Primary 3 MOE/SEAB Mathematics Examinations | 2027 Number Patterns, Missing Digits and Sequences to 10,000

Primary 3 Mathematics number-pattern questions become easier when pupils stop guessing the next digit and instead measure the change between consecutive numbers. The MOE Primary Mathematics syllabus includes whole numbers up to 10,000, place value, comparing and ordering numbers, and number patterns. A 2027 school assessment may ask for a missing term, the next value, an earlier value or a missing digit that satisfies a comparison. The most reliable strategy is to find a rule and test it across every given transition.

This guide gives original worked examples for the Primary 3 level. Singapore P3 Mathematics is assessed by individual schools, not through a national SEAB P3 paper. School notices determine which chapters appear in any 2027 weighted assessment. Use the official syllabus to identify age-appropriate learning and use the school’s actual scope to decide which examples to practise.

First step: Subtract adjacent terms to discover the repeated step.
Second: Test the same step across the other terms, including when a number crosses a thousand.
Third: Use place value to decide missing digits or ordering constraints.
Fourth: Work backward with the inverse step when the blank comes before the first number.
Final check: Substitute your proposed term into the complete sequence and verify the rule remains consistent.
Scope: This guide uses P3 whole-number reasoning rather than upper-primary algebraic formulas.

What MOE teaches at P3 about number patterns

The Primary Three whole-number strand includes number notation and place value within 10,000, comparing and ordering numbers, and number patterns. These ideas belong together. A child who cannot recognise that 3,000 follows 2,900 when adding one hundred will struggle to follow a sequence through the thousands boundary, even if they can recite ‘add a hundred’.

The purpose of pattern work is not to guess from the final two digits. It is to recognise numerical structure: a repeated addition, repeated subtraction or a relationship between places. The number line, place-value chart and difference between adjacent terms are all legitimate ways to reveal that structure.

Do not present every complex alternating sequence or algebraic nth-term formula as a compulsory Primary 3 examination topic. The official curriculum sets the content boundary, and the school specifies the assessed scope. A sensible P3 problem can be challenging without requiring later-year notation.

How to find a missing number in a sequence

Take 2,450, 2,650, 2,850, ___. The first difference is 200; the second is also 200. Add 200 to the last value to get 3,050. The thousands digit changes, but the step remains exactly two hundreds. A child who writes 2,1050 has not understood place-value regrouping.

For a missing middle term, use the same relationship in both directions. In 3,400, ___, 3,800, the overall change is 400 across two equal steps, so each step is 200 and the middle number is 3,600. Check 3,400 + 200 = 3,600 and 3,600 + 200 = 3,800.

For a missing first term, reverse the step. In ___, 5,150, 5,350, the repeated increase is 200, so the previous term is 4,950. Do not start adding from the blank without knowing its value; use the known adjacent numbers to infer the rule, then work backward.

Number ordering and missing digits use the same place-value logic

Suppose a question asks for a number 6,_45 that lies strictly between 6,345 and 6,545. The missing hundreds digit must be 4, giving 6,445. A pupil who checks only the final digit may miss that the hundreds column decides the comparison.

Another question may have several valid missing digits. If 7,_20 must be larger than 7,320 but smaller than 7,720, the hundreds digit can be 4, 5 or 6. Do not force a single answer when the conditions allow several. This is a useful exercise in careful reading and mathematical justification.

Place-value comparison should always proceed from the largest place to the smallest. The first unequal digit determines which whole number is larger. This is true for four-digit numbers with internal zeros as well as for familiar three-digit values.

Thirty-six original number-pattern and missing-number problems

Try each question without looking at the answer. The explanation shows why the pattern works; the changed-case instruction asks the child to transfer the idea to another example. These are original practice items, not claims about confidential 2027 school papers.

Sequence 1: adding 100

Question: Complete ___, 1,350, 1,450, 1,550, 1,650. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 1,250. The sequence increases by 100 each time. The complete sequence is 1,250, 1,350, 1,450, 1,550, 1,650. Check two neighbouring transitions: the numerical difference is 100 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 1,150. What would the next term after the five displayed positions be? 1,750. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 2: adding 200

Question: Complete 2,340, 2,540, ___, 2,940, 3,140. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 2,740. The sequence increases by 200 each time. The complete sequence is 2,340, 2,540, 2,740, 2,940, 3,140. Check two neighbouring transitions: the numerical difference is 200 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 2,140. What would the next term after the five displayed positions be? 3,340. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 3: adding 50

