Renaming numbers: a week of ready-to-teach maths
Five days of lessons for Year 2 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out 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.
- Cut out the two card sheets once; they are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and when.
- 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 model answers, so you can walk in and teach it.
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 lesson can also split into a short warm-up and a main session if your timetable runs small blocks.
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 | Take a number apart | Partition three-digit numbers into hundreds, tens and ones | The sausage sizzle stocktake |
| 2 | The same number, a new cut | Rename a hundred as ten tens and write non-standard partitions | One bar, many cuts |
| 3 | Count in tens | Rename across places: 35 tens is 350; read packs and singles as a number | The stocktake shorthand |
| 4 | The zero holds a seat | See what a zero digit does and why it cannot be dropped | The quiet zero |
| 5 | Rename for a reason | Tell true names from false ones and regroup to be ready to add | True name or false name? |
How the week builds
Day 1 takes numbers apart the standard way; Day 2 cuts them a new way; Day 3 counts them in tens; Day 4 puts the zero to work; and Day 5 renames them for a reason. It builds on Numbers to 1000 from earlier this year, and it opens the way to column addition and subtraction next term, when a ten will have to become ten ones on the spot.
Materials for the week (one trip)
- From the classroom: scissors, pencils, this pack printed.
- From home or the craft box: a handful of straws, matchsticks or dry pasta to bundle into tens, with elastic bands.
- Cut out once, use all week: the place-value cards, the bundling cards and the rename mat in this pack. No maths equipment to buy.
Dear families
This week in maths, Year 2 learns to rename numbers. We take a number apart into hundreds, tens and ones, then cut it new ways: 354 can be 3 hundreds, 5 tens and 4 ones, or 35 tens and 4 ones, and it is still the very same number.
Try this at home
- Pick a number of the day: a page number, a door number, a footy score. Say how many hundreds, tens and ones it has.
- Then rename it: how many tens are in the whole number? (240 has 24 tens.)
- Find a number with a zero (a price, a house number). Ask what the zero is doing, and what would go wrong without it.
- Swap ten single things for one bundle of ten, and back again. Did the amount change?
My numbers this week
Fill one row a day. Tick when you have renamed your number a new way.
| Day | My number | Tens in all | I renamed it | Another name for it |
|---|---|---|---|---|
| Monday | □ | |||
| Tuesday | □ | |||
| Wednesday | □ | |||
| Thursday | □ | |||
| Friday | □ |
Printed from the free seegongsik Renaming Numbers teaching pack · seegongsik.com/au/y2/number/AC9M2N02/pack
Take a number apart
Every three-digit number can be shared into hundreds, tens and ones. Today children take numbers apart the tidy, standard way, and meet the delivery bench where a hundred, a ten and a one are a box, a pack and a single.
We are learning to
- partition a three-digit number into hundreds, tens and ones,
- build that number with trays of a hundred, bundles of ten and single ones,
- write the standard partition, such as 462 is 4 hundreds, 6 tens and 2 ones.
Success criteria
- I can partition a number into hundreds, tens and ones.
- I can build a number and say how many of each it has.
You need
A handful of straws, matchsticks or dry pasta bundled into tens, with elastic bands. The place-value cards (cut-out sheet 1), one set per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Sort the bench Tip out a jumble of singles, tens and hundreds. Children sort them into three trays and say what each tray is worth. Ask: “One box, or a whole handful of singles — which is worth more, and how do you know?” |
| 30 min | Take it apart Call a number: 462. Pairs build it with cards or bundles and write 4 hundreds, 6 tens, 2 ones. Repeat with 508 (no tens) and 730 (no ones). Ask: “How many hundreds does 462 have? How many tens? How many ones? Say its tidy name.” |
| 10 min | Read it back Show a built number; children write how many hundreds, tens and ones. Ask: “Take the tens tray away. What is left, and what was that tray worth?” |
Two half-sessions instead? End Session A after 462. Start Session B by rebuilding 462 from memory, then go on to 508 and 730.
