Making Ten | Primary 1 Mental Addition Strategy

Eight plus five.

A Primary 1 learner can solve it by counting five steps forward from eight:

9, 10, 11, 12, 13.

That works.

But there is another route.

Eight is close to ten. It needs two.

Five can be split into two and three.

So:

8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.

Nothing magical happened. No shortcut changed the mathematics.

The learner simply reorganised the same quantity around a more useful landmark.

Making ten is not really a trick for addition. It is an early lesson in choosing a better representation.

That is why the strategy matters far beyond one-digit sums. It teaches children to notice structure, decompose numbers deliberately, use the base-ten system and recombine quantities without changing their value.

Those are habits that continue through mental arithmetic, place value, regrouping, decimals, percentages, algebra and problem solving.

The quick answer: what does “make ten” mean?

The make-ten strategy solves an addition problem by first completing one addend to 10.

For 9 + 6:

9 needs 1 to make 10.
Split 6 into 1 and 5.
Combine 9 and 1.
Then add the remaining 5.

So:

9 + 6 = 10 + 5 = 15.

The strategy is sometimes called bridging through ten, making a ten, or decomposing to ten.

Different names point to the same structure: use a number bond to complete 10, then add what remains.

Why ten is such a powerful landmark

Our everyday number system is base ten.

Ten ones make one ten. Ten tens make one hundred. Place-value notation is organised around powers of ten.

That means 10 is not just another number between 9 and 11. It is a structural boundary.

Compare the mental effort in these two expressions:

8 + 5
10 + 3

They have the same value when the 5 has been split correctly, but 10 + 3 is easier to see because the place-value structure is transparent.

The strategy therefore uses a general mathematical principle:

If two forms have the same value, choose the form that makes the useful structure easier to see.

Primary 1 learners meet this principle through small numbers. Older learners use the same idea when they rewrite 49 as 50 − 1, 0.25 as 1/4, or a quadratic expression in factored form.

Making ten depends on earlier knowledge

A learner cannot use the strategy reliably just because an adult demonstrates the steps.

Several prerequisite ideas must already be available.

1. The learner must recognise quantities

If 8 is still eight separate objects that must be recounted from one, the learner has more cognitive work to do before reorganising it efficiently.

2. The learner must know bonds to 10

The child needs relationships such as 9 + 1, 8 + 2, 7 + 3, 6 + 4 and 5 + 5.

3. The learner must be able to decompose the second addend

To solve 8 + 5, knowing that 8 needs 2 is not enough. The learner must also split 5 into 2 and 3.

4. The learner must understand that decomposition does not change the total

Five is still five when it becomes 2 + 3.

5. The learner must understand teen numbers

After making 10, the learner needs to recognise 10 + 3 as 13, 10 + 5 as 15, and so on.

This dependency chain explains why “make ten” sometimes feels impossible to a child even after many demonstrations. The visible step may not be the broken step.

The ten-frame shows the strategy before symbols do

Place eight counters on a ten-frame.

Two spaces are empty.

Now place five counters beside the frame.

Move two of those five counters into the empty spaces.

The frame is full. Ten has been made. Three counters remain outside.

The learner can see:

8 + 5 became 10 + 3.

The physical movement represents the decomposition:

5 = 2 + 3.

The ten-frame therefore does several jobs at once. It makes the complement to ten visible, shows why the addend is split, preserves the total quantity, and reveals the teen number as ten plus some ones.

This is why a representation can be powerful when it is connected explicitly to the mathematics. The frame should not become another object to manipulate without explanation.

Worked example 1: 9 + 4

Ask first:

What does 9 need to make 10?

Answer: 1.

Can 4 be split into 1 and something?

Yes: 4 = 1 + 3.

Therefore:

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

The child has not added extra value. Four was simply reorganised.

Worked example 2: 7 + 6

Seven needs 3 to make ten.

Split 6 into 3 and 3.

7 + 6 = 7 + 3 + 3 = 10 + 3 = 13.

Notice something interesting: 7 + 6 and 8 + 5 both become 10 + 3.

Different starting sums can be reorganised into the same benchmark form.

This is an opportunity to ask a deeper question:

What was preserved when the calculation was rewritten?

The total value.

