Composition of numbers to 9

Ten frames: how many, and how many more to make 9

Objective: Children read how many counters are on a ten frame and work out how many more are needed to make 9.

What to do

1. Gather the group on the carpet around the large ten frame and show them 9 counters in the bag.
2. Turn over the top ten frame card and ask a child to place that many counters onto the large frame, matching the pattern on the card.
3. Ask the group to count the counters together, touching each one.
4. Ask the key question: how many more counters do we need to fill the frame up to 9?
5. Invite a different child to take that many more counters from the bag and fill the empty spaces until the frame shows 9.
6. Say the matching number fact together, for example 'and make 9'.
7. Empty the frame and repeat with the next card, passing the soft toy so a new child goes first each round.
8. For the card showing 9, ask how many more are needed, so children notice that 9 and 0 make 9.

Misconceptions

Adapting

• Support: Use frames showing only 0, 1, 2 and 3 first, and let the child place one counter at a time while the adult says each number aloud.
• Challenge: Hide the ten frame card after a quick look and ask the child to say how many more make 9 from memory before checking.
• SEND and EAL: Use consistent, simple language each round ('how many more to make 9?'), pair the spoken number with a hand signal, and let children point to the frame instead of answering verbally if that is easier.

Look for

• Children count counters accurately without recounting from 1 every time.
• Children can say how many more are needed without filling every space first.
• Children use the vocabulary 'more' and 'make' when describing the frame.
• Children notice the pattern that the counted amount and the amount more always make 9.

Picture cards for this session

Part-whole: composition of 7 and 8

Objective: Children partition a group of 7 or 8 real objects into two parts in different ways, and match their partitions to a part-whole model, building their understanding that 7 and 8 can each be made of two smaller parts.

What to do

1. Gather the group on the carpet and show everyone 7 objects in the whole hoop of one mat. Say, 'This whole is 7. Watch what happens when I split it into two parts.'
2. Slide a small handful of the objects into one of the small hoops and the rest into the other hoop, counting each part out loud as you go.
3. Hold up the matching picture card (for example 2 and 5 make 7) and say, 'My two parts match this card: 2 and 5 make 7.'
4. Give each child 7 objects and their own mat. Ask them to split their 7 into two parts in their own way, counting each part as they place it.
5. Go round the group and ask each child to say their own part-whole sentence out loud, for example 'My parts are 3 and 4. 3 and 4 make 7.'
6. Find and hold up the picture card that matches each child's split so they can see their real objects mirrored in the picture.
7. Ask, 'Can you split your 7 into two parts in a different way?' and let children rearrange and recount.
8. Swap the baskets for 8 objects. Repeat the splitting, saying and matching-the-card process for 8.
9. Introduce the feely bag: put 8 objects in, let a child pull some out without looking, then count what's left in the bag and what's in their hand, saying the part-whole sentence for 8.
10. Finish by laying out several of the picture cards and asking children to build the matching split with their own objects on their mat.

Misconceptions

Adapting

• Support: Use 7 only, and give the child a mat with the two part-hoops already a visibly different size so one part is obviously smaller, supporting one-to-one counting with fewer objects to track.
• Challenge: Ask the child to find every different way to split 8 across two parts and lay all their findings out at once, then compare which picture cards match.
• SEND and EAL: Pair the sentence 'X and Y make Z' with consistent hand gestures (two hands apart for parts, hands coming together for the whole) and real objects throughout, repeating the same sentence structure every time so the pattern becomes familiar regardless of spoken English level.

Look for

• Counts each part accurately using one-to-one correspondence
• Uses the language 'and' and 'make' when describing their split
• Finds more than one way to split the same whole
• Matches their own arrangement of real objects to the correct picture card
• Recounts to check the two parts still make the whole after moving objects

Picture cards for this session

Composition of 9: every way to make 9

Objective: Children explore and record every way to partition 9 into two parts, using real objects and a part-whole frame, building towards a secure understanding that 9 can always be split into two parts whose total stays 9.

What to do

1. Adult says: 'We have 9 conkers in our whole hoop. Let's count them together to check.' Adult counts all 9 objects with the children, touching each one.
2. Adult says: 'I'm going to split our 9 into two parts.' Adult moves some objects into one small hoop and the rest into the other, for example 1 object into one hoop and 8 into the other.
3. Adult says: 'Let's count each part.' Adult counts each small hoop aloud with the children, then says the stem sentence: '1 and 8 make 9.'
4. Adult turns over the matching part-whole picture card (1 and 8 make 9) and places it next to the hoops, saying: 'Look, this picture shows the same thing.'
5. Adult invites a child to move the objects to make a different split, for example 2 and 7, and supports the child to say: '2 and 7 make 9.' Adult finds and places the matching picture card.
6. Adult continues around the group, giving each child a turn to make a new split (3 and 6, 4 and 5, 5 and 4, 6 and 3, 7 and 2, 8 and 1), checking each total by recounting and matching the picture card each time.
7. Adult says: 'What if I don't move any conkers at all?' Adult shows the empty small bowl next to the full hoop and models: '0 and 9 make 9.' Adult repeats the other way round: '9 and 0 make 9.'
8. Adult lines up the picture cards children have matched so far and says: 'Let's look at our pictures in order. Have we found every single way to make 9, or are there any missing?' Adult supports children to check against the numeral cards 0 to 9.
9. Adult hides the 9 objects briefly under the cloth and says: 'I've got 9 conkers under here split into two parts. Can you guess what the two parts might be?' Children suggest a split, then adult reveals to check.