Watch for these ideas
- Reading 462 as the digits 4, 6 and 2 rather than 400, 60 and 2.
- Counting 4 hundreds as 4, forgetting each hundred is worth 100.
- With 508, dropping the empty tens and writing 58.
Answers
- 462 is 4 hundreds, 6 tens, 2 ones. 508 is 5 hundreds, 0 tens, 8 ones. 730 is 7 hundreds, 3 tens, 0 ones.
- 275 is 2 hundreds, 7 tens, 5 ones. 640 is 6 hundreds, 4 tens, 0 ones. 906 is 9 hundreds, 0 tens, 6 ones.
- Build-your-own varies: check no column holds ten or more, and the drawing matches the digits.
Take it apart
Build each number with trays of 100, bags of 10 and single ones. Draw what you build, then write how many of each.
462
462 is ____ hundreds ____ tens ____ ones.
508
508 is ____ hundreds ____ tens ____ ones. Careful: what does the 0 tell you?
Just write how many
| Number | Hundreds | Tens | Ones |
|---|---|---|---|
| 275 | |||
| 640 | |||
| 906 |
Your own number
Choose a number between 100 and 999. Build it, draw it, and write it here: ____
The same number, a new cut
462 is 4 hundreds, 6 tens and 2 ones. It is also 3 hundreds, 16 tens and 2 ones. Today children learn that one number can be cut many ways and stay exactly the same number.
We are learning to
- rename one hundred as ten tens, and ten tens back as one hundred,
- write a non-standard partition, such as 245 is 1 hundred, 14 tens and 5 ones,
- check that a new cut still makes the same number.
Success criteria
- I can rename a hundred as ten tens without changing the number.
- I can write a number a non-standard way and show it is the same.
You need
The place-value cards (cut-out sheet 1). The bundling cards and the rename mat (cut-out sheet 2), one set per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | One hundred, ten tens Children swap one hundred card for ten tens on the rename mat, then swap them back, and check the amount each time. Ask: “I traded a hundred for ten tens. Did the amount get bigger, get smaller, or stay the same?” |
| 30 min | Cut it a new way Build 245 the tidy way, then cut a hundred into tens: 1 hundred, 14 tens, 5 ones. Record both. Repeat with 362, cutting to 2 hundreds, 16 tens and 2 ones. Ask: “We have not added a single thing. Why is 1 hundred, 14 tens and 5 ones still 245?” |
| 10 min | Prove it Children show one number two ways on the mat, then add the new cut to check. Ask: “Add up your new cut. Do you land back on the same number?” |
Two half-sessions instead? End Session A after 245. Start Session B with 362, then the worksheet.
Watch for these ideas
- Thinking that cutting a hundred into tens makes a bigger number because there are more pieces.
- Writing 14 into the tens place, so 245 is misread as 145.
- Losing the ones while busy cutting the hundreds.
Answers
- 245 is 1 hundred, 14 tens and 5 ones. 362 is 2 hundreds, 16 tens and 2 ones.
- New cuts: 173 is 17 tens and 3 ones; 428 is 3 hundreds, 12 tens and 8 ones; 590 is 4 hundreds, 19 tens and 0 ones.
- The two drawings of 245 show the same amount: one hundred has simply become ten tens.
One number, a new cut
Cut one hundred into ten tens. The number does not change. Fill in the missing tens.
245
245 is 2 hundreds, 4 tens and 5 ones. Cut one hundred into tens: 245 is 1 hundred, ____ tens and 5 ones.
362
362 is 3 hundreds, 6 tens and 2 ones. Cut one hundred into tens: 362 is 2 hundreds, ____ tens and 2 ones.
