Composition of numbers to 6

Ten frames: how many, and how many more to make 6

Objective: Children find how many counters are on a ten frame and work out how many more counters are needed to fill it to 6, deepening their understanding of the composition of 6.

What to do

1. Gather the group and show the empty ten frame. Say: 'Look, our frame is empty.' Hold up the ten frame showing 0 card and say: 'Zero - no counters at all.'
2. Put 4 counters into the frame one at a time, counting aloud together as each one is placed: 'one, two, three, four'. Hold up the ten frame showing 4 card to match.
3. Ask: 'How many counters are on our frame?' Point to the ribbon marking the sixth space and say: 'We are filling up to here today - our six.'
4. Ask: 'How many more do we need to make 6?' Invite a child to count the empty spaces up to the ribbon only, then add that many counters one at a time.
5. Count the whole frame together to check: 'four and two make six.' Repeat the sentence together as a group.
6. Pass the frame to the next child and tip a different amount of counters in (try 1, then 3, then 5 across turns), repeating the same questions and sentence pattern each time.
7. Introduce the feely bag with the remaining picture cards inside. Let a child pull out a card without looking, show it to the group, and ask them to build that amount on the real frame before working out how many more are needed to make 6.
8. Use the soft toy to 'nibble away' some counters from a full frame of 6 while children close their eyes. On 'open your eyes', ask how many are left and how many more the toy needs to give back to make 6 again.

Misconceptions

Adapting

• Support: Work with smaller starting amounts first (0, 1 or 2), use hand-over-hand support to place counters one at a time, and let the child use their fingers alongside the frame to check.
• Challenge: Show the frame briefly, cover it, and ask the child to say how many more are needed from memory; or ask them to find more than one way to make 6 on the frame and compare the ways using the picture cards.
• SEND and EAL: Use the real counters for children to touch and move rather than relying on spoken instructions alone; pair the word 'more' with a simple adding gesture; repeat the same short sentence frame every turn; use the matching picture card alongside the real frame as extra visual support; pair the child with a talk partner who models the vocabulary.

Look for

• Can the child say how many counters are on the frame without recounting each one (subitising small amounts)?
• Does the child count on from the number already on the frame, rather than starting again at 1, when finding how many more are needed?
• Does the child use or join in with the sentence '... and ... make 6'?
• Does the child understand that today's target is the sixth space, rather than treating all ten spaces on the frame as the target?

Picture cards for this session

Part-whole: composition of 4 and 5

Objective: Children explore the composition of 4 and 5: they split a whole group of real objects into two parts in different ways and check that the parts still make the same whole, matching their work to part-whole picture models.

What to do

1. Say: 'Today we are finding different ways to split a group into two parts.' Ask each child to count out 4 counters into the whole circle of their mat.
2. Show picture card 1 (1 and 3 make 4). Say: 'Can you split your 4 so that one part has 1 and the other part has 3?' Model moving 1 counter into one part circle and 3 into the other.
3. Ask the children to check their two parts by counting each part out loud, then count both parts together to check they still make 4.
4. Show picture card 2 (2 and 2 make 4). Say: 'Let's move the counters around. Can you make 2 and 2 instead?' Give children time to rearrange their own counters.
5. Show picture card 3 (3 and 1 make 4). Ask: 'What if the big part is on the other side this time, with 3 and 1?' Let children try this arrangement themselves.
6. Use the puppet to hide one part of the 4 under the cloth and ask: 'The puppet can see 1 part. If the whole is 4, how many is the puppet hiding?'
7. Ask the children to now count out 5 counters into the whole circle of their mat.
8. Show picture card 4 (1 and 4 make 5). Say: 'Can you split your 5 into a part with 1 and a part with 4?' Model this with your own counters alongside them.
9. Show picture card 5 (2 and 3 make 5). Ask the children to rearrange their counters into a part of 2 and a part of 3, then check both parts together make 5.
10. Show picture card 6 (3 and 2 make 5). Ask: 'Can you flip it round, so the part of 3 is on the other side?' Encourage children to try this with their own counters.
11. Show picture card 7 (4 and 1 make 5). Say: 'One more way - can you make a part of 4 and a part of 1?' Let children arrange this themselves.
12. Finish by hiding one part of 5 under the cloth again and asking the children to work out the hidden part, checking by tipping the cloth away to reveal it.

Misconceptions

Adapting

• Support: Work only with 4 first and use a five frame or part-whole mat with large, clear circles. Let the child move one object at a time between parts while the adult counts aloud with them.
• Challenge: Ask the child to find all the ways to split 5 without being shown the picture cards first, then check their own ways against the cards.
• SEND and EAL: Use real objects the child can touch and move rather than relying on spoken instructions alone; pair key words (whole, part, split) with gestures, and repeat each instruction while pointing to the mat.