Question: Complete 2,800, 2,850, 2,900, 2,950, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 3,000. The sequence increases by 50 each time. The complete sequence is 2,800, 2,850, 2,900, 2,950, 3,000. Check two neighbouring transitions: the numerical difference is 50 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 2,750. What would the next term after the five displayed positions be? 3,050. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 4: adding 20

Question: Complete 2,990, 3,010, 3,030, ___, 3,070. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 3,050. The sequence increases by 20 each time. The complete sequence is 2,990, 3,010, 3,030, 3,050, 3,070. Check two neighbouring transitions: the numerical difference is 20 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 2,970. What would the next term after the five displayed positions be? 3,090. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 5: adding 250

Question: Complete ___, 5,000, 5,250, 5,500, 5,750. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,750. The sequence increases by 250 each time. The complete sequence is 4,750, 5,000, 5,250, 5,500, 5,750. Check two neighbouring transitions: the numerical difference is 250 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 4,500. What would the next term after the five displayed positions be? 6,000. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 6: subtracting 1,000

Question: Complete 8,000, 7,000, ___, 5,000, 4,000. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 6,000. The sequence decreases by 1,000 each time. The complete sequence is 8,000, 7,000, 6,000, 5,000, 4,000. Check two neighbouring transitions: the numerical difference is 1,000 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 9,000. What would the next term after the five displayed positions be? 3,000. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 7: subtracting 200

Question: Complete 9,300, 9,100, 8,900, 8,700, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 8,500. The sequence decreases by 200 each time. The complete sequence is 9,300, 9,100, 8,900, 8,700, 8,500. Check two neighbouring transitions: the numerical difference is 200 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 9,500. What would the next term after the five displayed positions be? 8,300. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 8: subtracting 20

Question: Complete 7,020, 7,000, 6,980, ___, 6,940. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 6,960. The sequence decreases by 20 each time. The complete sequence is 7,020, 7,000, 6,980, 6,960, 6,940. Check two neighbouring transitions: the numerical difference is 20 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 7,040. What would the next term after the five displayed positions be? 6,920. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 9: adding 100

Question: Complete ___, 1,705, 1,805, 1,905, 2,005. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 1,605. The sequence increases by 100 each time. The complete sequence is 1,605, 1,705, 1,805, 1,905, 2,005. Check two neighbouring transitions: the numerical difference is 100 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 1,505. What would the next term after the five displayed positions be? 2,105. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 10: adding 50

Question: Complete 4,850, 4,900, ___, 5,000, 5,050. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,950. The sequence increases by 50 each time. The complete sequence is 4,850, 4,900, 4,950, 5,000, 5,050. Check two neighbouring transitions: the numerical difference is 50 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 4,800. What would the next term after the five displayed positions be? 5,100. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 11: subtracting 250

Question: Complete 9,900, 9,650, 9,400, 9,150, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 8,900. The sequence decreases by 250 each time. The complete sequence is 9,900, 9,650, 9,400, 9,150, 8,900. Check two neighbouring transitions: the numerical difference is 250 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 10,150. What would the next term after the five displayed positions be? 8,650. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 12: adding 1,000

Question: Complete 1,111, 2,111, 3,111, ___, 5,111. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,111. The sequence increases by 1,000 each time. The complete sequence is 1,111, 2,111, 3,111, 4,111, 5,111. Check two neighbouring transitions: the numerical difference is 1,000 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 111. What would the next term after the five displayed positions be? 6,111. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 13: subtracting 500

Question: Complete ___, 4,000, 3,500, 3,000, 2,500. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,500. The sequence decreases by 500 each time. The complete sequence is 4,500, 4,000, 3,500, 3,000, 2,500. Check two neighbouring transitions: the numerical difference is 500 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 5,000. What would the next term after the five displayed positions be? 2,000. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 14: adding 150

Question: Complete 6,550, 6,700, ___, 7,000, 7,150. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 6,850. The sequence increases by 150 each time. The complete sequence is 6,550, 6,700, 6,850, 7,000, 7,150. Check two neighbouring transitions: the numerical difference is 150 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 6,400. What would the next term after the five displayed positions be? 7,300. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 15: subtracting 50

Question: Complete 3,050, 3,000, 2,950, 2,900, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 2,850. The sequence decreases by 50 each time. The complete sequence is 3,050, 3,000, 2,950, 2,900, 2,850. Check two neighbouring transitions: the numerical difference is 50 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 3,100. What would the next term after the five displayed positions be? 2,800. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 16: subtracting 100

