Teaching pack: Breaking Numbers Apart (Year 1) -- a week of maths lessons

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Teaching pack · Year 1 Numberseegongsik /au

Breaking Numbers Apart: a week of ready-to-teach maths

Five days of lessons for Year 1 Number, all about partitioning: breaking a number into parts, and putting the parts back together. Children split one-digit numbers two ways, learn the most useful split of all — a two-digit number into tens and ones — and see that the same number can come apart in many ways while the total never changes. 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.

AC9M1N02

partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones

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; the ten-coins, one-coins and part-part-whole mats 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 muddles 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 40 minutes a day. Run them in order: each day builds on the day before, growing from splitting small numbers to partitioning into tens and ones and counting with ten-coins. Every lesson can also split into a carpet warm-up and a table task if your morning runs in small blocks.

On the board

This pack is the printable half of a free interactive unit, “Breaking Numbers Apart”. The on-screen half has five interactive pictures: “Break a Number Apart”, “Tens and Ones”, “Many Ways, Same Number”, “Build It from Parts” and “Counting with Ten-Coins”. Show the matching picture at the point each plan names.

seegongsik.com/au/y1/number/AC9M1N02

Aligned to the Australian Curriculum V9 (AC9M1N02). This pack is original material from seegongsik, independently produced and not endorsed by ACARA. Curriculum content descriptors are (c) ACARA, licensed under CC BY 4.0. Free to print and use in class.

The week at a glance5 lessons

The week at a glance

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

Day	Lesson	Children learn and do	On screen
1	Break a number apart	Split a one-digit number into two parts; the parts always add back to the whole	“Break a Number Apart”
2	Tens and ones	Partition a two-digit number into tens and ones: 34 is 3 tens and 4 ones, or 30 and 4	“Tens and Ones”
3	Many ways, same number	Split the same number many ways; the total never changes	“Many Ways, Same Number”
4	Build it from parts	Join parts back into a whole, and find a missing part	“Build It from Parts”
5	Counting with ten-coins	Make and break numbers with ten-coins and one-coins	“Counting with Ten-Coins”

How the week builds

Day 1 breaks a small number into two parts and shows that the parts always add back to the whole. Day 2 meets the split that matters most: a two-digit number into tens and ones, so 34 is 3 tens and 4 ones, which is 30 and 4. Day 3 finds many different ways to split one number. Day 4 turns it around and builds a number from its parts, then finds a missing part. Day 5 makes and breaks numbers with ten-coins and one-coins. It builds on knowing numbers to 20, and it lays the place-value ground that addition and subtraction stand on.

Materials for the week (one trip)

From the classroom: scissors, pencils, this pack printed.
A small tub of counters or buttons, and some coins if you have them, for making and breaking numbers.
Ten-strips or bundles of ten, if you have them, to sit beside the printed ten-coins.
Cut out once, use all week: the ten-coins, one-coins and part-part-whole mats in this pack. No special equipment to buy.

A note homeHome practice

Dear families

This week in maths, Year 1 is breaking numbers apart. We split a number into two parts, we break a two-digit number into tens and ones, and we put the parts back together again. It is called partitioning, and it is the ground that adding and taking away are built on. You can help in a few playful minutes a day.

Try this at home

Hold up some fingers on two hands. Six is four and two, or five and one. How else can you make six?
Find a two-digit number on a door or a bus, like 27. Say it as 2 tens and 7 ones, which is 20 and 7.
Share a small handful of coins or buttons into two piles. How many in each? How many altogether?
Play a missing-part game: I have 4, how many more to make 10? Swap over and take turns.

My breaking numbers this week

Fill one row a day. Tick when you broke a number into parts and said how you know.

Day	The number I broke	The two parts	I could do it
Monday			□
Tuesday			□
Wednesday			□
Thursday			□
Friday			□

Printed from the free seegongsik Breaking Numbers Apart teaching pack · seegongsik.com/au/y1/number/AC9M1N02/pack

Day 1 · Teacher planDay 1 of 5

Break a number apart

The week starts by breaking a small number into two parts. Seven can be four and three, or five and two, or six and one, and it is still seven. The big idea to hold onto all week: the two parts always add back to the whole. That is what partitioning means.