Look for

• Child counts each part accurately before counting the whole
• Child can rearrange the same whole into a different pair of parts without recounting from scratch
• Child uses the words 'part' and 'whole' when describing what they have done
• Child notices that swapping the two parts still makes the same whole
• Child can say the hidden part when shown one part and told the whole

Picture cards for this session

Composition of 6: every way to make 6

Objective: Children explore, using real objects, that 6 can be split into two parts in different ways and say the matching number fact each time, for example 2 and 4 make 6.

What to do

1. Gather the group and show your hoop with all 6 objects inside. Say: 'All 6 are together right now - this is the whole.'
2. Model splitting the 6 objects into the two part plates, for example 2 in one and 4 in the other. Count each part aloud, then say: '2 and 4 make 6.'
3. Hide one part plate under the cloth. Say: 'I can see 4. How many do you think are hiding, so we still have 6 altogether?' Reveal the hidden part to check.
4. Give each child their own 6 objects and two part plates. Invite them to split their 6 their own way, count each part, and say the fact aloud, for example 'my parts are 3 and 3, that makes 6.'
5. Turn over one part-whole picture card at a time (1 and 5, 2 and 4, 3 and 3, 4 and 2, 5 and 1). For each card, ask children to copy that split with their own objects and check it by counting both parts.
6. Ask: 'Can you find a way to split your 6 that nobody in our group has made yet?' Support children to swap their two parts over and notice what happens.
7. As each new way is found, place it on the shared tray in order, and count together how many different ways the group has made.
8. Close by choosing a favourite way together and saying the fact one more time, for example '5 and 1 make 6.'

Misconceptions

Adapting

• Support: Start with fewer objects at a time and guide the first split hand-over-hand. Begin with 5 and 1, since it links to the child's existing knowledge of 5, and keep repeating the same sentence pattern 'X and Y make 6' for every split.
• Challenge: Ask the child to work out a hidden part when only one part is shown and the other is covered, before checking. Invite them to predict their next split before moving the objects, and to keep going until they have found every way to make 6.
• SEND and EAL: Use the real objects and gestures alongside the words, for example open arms for 'whole' and two fists tapped together for 'parts'. Repeat the same sentence stem every time, point to the matching picture card as you say the fact, and accept pointing or counting as an answer rather than requiring spoken English.

Look for

• Children who can find a new way to split 6 without repeating a way already made
• Children who recognise 3 and 3 as equal parts without needing to count each one
• Children who predict the hidden part before counting to check
• Children who understand that swapping the two parts over keeps the whole the same
• Children who can match a part-whole picture card to their own split of real objects confidently

Picture cards for this session

Number bonds to 6, including zero and take away

Objective: Children find and show all the ways to split 6 objects into two parts (part-whole bonds for 6, including zero), and record that 'take away' is a related idea to composition.

What to do

1. Gather the group on the carpet and count the 6 shells together into the whole section of the plate, saying 'We have 6 shells altogether.'
2. Say: 'The number dragon is hungry. Watch how many he moves to the other side.' Move the dragon to push 0 shells across, then say 'Look, 0 and 6 still make 6.'
3. Ask a child to move the dragon and slide 1 shell across the string divider. Say together: '1 and 5 make 6.'
4. Keep going round the group, each child taking a turn to slide a different amount across: 2 shells (saying '2 and 4 make 6'), then 3 shells ('3 and 3 make 6'), then 4 shells ('4 and 2 make 6'), then 5 shells ('5 and 1 make 6'), then all 6 shells ('6 and 0 make 6').
5. After each move, pause and check together: push the two parts back together and recount to 6 to prove the whole hasn't changed.
6. Bring out the rekenrek. Slide beads across to match each split children made (for example 2 red and 4 white), and ask children to spot the matching part-whole plate from earlier.
7. Link to take away: say 'If 6 shells start on the plate and the dragon takes away 2, how many are left?' Move 2 shells off and count the remaining 4 together.
8. Repeat the take-away question with a different amount, each time starting from 6 shells and checking the answer by recounting.

Misconceptions

Adapting

• Support: Use fewer turns per child and keep the string divider still while an adult moves the shells, letting the child only count and say the matching number sentence.
• Challenge: Ask children to predict the missing part before moving any shells, and to find a split that has not been shown yet without adult prompting.
• SEND and EAL: Pair the puppet's actions with real shells every time so the language 'and... make 6' is always linked to a concrete action, and model the sentence slowly for children to repeat.

Look for

• Child recounts the whole after a split to check it is still 6
• Child uses the words 'and' and 'make' when describing a split
• Child recognises 0 as a valid part without adult prompting
• Child links a take-away action to the matching part-whole split

Picture cards for this session

Observation prompts: eyfs.ma.number.1

Look for

• Child splits a group of up to 6 pebbles, shells or counters into two parts on a tuff tray and can say how many are in each part.
• Child fills a ten frame with up to 6 counters and works out how many more are needed to make 6.
• Child notices that 2 and 4 make 6 in the same way as 4 and 2, perhaps by turning a part-whole mat around.
• Child uses fingers, a show-me board or two hoops to display two parts that make 6.
• Child acts out 0 and 6 make 6 in role play, for example an empty basket and a full basket of 6 toy fruits.
• Child uses the part-whole model (for example two plates and a whole tray) to find more than one way to make 6 during continuous provision.

