Primary 1 number patterns are about noticing what changes from one number to the next, then using that rule to find a missing or following number. The Singapore MOE P1 Mathematics syllabus explicitly includes patterns in number sequences within the whole-number strand up to 100. Children should be able to explain a simple sequence, not just guess a numeral because it looks familiar.
A reliable learner can say ‘31, 41, 51, 61 increases by ten each time’, explain that the tens digit increases while the ones digit stays one, and use the same rule to solve a new sequence. A child who keeps writing 71 when the sequence is decreasing may be copying a visible digit pattern without checking the direction. Use number cards, ten-bundles and number lines to build the underlying relationship.
- Official P1 basis: number patterns within the Numbers up to 100 strand; compare and order numbers and understand tens and ones.
- Immediate strategy: compare two neighbouring numbers, determine how much was added or removed, and check the same change again.
- Examples: 21, 22, 23; 35, 45, 55; 30, 28, 26; 75, 65, 55.
- Common mistake: filling a blank using the nearest printed digit rather than a rule that works throughout.
- Assessment: Singapore has no weighted P1 exam or SEAB national P1 Mathematics paper; these are learning and teacher-feedback exercises.
What the MOE Primary 1 Mathematics syllabus says about number patterns
The MOE 2021 Primary Mathematics syllabus, updated October 2025, names ‘patterns in number sequences’ as item 1.6 under Primary One Whole Numbers. It sits beside counting sets, place value, comparing and ordering numbers, and ordinal positions. A sequence is not an isolated guessing puzzle; it is an application of number order and mathematical relationships.
The official line does not publish a fixed exhaustive menu of possible steps for every P1 worksheet. The patterns below are examples designed for age-appropriate teaching, with a few clearly marked extensions. They are not predictions of exam questions. MOE removed P1 and P2 weighted assessments and examinations from 2019, so classroom feedback rather than a national paper should guide practice.
The four-step method for solving a missing-number pattern
- Read the direction: do the numbers increase, decrease or stay unchanged?
- Measure one step: count how much changes between two neighbouring values.
- Check another step: the same rule must work across the given sequence.
- Fill the blank and test: read the complete sequence and verify the change on both sides of the missing entry.
For example, 14, 16, □, 20. The first difference is two. A candidate answer of 18 makes the next step from 18 to 20 also two. By contrast 19 would make the two steps plus three then plus one, so it does not fit this constant-step pattern. The child should say why 18 is correct, not merely write it.
Patterns that increase by one
Start with 26, 27, 28, 29, 30. Count forwards one at a time. Crossing from 29 to 30 is important: the ones column goes from nine to zero while the tens column increases. Build 29 as two tens and nine ones, add one, and regroup into three tens. The number line and ten-bundles now tell the same story.
Worked example: 47, 48, □, 50
From 47 to 48 the increase is one. Next is 49, then 50. The blank is 49. Ask the learner to read the whole sequence and show the step from 49 to 50. This is particularly useful when the child has trouble crossing a tens boundary.
Patterns that decrease by one
Counting backwards uses the same number order in reverse: 64, 63, 62, 61, 60. A learner who always counts forwards might write 65 after 64. Put the sequence on a number line and move one position left at each step. Ask whether every new number is greater or smaller than the previous one.
Worked example: 71, 70, □, 68
From 71 to 70 is minus one. Therefore the next number is 69 and the final 68 confirms the rule. The blank is 69. If the child says 60, use a number chart to distinguish stepping back one from dropping a whole ten.
Patterns that increase or decrease by two
A simple ‘add two’ pattern might be 12, 14, 16, 18, 20. Each value is two more than the previous one. With counters, add a pair at each stage. A ‘subtract two’ pattern could be 19, 17, 15, 13, 11. The child can count back two individual positions along a number line. The essential idea is a repeatable change, not memorising a special sequence.