Question: Complete 9,750, 9,650, 9,550, ___, 9,350. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 9,450. The sequence decreases by 100 each time. The complete sequence is 9,750, 9,650, 9,550, 9,450, 9,350. Check two neighbouring transitions: the numerical difference is 100 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 9,850. What would the next term after the five displayed positions be? 9,250. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 17: adding 25

Question: Complete ___, 6,050, 6,075, 6,100, 6,125. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 6,025. The sequence increases by 25 each time. The complete sequence is 6,025, 6,050, 6,075, 6,100, 6,125. Check two neighbouring transitions: the numerical difference is 25 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 6,000. What would the next term after the five displayed positions be? 6,150. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 18: adding 300

Question: Complete 4,700, 5,000, ___, 5,600, 5,900. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 5,300. The sequence increases by 300 each time. The complete sequence is 4,700, 5,000, 5,300, 5,600, 5,900. Check two neighbouring transitions: the numerical difference is 300 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 4,400. What would the next term after the five displayed positions be? 6,200. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 19: adding 400

Question: Complete 2,800, 3,200, 3,600, 4,000, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,400. The sequence increases by 400 each time. The complete sequence is 2,800, 3,200, 3,600, 4,000, 4,400. Check two neighbouring transitions: the numerical difference is 400 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 2,400. What would the next term after the five displayed positions be? 4,800. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 20: subtracting 750

Question: Complete 9,000, 8,250, 7,500, ___, 6,000. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 6,750. The sequence decreases by 750 each time. The complete sequence is 9,000, 8,250, 7,500, 6,750, 6,000. Check two neighbouring transitions: the numerical difference is 750 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 9,750. What would the next term after the five displayed positions be? 5,250. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 21: adding 100

Question: Complete ___, 4,450, 4,550, 4,650, 4,750. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,350. The sequence increases by 100 each time. The complete sequence is 4,350, 4,450, 4,550, 4,650, 4,750. Check two neighbouring transitions: the numerical difference is 100 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 4,250. What would the next term after the five displayed positions be? 4,850. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 22: subtracting 200

Question: Complete 5,800, 5,600, ___, 5,200, 5,000. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 5,400. The sequence decreases by 200 each time. The complete sequence is 5,800, 5,600, 5,400, 5,200, 5,000. Check two neighbouring transitions: the numerical difference is 200 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 6,000. What would the next term after the five displayed positions be? 4,800. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 23: adding 100

Question: Complete 1,234, 1,334, 1,434, 1,534, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 1,634. The sequence increases by 100 each time. The complete sequence is 1,234, 1,334, 1,434, 1,534, 1,634. Check two neighbouring transitions: the numerical difference is 100 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 1,134. What would the next term after the five displayed positions be? 1,734. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 24: subtracting 100

Question: Complete 9,876, 9,776, 9,676, ___, 9,476. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 9,576. The sequence decreases by 100 each time. The complete sequence is 9,876, 9,776, 9,676, 9,576, 9,476. Check two neighbouring transitions: the numerical difference is 100 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 9,976. What would the next term after the five displayed positions be? 9,376. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 25: adding 250

Question: Complete ___, 2,750, 3,000, 3,250, 3,500. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 2,500. The sequence increases by 250 each time. The complete sequence is 2,500, 2,750, 3,000, 3,250, 3,500. Check two neighbouring transitions: the numerical difference is 250 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 2,250. What would the next term after the five displayed positions be? 3,750. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 26: adding 900

Question: Complete 3,100, 4,000, ___, 5,800, 6,700. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,900. The sequence increases by 900 each time. The complete sequence is 3,100, 4,000, 4,900, 5,800, 6,700. Check two neighbouring transitions: the numerical difference is 900 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 2,200. What would the next term after the five displayed positions be? 7,600. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 27: subtracting 400

Question: Complete 7,900, 7,500, 7,100, 6,700, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 6,300. The sequence decreases by 400 each time. The complete sequence is 7,900, 7,500, 7,100, 6,700, 6,300. Check two neighbouring transitions: the numerical difference is 400 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 8,300. What would the next term after the five displayed positions be? 5,900. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 28: adding 10

Question: Complete 4,010, 4,020, 4,030, ___, 4,050. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,040. The sequence increases by 10 each time. The complete sequence is 4,010, 4,020, 4,030, 4,040, 4,050. Check two neighbouring transitions: the numerical difference is 10 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 4,000. What would the next term after the five displayed positions be? 4,060. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 29: adding 200