Listen for

• "3 and 3 make 6."
• "I've got 2 over here and 4 over there, so that's 6 altogether."
• "How many more do I need to make 6?"
• "0 and 6 still makes 6, because 0 is nothing."
• "If I take one away from this pile, I need one more on the other pile to still make 6."
• "2 and 4 make 6, same as 4 and 2, just swapped round."

Next steps

• Not yet there: give the child groups of up to 4 objects to split into two parts first, using real objects such as conkers or buttons, before moving on to 6.
• Not yet there: model composition of 6 using two hoops on the carpet, physically moving objects between them while counting each part aloud with the child.
• Not yet there: use a ten frame with the practitioner, filling it together and asking the child to count how many more make 6, supporting with a number line showing 0 to 6.
• Secure: challenge the child to find every way to make 6 using the part-whole model, checking they have found all of 0 and 6, 1 and 5, 2 and 4, 3 and 3, 4 and 2, 5 and 1, 6 and 0.
• Secure: link composition to take away, asking the child what is left if 2 are taken from a group of 6, connecting it to the matching bond they already know.
• Secure: encourage the child to predict a missing part of 6 without recounting everything, using a known fact such as 4 and 2 make 6.

Observation prompts: eyfs.ma.patterns.3

Look for

• A child splits a group of 6 objects (for example conkers, shells or teddies) between two hoops or pots in different ways, such as 3 and 3, then 2 and 4.
• A child uses a ten frame with 6 counters placed and points to or counts the empty spaces to work out how many more are needed to make 6.
• A child notices that one part can be empty, for example pushing all 6 objects into one pot and none into the other, and still calls this 6.
• A child physically removes some objects from a group of 6 (a take-away context, such as eating pretend grapes or posting bears into a den) and recounts what is left.
• A child rearranges the same 6 objects into a new split after being asked, 'Is there another way?', rather than only finding one combination.
• A child matches two part groups side by side (for example two towers of cubes) to check that the parts together still total 6.

Listen for

• "3 and 3 makes 6."
• "I've got 4 here, so I need 2 more to make 6."
• "0 and 6 still makes 6, because I didn't take any away."
• "6 take away 2 leaves 4."
• "There's another way: 1 and 5."
• "Altogether that's the same as 6."

Next steps

• Not yet there: give the child a consistent small quantity, always 6 of the same object, with two clearly separate mats or hoops, so they can physically move objects between the two parts and recount the total each time.
• Not yet there: model one split at a time using a ten frame filled with 6 counters, asking the child to point to the filled spaces and then the empty spaces before introducing a second combination.
• Not yet there: use fingers alongside the ten frame, showing 6 fingers then folding some down, to link the physical action to the idea of two parts making 6.
• Secure: challenge the child to find every way to make 6 using real objects and record each combination practically, for example by photographing each split or building it with duplo, rather than writing it down.
• Secure: ask the child directly what happens when one part has nothing in it, to draw out 0 and 6 make 6 alongside the other combinations.
• Secure: extend into take-away play, starting with 6 objects and hiding or removing some under a cloth or in a bag, so the child links the bonds they already know to how many are left.

Dear families,

This term in maths, your child is getting to know the numbers 0 to 6 really well. We are exploring how each number is made up of smaller parts, so children start to see numbers as flexible rather than just something to count up to.

We began by using ten frames to help children see at a glance how many dots are shown and how many more are needed to make 6. We then looked closely at the numbers 4 and 5, splitting them into two parts in different ways, before moving on to find every single way to make 6 (for example, 1 and 5, or 3 and 3).

In our final sessions, we are learning number bonds to 6, including what happens when one part is 0, and what happens when we take some away. Playing with real objects helps children feel these ideas in their hands before they ever need to write a number down.

Ideas to try at home

• At snack time, put out 6 raisins or grapes and ask your child to split them between two plates. Can they find a different way to split them next time?
• Line up 6 toy cars, cover some with a cloth, and ask 'how many am I hiding?' so your child practises working out the missing part.
• In the bath, float 6 bath toys and take some away one at a time, asking 'how many are left?' each time.
• Build a tower of 6 bricks, then knock off a few. Ask your child how many fell and how many are still standing, and see if they can say the whole fact, like '4 and 2 make 6'.
• On a walk, spot 6 of something (leaves, stones, buttons) and ask your child to arrange them into two groups in as many ways as they can find.

With thanks for your support at home, The Reception Team