Worked example: 34, 36, □, 40
Compare 34 and 36: the increase is two. The blank must be 38, and 38 plus two gives 40, confirming the rule. If the learner writes 37, ask whether 36 to 37 and 37 to 40 are equal changes. The unequal steps show why a local guess is insufficient.
Patterns that change by five
A pattern can move by five: 10, 15, 20, 25, 30. Another begins at 3: 3, 8, 13, 18, 23. For a child already secure with tens and ones, adding five can be demonstrated by counters or a number line. When crossing a tens boundary, ask what happens to the tens and ones rather than treating the pattern as a wordless chant.
Worked example: 32, 37, 42, □
Each step adds five, so the next number is 47. Check from 37 to 42 and from 42 to 47. If a child sees only the changing ones digits and guesses 52, return to the actual five-unit increase. This is a teacher-created example, not a claim that every P1 class is formally tested on increments of five.
Patterns that change by ten
Numbers such as 24, 34, 44, 54, 64 all have four ones. The tens increase by one group of ten each time. A child who understands place value can show this by adding one ten-straw bundle at every step. On a hundred chart, the numbers appear at regular intervals in the standard grid, but students still need to explain the value change.
Worked example: 81, 71, 61, □
The sequence decreases by ten each time. From 81 to 71 is minus ten, and from 71 to 61 is also minus ten. Therefore the missing number is 51. The ones digit stays one; one group of ten is removed at each step. A learner who writes 60 is changing the ones incorrectly.
The missing entry may be at the beginning, middle or end
A child might solve 5, 10, 15, □ but not □, 10, 15, 20 because they expect the blank at the right-hand end. Present both. For the second sequence, the repeated change is plus five, so the number before 10 must be 5. Asking for the first value makes the child reason backwards from the rule. Similar tasks can use plus one, plus two or plus ten.
A gap in the middle needs checking on both sides. In 20, 30, □, 50, the candidate 40 sits ten after 30 and ten before 50. In 20, □, 40, 50, the blank is 30. A child who can only continue from the last number should practise these alternate blank positions using physical number cards.
Number patterns and place value reinforce one another
Consider 39, 49, 59, 69. The ones digit remains nine while the tens digit rises: three tens, four tens, five tens and six tens. This helps the child see that addition of ten changes the tens but not the ones. For 29, 30, 31, the rule is plus one, but the crossing of 29 to 30 changes both printed digits. Counting actual quantities prevents the misconception that every sequence changes only one printed digit.
The sequence 90, 80, 70, 60, 50 is a reduction by one ten each time. Ask the child to move one ten-bundle out of a collection at each stage. If they can explain how many bundles are removed, they are building a reasoned method that later helps with mental subtraction of tens.
Forty-five original P1 number sequence questions and answers
These examples are arranged from simple to more demanding. A few are useful extension exercises and may not match the exact stage of a child’s current classroom teaching. Ask the child for the repeated change before accepting an answer. The questions are not leaked or official exam items.
- 1, 2, 3, __, 5 Answer: 4. Rule/check: +1.
- 7, 8, __, 10 Answer: 9. Rule/check: +1.
- 18, 19, __, 21 Answer: 20. Rule/check: +1 across the tens boundary.
- 38, 39, __, 41 Answer: 40. Rule/check: +1 across a ten.
- 97, 98, __, 100 Answer: 99. Rule/check: +1.
- 10, 9, 8, __ Answer: 7. Rule/check: −1.
- 25, 24, __, 22 Answer: 23. Rule/check: −1.
- 71, 70, __, 68 Answer: 69. Rule/check: −1.
- 52, 51, 50, __ Answer: 49. Rule/check: −1.
- 40, 39, 38, __ Answer: 37. Rule/check: −1.
- 2, 4, 6, __ Answer: 8. Rule/check: +2.
- 12, 14, __, 18 Answer: 16. Rule/check: +2.
- 34, 36, __, 40 Answer: 38. Rule/check: +2.
- 81, 83, 85, __ Answer: 87. Rule/check: +2.
- 21, 19, 17, __ Answer: 15. Rule/check: −2.