Worked example 3: 6 + 8

A learner may make ten from the first addend:

6 needs 4, so split 8 into 4 + 4.

6 + 8 = 6 + 4 + 4 = 10 + 4 = 14.

But addition is commutative, so the learner could also think:

8 needs 2, split 6 into 2 + 4.

8 + 6 = 8 + 2 + 4 = 10 + 4 = 14.

Both are correct.

This matters because mathematics should not teach children that there is always one authorised mental route. The learner should gradually choose the route that is easiest to see and explain.

Why counting on is still useful

Making ten is powerful, but it should not replace every other mental strategy.

For 9 + 2, counting on two steps may be perfectly efficient:

10, 11.

For 6 + 6, a known double may be faster.

For 7 + 8, a learner might use a near-double:

7 + 7 = 14, so 7 + 8 = 15.

Or make ten:

8 + 2 + 5 = 15.

Both are legitimate.

The long-term goal is strategy flexibility: recognising the structure of the numbers and selecting a sensible method.

A learner who mechanically applies make ten to every sum has learned a procedure. A learner who knows when make ten is useful has begun to learn mathematics.

The hidden role of number bonds

Make ten is built from two decompositions.

Take 8 + 5.

First bond:

8 + 2 = 10.

Second bond:

5 = 2 + 3.

Then the remaining quantity is recombined:

10 + 3 = 13.

If any one of those relationships is weak, the strategy becomes slow or error-prone.

This is why repeatedly demonstrating the final algorithm may not help a struggling learner. The repair may need to happen one layer earlier.

The hidden role of teen-number place value

After the learner makes ten, another piece of knowledge is required.

10 + 4 must be recognised as 14.

10 + 7 must be recognised as 17.

If a child sees 14 only as a memorised word in the counting sequence, then making ten does not simplify the calculation as much as expected.

The learner needs to understand:

14 = one ten and four ones.

That is why make-ten strategy and teen-number place value belong close together conceptually.

The associative property is present even if Primary 1 never names it

When we rewrite:

8 + 5

8 + (2 + 3)

and then regroup it as

(8 + 2) + 3,

we are relying on a property of addition: changing the grouping does not change the sum.

A Primary 1 child does not need the phrase “associative property” in order to use the relationship meaningfully.

But adults should understand that the method is mathematically principled. We are not teaching children to manipulate numbers arbitrarily. We are teaching a lawful reorganisation of addition.

A common error: the child takes from the wrong number

Consider 8 + 5.

The learner knows “8 needs 2” but then writes:

8 + 2 + 5 = 15.

The child has created an extra 2 instead of taking the 2 from the original 5.

This is not merely a careless arithmetic error. It may show that decomposition is not yet understood.

The repair is to make conservation visible.

Start with five counters. Move two to join the eight. Ask how many of the original five remain.

The learner should see:

5 did not become 2 + 5. It became 2 + 3.

The total addend is conserved.

Another common error: making ten but forgetting the remainder

A learner solves 8 + 5 by moving two counters to make ten, then answers 10.

The child understood the first goal but lost the remaining three.

This can happen when the procedure is remembered as “make ten” rather than “reorganise the whole sum around ten”.

Ask the learner to account for every original counter.

Where are the eight?

Where are the five?

Which two moved?

Which three remained?

What is the final total?

Concrete accounting repairs a symbolic shortcut that has become detached from meaning.

A third error: choosing an incorrect complement to ten

If a learner thinks 7 needs 2 to make ten, every later step will fail even if the procedure is followed perfectly.

That error belongs to the ten-bond layer.

Return to a ten-frame or finger pattern. Show seven filled places and three empty places. Vary the representation until 7 + 3 = 10 becomes a relationship the child can reconstruct, not merely a phrase to memorise.

Then retest make ten.

This is what diagnostic teaching looks like: repair the earliest broken dependency instead of repeating the final procedure louder.

A fourth error: the learner can do the worksheet but not the story problem

A child may complete twenty make-ten equations accurately and still fail to use the strategy when addition is embedded in language.

For example:

Amir has 8 marbles. His sister gives him 5 more. How many marbles does he have now?

Before any strategy can operate, the learner must recognise that the quantities are being joined and that the question asks for the new total.