Fill in the new cut
| Number | Standard name | A new cut |
|---|---|---|
| 173 | 1 hundred, 7 tens, 3 ones | 0 hundreds, ____ tens, 3 ones |
| 428 | 4 hundreds, 2 tens, 8 ones | 3 hundreds, ____ tens, 8 ones |
| 590 | 5 hundreds, 9 tens, 0 ones | 4 hundreds, ____ tens, 0 ones |
Show it two ways
Draw 245 as 2 hundreds, 4 tens and 5 ones. Then draw it again as 1 hundred, 14 tens and 5 ones.
Count in tens
How many tens are in 350? Not five — thirty-five. Today children rename across places: they work out what a pile of tens is worth, and read a whole number as a count of tens.
We are learning to
- work out the value of a pile of tens, such as 13 tens is 130,
- rename a whole number as tens and ones, such as 350 is 35 tens,
- read a bench of packs and singles as one number, tens first.
Success criteria
- I can say how many tens are in a whole number, like 35 tens in 350.
- I can read a bench of packs and singles as one number.
You need
The place-value cards and the bundling cards (cut-out sheets 1 and 2). The worksheet, one per child. A board for the class count.
Lesson flow (about 50 minutes)
| 10 min | Worth of the pile Show 13 tens. The class works out that ten tens are a hundred, so thirteen tens are 130. Ask: “Ten tens make one hundred, so what are thirteen tens worth?” |
| 30 min | Read the bench Count 13 packs and 6 singles, tens first: 130, then 136. Then the sly one: 8 packs and 12 singles, where the twelve singles hide a ten, so the count is 92. Ask: “Twelve singles — are they allowed to just sit there? What is hiding among them?” |
| 10 min | How many tens? Ask how many tens are in the whole of 240, 480 and 90. Ask: “How many tens are in the whole of 240, both packed and loose?” |
Two half-sessions instead? End Session A after the bench count. Start Session B with the how-many-tens round.
Watch for these ideas
- Saying 350 has 5 tens (only the tens digit) when the whole number holds 35 tens.
- Reading 13 packs and 6 singles as 136 by gluing digits: it works here by luck, but breaks on 8 packs and 12 singles.
- Leaving twelve singles unbundled, so the count comes out wrong.
Answers
- 12 packs and 4 singles make 124. 15 packs and 0 singles make 150. 9 packs and 13 singles make 103. 18 packs and 5 singles make 185.
- 260 has 26 tens. 830 has 83 tens. 400 has 40 tens. 70 has 7 tens.
- 45 tens is the same as 450.
Count in tens
Count the packs of ten first, then the singles. Write the number. Watch for singles that hide a ten.
Read the bench
| Packs of ten | Singles | The number |
|---|---|---|
| 12 | 4 | |
| 15 | 0 | |
| 9 | 13 | |
| 18 | 5 |
How many tens are in the whole number?
| Number | Tens in all |
|---|---|
| 260 | |
| 830 | |
| 400 | |
| 70 |
One more
45 tens is the same as ____.
The zero holds a seat
In 506 the zero looks like nothing, but it does the biggest job on the page: it holds the tens seat so the 5 and the 6 stay where they belong. Today children learn what a zero digit is for.
We are learning to
- explain what a zero digit shows in a number,
- show why 506 and 56 are different numbers,
- write numbers with a zero in the tens place or the ones place.
Success criteria
- I can say what the zero is doing in a number like 506 or 340.
- I can explain why the zero cannot just be dropped.
You need
The place-value cards and the rename mat (cut-out sheets 1 and 2). The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | The empty seat Build 506 on the mat. The tens column sits empty. Ask how a reader will know the 5 means five hundreds. Ask: “The tens seat is empty. If we write nothing there, how will anyone know the 5 means five hundreds?” |
| 30 min | Pull the zero Build 506, take the zero out and slide the digits together into 56. Compare the two on the mat. Repeat with 340 (zero in the ones) and 703. Ask: “Take the zero out of 506. What number do the digits make now? Is it bigger or smaller, and by how much?” |
| 10 min | Zero hunt Children write three numbers that each have a zero and say what the zero is doing. Ask: “Where is the empty seat in your number: the tens or the ones?” |
Two half-sessions instead? End Session A after pulling the zero from 506. Start Session B with 340 and 703.