- 30, 28, __, 24 Answer: 26. Rule/check: −2.
- 18, 16, 14, __ Answer: 12. Rule/check: −2.
- 93, 91, __, 87 Answer: 89. Rule/check: −2.
- 5, 10, 15, __ Answer: 20. Rule/check: +5.
- 20, 25, __, 35 Answer: 30. Rule/check: +5.
- 32, 37, 42, __ Answer: 47. Rule/check: +5.
- 60, 55, __, 45 Answer: 50. Rule/check: −5.
- 47, 42, 37, __ Answer: 32. Rule/check: −5.
- 11, 16, __, 26 Answer: 21. Rule/check: +5.
- 82, 77, __, 67 Answer: 72. Rule/check: −5.
- 10, 20, 30, __ Answer: 40. Rule/check: +10.
- 24, 34, __, 54 Answer: 44. Rule/check: +10.
- 37, 47, 57, __ Answer: 67. Rule/check: +10.
- 63, 73, __, 93 Answer: 83. Rule/check: +10.
- 90, 80, 70, __ Answer: 60. Rule/check: −10.
- 81, 71, __, 51 Answer: 61. Rule/check: −10.
- 65, 55, 45, __ Answer: 35. Rule/check: −10.
- 100, 90, 80, __ Answer: 70. Rule/check: −10.
- __, 10, 15, 20 Answer: 5. Rule/check: +5, missing start.
- __, 21, 22, 23 Answer: 20. Rule/check: +1, missing start.
- 30, __, 50, 60 Answer: 40. Rule/check: +10.
- 12, __, 16, 18 Answer: 14. Rule/check: +2.
- 50, __, 40, 35 Answer: 45. Rule/check: −5.
- 45, __, 25, 15 Answer: 35. Rule/check: −10.
- 33, 34, 35, __, 37 Answer: 36. Rule/check: +1.
- Which sequence is decreasing: 10,20,30 or 30,20,10? Answer: 30, 20, 10. Rule/check: Every entry gets smaller.
- What is the rule for 41,51,61? Answer: +10. Rule/check: Tens increase while ones stay one.
- What is the rule for 17,15,13? Answer: −2. Rule/check: Take away two every time.
- Does 4,7,10,14 have constant +3 steps? Answer: No. Rule/check: The final increase is four.
- What follows 88,90,92? Answer: 94. Rule/check: +2.
Common pattern errors and their precise repairs
Guessing the next visible digit
The child notices 21, 31, 41 but writes 42 because the digits nearby look familiar. Repair: Ask for the difference between 21 and 31, then 31 and 41. If the change is ten both times, the next value is 51. Ask for a new sequence with different starting values to check independent reasoning.
Forgetting the direction
A decreasing sequence is filled by adding, because the learner habitually counts forwards. Repair: Have the student point left on a number line, say ‘smaller each step’, then count back using the real amount. Ask for a new sequence with different starting values to check independent reasoning.
Checking only one pair
A proposed number matches the first gap but not the gap after the blank. Repair: Test the repeated change on both sides. The rule must explain all given entries, not one convenient pair. Ask for a new sequence with different starting values to check independent reasoning.
Confusing ones with tens
For 25, 35, 45 a child writes 46. Repair: Build tens bundles and five singles; add one ten bundle at each step while retaining the five singles. Ask for a new sequence with different starting values to check independent reasoning.
Incorrect crossing at 29 or 39
Counting forwards from 29 becomes 210 or 20. Repair: Group ten ones into a new ten to show 30, then read the numeral and continue from there. Ask for a new sequence with different starting values to check independent reasoning.
Treating a missing-start question as impossible
The child can say the next number but cannot find the first one. Repair: Work backwards one step using the inverse change: if the rule adds five to reach 10, start from 5. Ask for a new sequence with different starting values to check independent reasoning.
Using two different step sizes unintentionally
For 12,14,16,18 the child writes 21 next. Repair: Count the constant difference of two at each gap and verify with a number line. Ask for a new sequence with different starting values to check independent reasoning.
