P2 Missing Number Sums & Number Bonds

For a Primary 2 missing-number sum, identify which quantity is the whole and which is the unknown part before choosing an operation. If □ + 48 = 125, the missing part is 125 − 48 = 77. Check it by substituting the answer: 77 + 48 = 125. The box is not an instruction to add every number printed on the page.

Singapore Primary 2 pupils no longer have formal school examinations or weighted assessments under MOE’s current framework, and there is no national SEAB P2 Maths paper. This guide uses boxes, number bonds and part–whole pictures as teaching representations of the arithmetic and number relationships in the MOE syllabus—not as invented national exam formats or predictions.

Starting point: identify the whole, the known part and the missing part.
Methods: number bonds, start–change–finish diagrams, inverse operations and fact families.
Question types: unknown addends, minuends, subtrahends, factors, divisors and group counts.
Additional practice: simple money, time and picture-graph missing quantities with proper units.
Included: twenty worked solutions, thirty-six checked questions, common-error fixes and a family plan.

The syllabus basis, and why a square box is not a separate national test

The MOE Primary Mathematics Syllabus (October 2025 update) explicitly includes Primary Two addition and subtraction algorithms up to three digits, mental addition and subtraction of three-digit numbers with ones, tens and hundreds, and multiplication/division within the 2, 3, 4, 5 and 10 tables. These operations form the mathematical content of the exercises here.

What is not explicitly promised is a particular future SEAB Primary 2 examination paper, a section worth a particular number of marks or a fixed number of missing-box questions. The box is a convenient representation used in classroom practice. It marks a quantity that is unknown while the relationship stays the same.

When children learn this idea, the answer may be shown with counters, number bonds, bars, number sentences or a spoken explanation. Different representations serve different learners. A diagram is useful if it shows what the numbers count; it becomes unnecessary decoration if the child draws it mechanically without linking it to the story.

Some adults describe missing-number questions as early algebra. That can be a reasonable way to discuss reasoning about unknowns, but formal equations with letters and symbolic manipulation are not the specific compulsory P2 whole-number outcome. Keep the child grounded in familiar arithmetic and meaningful units.

A number bond makes a whole and two parts visible

Place twelve counters on a table, five red and seven blue. The whole is twelve counters and the two parts are five and seven. Draw a larger circle labelled twelve, connected to two smaller circles labelled five and seven. The relationship is 5 + 7 = 12. If one small circle is covered, the missing part can be found from the whole minus the other part.

For three-digit quantities, imagine a collection of 425 items containing a known group of 180 and an unknown remainder. The number bond has the whole 425 and parts 180 and □. Subtract 425 − 180 = 245. Both parts are counted in the same unit, so 180 + 245 must return to 425.

Ask the child to name the whole before calculating. If the larger circle is mistakenly treated as one part, the operation can be chosen incorrectly even when arithmetic skills are strong. A number bond is meant to show a relationship, not to be a shape students fill in by memorised position alone.

The same relationship may be shown by a long bar divided into two adjoining sections. The whole bar is 425, the first part is 180 and the second is 245. Use whichever representation the learner can explain accurately. The mathematical content remains unchanged.

The equal sign means two expressions have the same value

A child may think an equal sign means “write the answer after this”. That habit fails when the equation is 42 = 18 + □. Instead, explain that both sides of an equality name the same amount. The missing value is 24, because 18 + 24 = 42. Turning the equation around does not change the relationship.

Compare □ + 9 = 15 with 15 = 9 + □. Both need six. A child who solves the first but treats the second as nonsensical has learnt the page layout rather than equality. Use counters to show fifteen objects split into nine and six, then read both equations aloud.

For an answer-checking routine, replace the square with the proposed value and evaluate the two sides. If they are equal, the answer fits. For example, proposing 25 in 42 = 18 + □ fails because 18 + 25 = 43. The student can catch the discrepancy independently without waiting for an adult’s tick or cross.

