Composition of numbers to 7

Ten frames: how many, and how many more to make 7

Objective: Children work out how many counters are shown on a ten frame (0 to 7) and how many more are needed to fill it to 7, building a secure sense of the pairs that make 7.

What to do

1. Gather the group and place the empty ten frame mat in the middle. Say: 'This is our ten frame. Today we are finding out how many we can see, and how many more we need to make 7.'
2. Turn over the first ten frame picture card (showing 4). Say: 'Let's build what the card shows.' Help children place counters onto the real ten frame mat to match.
3. Say: 'Let's count together how many counters are on our frame.' Count the filled spaces aloud, touching each one.
4. Say: 'We need 7 altogether. How many more counters do we need to add to make 7?' Let children work out the missing amount by adding counters one at a time while counting on.
5. Once the frame shows 7, say: 'Now our frame has 7. Let's check by counting all of them.' Count all 7 together.
6. Turn over the next picture card and repeat the process, working through several of the cards (0, 1, 2, 3, 5, 6, 7) so children see different starting amounts.
7. For the card showing 0, say: 'Look, this frame has nothing on it yet. How many counters do we need to make 7?' Guide children to add all 7 counters one by one.
8. For the card showing 7, say: 'This frame is already showing 7. How many more do we need?' Help children notice that 0 more are needed because it already makes 7.

Misconceptions

Adapting

• Support: Use only the cards showing 0, 1, 2 and 3 first, and let the child physically move each counter into a space while the adult counts alongside them.
• Challenge: Show a card and ask the child to say both facts straight away without building it first, for example 'that shows 5, so we need 2 more,' then check by building it.
• SEND and EAL: Pair every number word with a consistent gesture (e.g. tapping the frame) and the matching numeral shown next to the frame, keep sentences short and repeated each turn, and allow extra time for the child to place and count counters at their own pace.

Look for

• Child recognises small amounts on the ten frame without recounting every time
• Child counts filled counters accurately with one-to-one correspondence
• Child works out the missing amount needed to reach 7
• Child uses counting on from the known amount rather than starting from 1
• Child uses vocabulary such as 'more', 'altogether' or 'makes' during the activity

Picture cards for this session

Part-whole: composition of 5 and 6

Objective: Children will explore different ways to partition 5 and 6 into two parts, using real objects and part-whole models, and begin to see that the same whole can be made of different pairs of parts.

What to do

1. Gather the group on the carpet around the large part-whole model and say, 'Today we are finding all the ways to make 5 and 6 using two parts.'
2. Ask each child to tip out 5 conkers onto the 'whole' space on their mat and count them together as a group: 'Let's check, how many conkers in the whole?'
3. Model splitting the 5 conkers into two parts on the large floor model, for example 1 conker in one part and 4 conkers in the other, saying, '1 and 4 make 5.'
4. Turn over picture card 1 (1 and 4 make 5) and hold it next to the real conkers so children can match the model to the picture.
5. Invite each child to split their own 5 conkers into two parts on their mat in a different way, and ask them to say the matching sentence aloud: '___ and ___ make 5.'
6. Reveal picture cards 2, 3 and 4 one at a time (2 and 3; 3 and 2; 4 and 1) and ask children to rebuild each one with their own conkers, checking the whole stays 5 each time by recombining and recounting.
7. Add one more conker to each child's pot so they now have 6, and repeat the process, splitting into two parts and saying the sentence, matching to picture cards 5 to 9 (1 and 5; 2 and 4; 3 and 3; 4 and 2; 5 and 1).
8. Hide one part under the cloth each time and ask, 'I can see ___ here, how many are hiding?' before lifting the cloth to check.
9. Finish by laying out all the picture cards the group has matched and counting together how many different ways they found to make 5 and how many to make 6.

Misconceptions

Adapting

• Support: Work with 5 only and keep the number of conkers small and identical in colour and size. Let the child move one conker at a time between parts while the adult says the sentence, anchoring each count with fingers held up alongside the mat.
• Challenge: Ask the child to find every possible way to make 6 before being shown a new picture card, then match their own arrangement to the matching numeral cards and say the full sentence independently.
• SEND and EAL: Repeat the same sentence frame, '___ and ___ make ___', every time, pairing it with pointing to each part and the whole. Let the child respond by moving objects or pointing to picture cards rather than only speaking, and use gesture (two hands coming together for the whole) alongside the words.

Look for

• Child recombines the two parts and recounts to check the whole stays the same
• Child uses the sentence 'and' and 'make' independently when describing their arrangement
• Child matches their own built arrangement correctly to the matching picture card
• Child starts to predict the missing part before checking under the cloth
• Child notices that swapping the parts still makes the same whole

Picture cards for this session

Composition of 7: every way to make 7

Objective: Children compose and decompose 7, finding different ways to split 7 into two parts using real objects and part-whole models.