Mistaking a decorative picture pattern for the same syllabus item
A learner is drilled on complex shape attributes instead of numeric sequences. Repair: P1 explicitly lists number sequence patterns. More formal patterns with 2D shapes are separately described at P2. Practise the child’s current objective. Ask for a new sequence with different starting values to check independent reasoning.
The home lesson: paper number cards and an empty number line
Prepare ten small cards with consecutive numbers such as 21 through 30. Mix the cards and ask the child to put them in order. Hide one card and ask what is missing. Once the missing entry can be found reliably, create cards with two-unit gaps, such as 32, 34, 36 and 38, and ask for the rule. The child should say what changes rather than merely recognise the visual pattern.
For tens sequences, use bundles of ten objects. Add one complete bundle at every step. For a decreasing pattern, remove one bundle. This physical action makes ‘plus ten’ and ‘minus ten’ visible. Revisit with new starting points such as 17, 27, 37 and 74, 64, 54. If the child can now solve without bundles, the concept is becoming portable.
Four weeks of short, targeted number-sequence practice
Week 1
Forward and backward counting by one, including crossing tens boundaries. Use ten-minute or shorter focused sessions and one independent sequence at the end. Keep a one-line note of errors that recur; revisit those after two days with different numbers instead of assigning a large timed worksheet.
Week 2
Recognise step sizes of two and five using a number line and repeated additions or subtractions. Emphasise that the same amount must change each time. Keep a one-line note of errors that recur; revisit those after two days with different numbers instead of assigning a large timed worksheet.
Week 3
Practise +10 and −10 using tens and ones, and place blanks in the middle or beginning as well as at the end. Keep a one-line note of errors that recur; revisit those after two days with different numbers instead of assigning a large timed worksheet.
Week 4
Mix familiar constant-step patterns with one unfamiliar arrangement. Ask the child to justify the rule and check both neighbouring gaps before recording the answer. Keep a one-line note of errors that recur; revisit those after two days with different numbers instead of assigning a large timed worksheet.
Parent and student FAQ
Are number patterns part of Primary 1 Mathematics?
Yes, the MOE P1 Whole Numbers strand explicitly includes patterns in number sequences. The exact worksheet format depends on the school and teacher.
Is there a 2027 P1 number-pattern examination?
No national SEAB P1 Mathematics examination exists, and MOE removed all P1 weighted assessments and examinations from 2019.
Must every P1 pattern use a step of two, five or ten?
No. These are useful practice examples, not an exhaustive official list. Focus on how the child recognises and explains a repeatable numerical change.
What if the pattern decreases?
Find how many are subtracted at each step. Moving backward is as meaningful as counting forwards.
Why does my child say 29, 210 instead of 30?
They may not yet understand exchanging ten ones for another ten. Rebuild 29 with bundles and add one object.
Why use missing-number questions in the middle?
They require checking the rule on both sides instead of simply extending a memorised series.
Can a child use a number line?
Yes. The number line can visualise addition and subtraction of steps. Ask the learner to explain the move and later try without the representation.
Are shape-colour patterns a P1 Mathematics examination expectation?
P1 specifies patterns in number sequences. The formal P2 Geometry content includes shape patterns by attributes. Playful shape patterns are fine, but should not be mislabelled as guaranteed P1 examination questions.
What if a child sees many rules?
Start with the simplest rule that explains every given term, then check all gaps. If the sequence is ambiguous, the adult should clarify the intended rule instead of punishing a defensible alternative.
Does a missing number have to be at the end?
No. Gaps can be before, between or after known entries. Children should use a consistent rule in either direction.
Should a learner memorise sequences instead of reasoning?
Fluency helps, but the child should demonstrate that each step changes by a known amount and can apply the same structure to different starting numbers.
When might a Maths tutor help?
When the child repeatedly loses the rule despite feedback. A tutor can check number sense, place value and forward/backward counting before applying the sequence independently.