Keep this reasoning concrete. Equality is an important mathematical idea, but there is no need to introduce formal algebraic transformations just to teach a child that 42 and 18 + 24 describe one quantity.

Missing addends: what must join the known part?

Take □ + 48 = 125. The total 125 is known and one part is 48. The missing part is 125 − 48 = 77. When 77 replaces the square, 77 + 48 = 125, so the equation is true. The operation is subtraction because the whole and one part were given.

For 235 + □ = 400, the unknown is 165. A number line can bridge from 235 to 300 by adding 65, then from 300 to 400 by adding 100. The required increase is 65 + 100 = 165. This gives a second explanation beyond a vertical subtraction algorithm.

Reverse the layout: 400 = □ + 235. The unknown remains 165 because the whole and parts have not changed. Ask the learner what stayed constant and what changed. They should say that only the position in the written sentence changed.

One frequent mistake is to add the two visible numerals, giving 235 + 400 = 635. The problem is not necessarily calculation. It is failure to recognise that 400 is already the whole. Draw the bar and place 235 inside it, leaving the unfilled section to be found.

Missing minuends: finding the amount before something was removed

Suppose □ − 85 = 317. The original whole is missing. Since eighty-five was removed and three hundred seventeen remain, restore what was removed: 317 + 85 = 402. Check 402 − 85 = 317. A story about a cupboard of pencils can make the relationship visible.

A learner who answers 232 may have subtracted 85 from the remainder, moving backwards again instead of reconstructing the start. Ask whether the cupboard could have begun with fewer than 317 pencils if 85 were subsequently removed and no others were added. The story makes the implausibility clear.

Compare □ − 176 = 324. The missing start is 500 because 324 + 176 = 500. The fact that the total ends with zeroes does not change the operation. It may require regrouping when the student checks by subtraction, so use the corresponding three-digit algorithm guide if that is the first point of difficulty.

Another way to represent the relationship is with three labels: start, change, finish. Place the unknown in the start box, 85 in the change box and 317 in the finish box. The diagram tells the learner what to find without needing to memorise a special rule for the location of the square.

Missing subtrahends: finding what was taken away

For 500 − □ = 324, the starting amount and the remainder are known. The missing amount removed is 500 − 324 = 176. Verify by adding the removed and remaining parts: 176 + 324 = 500. The missing value should be positive and smaller than the starting total in this ordinary P2 story.

In 703 − □ = 650, the missing quantity is 53. One mental approach counts from 650 to 700, a jump of 50, and then to 703, a jump of 3. The total difference is 53. Check 703 − 53 = 650. The number line exposes the same relationship as the number bond.

A child who writes 350 for the missing value might have mixed hundreds and tens or mistaken the requested difference. Ask them to substitute 350 back into the original equation. Because 703 − 350 is not 650, the error becomes visible without an adult giving away the answer.

Keep the question in context: “A collection begins with five hundred items, some are removed, and three hundred twenty-four remain.” The square counts the removed items. The number sentence is a compact record of that story.

Four related addition and subtraction facts

Take three related quantities: 245, 180 and 425. Two addition statements are 245 + 180 = 425 and 180 + 245 = 425. Two subtraction statements are 425 − 180 = 245 and 425 − 245 = 180. All four form a fact family because they describe the same whole and two parts.

Draw one number bond for the whole 425 and parts 245 and 180, then cover a different value each time. With the whole hidden, add the parts. With one part hidden, subtract the known part from the whole. This sequence makes the choice of operation depend on the missing quantity rather than on the surface appearance of a worksheet.

A useful self-check uses the inverse operation. If 425 − 245 is believed to be 190, add 190 + 245 and see that it gives 435, not 425. The failed inverse signals a calculation mistake. The correct difference is 180.

When children work confidently, ask them to create their own fact family with three-digit numbers whose whole remains within the P2 range. They may choose 150, 275 and 425, then explain each statement. Constructing a valid family demonstrates deeper understanding than filling in an already-labelled diagram.