Watch for these ideas
- Believing the zero means nothing, so 506 and 56 are the same number.
- Dropping a final zero, so 340 is read as 34.
- Not knowing which seat is empty, so the zero lands in the wrong place.
Answers
- 506 is 5 hundreds, 0 tens, 6 ones. The zero is in the tens seat. Without it, 506 becomes 56.
- 340 is 3 hundreds, 4 tens, 0 ones. The zero is in the ones seat. Without it, 340 becomes 34.
- 604: the zero holds the tens seat. 190: the zero holds the ones seat. 800: the zeros hold both the tens seat and the ones seat.
The quiet zero
Each number has a zero. Say which seat it holds, and what would go wrong without it.
506
506 is ____ hundreds, ____ tens and ____ ones. The zero is in the ____ seat. Take the zero out and 506 becomes ____.
340
340 is ____ hundreds, ____ tens and ____ ones. The zero is in the ____ seat. Take the zero out and 340 becomes ____.
Find the empty seat
| Number | Hundreds | Tens | Ones | The zero holds the ... |
|---|---|---|---|---|
| 604 | ||||
| 190 | ||||
| 800 |
Two different numbers
Draw 506 and 56 side by side. Then write why they are not the same number.
Rename for a reason
Why bother renaming? Because next term, when a subtraction runs out of ones, a ten will have to become ten ones on the spot. Today children choose good renames and catch the imposters, the names that look right but make a different number.
We are learning to
- check whether a new name really makes the same number,
- rename a number to get more ones or more tens when we need them,
- explain why renaming does not change the number.
Success criteria
- I can tell a true rename from a false one.
- I can open a ten to get more ones when I need them.
You need
The place-value cards, the bundling cards and the rename mat (cut-out sheets 1 and 2). The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | True or false name Show 270 with the name 27 tens (true), then with 2 hundreds and 7 ones (which makes 207). Children vote, then prove it on the mat. Ask: “Does 27 tens really make 270? Prove it before you vote.” |
| 30 min | Rename to be ready Pose 42 take away 7. There are only 2 ones, so open a ten: 42 becomes 3 tens and 12 ones, and now there are enough. Try 63 take away 15 the same way. Ask: “You need to take 7 ones from 42, but there are only 2 ones. What can you open to get more ones?” |
| 10 min | Catch the imposter Children mark the true and false names on the worksheet, adding each one up to be sure. Ask: “This name looks right. Add it up. Does it land on the number?” |
Two half-sessions instead? End Session A after the true-or-false round. Start Session B with rename to be ready.
Watch for these ideas
- Judging a name by how the digits look (27 tens looks like 27) instead of by its value.
- Thinking that opening a ten to get more ones changes how much there is.
- Opening a hundred but forgetting to add the ten new tens to the tens already there.
Answers
- For 260, the true names are 26 tens; 2 hundreds and 6 tens; 1 hundred and 16 tens. The false one is 2 hundreds and 6 ones, which makes 206.
- For 405, the true names are 40 tens and 5 ones; 4 hundreds and 5 ones. The false ones are 4 hundreds and 5 tens (450) and 45 tens (450).
- Rename to be ready: 62 becomes 5 tens and 12 ones; 43 becomes 3 tens and 13 ones; 152 becomes 0 hundreds, 15 tens and 2 ones.
True name, false name
Add up each name to see what it makes. Then write true if it makes the number, or false if it does not.
