from the smaller number to the larger one.
- I can add my jumps to find the difference.
You need
A long empty line drawn on the board. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | How far apart? Two children stand at 167 and 523 on a pretend line. Ask how far apart they are, then draw the jumps 167 to 170, 200, 500 and 523 on the board. Ask: “Why jump to 170 first? Why is 200 a good place to land?” |
| 30 min | Jump and add Count up on the board (see the box), adding the jumps as you go: 3 + 30 + 300 + 20 + 3 = 356. Children do the worksheet lines and the two stories. Ask: “Is there a quicker set of jumps? Does a different path give the same answer?” |
| 10 min | Take away or count up? Write 805 − 348 and 700 − 695. Children vote on the way they would use for each. Ask: “When is counting up quicker than taking away?” |
Two half-sessions instead? Split after 523 − 167; start Session B with the worksheet lines.
Watch for these ideas
- Answering with the number landed on (523) instead of the total of the jumps.
- Forgetting a jump when adding them up. Write each jump above its arc.
- Thinking a difference needs taking away. Counting up gives the same answer.
Answers
- 640 − 275: 275 to 280 (5), 300 (20), 600 (300), 640 (40) = 365.
- 800 − 326: 326 to 330 (4), 400 (70), 800 (400) = 474. 403 − 188: 188 to 190 (2), 200 (10), 400 (200), 403 (3) = 215.
- Stories: 312 − 145 = 167 pages; 600 − 465 = 135 seats. Any correct set of jumps is fine.
- Take away or count up: 805 − 348 = 457; 700 − 695 = 5 (counting up is quickest).
Count up the gap
Draw jumps up the line from the smaller number to the larger one. Write each jump. Add the jumps.
640 − 275 Jumps: ____ + ____ + ____ + ____ = ________
800 − 326 Jumps: ____ + ____ + ____ + ____ = ________
403 − 188 Jumps: ____ + ____ + ____ + ____ = ________
Story problems
1. A book has 312 pages. Ella has read 145 pages. How many pages are left?
Answer: ________
2. The school hall has 600 seats. 465 tickets are sold. How many seats are still free?
Answer: ________
Make it easy first
A number near a round one is a gift: add the round number, then adjust. Reordering can make friendly pairs too. Good calculators look at the numbers first, then choose the way.
We are learning to
- round a number to a friendly hundred, calculate, then adjust,
- reorder numbers to make friendly pairs that add to a ten or a hundred,
- choose a strategy that suits the numbers, and explain the choice.
Success criteria
- I can use round and adjust to add or subtract quickly.
- I can choose a strategy and say why it suits the numbers.
You need
The strategy cards (cut-out sheet 2), one set per group. The worksheet. The unit’s self-check quiz.
Lesson flow (about 50 minutes)
| 10 min | Spot the gift Show the trick on the board (see the box). Then ask for 365 + 199 in heads: 365 + 200 is 565, take 1 back, 564. Ask: “We added 200 but only needed 199. Do we take 1 back or add 1 more? Why?” |
| 25 min | Sort and solve Groups sort the strategy cards under the four headings, solve them, and compare choices. Then the worksheet. Ask: “Two of you chose different ways for 700 − 498. Did you get the same answer?” |
| 15 min | Class quiz Run the self-check quiz as a team game: teams hold up one, two or three fingers for their choice. Ask: “Which strategy did your team use for that one?” |
Two half-sessions instead? Split after the card sort; start Session B with the worksheet and the quiz.
Watch for these ideas
- Adjusting the wrong way. If we added too much, take some back; if we took too much, give some back.
- In 452 − 199, taking 200 and then taking 1 more. We took 1 too many, so add 1 back: 253.
- Thinking there is one right way. Any strategy that works is right; the best one is quick and safe.
Answers
- Round and adjust: 564; 525; 833; 713; 452 − 199 = 253.
- Friendly pairs: 46 + 54 + 125 = 225; 175 + 25 + 38 = 238.
- Choose: 600 − 397 = 203 (count up or round); 254 + 333 = 587 (split); 498 + 236 = 734 (round); 512 − 487 = 25 (count up).
- Strategy cards: the answers are under the cards on cut-out sheet 2.
Make it easy first
Round and adjust
Example: 348 + 199 = 348 + 200 − 1 = 547.
365 + 199 = ________ + ________ ________ = ________
427 + 98 = ________ + ________ ________ = ________
538 + 295 = ________ + ________ ________ = ________
614 + 99 = ________ + ________ ________ = ________
452 − 199 = ________ + ________ ________ = ________
Make friendly pairs
46 + 125 + 54 = ________
175 + 38 + 25 = ________
Choose your strategy
| Calculation | My strategy (split, open a ten, count up, round and adjust) | Answer |
|---|---|---|
| 600 − 397 | ||
| 254 + 333 | ||
| 498 + 236 | ||
| 512 − 487 |
Place-value mat
One mat per pair. Build the top number in the upper row and the second number in the lower row, then work one place at a time. When a place holds ten or more, bundle ten and move them one place to the left. To take away, open one of a place into ten of the next place to the right.
Teacher note: base-ten blocks or bundles of ten sticks work on the mat. A flat of a hundred, or ten bundles held together, fills the hundreds box.
Strategy cards
Cut out the cards. Lay the four headings in a row. For each calculation card, choose the way you would work it out, place it under that heading, then solve it. More than one heading can be right.
Answers (fold this line under before cutting): 312 + 245 = 557; 199 + 365 = 564; 700 − 498 = 202; 456 − 123 = 333; 640 − 275 = 365; 247 + 98 = 345; 503 − 297 = 206; 128 + 370 = 498; 800 − 326 = 474; 264 + 199 = 463; 425 − 150 = 275; 333 + 167 = 500.
What we know: Add and Subtract to Three Digits
Work on your own. No calculators. Show your thinking if you can.
- Split and add: 462 + 325 = ______ + ______ + ______ = ______
- 268 + 157 = ______
- Which place regroups in 347 + 26? Circle one: ones tens none
- 853 − 427 = ______
- 603 − 257 = ______
- Count up to find 400 − 165. Show your jumps: ______________________ = ______
- A quick way to work out 456 + 299: ______________________ = ______
- A school has 386 students. 147 go on an excursion. How many stay at school? ______
Answers and marking guide
Answers
- 700 + 80 + 7 = 787.
- 425 (the ones make 15 and the tens make 12, so both regroup).
- The ones (7 + 6 = 13).
- 426 (open a ten: 853 is 800 + 40 + 13).
- 346 (open a hundred across the zero tens, then a ten).
- 165 to 170 (5), 200 (30), 400 (200): 235.
- 456 + 300 = 756, take 1 back: 755.
- 239 (386 − 147; any correct strategy).
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Partition (Q1, Q2) | adds two-digit numbers by place | splits three-digit numbers, adds each place and puts the parts back together | explains what happens to a place that makes ten or more |
| Regroup (Q3, Q4, Q5) | regroups with blocks on the mat | predicts the regrouping place and subtracts with an opened ten or hundred, including across a zero | checks each subtraction by adding without being asked |
| Rearrange and choose (Q6, Q7, Q8) | uses one strategy for everything | counts up a gap and rounds and adjusts, adjusting the right way | chooses the quickest strategy for the numbers and explains why |
Eight questions, three ideas. A child at standard answers most questions and can show the parts, the regrouping or the jumps behind each answer.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Partitions | Regroups (add) | Opens a ten | Counts up | Rounds, adjusts |
|---|---|---|---|---|---|
The five columns are the five days: partition, regroup in addition, open a ten in subtraction, count up, and round and adjust.