We are learning to

split a one-digit number into two parts,
find more than one way to break the same number,
see that the two parts always join back to make the whole.

Success criteria

I can break a number into two parts.
I can check that my two parts add back to the whole.

You need

A tub of counters or buttons, and the part-part-whole mats (cut-out sheet 2), one mat per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Show it on two hands Ask children to make seven on two hands: four on one, three on the other. Then find another way, like five and two. Ask: “You made seven as four and three. Show me seven a different way. Is it still seven?”
20 min	Break it on the mat Put seven counters on a part-part-whole mat, then slide some into each part box. Children read the two parts, then break six, eight and nine the same way. Ask: “Six is in the whole. Push some into each part. How many in each? Do they make six again?”
10 min	Another way Keep the same whole and slide one counter across to the other part. Ask: “I moved one across. The parts changed. Is it still the same number altogether? How do you know?”

Two half-sessions instead? End Session A after break it on the mat. Start Session B with another way, then the worksheet.

On the board

Open the interactive unit and show “Break a Number Apart”. Move the divider with the plus and minus buttons: seven splits into two parts and the caption keeps the running total. Ask the class to read the two parts each time, and to notice that it is still seven altogether.

seegongsik.com/au/y1/number/AC9M1N02

Watch for these ideas

The two parts do not add back to the whole: this is the key check. Count the parts together and compare with the whole.
Thinking a number breaks only one way: six is five and one, and also four and two, and three and three.
Losing a counter when sliding it across: the whole must stay the same, so count it again at the end.

Answers

Worked example: 7 is 5 and 2.
Break 6: any two parts that make 6, such as 4 and 2 (also 1 and 5, 2 and 4, 3 and 3).
Break 8: any two parts that make 8, such as 5 and 3 (also 6 and 2, 4 and 4, 7 and 1).
Break 9: any two parts that make 9, such as 6 and 3 (also 5 and 4, 7 and 2, 8 and 1).
Check every answer by adding the two parts: they always come back to the whole.

Day 1 · Worksheet

Break a number apart

NameClassDate

Break each number into two parts. Fill the two boxes. Then check: do the parts add back to the whole?

Here is how

7 is broken into 5 and 2. The two parts add back to make 7.

Break 6 into two parts

6 is ____ and ____

Break 8 into two parts

8 is ____ and ____

Break 9 into two parts

9 is ____ and ____

Think about it

You broke 8 into two parts. Can you break 8 a different way? Draw or write another way here.

8 is ____ and ____

Day 2 · Teacher planDay 2 of 5

Tens and ones

Today the class meets the most useful split of all: a two-digit number into tens and ones. Thirty-four is 3 tens and 4 ones, which is 30 and 4. The danger to head off is reading the digits as loose ones, so 34 becomes 3 and 4. The ten-strips make the tens count as tens.

We are learning to

partition a two-digit number into tens and ones,
say that the tens digit counts whole tens, not ones,
write the number as tens plus ones, like 30 and 4.

Success criteria

I can say how many tens and how many ones are in a number.
I can write it as tens plus ones, like 20 and 7.

You need

Ten-strips or bundles of ten, and single counters, or the printed ten-coins and one-coins (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Count in tens Lay out ten-strips one at a time and count: 10, 20, 30. Add a few single ones: 31, 32, 33, 34. Ask: “Three strips is thirty, not three. Why does one strip count as ten?”
20 min	Split into tens and ones Build 34, then 27, 40 and 63 with strips and ones. Children say the tens and the ones, then write it as 30 and 4. Ask: “Twenty-seven. Grab the tens first. How many strips? How many ones are left over?”
10 min	Is Sam right? Tell the class Sam says 34 is 3 and 4. Ask them to prove it with strips. Ask: “Sam says 34 is 3 and 4. Show me with the strips. Is Sam right, or is it 30 and 4?”

Two half-sessions instead? End Session A after split into tens and ones. Start Session B with is Sam right.