Equal groups and missing multiplication or division values

Imagine twenty pencils arranged in five equal groups of four. Multiplication describes the whole: 5 × 4 = 20. Division can find the number of groups when the group size is known: 20 ÷ 4 = 5. It can also find the size of each group when the group count is known: 20 ÷ 5 = 4.

For □ × 4 = 20, the missing factor is five. Ask the child to point to one group of four, then count how many groups can be made from twenty counters. The result counts groups. For 24 ÷ □ = 6, the missing divisor is four, because six groups of four total twenty-four.

For □ ÷ 3 = 8, the missing dividend is twenty-four. There must be enough items to make eight groups of three, so multiply 8 × 3 = 24. Use the P2 multiplication tables of 2, 3, 4, 5 and 10 to develop these links. A quotient can be another number, but the underlying facts should remain accessible within those tables.

Do not treat the numerical answer as the whole story. Five groups is different from five items in each group. A child can calculate 20 ÷ 4 correctly yet answer the wrong question if the unit is omitted. Label the drawing and say what the unknown counts.

Comparison word problems with the unknown in a different place

“Mei has 28 more stickers than Eli, who has 135” asks for Mei’s amount. Add 135 + 28 = 163. “Mei has 163 stickers, 28 more than Eli” asks for Eli’s amount. Subtract 163 − 28 = 135. The word “more” appears in both versions, but the operation differs because the unknown moved.

A comparison bar can show Eli’s amount as the shorter bar and Mei’s as a longer bar with an additional segment of twenty-eight. The gap is not a second collection belonging to someone else; it is the difference between the two totals. This is why the correct drawing matters.

In empty-box notation, the two examples become □ = 135 + 28 and 163 = □ + 28. The child should be able to say which amount the square represents before calculating. If they immediately add 163 and 28 in the second example, they have overlooked the fact that 163 is already the larger total.

Ask the child to invent a pair of related stories using the same three quantities. One should ask for the larger amount and one for the smaller. Successful story creation shows that the relation has transferred beyond a fixed model-solution pattern.

Money, time and graph blanks: a quantity always has a unit

A fictional item costs 235 cents and is paid for with 500 cents. The change is the missing part of the payment: 500 − 235 = 265 cents, or $2.65. The number bond describes an entire payment separated into cost and change, but the answer must be expressed in the unit requested.

For time, one hour and twenty-five minutes equals □ minutes. One hour contributes sixty minutes, so the missing value is 85 minutes. This is a unit conversion, not a new algebra topic. The child should explain why an hour is not counted as a hundred minutes.

For a scaled picture graph, suppose each star represents two children and a category shows five stars. The category value is ten children, because five equal groups of two total ten. If a category value is given as ten children, the missing symbol count is five. The relationship reverses through division.

Use such cross-topic tasks carefully. A wrong answer in a money problem may stem from confusing $2.05 with $2.50. A wrong graph blank may stem from ignoring the scale key. The square is simply the presentation format; the actual teaching gap may be elsewhere.

A reliable five-step routine for any box

Read everything: What does each visible number represent?
Identify the missing quantity: whole, part, beginning, change, finish, group size or group count?
Represent the structure: number bond, short bar, counter groups or a simple start–finish line.
Choose a suitable operation: add, subtract, multiply or divide based on the structure.
Replace the box and verify: the original equality and units must make sense.

This routine should become shorter as the child grows independent. Initially an adult may ask each question. Later the child can use a small card. Finally remove the card and ask for a spoken explanation. The goal is to reduce prompts rather than create a permanent dependence on a five-step script.

If the child’s answer is correct but the explanation is wrong, do not assume the concept is secure. They may have guessed or matched a familiar surface pattern. Change one known number and ask how the unknown should respond. A learner who understands the relationship can predict the direction of change before calculating.