How to distinguish a pattern from a list of unrelated numbers
A number sequence has an order. The learner looks for a relationship between each neighbouring pair that can help determine another entry. The list 12, 14, 16, 18 is useful because every step adds two. The list 12, 14, 17, 18 may be perfectly valid as a record of real events, but it does not follow that same constant +2 rule. A child should be encouraged to test the proposed rule across the entire sequence, not only its first two entries.
There are also sequences that could fit several different rules when too few numbers are shown. For example, the two values 2 and 4 might begin 2, 4, 6, 8, or another mathematical relationship entirely. At Primary 1, a fair learning task should provide enough context or entries for its intended simple pattern to be clear. If a child offers a different defensible rule, discuss the evidence rather than insisting that the adult’s unstated pattern was the only possible answer.
Eight worked cases where children need more than a guess
Case 1: from 28 to 32 with a missing number
Look at 28, 30, □, 34. The first gap is plus two. If the blank is 32, the next gap from 32 to 34 is also plus two. Both sides confirm the rule. If the child proposes 31, the two steps would be plus one and plus three, which is inconsistent. Ask the learner to mark the steps on a number line to make the equal change visible.
Case 2: from 90 down to 60
Consider 90, 80, □, 60. The first step removes ten, so the next value must be 70. From 70 removing ten leaves 60. Show nine ten-bundles, remove one bundle for each step and count the remaining bundles. The model explains why it is the tens digit that changes while the ones stay at zero.
Case 3: filling the first blank
Consider □, 26, 28, 30. The visible gap from 26 to 28 and from 28 to 30 is plus two. To recover the starting value, move two backward from 26. The blank is 24. This tests understanding of the rule in both directions rather than only continuing a chant from a visible starting number.
Case 4: crossing the tens boundary
Consider 96, 97, 98, □, 100. The next value is 99. From 99 to 100 is one further step. If the child finds the last transition confusing, create nine groups of ten and nine single counters, then add one to exchange the ten singles for one more bundle. The hundred is ten complete groups of ten.
Case 5: a fixed ones digit with changing tens
Look at 13, 23, 33, 43, □. The rule adds ten each time, and the three ones remain unchanged. The next value is 53. Ask the child to point to the ones digit across the whole sequence. Then ask which digit carries the repeated change. This connects number patterns with place value rather than treating them as separate topics.
Case 6: a constant subtraction of five
Look at 83, 78, 73, □. Each value is five less than the previous one, so the next is 68. Check from 78 to 73 and from 73 to 68. A learner who writes 63 may have subtracted ten on the last step instead. Use counters or a number line to make the five-unit movement clear.
Case 7: recognise a rule that fails
A child says the rule for 5, 10, 15, 21 is plus five. The first two gaps support the claim, but the final gap is plus six, so the complete sequence does not obey that constant-step rule. Ask whether the list might contain a mistake or be governed by another stated rule. Do not pretend it is automatically correct merely because the first two pairs looked promising.
Case 8: the same step from a new starting point
The child can solve 10, 20, 30, 40 by memory, so present 17, 27, 37, □. The rule is still plus ten, and the answer is 47. If the child struggles, show one ten-bundle being added to seventeen. A skill becomes reliable when it works for unfamiliar starting values, not only a sequence of familiar round numbers.
Fifteen mixed transfer questions with explanations
- Write the next two numbers after 24, 25, 26. 27, 28. The step is one.
- Write the previous number before 40, 42, 44. 38. Each value increases by two.
- Complete 19, 29, 39, □, □. 49, 59. Add a ten each time.
- Complete 87, 82, 77, □, □. 72, 67. Subtract five each step.
- What is the rule for 16, 18, 20, 22? Plus two. Every adjacent difference is two.
- What is the rule for 72, 62, 52, 42? Minus ten. Ones remain two while tens decrease.
- Complete □, 45, 50, 55. 40. Go back five from 45.
- Complete □, 70, 60, 50. 80. Go back one step by adding ten.