On the board

Show “Tens and Ones”. Press “Split into tens and ones” and 47 comes apart into 4 tens and 7 ones; press “Put back together” to close it again. Ask the class to read the tens and the ones before you split, and to check after.

seegongsik.com/au/y1/number/AC9M1N02

Watch for these ideas

Reading 34 as 3 and 4: the 3 stands for 3 tens, which is 30, so 34 is 30 and 4.
Forgetting the ones when there are none: 40 is 4 tens and 0 ones, a full set of tens.
Counting the tens in ones: slide a whole strip and count it as ten, not one.

Answers

Worked example: 34 is 3 tens and 4 ones, which is 30 and 4.
27 is 2 tens and 7 ones, which is 20 and 7.
40 is 4 tens and 0 ones, which is 40 (40 and 0).
63 is 6 tens and 3 ones, which is 60 and 3.
Is Sam right? No. The 3 in 34 stands for 3 tens, so 34 is 30 and 4, not 3 and 4.

Day 2 · Worksheet

Tens and ones

NameClassDate

Break each number into tens and ones. The ten-strips are tens; the little cubes are ones.

Here is how

34 is 3 tens and 4 ones. That is 30 and 4.

34 is 3 tens and 4 ones.
34 is 30 and 4.

Break 27 into tens and ones

2727 is ____ tens and ____ ones.
27 is ____ and ____.

Draw 27 as ten-strips and ones

Break 40 into tens and ones

4040 is ____ tens and ____ ones.
40 is ____ and ____.

Draw 40 as ten-strips and ones

Break 63 into tens and ones

6363 is ____ tens and ____ ones.
63 is ____ and ____.

Draw 63 as ten-strips and ones

Is Sam right?

Sam says 34 is 3 and 4. Use tens and ones to check. Is Sam right? Write yes or no and say why.

No, because...

Day 3 · Teacher planDay 3 of 5

Many ways, same number

A number does not break only one way. Eight is 8 and 0, and also 7 and 1, 6 and 2, 5 and 3, 4 and 4. Whichever way we split it, the total is still eight. Seeing the many splits of one number is what builds a strong sense of how numbers are made.

We are learning to

find more than one way to split the same number,
record each way as two parts,
see that every way still makes the same total.

Success criteria

I can find three ways to make a number.
I can find all the ways to make five.

You need

Counters, and the part-part-whole mats (cut-out sheet 2). The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	One more way Make eight on a mat as 5 and 3. Slide one counter across: now 4 and 4. Keep going. Ask: “We had 5 and 3. I slid one across. What are the parts now? Is it still eight?”
20 min	Find every way Children find three ways to make eight, then three ways to make ten, recording each on a mat. Then find every way to make five, in order. Ask: “Start with 5 and 0. Move one across each time. How will you know when you have them all?”
10 min	In good order Line up the ways to make five in order: 5 and 0, 4 and 1, 3 and 2, and so on. Ask: “As the first part goes down by one, what happens to the second part? Can you hear the pattern?”

Two half-sessions instead? End Session A after find every way. Start Session B with in good order.

On the board

Show “Many Ways, Same Number”. Press “Another way” and 36 splits a new way each time: 30 and 6, then 20 and 16, then 10 and 26. The bar and the total show that however it splits, it is always 36.

seegongsik.com/au/y1/number/AC9M1N02

Watch for these ideas

Thinking a number has only one pair of parts: eight has many, and they all still make eight.
Stopping too soon on five: work in order so no way is missed.
Forgetting the zero splits: 5 and 0 is a way to make five, and so is 0 and 5.

Answers

Three ways to make 8: any three of 8 and 0, 7 and 1, 6 and 2, 5 and 3, 4 and 4 (parts may be swapped over).
Three ways to make 10: any three of 10 and 0, 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5.
All the ways to make 5: 5 and 0, 4 and 1, 3 and 2, 2 and 3, 1 and 4, 0 and 5 (six ways in all).
Every way still makes the same total.

Day 3 · Worksheet

Many ways, same number

NameClassDate

One number can break many ways. Find the parts and fill each mat. The whole never changes.

Find 3 ways to make 8

Find 3 ways to make 10

Find every way to make 5

Work in order. Start with 5 and 0. Fill a row for each way.