Twenty worked missing-number examples with full reasoning

These twenty examples are original classroom-style practice. They include several positions of the unknown so that children cannot pass by simply performing the operation sign they first see. Each solution is accompanied by an inverse check or an explanation of what the unknown counts.

Worked problem 1: Missing addend

Question: □ + 48 = 125. Missing value: 77.

Why: 125 − 48 = 77, then 77 + 48 = 125.

Try a changed case: Move the unknown to another position in the same fact family, or change one known amount while keeping the relationship. Ask for the correct unit and an inverse check rather than a guessed number.

Worked problem 2: Missing second part

Question: 235 + □ = 400. Missing value: 165.

Why: 400 − 235 = 165, then 235 + 165 = 400.

Worked problem 3: Reversed equality

Question: 42 = 18 + □. Missing value: 24.

Why: 42 − 18 = 24; both sides then equal 42.

Worked problem 4: Another reversed equality

Question: 125 = □ + 77. Missing value: 48.

Why: 125 − 77 = 48; 48 + 77 returns 125.

Worked problem 5: Unknown starting whole

Question: □ − 85 = 317. Missing value: 402.

Why: 317 + 85 = 402; restored removed value.

Worked problem 6: Unknown amount removed

Question: 402 − □ = 317. Missing value: 85.

Why: 402 − 317 = 85; verify 317 + 85 = 402.

Worked problem 7: Unknown whole across a hundred

Question: □ − 176 = 324. Missing value: 500.

Why: 324 + 176 = 500; check 500 − 176 = 324.

Worked problem 8: Unknown amount removed with zero tens

Question: 703 − □ = 650. Missing value: 53.

Why: 703 − 650 = 53; 650 + 53 = 703.

Worked problem 9: Whole and part

Question: □ + 180 = 425. Missing value: 245.

Why: 425 − 180 = 245; sum of two parts is 425.

Worked problem 10: Subtraction fact family

Question: 425 − □ = 245. Missing value: 180.

Why: 425 − 245 = 180; the removed and remaining amounts sum to 425.

Worked problem 11: Multiplication factor

Question: □ × 4 = 20. Missing value: 5.

Why: 20 ÷ 4 = 5; five groups of four make twenty.

Worked problem 12: Another multiplier

Question: 5 × □ = 35. Missing value: 7.

Why: 35 ÷ 5 = 7 items per group; five groups give 35.

Worked problem 13: Unknown dividend

Question: □ ÷ 4 = 6. Missing value: 24.

Why: Six groups of four make 24.

Worked problem 14: Unknown divisor

Question: 24 ÷ □ = 6. Missing value: 4.

Why: Six groups of four make 24, so the group size is four.

Worked problem 15: Division with table five

Question: 30 ÷ □ = 6. Missing value: 5.

Why: Six groups of five make thirty.

Worked problem 16: Comparison larger unknown

Question: □ = 135 + 28. Missing value: 163.

Why: The smaller amount plus the gap equals the larger amount.

Worked problem 17: Comparison smaller unknown

Question: 163 = □ + 28. Missing value: 135.

Why: Remove the gap 28 from the larger amount.

Worked problem 18: Money remainder

Question: 500 − □ = 235. Missing value: 265.

Why: 500 cents paid minus 235 cents cost gives 265 cents change.

Worked problem 19: Hours to minutes

Question: One hour and 25 minutes = □ minutes. Missing value: 85.

Why: One hour is 60 minutes, so 60 + 25 = 85.

Worked problem 20: Scaled graph

Question: Five pictures, each worth two objects = □ objects. Missing value: 10.

Why: Five groups of two represent ten objects.

Thirty-six missing-number problems and independently checked answers

Use this worksheet without timing. Have the child substitute each proposed answer into the original statement. If the two sides do not agree, revisit the relationship before seeking another answer from the key. All questions are original illustrations of familiar Primary Two arithmetic.