- What comes after 89, 90, 91? 92. Continue plus one.
- What comes before 31, 30, 29? 32. The list decreases by one.
- Complete 5, 7, 9, □, 13. 11. Plus two works on both sides.
- Complete 100, 95, 90, □. 85. Subtract five each step.
- Complete 6, 16, 26, □. 36. Add ten without changing the ones.
- Does 4, 9, 14, 19 have a constant step? Yes, plus five. Verify every gap.
- Does 2, 4, 7, 9 have a constant plus-two step? No. The middle gap is plus three.
What to do when a child can recite a sequence but cannot fill a blank
The learner may have memorised 10, 20, 30, 40, 50 as a song or chant. Present 25, 35, 45, □ and ask what changed. If the student cannot identify the next value, build 25 as two tens and five ones, add another ten, and repeat. The movement is structurally the same as the familiar chant but starts from a different amount.
A number line can make one-unit and two-unit movements visible. With a hundred chart, ask the child to explain why a vertical move in a standard layout often changes the value by ten. Emphasise that these tools are representations. To check independent understanding, remove the chart after practice and give one new sequence on plain paper.
Learning checks for an independent child, a child who needs repair and a child ready to extend
Secure but cautious: The child finds a missing value correctly but needs a little thinking time. Ask for a second similar example with a new start, and do not impose a speed target. Correct understanding can be deliberate. Needs repair: The child cannot tell whether the sequence is increasing or decreasing. Return to physical objects, count one step at a time, and practise a shorter three-number pattern before the longer version.
Ready to extend: The learner explains simple changes by one, two, five and ten without help. Ask them to create a four-number sequence and hide one entry for a family member to solve. They must explain a rule that works for every gap. The ability to generate and justify a new pattern is a strong indication that the child is reasoning instead of copying an existing format.
Weekly family practice without turning Primary 1 into an exam year
Choose one small pattern challenge during an everyday activity. Number library books on a shelf, count steps taken in pairs, identify numbers on calendar dates, or construct a card sequence while waiting for an activity to begin. Do not require every real-life sequence to follow a perfect arithmetic rule; ask whether one exists, how it can be checked and what information is needed.
At the end of the week, review the child’s earlier mistakes. If they once wrote 60 after 39 in a plus-one sequence, show 39, 40, 41 with counters and have them build the transition. If they once added instead of subtracting, ask them to place decreasing number cards in order. Short, meaningful rechecks are more useful than demanding a formal score for a grade that does not have weighted examinations.
How to respond to a pattern the child can justify differently
Do not present a short, ambiguous string of numbers and then insist that there is only one possible mathematical rule. If the first terms are 1, 2 and 3, a continuation of 4 is natural under a constant plus-one pattern, but a creative learner might imagine a more complicated relationship. At P1, supply enough terms and make the intended simple change clear. The aim is to teach a repeatable rule supported by evidence, not reward guessing the teacher’s hidden intention.
When a child suggests a missing number, ask three questions: ‘What changes from the first number to the second?’, ‘Does the same change work for the next pair?’, and ‘Does your answer keep the pattern going?’ If the proposal fails, demonstrate the mismatched gap gently and let the learner try again. This gives children a reasoned checking process they can use without an adult correcting every answer.
For a final review, ask the student to invent a sequence with four terms, leave one blank and describe the rule to a parent. A sequence such as 17, 27, □, 47 can be solved as plus ten; a sequence such as 42, 40, □, 36 uses minus two. Explaining their own created sequence is a richer achievement than repeating an identical prepared question.
Related guides and official references
Start with Numbers to 100, Tens and Ones, then continue to Number Bonds and Missing Numbers. For further reading use the eduKate Mathematics Learning Hub.
Official sources: MOE Primary Mathematics Syllabus, October 2025, P1 Numbers up to 100, page 31 and MOE P1/P2 assessment policy. This is independent original learning guidance, not an official MOE/SEAB paper. Reviewed November 2026 for 2027 preparation.