Mathematics Tutor Singapore | Primary 1 Make Ten

Mathematics Tutor Singapore | Primary 1 Maths tuition is often considered when a child counts carefully on their fingers but becomes uncertain as soon as an addition question changes its wording. I do not begin by asking the child to become faster. I ask whether they can see a whole number as two parts, and whether those parts can be rearranged without changing the total.

Number bonds, ten-frames and make-ten addition are more than beginner tricks. They teach children to decompose quantities, choose efficient calculations and reverse addition through subtraction. A child who can explain why 9 + 6 equals 10 + 5 has discovered a conservation idea that will still matter in Primary problem sums, fractions and Secondary algebra.

In this guide I work through Primary 1 number bonds, make-ten and subtract-from-ten strategies, compare three common word-problem structures and show how parents can check progress without turning early Mathematics into a daily race. The learning scope is consistent with the current MOE Primary Mathematics syllabus, and the examples are original.

Explore Primary 1 Mathematics teaching chapters

Number bonds are part–whole relationships
Why ten is such a helpful landmark
Worked example: make ten when adding 9 + 6
Another route for 8 + 7
Subtraction as undoing a relationship
Missing-number sentences and the equal sign
More than, fewer than and comparison stories
From a ten-frame to mental strategies
Seven early-primary mistakes worth diagnosing
Fourteen P1 make-ten and number-bond problems
A one-week family practice routine
When Primary 1 Mathematics tuition is genuinely useful
Primary 1 to PSLE and later Mathematics
Frequently asked parent questions
MOE syllabus, trusted learning routes and support

Number bonds are part–whole relationships

If seven counters are on a table and three are blue, four are not blue. We can describe the total as 7 = 3 + 4. The same seven counters might be divided into five and two, or six and one. None of those decompositions creates or loses a counter. They describe the same whole in different ways.

A number bond is the relationship between a whole and its parts. In Primary 1, building secure number bonds for numbers up to ten makes many later addition and subtraction calculations easier. Instead of counting every object anew, the child can see five and three as a total of eight.

Whole	Two parts	Check
7	3 and 4	3 + 4 = 7
8	5 and 3	5 + 3 = 8
9	6 and 3	6 + 3 = 9
10	4 and 6	4 + 6 = 10
10	7 and 3	7 + 3 = 10

The whole stays fixed even when the parts are grouped differently.

I would lay out eight small counters and ask a child to cover some with a sheet of paper. If five remain visible, how many are hidden? Three. Now reveal the hidden group so the child can check. This makes a missing-number question concrete without handing the answer to them.

Number bonds are not only lists to memorise. The important underlying idea is that knowing the whole and one part lets us recover the other part. That idea will later be used with money, time, ratios and algebraic unknowns.

Why ten is such a helpful landmark

Our place-value system groups in tens, so the number ten makes an efficient anchor for calculations within twenty. A ten-frame is a rectangle containing ten equal positions, often shown as two rows of five. When a learner sees nine occupied positions, they can recognise that exactly one more makes ten.

This recognition is useful because adding one to nine is easier than recounting ten items one by one. Once the child sees “nine needs one to become ten”, a question such as 9 + 6 can be reorganised. The six contains one and five, so one completes the ten and five remain.

I ask the learner to move a real counter rather than merely watch a teacher draw an arrow. When the child transfers one counter from the six-group into the nine-group, the two groups become ten and five. The overall number of counters is still fifteen.

Represent a group of ten using a ten-frame or ten counters.
Identify the complement of ten: 9 needs 1, 8 needs 2 and 7 needs 3.
Split the second addend into the amount needed to make ten and a remainder.
Regroup without increasing or decreasing the combined total.
Check the answer by counting once or by using a related subtraction fact.

The child should eventually be able to imagine the frame rather than physically draw it for every example. Concrete objects are a bridge to independence, not a requirement that the learner always carry counters to a test.

Worked example: make ten when adding 9 + 6

Here is the full process I would teach. Start with nine counters and six more. Nine needs one to become ten. Break six into one and five. Move the one into the group of nine, leaving a group of five. Now 9 + 6 = 9 + 1 + 5 = 10 + 5 = 15.