Misconceptions

Adapting

• Support: Work with fewer objects moved at a time and let the child move one object across at a time while the adult counts aloud, focusing only on a couple of ways to make 9 (such as 1 and 8, then 8 and 1) rather than all of them.
• Challenge: Ask the child to find and order all the ways to make 9 independently using the numeral cards, predicting the next split before trying it, and checking their own matching picture card.
• SEND and EAL: Pair every number word with the matching numeral card and the real objects, model the stem sentence slowly with gesture (hands apart for the two parts, hands together for the whole), and allow the child to point to or move objects instead of speaking the sentence aloud.

Look for

• Child recounts each part and the whole to check the total is correct.
• Child notices and comments that swapping the two parts does not change the whole.
• Child accepts 0 as a valid part when shown the empty bowl.
• Child uses a system (such as following the numeral cards in order) rather than moving objects randomly.
• Child uses the stem sentence '... and ... make 9' independently.
• Child matches their own split correctly to one of the part-whole picture cards.

Picture cards for this session

Number bonds to 9, including zero and take away

Objective: Children find and say the pairs of numbers that make 9, including 0 and 9, and use take away to explain how the two parts are connected.

What to do

1. Gather the group and show the pot of 9 objects. Count them together into the top part of the part-whole mat: '1, 2, 3... let's check, how many have we got altogether?'
2. Say: 'I'm going to split our 9 into two parts.' Slide some objects into one bottom circle and the rest into the other bottom circle, for example 3 and 6. Ask the children to count each part.
3. Say the sentence together: '3 and 6 make 9.' Find the matching number cards and place them under each part.
4. Pass the rekenrek to a child. Ask them to slide beads so that some are red on one side and white stay on the other, matching the same split (3 red, 6 white). Count each colour together.
5. Hide the 9 objects under the drawstring bag. Take some out in full view and ask, 'If I take away 2, how many are left under the bag?' Reveal to check, then say the bond: '2 and 7 make 9.'
6. Repeat with a new split each time, moving towards the zero fact: slide all 9 beads to one side so none are left on the other. Ask, 'What if I take nothing away? How many parts do we really have?' Introduce '0 and 9 make 9.'
7. Let each child take a turn choosing a split on the rekenrek or part-whole mat while the rest of the group checks by counting both parts and saying the bond sentence.
8. Finish by lining up the number cards in order and reading all the pairs the group found for 9, including 0 and 9.

Misconceptions

Adapting

• Support: Work with objects only to begin with, splitting 9 into just two groups the child can touch and move. Use a five-frame style row (5 and then extra) to help them see parts without the rekenrek's extra rows. Keep numbers to one bond at a time before moving on.
• Challenge: Ask the child to predict the missing part before counting, for example 'If one part is 6, how many is the other part, before we check?' Encourage them to record each bond they find using the number cards in order and spot that the pairs reverse once they pass the middle.
• SEND and EAL: Use the same real objects and rekenrek every session so the resource itself is familiar. Pair each spoken number with a number card and a clear gesture (two open hands for the two parts). Keep sentences short and consistent: '3 and 6 make 9.' Allow extra processing time and model the sentence before asking the child to repeat it.

Look for

• Child counts each part accurately without recounting the whole from the start
• Child can say the bond sentence using both parts and the whole, for example '2 and 7 make 9'
• Child recognises that swapping the two parts still makes the same bond
• Child accepts 0 as a valid part when a group is empty
• Child links taking away from the whole to finding the matching part that is left
• Child begins to predict the second part when given the first, without needing to count both from scratch

Picture cards for this session

Observation prompts: eyfs.ma.number.1

Look for

• Child splits a group of 9 objects into two parts (for example onto two plates or two hoops) and can say how many are in each part
• Child uses a ten frame to show 9 counters and points to the empty space to say how many more are needed to make 9
• Child rearranges 9 objects into a different split (such as 3 and 6, then 6 and 3) and notices the total is still 9
• Child matches a part to its missing part without counting from 1 again, for example seeing 6 and knowing 3 more makes 9
• Child uses fingers, a number line, a bead string or small-world objects (such as 9 conkers, 9 shells or 9 toy cars) to explore the different ways to make 9
• Child represents a split using a part-whole model (two circles joined to one circle) with real objects or pictures
• Child checks their own work by counting the two parts together to see if they make 9

Listen for

• "I've got 4 and 5, that's 9 altogether."
• "If I take 2 away from 9 I've got 7 left."
• "3 and 6 make 9, and 6 and 3 make 9 as well, it's the same numbers swapped round."
• "There's 0 in this hoop and 9 in the other one, so it's still 9."
• "I need 1 more to make 9."
• "8 and 1 make 9, I didn't even need to count them all again."