What to do

1. Gather the children in a small circle and show the pot of 7 objects. Count them together into the whole circle on one mat: 'Let's check - how many altogether?'
2. Model tipping the 7 objects into the two part circles so there is 1 in one part and 6 in the other. Turn over the first picture card (1 and 6 make 7) and hold it next to the mat so children can match the real objects to the picture.
3. Say: '1 and 6 make 7. Let's check by counting all the parts together.' Count both parts and the whole with the children.
4. Invite a child to move one object across so the split changes. Count the new parts together and turn over the matching picture card (2 and 5 make 7) to check it matches.
5. Give each child their own mat and objects. Ask them to find their own way to split 7, then say the number sentence out loud, e.g. '3 and 4 make 7'. Turn over the picture card (3 and 4 make 7) to confirm.
6. Ask children to swap the amount in each part (e.g. from 3 and 4 to 4 and 3) and notice what happens. Show the matching picture card (4 and 3 make 7) and ask if the total has changed.
7. Continue around the group so each child has a turn finding a new split, checking against the remaining picture cards (5 and 2 make 7, and 6 and 1 make 7) as they come up.
8. Finish by lining up all six picture cards in order and counting through them together, checking each one still makes 7.

Misconceptions

Adapting

• Support: Work with one split at a time, keeping the same mat and objects for several turns. Use larger, easy-to-grasp objects and hand-over-hand support to move them between parts, focusing on matching real objects to just one or two picture cards.
• Challenge: Ask children to find all six ways to split 7 in order without adult prompting, then predict which split comes next before checking with the picture card. Encourage them to explain in a full sentence why swapping the parts still makes 7.
• SEND and EAL: Use the part-whole mat consistently so the layout becomes familiar, pair every spoken number with a gesture (hands apart for the two parts, hands together for the whole), and model the sentence stem '___ and ___ make 7' for children to repeat, allowing home-language versions where known.

Look for

• Child counts each part accurately before counting the whole.
• Child recognises the total stays 7 no matter how it is split.
• Child independently moves an object to create a new, correct split.
• Child uses the words 'part', 'whole' or 'altogether' during the activity.
• Child notices that swapping the parts (e.g. 2 and 5 to 5 and 2) still makes 7.

Picture cards for this session

Number bonds to 7, including zero and take away

Objective: Children secure the number bonds to 7, including the bond with zero, and begin to see finding the two parts of 7 and taking away from 7 as connected, using real objects, a rekenrek and part-whole models.

What to do

1. Say: 'We have 7 conkers each today. Let's find all the different ways we can split 7 into two groups.'
2. Ask children to put all 7 objects into one hoop and leave the other hoop empty. Say: 'How many are in this hoop? How many are in this one?' Reveal the part-whole picture showing 0 and 7 make 7, then the rekenrek picture with 0 red and 7 white beads, and ask children to check their hoops match.
3. Ask a child to move 1 object across to the empty hoop. Say: 'What's happened now?' Reveal the part-whole picture for 1 and 6, then the matching rekenrek picture, and ask children to check their own hoops against it.
4. Keep moving one object at a time, revealing the matching part-whole and rekenrek pictures in turn: 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1, finishing at 7 and 0. Each time, ask: 'Is this a way we've already made, or a new one?'
5. Pause at 3 and 4 and 4 and 3. Ask: 'What do you notice about these two?' Encourage children to physically swap the hoops over to see that the parts have swapped but the whole is still 7.
6. Introduce take away. Show 7 objects in one hoop. Say: 'Watch carefully.' Take some away and hide them in the bag, e.g. take away 3. Ask: 'How many did I take away? How many are left in the hoop?'
7. Repeat the take-away game with different amounts, including taking away 0 (say: 'I took none away, what's left?') and taking away all 7 (say: 'I took them all away, what's left?').
8. Let each child take a turn making their own split of 7 with their objects and hoops, matching it to a part-whole picture, then challenge their neighbour to say how many they would need to take away to get back to one part.

Misconceptions

Adapting

• Support: Work with smaller, more familiar totals first (e.g. recap bonds to 4 or 5 with the same hoops) before returning to 7. Let the child physically move one object at a time rather than predicting, and have the adult say each total out loud as it changes.
• Challenge: Ask the child to predict how many will be in the second hoop before moving any objects across, and to find a bond to 7 using the rekenrek alone, sliding beads without counting from 1. Ask them to explain how taking away 2 and taking away 5 are connected.
• SEND and EAL: Pair every number word with the matching real object group and gesture (e.g. open hands for 'none', a sweeping motion for 'altogether'). Keep the part-whole and rekenrek pictures visible throughout as a visual anchor, repeat key phrases consistently each time, and allow the child to respond by moving objects rather than only speaking.