Step	Representation	Reason
Begin	9 + 6	Two groups of counters
Identify missing part	9 + 1 = 10	One makes the next ten
Split six	6 = 1 + 5	The original group is conserved
Regroup	(9 + 1) + 5	Combine a convenient pair first
Answer	10 + 5 = 15	Total unchanged
Check	15 − 6 = 9	Related inverse fact

The split is valid because one and five together are the original six.

A child who writes 9 + 6 = 10 + 6 = 16 may have made ten but failed to remove the one from the six-group. They effectively counted that transferred counter twice. I call this a conservation error rather than a simple careless mistake, and I ask the learner to show exactly where the one came from.

A second child may choose to count on six steps from nine: ten, eleven, twelve, thirteen, fourteen, fifteen. Counting on is valid, especially early in learning. The goal is to develop a more flexible strategy for larger calculations, not to shame the child for using a method that still works.

Another route: 8 + 7

Eight needs two to make ten, so we split seven into two and five. The calculation becomes 8 + 7 = (8 + 2) + 5 = 10 + 5 = 15. The learner can place two counters into the two empty positions of an eight-filled ten-frame.

Notice that both 9 + 6 and 8 + 7 give fifteen. The different starting groups do not matter because each pair rearranges to ten and five. This invites a useful pattern conversation: to keep the same total, increasing one addend by one requires decreasing the other by one.

Expression	Make ten	Same total
9 + 6	10 + 5	15
8 + 7	10 + 5	15
7 + 8	10 + 5	15
6 + 9	10 + 5	15

Rearranging part sizes can preserve a fixed total.

For a learner ready for a challenge, I might ask for another pair that totals fifteen without supplying the numbers. If the child offers ten and five, eleven and four, or twelve and three, they have begun to generalise the relationship. We can choose which pairs are suitable for their current Primary One number range.

Subtraction as undoing a relationship

Subtraction is not only counting backwards. It can recover a missing part. Consider 15 − 6. If the child already knows 9 + 6 = 15, then 15 − 6 = 9. Addition and subtraction describe the same part–whole relationship from different directions.

Another approach uses ten as a landmark. To calculate 14 − 6, first subtract four to reach ten, then subtract the remaining two. That gives 14 − 4 − 2 = 10 − 2 = 8. The six has been divided into four and two, so no amount was lost or counted twice.

Problem	First move	Second move	Answer
14 − 6	14 − 4 = 10	10 − 2 = 8	8
13 − 5	13 − 3 = 10	10 − 2 = 8	8
16 − 9	16 − 6 = 10	10 − 3 = 7	7
12 − 7	12 − 2 = 10	10 − 5 = 5	5

The subtracted quantity is divided into two parts, not enlarged.

The fragile step is often choosing the wrong remainder. If a pupil takes four away from fourteen and then subtracts six again, they have subtracted ten in total rather than the required six. I ask them to check the decomposition 6 = 4 + 2 before proceeding.

The lesson connects back to number bonds: ten is made from six and four, or seven and three. Those facts help the learner cross the ten boundary during subtraction without a long sequence of counting-back steps.

Missing-number sentences and the meaning of equals

An equal sign tells us two expressions have the same value. It does not simply mean “write the answer after this symbol”. Consider 4 + □ = 10. The box must contain six because four and six are parts of ten. Now consider 10 = □ + 4. The box is still six, even though the equation is written in a different order.

A child may become uncertain when the missing box appears at the beginning: □ − 3 = 5. We can ask which number becomes five after three are removed. It is eight, because 5 + 3 = 8. The inverse relationship makes the answer visible.

Missing-number equation	Part–whole interpretation	Answer
7 + □ = 10	What part completes ten from seven?	3
□ + 6 = 10	What part joins six to make ten?	4
10 = 2 + □	Which part joins two to equal ten?	8
□ − 3 = 5	Which whole leaves five after removing three?	8
9 = □ + 4	What part joins four to make nine?	5

The missing position changes, but equality and number bonds remain valid.

These small equations are the earliest foundations of algebraic reasoning. In Secondary school, the box may become x, but the idea has not changed: the equation imposes a relationship that must remain true.