Way	First part	Second part
1
2
3
4
5
6

How many ways did you find? ____

Day 4 · Teacher planDay 4 of 5

Build it from parts

So far the class has broken numbers apart. Today they go the other way: join the parts back into a whole. Thirty and seven make 37; five and three make eight. Then they meet a missing part: six and how many more make ten? Putting parts together is the twin of taking them apart.

We are learning to

join two parts to make the whole,
join tens and ones, like 30 and 7 to make 37,
find a missing part when we know the whole and one part.

Success criteria

I can join two parts to find the whole.
I can find the missing part to reach the whole.

You need

Counters, and the part-part-whole mats (cut-out sheet 2). The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Push them together Put five counters in one part and three in the other. Push the two parts into the whole and count. Ask: “Five here and three here. Push them together. How many is the whole now?”
20 min	Join tens and ones Join a ten-strip set with some ones: 30 and 7 make 37. Children join more part pairs and write the whole. Ask: “Thirty and seven. Do not count from one. Start at thirty and count on the ones: 31, 32...”
10 min	The missing part Fill the whole box with ten, put six in one part, and cover the other. Ask: “Ten altogether, and six in this part. How many are hiding in the other part?”

Two half-sessions instead? End Session A after join tens and ones. Start Session B with the missing part.

On the board

Show “Build It from Parts”. Use “Add ten”, “Remove ten”, “Add one” and “Remove one” to build 53 from tens and ones. The running number shows the parts joining into the whole; stop when the class reaches 53.

seegongsik.com/au/y1/number/AC9M1N02

Watch for these ideas

Miscounting when recombining: start from the bigger part and count on, rather than counting all from one.
Adding the digits of tens as ones: 30 and 7 is thirty-seven, not ten.
Guessing the missing part: count up from the known part to the whole to find it.

Answers

Join the parts: 30 and 7 make 37; 5 and 3 make 8; 50 and 2 make 52; 20 and 4 make 24.
Missing part: 6 and 4 make 10; 3 and 5 make 8; 5 and 4 make 9; 8 and 2 make 10.
Check each one by breaking the whole back apart: the parts return.

Day 4 · Worksheet

Build it from parts

NameClassDate

Now put the parts back together. Join them to find the whole, then find the missing part.

Join the parts

Add the two parts. Write the whole.

30 + 7 = ____

5 + 3 = ____

50 + 2 = ____

20 + 4 = ____

Find the missing part

You know the whole and one part. How many more make the whole? Fill the empty box.

6 + ____ = 10

3 + ____ = 8

5 + ____ = 9

8 + ____ = 10

Day 5 · Teacher planDay 5 of 5

Counting with ten-coins

The last day gathers the week with ten-coins and one-coins. A ten-coin is worth ten; a one-coin is worth one. So 45 is four ten-coins and five one-coins. Making and breaking numbers this way is exactly the tens-and-ones idea in a child’s hands, and it leads straight into the mini-check.

We are learning to

show a number with ten-coins and one-coins,
break a number into ten-coins and one-coins,
remember that a ten-coin is worth ten, not one.

Success criteria

I can show a two-digit number with ten-coins and one-coins.
I can say how many tens and ones I used.

You need

The ten-coins and one-coins (cut-out sheet 1), one set per pair. The worksheet, one per child, and the mini-check (back of the pack).

Lesson flow (about 40 minutes)

10 min	What is a ten-coin worth? Hold up a ten-coin and a one-coin. Count a small pile: 10, 20, then 21, 22, 23. Ask: “This coin says ten. When I add it, do I count on by one or by ten? Why?”
20 min	Make and break Children make 45 with coins, then 36, 52 and, for a challenge, 108. They say the tens and ones each time. Ask: “Fifty-two. Grab ten-coins first. How many? Then the one-coins. How many left over?”
15 min	Mini-check Hand out the mini-check. Children work on their own; you move around and note who partitions with ease.

Two half-sessions instead? End Session A after make and break. Start Session B with the mini-check.