Only then does 8 + 5 appear.

Transfer therefore requires more than arithmetic fluency. The learner must move from words to a mathematical representation, then choose a strategy.

A simple diagnostic decision tree

If a learner struggles with 8 + 5, do not immediately assign ten more examples of 8 + 5.

Can the child represent 8 and 5 accurately? If not, return to quantity and counting.
Does the child know what 8 needs to make 10? If not, repair bonds to ten.
Can the child split 5 into 2 and 3? If not, repair decomposition.
Can the child see that the 2 comes from the 5? If not, repair conservation of quantity.
Can the child combine 10 and 3 as 13? If not, repair teen-number place value.
Can the child record the steps correctly? If not, work on symbolic representation.
Can the child use the idea in a word problem? If not, work on translation and method selection.

One wrong answer can therefore correspond to several different learning needs.

When should the ten-frame disappear?

Not on a predetermined date.

The representation should fade when the learner can reconstruct the same structure mentally.

A useful progression is:

move actual counters;
look at a completed ten-frame;
draw the ten-frame;
write the number split;
say the split aloud without drawing;
solve mentally;
explain the mental route afterwards.

If removing the frame causes the reasoning to collapse, the representation was still carrying part of the thinking.

That is useful information, not a reason for embarrassment. Restore enough support for the learner to succeed, then fade again gradually.

Making ten should eventually become invisible

When fluency develops, an adult may no longer hear every intermediate step.

The learner sees 9 + 7 and answers 16.

If asked, the child may explain:

“I moved one from seven to nine. Ten and six is sixteen.”

That compressed explanation is a sign that the strategy is becoming internalised.

The goal is not to force the learner to write every decomposition forever. Written steps are useful while the structure is being built or when working needs to be communicated. Mental fluency eventually allows some intermediate work to be carried internally.

From 8 + 5 to 28 + 5

Once the learner understands place value, the same idea scales.

28 + 5.

Twenty-eight needs two to make thirty.

Split 5 into 2 and 3.

28 + 5 = 28 + 2 + 3 = 30 + 3 = 33.

Now the useful landmark is 30 rather than 10, but the reasoning is the same.

This is an important transfer. The child should eventually see make-ten as part of a broader family of make-a-friendly-number strategies.

From 48 + 7 to 50 + 5

Forty-eight needs two to make fifty.

Seven becomes two and five.

48 + 7 = 50 + 5 = 55.

The child is now using benchmark completion at a different scale.

Later, an adult may calculate 398 + 27 by making 400 first. The Primary 1 strategy has not disappeared. It has grown up.

Making ten and subtraction

The benchmark idea also helps with subtraction, although subtraction requires careful attention because the structure differs.

Consider 13 − 5.

One route is to subtract 3 to reach 10, then subtract the remaining 2:

13 − 5 = 13 − 3 − 2 = 10 − 2 = 8.

The learner decomposes 5 into 3 and 2 because 13 is three above ten.

Another learner may use the inverse relationship: 8 + 5 = 13, so 13 − 5 = 8.

Again, several valid strategies may coexist. The important question is whether the child understands the quantities and can justify the route.

A practice sequence that builds meaning before speed

Phase 1: complements to ten

Ask: “What does 6 need to make 10?” Use fingers, frames and objects until the relationship is clear.

Phase 2: decomposition

Ask learners to split numbers in several ways: 5 as 1 + 4, 2 + 3, 3 + 2 and so on.

Phase 3: concrete make ten

Move counters physically into a ten-frame.

Phase 4: pictorial make ten

Use drawings, frames or number-bond diagrams without movable counters.

Phase 5: symbolic recording

Write 8 + 5 = 8 + 2 + 3 = 13, making the decomposition explicit.

Phase 6: mental use

Present varied sums and ask the learner to choose a method.

Phase 7: transfer

Move to word problems and then to numbers such as 28 + 5 or 48 + 7 when place-value understanding is ready.

What parents can ask instead of “What is the answer?”

Which number is closer to ten?
How many does it need?
Can you split the other number to give it that amount?
Where did the remaining part go?
Can you show the same idea on a ten-frame?
Can you solve it a different way?
Which way feels easier, and why?
How can you check that you did not change the total?

