Making ten and the teen numbers
Breaking numbers apart within 10, finding the partner that makes 10, and seeing 11 to 19 as a ten and some more
About four lessons of 30 to 40 minutes
Ten fingers hide a big secret
Hold up all ten fingers. Now curl down 3. How many are still up? Seven. You just broke 10 into two parts, 7 and 3, without even thinking about it. Every number up to 10 can be split into two parts in more than one way, and knowing the splits by heart is one of the single most useful things you can learn in maths.
There is a special split worth knowing best of all: the partner that makes 10. If you have 6 fingers up, how many more do you need to get to a full 10? Four. Once making 10 feels easy, something magical happens: the numbers 11 to 19 are just 10 with a few more fingers held up on a second hand, and suddenly the teen numbers make sense too.
- 10 fingers split into 7 up, 3 down7 and 3 are a part-part-whole for the number 10
- 6 counters, how many more to make 10?6 needs 4 more, because 6 and 4 make 10
- One full hand plus 4 fingers on the otherthat is 10 and 4 more, which is 14
- 13 counters as one ten-frame full plus 313 is a ten and three ones
What students will be able to do
Students will break numbers up to 10 into two parts in more than one way, find the missing partner that makes 10 with a given number from 1 to 9, and see the numbers 11 to 19 as one ten plus some further ones.
- I can split a number up to 10 into two parts in more than one way.
- I can find the number that makes 10 when added to a number from 1 to 9.
- I can show a teen number, like 13, as one full ten and some more ones.
- I can explain why 10 and 4 make the number fourteen.
Standards this unit teaches
- K.OA.A.3Common Core (US)Decompose numbers within 10
Break apart numbers up to 10 into pairs of smaller numbers in more than one way, recording each as a drawing or equation.
- K.OA.A.4Common Core (US)Make 10 from any number
Find the number that makes 10 when added to a given number from 1 to 9, using objects or drawings.
- K.NBT.A.1Common Core (US)Numbers 11 to 19 as tens and ones
Break numbers from 11 to 19 into a group of ten and some further ones to build place value sense.
- AC9MFN03Australian Curriculum v9 (ACARA)Part-part-whole to 10 (Foundation)
Split and join collections of up to ten using part-part-whole thinking, naming the two parts that make the whole.
- AC9M1N02Australian Curriculum v9 (ACARA)Place value and the role of zero (Year 1 bridge)
Partition, regroup and rename two- and three-digit numbers in different ways. ACARA formalises the tens-and-ones split at Year 1, so this Kindergarten unit reaches toward that Year 1 descriptor.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Decompose
- break a number apart into two smaller parts
- Part-whole
- the whole is the total, the parts are the smaller groups that add up to it
- Partner to 10
- the number that, added to a given number, makes exactly 10
- Ten-frame
- a 2 by 5 grid used to show a number by how many boxes are filled
- Teen number
- one of the numbers from 11 to 19, each made of one ten and some more ones
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Breaking a number into two parts
ConcreteTake 8 counters and split them into two groups any way you like. Maybe 5 in one hand and 3 in the other. Both groups together are still 8, because you did not add or take any away, you only rearranged them. Say it as a sentence: 8 is 5 and 3.
The same number can be split more than one way. Split the same 8 counters again, differently: 6 and 2. Still 8 altogether. Split it again: 4 and 4. Every split is a valid way to break 8 into two parts, and finding several different splits for the same number is exactly what this section practises.
Record each split as a small drawing or as an equation, such as 8 = 5 + 3, so the split is not just something you did with your hands but something you can also write down and remember.
Split 7 counters into two parts in two different ways.
- First way: 4 in one group and 3 in the other. Check: 4 and 3 together is 7.
- Second way: 6 in one group and 1 in the other. Check: 6 and 1 together is 7.
- Both splits are correct because both pairs of parts make the same whole, 7.
Answer: 7 = 4 + 3, and also 7 = 6 + 1 (there are other correct splits too, such as 5 + 2).
- Split 6 counters into two parts. Now split the same 6 counters a different way. Are both splits correct?
- If one part of 9 is 4, what must the other part be?
2. Finding the partner that makes 10
PictorialOut of every possible split, one matters more than the rest: the partner to 10. Given a number from 1 to 9, the question is always the same: how many more to reach 10? A ten-frame makes this visible. Fill 6 boxes of a 2 by 5 ten-frame, and the 4 empty boxes are exactly how many more you need, because 6 and 4 together fill all 10 boxes.
Learning every partner to 10 by heart, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, is one of the most valuable things a young learner can do, because so much later addition and subtraction leans on bridging through 10.
What number makes 10 when added to 7?
- Picture a ten-frame with 7 boxes filled.
- Count the empty boxes: there are 3 left.
- 7 and 3 together fill all 10 boxes.
Answer: 3, because 7 + 3 = 10.
- What number makes 10 when added to 2?
- What number makes 10 when added to 5?
3. Teen numbers: one ten and some more ones
PictorialFill a whole ten-frame, all 10 boxes, and then add a few loose counters beside it. If you add 3 more counters next to the full ten-frame, you have 10 and 3 more, which is the number 13. Every number from 11 to 19 works exactly this way: one full ten plus some extra ones.
This is the very first taste of place value. The full ten-frame stands for one ten. The loose counters beside it are the extra ones. So 16 is one ten and 6 ones, and 19 is one ten and 9 ones, right up to the edge of a second full ten.