On the board

Show “Counting with Ten-Coins”. Press “Next amount” to step through 24, 60 and 38, each shown as ten-counters and single counters. Ask the class to read the tens and the ones for each amount before you move on.

seegongsik.com/au/y1/number/AC9M1N02

Watch for these ideas

Counting a ten-coin as one: a ten-coin is worth ten, so count it on by ten.
Using ten one-coins in place of a ten-coin: it works, but trade ten ones for one ten to see the tens.
Muddling the challenge 108: it is ten ten-coins and eight one-coins, a hundred and eight.

Answers

Worked example: 45 is 4 ten-coins and 5 one-coins.
36 is 3 ten-coins and 6 one-coins.
52 is 5 ten-coins and 2 one-coins.
108 is 10 ten-coins and 8 one-coins.

Day 5 · Worksheet

Counting with ten-coins

NameClassDate

A ten-coin is worth 10. A one-coin is worth 1. Show each number with ten-coins and one-coins.

Here is how

45 is 4 ten-coins and 5 one-coins.

Show 36

3636 is ____ ten-coins and ____ one-coins.

Draw 36 with ten-coins and one-coins

Show 52

5252 is ____ ten-coins and ____ one-coins.

Draw 52 with ten-coins and one-coins

Show 108 (challenge)

108108 is ____ ten-coins and ____ one-coins.

Draw 108 with ten-coins and one-coins

Cut-out cards 1 of 2Ten-coins and one-coins

Ten-coins and one-coins

Cut out the coins. A ten-coin is worth ten; a one-coin is worth one. Use them to make a number, then break it into tens and ones, all week. There are enough ten-coins to make a hundred and more, so the Day 5 challenge works too. One set per pair is plenty.

Ten-coins (each worth 10)

One-coins (each worth 1)

Teacher note: to show the tens clearly, trade ten one-coins for one ten-coin. These are the same tens and ones the on-screen picture “Counting with Ten-Coins” uses.

Cut-out cards 2 of 2Part-part-whole mats

Part-part-whole mats

Cut out the mats. Put a number of counters in the whole box, then break them into the two part boxes; or fill the parts and join them into the whole. The mat holds the big idea in view: the two parts always make the whole (Days 1, 3 and 4).

Teacher note: the same mat works for breaking a number apart and for building it back from its parts, so children see that the two are the same idea both ways round.

Mini-check · End of the weekBreaking numbers apart

What we know: breaking numbers apart

NameClassDate

Break each number into parts. Fill the boxes and the blanks. You may use counters or coins.

1Break 7 into two parts: 7 is ____ and ____

24848 is ____ tens and ____ ones.
48 is ____ and ____.

3. Write two ways to make 9.

4Join the parts: 20 + 6 = ____

5Find the missing part: 6 + ____ = 10

Mini-check · Answers and markingFor the teacher

Answers and marking guide

Answers

1. Any two parts that make 7, such as 5 and 2	2. 4 tens and 8 ones, which is 40 and 8
3. Any two different ways to make 9, such as 5 and 4, and 6 and 3	4. 26
5. 4 (6 and 4 make 10)

Question 1: accept 6 and 1, 5 and 2, 4 and 3 or their reverses, as long as the two parts add back to 7. Question 3: the two ways must be different, and each pair must make 9.

A quick three-level guide

Idea	Working towards	At standard	Beyond
Break apart (Q1)	is unsure how to split it	breaks a number into two parts that add back to the whole	breaks it several ways with ease
Tens and ones (Q2)	reads the digits as loose ones	partitions into tens and ones, like 4 tens and 8 ones	also writes it as 40 and 8
Many ways (Q3)	finds only one way	finds two ways to make the number	finds several, working in order
Build from parts (Q4, Q5)	miscounts when rejoining	joins parts and finds a missing part	does it by counting on from the bigger part

Five questions, four ideas. A child at standard breaks a number into two parts, partitions a two-digit number into tens and ones, and joins parts back into the whole. Watch how they work as much as what they write: the surest sign is checking that the parts add back to the whole.

Weekly recordClass checklist

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	Break apart	Tens and ones	Many ways	Build from parts	Ten-coins

The five columns are the five days: break a number apart, tens and ones, many ways, build it from parts, and counting with ten-coins.