Which names really make 260?
| Name | It makes | True or false? |
|---|---|---|
| 26 tens | ||
| 2 hundreds and 6 tens | ||
| 2 hundreds and 6 ones | ||
| 1 hundred and 16 tens |
Which names really make 405?
| Name | It makes | True or false? |
|---|---|---|
| 40 tens and 5 ones | ||
| 4 hundreds and 5 tens | ||
| 4 hundreds and 5 ones | ||
| 45 tens |
Rename to be ready
62 is 6 tens and 2 ones. Open one ten. Now 62 is ____ tens and ____ ones.
You need to take 5 ones from 43, but there are only 3 ones. Open a ten. Now 43 is ____ tens and ____ ones.
152 is 1 hundred, 5 tens and 2 ones. Open one hundred. Now 152 is ____ hundreds, ____ tens and 2 ones.
Place-value cards
Cut out the cards. To build a number, put a hundreds card down, lay a tens card to its right, then a ones card, and read the number they make. To rename, swap one card for smaller ones on the mat. One set per pair is plenty.
Hundreds
Tens
Ones
Teacher note: the cards get shorter as the place gets smaller, so a built number reads left to right like the digits do. This is the same idea “The sausage sizzle stocktake” uses on screen.
Bundling cards and a rename mat
Cut out the bundling cards to trade one big card for ten smaller ones. Lay a number on the rename mat, then rename it by swapping a card across a column. Nothing is added or taken away, so the number never changes.
Ten tens for one hundred
Cover the 100 card with these ten tens. The amount is exactly the same.
Ten ones for one ten
Cover the 10 card with these ten ones. The amount is exactly the same.
The rename mat
| Hundreds | Tens | Ones |
|---|---|---|
Teacher note: renaming on the mat is what the numbers do on screen when you press “Open a box” in “The sausage sizzle stocktake”, or “Cut a hundred into tens” in “One bar, many cuts”.
What we know: renaming numbers
Work on your own. Show your thinking if you can.
- 486 is ____ hundreds, ____ tens and ____ ones.
- Fill in the new cut: 316 is 2 hundreds, ____ tens and 6 ones.
- How many tens are in 620? ____
- 7 packs of ten and 14 singles make ____.
- In 803, what job is the zero doing? ________________________
- Take the zero out of 730. The digits now make ____.
- True or false: 6 hundreds and 5 ones make 650. If it is false, what do they really make? ____
- 72 is 7 tens and 2 ones. Open one ten. Now 72 is ____ tens and ____ ones.
Answers and marking guide
Answers
- 4 hundreds, 8 tens and 6 ones.
- 11 tens (100 and 110 and 6 make 316).
- 62 tens.
- 84 (7 tens is 70, and 14 singles is a ten and 4, so 84).
- It holds the empty tens place: 803 has no tens, and the zero keeps the 8 and the 3 in their places.
- 73 (the digits slide together once the empty tens place is dropped).
- False. 6 hundreds and 5 ones make 605, not 650.
- 6 tens and 12 ones.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Partition (Q1, Q2) | partitions the standard way with materials | partitions 486 as 4 hundreds, 8 tens and 6 ones, and finds a non-standard cut (316 as 2 hundreds, 11 tens and 6 ones) | gives several names for a number and shows they match |
| Rename across places (Q3, Q4) | counts a pile of tens with help | renames between tens and a number: 620 has 62 tens, and 7 packs with 14 singles make 84 | regroups spare singles on sight, tens first |
| The role of zero (Q5, Q6) | reads a number that has a zero | explains the zero holds an empty place, and shows 730 becomes 73 without it | explains why 730 is ten times as much as 73 |
| Rename for a reason (Q7, Q8) | checks a name with materials | catches the false name (605, not 650) and opens a ten to get more ones (72 as 6 tens and 12 ones) | picks a rename that makes adding or subtracting easier and says why |
Eight questions, four ideas. A child at standard answers most questions and can explain why a number keeps its value when it is renamed.
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 | Partition | New cuts | Count in tens | The zero | Rename for a reason |
|---|---|---|---|---|---|
The five columns are the five days: take a number apart, cut it a new way, count in tens, mind the zero, and rename for a reason.