Next steps

• For children not yet secure: work with smaller totals first (within 5), using real objects the child can move and group with their hands, such as 5 teddy bears split between two baskets, before returning to 9
• For children not yet secure: use a ten frame with 9 counters already placed and ask the child to cover different parts with a cloth, counting what is hidden and what is showing each time
• For children not yet secure: pair the child with a confident peer during continuous provision, such as a den role-play area with 9 pretend eggs to share between two nests, so they hear the number talk
• For children secure in this goal: challenge them to find every way to make 9 and show when they have found them all, recording each split with objects, a drawing or a part-whole model
• For children secure in this goal: introduce the related take-away fact, for example starting with 9 objects, removing a part, and saying what is left
• For children secure in this goal: ask them to predict a missing part before checking, for example "if I can see 2, how many are hiding to make 9?", to build fluency without recounting

Observation prompts: eyfs.ma.patterns.3

Look for

• A child splits a group of 9 conkers, buttons or cubes into two parts on a part-whole mat or two hoops, and tries more than one way of doing it.
• A child uses a ten frame to show 9, then covers or removes counters to check how many more are needed to make 9.
• A child lines objects up in pairs to check whether an amount can be shared with no one left out, or has one odd one over.
• A child shares 9 items between two friends, two plates or two hands and notices the amounts are not equal.
• A child swaps the two parts of 9 around on the part-whole mat (for example moving from 3 and 6 to 6 and 3) and notices it is still 9 altogether.
• A child uses fingers, a bead string or natural materials outdoors to build or represent 9 in more than one way.
• A child takes some away from a group of 9 and works out how many are left, including when all 9 are taken away.

Listen for

• "4 and 5 make 9."
• "If I move one over, it's 2 and 7 instead of 3 and 6."
• "I can't share 9 fairly between the two of us, someone gets one more."
• "0 and 9 make 9 as well, that's none on this side and all of them on the other."
• "That's the same two numbers, just swapped round."
• "9 take away 9 leaves 0."
• "I only need 1 more to get to 9."

Next steps

• Not yet there: give fewer objects to compare first (for example sharing 6 or 8 fairly) before returning to 9, so the child has a secure sense of equal and unequal groups.
• Not yet there: use a ten frame alongside real objects so the child can see and touch each part of 9 rather than relying on counting in their head.
• Not yet there: pair objects physically (lining shoes up two by two, or holding hands in twos on the carpet) to build the idea of odd and even before linking this back to 9.
• Not yet there: use familiar contexts such as sharing snack or sharing crayons between two children, so composition of 9 is grounded in something meaningful.
• Those who are ready: ask the child to find and record every way to make 9, checking they have included 0 and 9.
• Those who are ready: pose the question of whether 9 can ever be shared equally between two people, and ask them to explain why or why not.
• Those who are ready: extend the challenge to doubles within the numbers to 9 (for example checking whether 4 and 4 or 3 and 3 make an even total) and link this to the odd result when sharing 9.
• Those who are ready: offer missing-number problems within 9, including take-away and zero, such as finding what is left when some are hidden or removed.

Dear families,

This half term in Reception your child is exploring how numbers up to 9 can be split into two smaller parts and put back together again. They have been building numbers on ten frames, working out how many more are needed to make 9, and exploring the different ways to break apart 7 and 8.

By the end of the unit, children will know all the ways to make 9 from two parts, such as 4 and 5, or 3 and 6. They are also learning about zero as a part (for example, 9 and 0 still make 9) and starting to connect this to simple take-away, such as knowing that if 9 take away 2 leaves 7, then 2 and 7 must make 9.

Ideas to try at home

• At snack time, put out 9 grapes, raisins or crackers and ask your child to share them between two bowls in a few different ways, saying the numbers each time.
• Use a muffin tin or egg box with two sections and 9 small items (buttons, pasta shapes, pom-poms) to explore how many could go in each part.
• Hide some of a group of 9 toys or coins under a cup and ask your child to work out how many are hidden without lifting it.
• In the bath or garden, line up 9 toys or stones and take some away, asking how many are left and how many were taken.

Thank you for your support at home.