More than, fewer than and comparison stories

A story can use numbers that look like an addition question but actually require subtraction. “Mira has nine stickers. Jo has four fewer stickers. How many does Jo have?” The answer is five. Jo’s group is smaller than Mira’s by four.

Now change the question: “Jo has five stickers. Mira has four more. How many does Mira have?” The answer is nine. Both stories involve a difference of four; the task changes which group is known. A child who always adds when they see “more” may fail a comparison question that asks for the smaller group.

I draw two short bars, one longer than the other, label the difference and ask which quantity is unknown. That representation is a gentle beginning for the model method used in upper-primary Mathematics. It is much more important that the child understands the comparison than that their drawing looks perfect.

From ten-frames to flexible mental strategies

Once children know complements of ten, we can ask whether one method is more convenient than another. For 9 + 8, making ten gives 10 + 7 = 17. For 8 + 8, doubling eight gives 16. For 8 + 9, the commutative property gives the same seventeen as 9 + 8. Different correct routes are useful.

I want students to recognise that the strategy should fit the numbers. Make-ten is excellent for nine plus a number, but it need not be compulsory for every small addition. If a child already knows 6 + 6 = 12 fluently, forcing them to split a six into four and two may be longer than using the known double.

As competence grows, the tutor can present two solutions and ask the child to compare them. The important question is not “which answer did you copy?” but “why is this shortcut true, and when would you choose it?”

Seven early-primary mistakes worth diagnosing

Mistake	Likely reason	Useful next prompt
9+6 becomes 10+6	Transferred one was counted twice	Where did the one come from?
14−6 becomes 10−6	Breaks six incorrectly across ten	How much of six was already subtracted?
10=4+□ is confusing	Equals treated as end-of-sentence symbol	Can both sides be shown with counters?
Counts every counter from one every time	Part–whole structure not recognised	Can you see five and three without recounting?
Adds when asked ‘how many fewer’	Comparison not represented	Which group is larger and by how much?
Says 8+7 differs from 7+8	Group order confused with total	Rotate or swap the two groups
Can answer only with a teacher pointing	Prompt dependency	Try one changed question alone

The teaching response should repair the precise misunderstanding.

The wrong final number is not always evidence of poor effort. A child may have counted accurately while misunderstanding what the problem asked. A useful tutor watches the learner’s method, not only the score.

Fourteen P1 number-bond and make-ten questions

1. Complete ten

Seven plus what equals ten? Three, because 7 + 3 = 10.

After solving, ask the child to explain which two parts form the whole and to verify with objects or an inverse calculation. If they succeed only with the exact same numbers, offer a small changed example on another day.

2. Complete another ten

Eight plus two equals ten. Two is the complement of eight.

3. Add nine and four

9 + 4 = 9 + 1 + 3 = 10 + 3 = 13.

4. Add nine and seven

9 + 7 = 9 + 1 + 6 = 10 + 6 = 16.

5. Add eight and five

8 + 5 = 8 + 2 + 3 = 13.

6. Add seven and six

7 + 6 = 7 + 3 + 3 = 13.

7. Subtract across ten

12 − 5 = 12 − 2 − 3 = 7.

8. Subtract from fourteen

14 − 6 = 14 − 4 − 2 = 8.

9. Use an inverse bond

□ + 6 = 15. The missing part is 9 because 9 + 6 = 15.

10. Find a missing whole

□ − 4 = 7. The whole is 11 because 7 + 4 = 11.

11. Recognise commutativity

6 + 9 and 9 + 6 both equal fifteen.

12. Compare groups

Mina has eight beads, Leo has five. Mina has three more beads.

13. Two-step expression

3 + 7 + 5 = 10 + 5 = 15. Choose the ten-making pair first.

14. Check by subtraction

For 8 + 7 = 15, the check 15 − 7 = 8 confirms the original sum.

A one-week family practice routine

Day	Gentle practice	What to notice
1	Ten-frame with 5–10 counters	Recognises complements of ten
2	Missing part of ten	Finds a bond without recounting
3	9 plus another one-digit number	Moves exactly enough to make ten
4	8 plus a number	Decomposes the second addend
5	Subtract through ten	Tracks both subtracted parts
6	Short comparison story	Identifies larger and smaller group
7	Mixed game after a pause	Explains without a prompt

Short sessions can be preferable to one long drill, depending on the child.