Look for

• Child recognises 0 and 7 make 7 without needing to count the empty hoop
• Child predicts the second part of 7 before moving the objects
• Child notices that swapping the two groups does not change the whole
• Child uses the remaining visible amount to work out how many are hidden, rather than recounting from 1
• Child notices that 7 cannot be split into two equal groups

Picture cards for this session

Observation prompts: eyfs.ma.number.1

Look for

• Splits a group of 7 objects into two parts (for example on a ten frame or in two hoops) and can say how many are in each part without recounting from one.
• Rearranges the same 7 objects into a different split and notices the total is still 7.
• Uses fingers, a part-whole mat, beads or counters to show 7 as two parts, including showing 0 and 7 (all on one side, none on the other).
• Checks a partner's split of 7 by counting both parts and adding them back together.
• Covers or hides part of a group of 7 and works out how many must be hidden for the whole to stay 7.

Listen for

• "3 and 4 make 7."
• "If I move 1 over, it's 6 and 1 now, but it's still 7 altogether."
• "There's 0 left in this pot because all 7 are in the other one."
• "I need 2 more to make 7."
• "7 take away 5 leaves 2."

Next steps

• Not there yet: give small groups of up to 7 objects to physically share between two hoops, pots or sides of a ten frame, counting the whole group first, then each part, then checking the parts together make the whole again.
• Not there yet: use a part-whole mat with a large whole of 7 objects and two smaller spaces, so the child moves real objects rather than holding numbers in their head.
• Not there yet: practise with a ten frame showing 7 counters, asking how many more are needed to fill all 7 spaces, moving counters in and out as a game.
• Ready to extend: challenge the child to find every different way to split 7 using small world objects or a shaking tin, and keep track of the ways they have already found by lining up their part-whole models side by side.
• Ready to extend: pose take-away stories with up to 7 objects (for example, 7 conkers and some roll away) and ask the child to work out how many are left without recounting every object.
• Ready to extend: ask the child to predict the hidden part when they can see one part and the whole is known to be 7, then check by counting.

Observation prompts: eyfs.ma.patterns.3

Look for

• Children splitting a group of up to 7 objects into two parts in different ways, for example 7 cubes shown as 3 and 4
• Children using ten frames, fingers or a part-whole model (two hoops, a bead string) to show both parts of 7 at once
• Children noticing that swapping the two parts still makes 7, for example moving from 2 and 5 to 5 and 2
• Children checking a total by recombining the two parts back into one group of 7
• Children spotting the pattern as one part goes down by 1 and the other goes up by 1, for example 6 and 1, then 5 and 2

Listen for

• "3 and 4 make 7"
• "If I move one over, it's 5 and 2 instead of 6 and 1, but it's still 7"
• "I've got 0 in this pot and 7 in the other, that still makes 7"
• "How many more do I need to make 7?"
• "I've already done 1 and 6, so now I'll try 2 and 5"

Next steps

• Not there yet: offer composition of 5 first with real objects in two hoops, counting each part and the whole every time, before moving back to 7
• Not there yet: use a ten frame with counters the child can physically slide from one side to the other while saying each new pair, such as 4 and 3
• Ready to extend: challenge the child to find every way to make 7 and check they have found all eight pairs, including 0 and 7 and 7 and 0
• Ready to extend: ask the child to predict the matching pair before checking, for example "if 2 and 5 make 7, what do you think 5 and 2 makes?"

Dear parents and carers,

This term in maths, your child is learning all about the number 7. They are discovering that numbers can be split into two smaller parts and put back together again, for example that 3 and 4 make 7, or that 5 and 2 make 7.

In class your child will play with ten frames to find how many more are needed to make 7, build and sort small groups to explore the parts that make 5 and 6, hunt for every way to make 7, and practise number bonds to 7, including what happens when there are 0 of something, or when some are taken away.

Your child explores all of this through hands-on, playful activities rather than sitting still: using toys, buttons, fingers and everyday objects to build towers, fill ten frames and sort groups, so the understanding really sticks.

Ideas to try at home

• At snack time, give your child 7 grapes or crackers and ask them to share them across two plates in different ways: 1 and 6, then 2 and 5, then 3 and 4.
• Use an egg box or muffin tray with 7 spaces as a ten frame. Drop in some buttons and ask how many more are needed to fill all 7 spaces.
• Line up 7 toys, cover some with a cloth, and ask your child how many are hiding without peeking.
• On a walk, collect up to 7 leaves or stones, then split them into two little piles and say the two numbers out loud together, for example '4 and 3 make 7'.
• Start with 7 of something (socks, spoons, toy cars) and take some away one at a time, asking how many are left each time, until none are left.

With thanks, The Reception Team