□ + 35 = 120
52 + □ = 145
210 = 80 + □
□ + 125 = 300
400 = □ + 235
□ + 47 = 200
□ − 20 = 380
□ − 85 = 317
□ − 46 = 159
□ − 128 = 272
□ − 15 = 600
□ − 249 = 351
500 − □ = 324
703 − □ = 650
400 − □ = 235
620 − □ = 570
900 − □ = 650
315 − □ = 200
□ × 2 = 16
□ × 3 = 21
4 × □ = 24
5 × □ = 35
□ × 10 = 90
□ × 4 = 32
20 ÷ □ = 5
□ ÷ 5 = 7
24 ÷ □ = 6
□ ÷ 3 = 8
40 ÷ □ = 8
□ ÷ 10 = 7
163 = □ + 28
425 = 180 + □
□ + 57 = 305
608 − □ = 408
200 = □ + 70
□ − 37 = 263

Answer key and method of verification

85. Substitute 85 into the box in □ + 35 = 120; the two sides then have equal values.
93. Substitute 93 into the box in 52 + □ = 145; the two sides then have equal values.
130. Substitute 130 into the box in 210 = 80 + □; the two sides then have equal values.
175. Substitute 175 into the box in □ + 125 = 300; the two sides then have equal values.
165. Substitute 165 into the box in 400 = □ + 235; the two sides then have equal values.
153. Substitute 153 into the box in □ + 47 = 200; the two sides then have equal values.
400. Substitute 400 into the box in □ − 20 = 380; the two sides then have equal values.
402. Substitute 402 into the box in □ − 85 = 317; the two sides then have equal values.
205. Substitute 205 into the box in □ − 46 = 159; the two sides then have equal values.
400. Substitute 400 into the box in □ − 128 = 272; the two sides then have equal values.
615. Substitute 615 into the box in □ − 15 = 600; the two sides then have equal values.
600. Substitute 600 into the box in □ − 249 = 351; the two sides then have equal values.
176. Substitute 176 into the box in 500 − □ = 324; the two sides then have equal values.
53. Substitute 53 into the box in 703 − □ = 650; the two sides then have equal values.
165. Substitute 165 into the box in 400 − □ = 235; the two sides then have equal values.
50. Substitute 50 into the box in 620 − □ = 570; the two sides then have equal values.
250. Substitute 250 into the box in 900 − □ = 650; the two sides then have equal values.
115. Substitute 115 into the box in 315 − □ = 200; the two sides then have equal values.
8. Substitute 8 into the box in □ × 2 = 16; the two sides then have equal values.
7. Substitute 7 into the box in □ × 3 = 21; the two sides then have equal values.
6. Substitute 6 into the box in 4 × □ = 24; the two sides then have equal values.
7. Substitute 7 into the box in 5 × □ = 35; the two sides then have equal values.
9. Substitute 9 into the box in □ × 10 = 90; the two sides then have equal values.
8. Substitute 8 into the box in □ × 4 = 32; the two sides then have equal values.
4. Substitute 4 into the box in 20 ÷ □ = 5; the two sides then have equal values.
35. Substitute 35 into the box in □ ÷ 5 = 7; the two sides then have equal values.
4. Substitute 4 into the box in 24 ÷ □ = 6; the two sides then have equal values.
24. Substitute 24 into the box in □ ÷ 3 = 8; the two sides then have equal values.
5. Substitute 5 into the box in 40 ÷ □ = 8; the two sides then have equal values.
70. Substitute 70 into the box in □ ÷ 10 = 7; the two sides then have equal values.
135. Substitute 135 into the box in 163 = □ + 28; the two sides then have equal values.
245. Substitute 245 into the box in 425 = 180 + □; the two sides then have equal values.
248. Substitute 248 into the box in □ + 57 = 305; the two sides then have equal values.
200. Substitute 200 into the box in 608 − □ = 408; the two sides then have equal values.
130. Substitute 130 into the box in 200 = □ + 70; the two sides then have equal values.
300. Substitute 300 into the box in □ − 37 = 263; the two sides then have equal values.