The number words can be tricky here, because thirteen says three before it says ten, in the opposite order to how the number is built. Keep the full ten-frame in view and count the extra ones out loud every time: ten... eleven, twelve, thirteen, so 13 is ten and three more.
Show 17 as a ten and some more ones.
- Fill one whole ten-frame: that is 10.
- Count out loose counters beside it until you reach 17: 11, 12, 13, 14, 15, 16, 17, which is 7 more counters.
- 17 is 1 ten and 7 ones.
Answer: 17 = 10 + 7, one ten and 7 more ones.
- How many tens and how many more ones are in 12?
- Which number is one ten and 9 more ones?
Common misconceptions and how to address them
MisconceptionWhen splitting a number into parts, the child believes only one split is correct, and rejects a different but equally valid split of the same number.
Why it happens: Early practice often shows just one example split per number, so the idea that many different splits can all be correct is not yet secure.
How to address it: Split the very same group of counters two or three different ways in a row, checking each time that both parts still add back to the same whole. Say clearly: there is more than one right answer.
MisconceptionFinding the partner to 10, the child counts the filled boxes again instead of counting the empty ones, and gives the wrong partner.
Why it happens: The habit of counting what is there (the filled boxes) is stronger than the newer skill of counting what is missing (the empty boxes).
How to address it: Physically point to and count only the empty boxes, ignoring the filled ones during that count. Say: I already know the filled part, I am hunting for the missing part.
MisconceptionA teen number is read backward, so 13 is thought to be 3 tens and 1 one, because the word 'thirteen' says the ones part first.
Why it happens: The number word order (three before ten in 'thir-teen') does not match the place value order (tens digit first), which is genuinely confusing for a beginner.
How to address it: Always build the ten-frame first and fill it completely before adding the extra ones, so the physical ten always comes first no matter what order the word says it in.
MisconceptionThe child thinks decomposing a number changes how many there are, so splitting 8 into 5 and 3 feels like it makes fewer than 8 altogether.
Why it happens: Splitting looks like something is being taken away, especially if the two parts are physically moved apart.
How to address it: After every split, push the two parts back together and recount to show the whole is unchanged: 5 and 3 pushed together is still 8, exactly what you started with.
Guided practice (with answers)
1. Split 9 into two parts. Give one way.
Answer: Any correct pair that makes 9, such as 6 and 3, or 5 and 4.
2. What number makes 10 when added to 4?
Answer: 6, because 4 + 6 = 10.
3. What number makes 10 when added to 8?
Answer: 2, because 8 + 2 = 10.
4. Show 15 as a ten and some more ones.
Answer: 15 is 1 ten and 5 ones, because 10 + 5 = 15.
5. One part of 7 is 2. What is the other part?
Answer: 5, because 2 and 5 together make 7.
6. How many tens and ones are in 19?
Answer: 1 ten and 9 ones, because 10 + 9 = 19.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Number bonds practise splitting and making 10, and the Kindergarten addition worksheet ties the parts back to a written equation.
Differentiation
- Stay with numbers to 5 for splitting practice before moving to numbers up to 10.
- Always use a physical ten-frame so the 10 boxes make missing-partner counting visible rather than mental.
- Build every teen number with a full ten-frame and loose counters before writing the number down.
- Give one split as an example and ask only for a second, different split, rather than starting from a blank page.
- Find every possible split of a number, such as all 5 ways to split 10 (1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5), and check none is missing.
- Play a fast partners-to-10 game: call a number from 1 to 9, the child says the partner instantly, no counting.
- Extend the ten-and-more idea past 19: show 24 as two tens and 4 more, as a bridge toward Grade 1 place value.
- Pose a missing-part word problem: there are 10 seats, 6 are full, how many are empty?
Assessment: exit ticket
A three-question exit ticket for the last five minutes, sampling a split, the partner to 10, and a teen number.
1. Split 6 into two parts.
Answer: Any correct pair, such as 4 and 2, or 3 and 3.
2. What number makes 10 when added to 3?
Answer: 7, because 3 + 7 = 10.
3. How many tens and ones are in 18?
Answer: 1 ten and 8 ones, because 10 + 8 = 18.
Teacher notes and timings
- Rough timing across four lessons: Lesson 1 decomposing numbers within 10 (section 1), Lesson 2 finding the partner to 10 (section 2), Lessons 3 to 4 teen numbers as a ten and some more (section 3) plus the exit ticket.
- These three standards sit together deliberately: decomposing numbers and making 10 are the same skill (part-whole splitting), and once making 10 is secure, seeing 11 to 19 as 10 plus a leftover part is a short, natural next step rather than a new idea.
- Language to keep saying: how many more to make 10, and one ten and some more ones. Both phrases pre-empt the most common slips in this unit.
- Curriculum note: US Kindergarten states decomposing within 10 (K.OA.A.3), making 10 (K.OA.A.4) and teens as ten-and-ones (K.NBT.A.1) as three separate standards. ACARA Foundation (AC9MFN03) covers part-part-whole to 10 as a single Foundation descriptor, and formalises the explicit tens-and-ones split one year later at Year 1 (AC9M1N02), so this unit reaches slightly ahead of the Foundation year for its teen-number section.
- Present mode and print both work: use the Print button for a student worksheet, or project the page and fill a real or on-screen ten-frame together as a class.