For many Primary 1 learners, a few minutes of deliberate practice can be useful; others may need more repetition or a different pace. Parents do not need to reproduce school every evening. A small set of counters, a ten-frame and one genuine conversation can provide helpful practice without unnecessary pressure.

It can be useful to end while the child is still engaged, not only after they are exhausted. Early mathematical confidence grows through understanding and manageable successes rather than speed contests.

When Primary 1 Mathematics tuition is genuinely useful

Extra tuition is not automatically necessary for every Primary 1 child. If the learner follows school lessons, enjoys numbers and can explain ordinary addition with reasonable support, school teaching and home conversation may be sufficient.

Where persistent uncertainty remains, a tutor can observe whether the problem is counting, recognising groups, understanding the equals sign, reading a word problem or choosing an operation. The appropriate lesson is determined by that observation.

Ask the child to show an existing strategy before demonstrating a new one.
Use physical objects when they clarify a new part–whole relationship.
Reduce prompts over time rather than supplying them throughout every worksheet.
Use short changed-number questions to check whether the idea transfers.
Coordinate with the child’s actual Primary 1 classwork and MOE syllabus.
Keep workload appropriate to age, rest, reading and play.
Avoid promising an eventual PSLE achievement level from an early-primary test.

How a number bond prepares the later Mathematics journey

The Primary 1 relationship 9 + 6 = 15 can later become the missing-number equation 9 + □ = 15 and, eventually, a Secondary algebraic relationship 9 + x = 15. The symbol changes, but the truth that a whole can be decomposed and reconstructed remains.

Make-ten strategies also underpin place value and regrouping. Fractions later ask students to split a whole into equal parts; ratio compares multiple parts; percentages use a named whole as one hundred per cent. A child does not have to study those advanced ideas in Primary 1, but number sense provides a foundation on which they will rest.

The long-term goal is not to accelerate immediately into upper-primary worksheets. It is to make the present mathematics clear enough that later learning has something solid to attach to.

Frequently asked parent questions

Should every Primary 1 learner enrol in Maths tuition?

No. Many children learn well through school teaching and manageable home support. Consider extra help when a persistent specific learning gap is visible.

Why does my child count on fingers?

Finger counting can support early number sense. The teaching goal is gradually recognising number bonds and more efficient structures, not simply banning fingers.

What does make ten mean?

Split an addend so part completes the first number to ten, then add the remainder, preserving the combined total.

Why is 9+6 not 10+6?

The one moved to complete ten came from the original six, so only five remain. Keeping all six would count one item twice.

Does the equal sign mean the answer comes next?

No. It means both expressions have equal value, so 10=4+6 is as valid as 4+6=10.

How much daily practice is enough?

There is no universal quota. Brief, engaged practice and an independent explanation can be more valuable than long repetitive worksheets.

What should I ask a prospective tutor?

Ask how they distinguish number-bond misunderstanding from word-problem comprehension or arithmetic fluency, and how they remove prompts over time.

Will an early head start guarantee top PSLE results?

No. Learning develops across many years and topics. Secure understanding now matters more than unsupported future-grade promises.

MOE syllabus, trusted learning routes and support

The MOE Primary Mathematics syllabus updated October 2025 includes number bonds up to ten, addition and subtraction, and make-ten or subtract-from-ten strategies within Primary 1. Use the learner’s school sequence to guide the amount and timing of practice.

Continue through the Mathematics Learning Hub. For wider place-value reasoning, read P1–P4 Maths Foundations Before Speed. For the next equal-group step, use Primary 2 Multiplication and Division Word Problems. These articles are distinct: this lesson owns number bonds and make-ten reasoning in early Primary 1.

The unchanged Secondary 1 Mathematics Tutor Clementi | Small Groups Tutorials shows a later example of targeted small-group Mathematics teaching. To ask about a child’s actual early-primary learning needs, arrange a parent–student consultation and bring a correct number bond plus a changed-wording question that the child found difficult.

Mathematics Tutor Singapore | Primary 1 Number Bonds and Make-Ten Addition