When an answer fails to match the original equality, it is more useful to revisit the choice of whole and part than to guess another number. For division, sketch equal groups. For a minus problem, label starting quantity, change and remainder. For a reversed equality, read both sides aloud before calculating.

Six wrong answers and the different lessons they suggest

Wrong response	Possible first misunderstanding	Correction question
□ + 48 = 125 answered 173	Known whole added to part	“Which visible number is already the total?”
□ − 85 = 317 answered 232	Start confused with remainder	“Could the start be smaller when items are removed?”
20 ÷ □ = 5 answered 5	Group count and group size confused	“How many items must be in one group?”
42 = 18 + □ rejected as invalid	Equality read in one direction only	“What must each side be worth?”
Correct number but wrong unit	Quantity target not identified	“Does the box count bags, items or cents?”
Succeeds only with an adult telling the operation	Method selection not independent	“Can you draw the whole and its parts?”

A wrong response alone is not a diagnosis. Inspect the child’s first working step. Someone who correctly chooses subtraction but miscalculates 125 − 48 needs place-value and regrouping support; someone who adds 125 and 48 needs help identifying the whole. Those are different interventions even though both lead to an incorrect box.

A two-week home-learning progression

Days 1–2: use counters and number bonds with small whole-number quantities. Days 3–4: hide each part in turn and teach the inverse relationship. Days 5–6: introduce missing minuends and subtrahends in simple start–change–finish stories. Days 7–8: use equal groups and inverse multiplication/division facts from the P2 tables. Days 9–10: compare greater and smaller amounts with the unknown moved. Days 11–12: practise mixed boxes without chapter headings. Days 13–14: retest a previously incorrect structure with different numbers.

This is an optional family sequence, not an MOE assessment calendar. Use a short number of meaningful questions per session. A child who can explain an unknown part with no adult hint is making useful progress even if they have not completed a long workbook.

Keep a tiny record of the first missing step: “Can solve □ + 27 = 95 but needs a bar to solve 95 = □ + 27.” That points to equality orientation. Another child may solve both but miscalculate subtraction across zero, requiring a different intervention. The smallest effective correction is usually the most efficient.

If a child becomes worried by timed drills, remove the timer. The objective here is relationship understanding and eventual independence, not a fabricated Primary 2 examination score.

Frequently asked Primary 2 missing-number questions

What is the easiest way to solve □ + 48 = 125?

Find the missing part by subtracting: 125 − 48 = 77. Check 77 + 48 = 125.

Why is □ − 85 = 317 solved by addition?

The original amount is missing; add the removed amount to the remainder: 317 + 85 = 402.

Is a missing-number box an official SEAB P2 exam format?

No national SEAB Primary 2 Maths paper applies. Boxes are a useful classroom representation of arithmetic relationships and should not be advertised as promised examination items.

Are number bonds and bar models the same?

They use different diagrams to show related part–whole or comparison relationships. Choose one that clarifies the given quantities.

Does the equal sign always come after a calculation?

No. Equality means the expressions on both sides have the same value. 42 = 18 + 24 is valid.

Should Primary 2 children learn formal x equations?

Formal symbolic algebra is not the P2 whole-number content listed in the referenced MOE syllabus. Familiar arithmetic can explain the unknown boxes here.

Sources, boundaries and next reading

Official curriculum: MOE Primary Mathematics Syllabus updated October 2025, Primary Two operations on printed page 33. Assessment framework: MOE Education Conversations, removal of P1/P2 formal exams and weighted assessments since 2019.

Continue with mental sums using ones, tens and hundreds, three-digit regrouping, multiplication and division fact families, word-problem method choice and fifty mixed P2 practice questions.

Reviewed 13 November 2026. All problems are original; no national P2 exam or search-ranking claim is implied.

Primary 2 MOE/SEAB Mathematics Examinations | P2 Missing Number Boxes, Number Bonds and Inverse Operations