Contents
Start here: quick setup and the key idea
Use one ten-frame, up to 10 identical counters, and two colours if you have them. The central idea is to keep three things separate all lesson: the counters you already have, the empty spaces you can still see, and the extra counters needed to make 10.
NSW Education defines a ten-frame here as a rectangle divided into 2 rows of 5, making 10 boxes altogether. Investigating ten-frames
Draw it quickly: sketch one rectangle, draw one line across the middle for 2 rows, then split each row into 5 equal boxes.
Set one class convention before you begin: fill from the top left across the first row of 5, then continue on the second row. This can help keep everyone's reading of the frame consistent.
Say this before the first example: 'Filled counters are what we count. Empty boxes are spaces where counters could go.' Then check whether pupils can use those words back to you.
NSW Education also highlights the middle split of a ten-frame as 5 and 5, and notes that this structure can help pupils use what they know about 5 instead of counting every object one by one. Investigating teen numbers with 10 frames
Worked hypothetical example: 7 + 3 = 10
NSW Education's ten-frame example shows that 10 can be made of 7 and 3, and also 3 and 7. Ten-frame filler
Classroom example: Hypothetical worked model, part 1: Place or draw 7 counters using the agreed fill order: 5 in the top row and 2 in the bottom row. Ask, 'How many counters can you see? How do you know?' Possible pupil responses: 'I can see 5 and 2 more,' 'It is 7,' or 'I counted them.'
Classroom example: Part 2: Keep the language separate. Say, 'There are 7 counters. There are 3 empty spaces. Empty spaces are not counters. They show how many more counters would fill the frame.' Then ask, 'So how many more counters do we need to make a full 10?'
Classroom example: Part 3: Add 3 counters in a second colour. Say, 'Now I have 7 counters and 3 more counters. Altogether there are 10 counters, so 7 + 3 = 10.'
Classroom example: Part 4: Read the same completed frame again. 'I can also say 3 + 7 = 10.' Ask, 'What stayed the same? What changed?' Possible pupil responses: 'The whole stayed 10' and 'we changed which part we said first.'
Classroom example: Hypothetical board note:
7 counters
3 empty spaces
7 + 3 = 10
3 + 7 = 10
A coherent lesson sequence
1. Notice the frame. Give pupils a blank frame to inspect or draw. Ask: 'What do you notice? How many boxes are in each row? How many altogether?' Keep returning to 5 and 5 making 10.
2. Show one part first. Place 7 counters and ask: 'How many counters are there? How do you see it? What is full already? What is not full yet?' If needed, accept counting, then revoice with structure: 'Yes, 5 and 2 more makes 7.'
3. Find the missing part without blurring spaces and counters. Ask in this order:
'How many counters are there?'
'How many empty spaces are there?'
'How many more counters would fill the frame?'
Only after that write 7 + 3 = 10.
England's national curriculum for mathematics says pupils should represent and use number bonds and related subtraction facts within 20. In the same programme of study, pupils should add and subtract one-digit and two-digit numbers to 20, including 0; the notes add that pupils memorise and reason with number bonds to 10 and 20 in several forms. National curriculum in England: mathematics programmes of study
NCETM describes 'seeing the numbers inside' other numbers as part of understanding composition, and one NCETM classroom discussion used 'What's the same?' and 'What's different?' to compare different ways of making 10. Exploring the composition of number Number bonds to 10 using bead strings: a lightbulb moment
4. Vary the reading of the same whole. Ask: 'If 7 + 3 = 10, what else is true?' Useful follow-ups are:
3 + 7 = 10
10 – 7 = 3
10 – 3 = 7
Then show another full frame such as 8 and 2 or 6 and 4.
5. Include zero carefully. Use a full frame of 10 counters and say, 'The whole is 10. One part is 10 counters. The other part is 0 counters.' This keeps zero as a part without using empty spaces to mean zero.
6. Check transfer. Cover part of a frame or switch to a missing-part equation such as 10 = 8 + __ or 10 = __ + 4. Ask pupils to explain whether they are using counters they can see, spaces they can see, or a known bond.
Optional variation for later in the lesson: show 10 as 3 + 4 + 3. Ask, 'How is this like 7 + 3? How is it different?' Then see whether pupils can combine 3 and 4 to notice the hidden 7.
Common sticking points and responsive teaching moves
Sticking point: a pupil says 'There are 10' because there are 10 boxes. Responsive move: ask them to touch or point only to filled counters while counting. Then say, 'There are 7 counters in 10 boxes.'
Sticking point: a pupil mixes up empty spaces and counters. Responsive move: keep the words separate every time: counter, box, space. Ask first for the number of counters, then for empty spaces, then for how many more counters are needed.
Valid starting strategy: a pupil counts from 1 to 7 each time. Responsive move: accept the count, then invite a more structural reading: 'What does this full row tell us?' and 'Can you see 5 and 2 more?'
Sticking point: a pupil thinks only one order is correct. Responsive move: point to the same completed frame and read it once as 7 + 3 = 10 and once as 3 + 7 = 10. Ask, 'What stays the same? What changes?'
Sticking point: a pupil treats zero as the same as empty spaces. Responsive move: use a full frame for 10 + 0 = 10 or 0 + 10 = 10. Here there are no empty spaces, which helps separate '0 counters in a part' from 'spaces not yet filled.'
Adaptation if pupils need a simpler entry: stay within the same ten-frame but begin with other visible parts such as 5 and 1, 5 and 2, or 8 and 2 before returning to 7 and 3.
Adaptation if pupils are ready to generalise: ask for another split of 10, then a three-part split such as 3 + 4 + 3, and compare what is the same and what is different.
Copyable practice and transfer questions
Copyable practice set:
1. Draw 6 counters on a ten-frame. How many empty spaces are there? How many more counters make 10?
2. 10 = 8 + __
3. 10 = __ + 4
4. Draw a full ten-frame to show 7 + 3 = 10 using two colours.
5. Write two number sentences for the same frame in question 4.
6. 10 = 10 + __
7. 10 = __ + 0
8. True or false: 3 empty spaces means there are 3 counters. Explain.
9. Optional transfer: Show 10 as 3 + 4 + 3. How is it like 7 + 3?
Classroom example: Explained answers:
1. 4 empty spaces and 4 more counters, because 6 counters need 4 more to fill 10 boxes.
2. 2.
3. 6.
4. Any full frame with 7 counters in one colour and 3 in another.
5. 7 + 3 = 10 and 3 + 7 = 10.
6. 0.
7. 10.
8. False. Empty spaces are positions, not counters.
9. It is like 7 + 3 because 3 and 4 can be combined to make 7, and both totals are 10.
Evidence-backed context and clear limits
Published guidance in England's early years materials emphasises composition of numbers to 10 and some number bonds to 10, and says understanding should be shown across different representations such as objects, fingers, frames and numerals rather than by rote counting alone. ELG: Number Development Matters
NCETM's representation guidance says a tens frame can be used with each counter valued at one, and that the representation should help pupils see the mathematical structure. The Five Big Ideas at Primary – Representation and Structure
NSW Education and NCETM both provide examples of seeing 10 in different partitions, including 8 and 2, 7 and 3, 3 and 7, and a three-part split such as 3 + 4 + 3. Ten-frame filler Number bonds to 10 using bead strings: a lightbulb moment
This page gives you an original lesson script, original teacher prompts, and hypothetical pupil responses built from those published ideas. Those exact prompts and examples are not quoted from the published pages.
The curriculum and guidance pages here come from specific jurisdictions and professional-development contexts. They are useful for lesson design, but they are not universal age placements, policy statements, or guarantees about what every class will do next.