These questions make the child explain structure rather than perform for the adult.

What tutors should record diagnostically

A useful lesson note is more precise than “weak at addition”.

Record which layer is secure:

quantity recognition;
counting on;
number bonds within 10;
complements to ten;
decomposition of the second addend;
conservation of the original total;
teen-number place value;
symbolic recording;
strategy selection;
transfer into word problems.

This turns “addition difficulty” into a repairable map.

What making ten can reveal — and what it cannot

A make-ten task can reveal whether a learner coordinates several early number ideas. It can show whether the child recognises ten partners, decomposes quantities and uses teen-number structure.

It cannot, by itself, tell us why all mathematics is difficult for a learner. It does not diagnose a clinical condition, and one slow performance does not prove a general weakness.

A tired child, an unfamiliar representation, weak language comprehension or simple inexperience can all affect performance.

Use repeated evidence across conditions before drawing broader conclusions.

How do we know this strategy matters?

The make-ten strategy is well established in mathematics education as a derived-fact strategy that exploits base-ten structure.

The Institute of Education Sciences’ Assisting Students Struggling with Mathematics practice guide gives make-a-10 as an important example of a derived addition strategy. The guide explains that successful use depends on knowing the partner that completes ten and on being able to break an addend into parts.

The Education Endowment Foundation’s early-mathematics evidence resources also illustrate bridging through ten using counters and ten-frames, while emphasising the need to connect manipulatives to the abstract idea they represent.

The broader early-mathematics evidence base emphasises developmental progressions, composition and decomposition, and multiple representations. None of this means every learner must use make ten for every addition fact. The evidence supports teaching useful strategies and underlying structure, not replacing mathematical judgement with one compulsory routine.

For Singapore curriculum context, the MOE Primary Mathematics syllabus places Primary 1 learners inside a wider programme of whole numbers, tens and ones, addition and subtraction, mental calculation, mathematical processes and problem solving.

A Primary 1 make-ten readiness checkpoint

Can the learner identify what 9 needs to make 10?
What 8 needs?
What 7 needs?
Can the learner split 5 into 2 and 3 without changing its value?
Can the learner split 6 into 3 and 3, or 4 and 2?
Can the learner show 8 + 5 with counters?
Can the learner move only two of the five counters to complete ten?
Can the learner explain why three remain?
Can the learner read 10 + 3 as 13?
Can the learner write the equation?
Can the learner solve a similar sum without the frame?
Can the learner choose another strategy when it is easier?

The final item matters. Strategy ownership is stronger than strategy obedience.

The deeper mathematics: preserve value, change form

Making ten teaches an idea that becomes increasingly important as mathematics becomes more abstract.

We can transform an expression without changing what it is worth.

8 + 5 becomes 10 + 3.

48 + 7 becomes 50 + 5.

199 + 36 can become 200 + 35.

Later, 25 × 16 can be reorganised as 100 × 4. An algebraic expression can be factorised. A fraction can be renamed with an equivalent denominator. A coordinate problem can be translated into an equation.

The surface changes so the structure becomes easier to use.

That is a major mathematical habit.

Do not alter the value. Alter the representation until the useful structure becomes visible.

Primary 1 learners first meet that habit with numbers small enough to hold in their hands.

Where this leads next

Once making ten is secure, the next conceptual question is why expressions such as 10 + 4 are so easy to read.

The answer is place value.

Fourteen is not merely the fourteenth word in a counting chant. It is one ten and four ones.

That understanding turns the make-ten landing point into a genuine base-ten structure.

It also prepares the learner for larger two-digit calculations, where friendly tens such as 20, 30, 40 and 50 become new landmarks.

For the wider Primary 1 map, see Understanding Primary 1 Mathematics and eduKateSG’s How Mathematics Works resources.

Final thought

There is a moment when 8 + 5 stops looking like two inconvenient numbers.

The learner sees something else:

Eight is almost ten.

Five contains the two that eight needs.

Ten and three is thirteen.

The answer has not become easier because the child memorised a magic instruction.

It became easier because the child learned to see a better structure.

Making ten is the first great lesson in mental arithmetic: when a problem is awkward, reorganise it around something you understand well.

Making Ten: The Mental Addition Strategy Every Primary 1 Learner Needs