Question: Complete ___, 5,400, 5,600, 5,800, 6,000. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 5,200. The sequence increases by 200 each time. The complete sequence is 5,200, 5,400, 5,600, 5,800, 6,000. Check two neighbouring transitions: the numerical difference is 200 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 5,000. What would the next term after the five displayed positions be? 6,200. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 30: adding 150

Question: Complete 3,700, 3,850, ___, 4,150, 4,300. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,000. The sequence increases by 150 each time. The complete sequence is 3,700, 3,850, 4,000, 4,150, 4,300. Check two neighbouring transitions: the numerical difference is 150 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 3,550. What would the next term after the five displayed positions be? 4,450. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 31: subtracting 150

Question: Complete 6,150, 6,000, 5,850, 5,700, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 5,550. The sequence decreases by 150 each time. The complete sequence is 6,150, 6,000, 5,850, 5,700, 5,550. Check two neighbouring transitions: the numerical difference is 150 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 6,300. What would the next term after the five displayed positions be? 5,400. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 32: adding 250

Question: Complete 7,750, 8,000, 8,250, ___, 8,750. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 8,500. The sequence increases by 250 each time. The complete sequence is 7,750, 8,000, 8,250, 8,500, 8,750. Check two neighbouring transitions: the numerical difference is 250 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 7,500. What would the next term after the five displayed positions be? 9,000. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 33: subtracting 300

Question: Complete ___, 4,100, 3,800, 3,500, 3,200. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 4,400. The sequence decreases by 300 each time. The complete sequence is 4,400, 4,100, 3,800, 3,500, 3,200. Check two neighbouring transitions: the numerical difference is 300 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 4,700. What would the next term after the five displayed positions be? 2,900. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 34: subtracting 500

Question: Complete 8,200, 7,700, ___, 6,700, 6,200. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 7,200. The sequence decreases by 500 each time. The complete sequence is 8,200, 7,700, 7,200, 6,700, 6,200. Check two neighbouring transitions: the numerical difference is 500 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 8,700. What would the next term after the five displayed positions be? 5,700. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 35: adding 500

Question: Complete 1,500, 2,000, 2,500, 3,000, ___. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 3,500. The sequence increases by 500 each time. The complete sequence is 1,500, 2,000, 2,500, 3,000, 3,500. Check two neighbouring transitions: the numerical difference is 500 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 1,000. What would the next term after the five displayed positions be? 4,000. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Sequence 36: subtracting 50

Question: Complete 7,050, 7,000, 6,950, ___, 6,850. The numbers are within the P3 whole-number range and follow a constant step. State the missing value and explain the rule rather than guessing from the visible digits.

Worked answer: 6,900. The sequence decreases by 50 each time. The complete sequence is 7,050, 7,000, 6,950, 6,900, 6,850. Check two neighbouring transitions: the numerical difference is 50 in each, even if the thousands or hundreds digit changes.

Transfer challenge: What would the term before the first value be? 7,100. What would the next term after the five displayed positions be? 6,800. If a new pupil instead suggests a number that looks similar in its last two digits, ask them to calculate the actual difference between terms and explain why that suggestion does or does not preserve the repeated rule.

Five types of number-pattern errors

Reading only the final digits

A child sees 2,990 to 3,010 and thinks the increase is 120. Subtract the complete numbers or count twenty along a number line.

Ask the child to say which number relationship was broken in the first incorrect attempt. Keep the original answer and let the pupil repair it independently. A different representation, such as a number line or place-value grid, can show the idea without merely repeating the same written operation.

Assuming the rule must be addition

Some sequences decrease. Calculate the signed change from the first to second number before deciding which operation repeats.

Filling the blank without checking both sides

A proposed middle term must match the step from the previous term and to the next. Test both transitions.

Confusing a missing digit with a missing term

A digit placeholder inside 5,_20 is a place-value condition; an entire missing term between 5,120 and 5,320 is a sequence relationship.

Treating one correct answer as mastery

A pupil may recognise a familiar worksheet pattern. Give a changed sequence with a new starting value and a blank in another position.

A seven-day practice plan

Day 1

Count by hundreds and thousands across a boundary, and read each number aloud.

Keep sessions short enough for the child to explain why a pattern works. Use the school’s confirmed 2027 scope to decide which exercises belong in immediate examination revision. Spaced practice and changed cases are more useful than copying the same number sequence repeatedly.

Day 2

Compare and order four-digit numbers with zeros in different places.

Day 3

Find constant positive steps of 20, 50, 100 and 200.

Day 4

Find negative steps and work backward from a known term.

Day 5

Solve missing middle terms, checking both adjacent differences.

Day 6

Solve missing-digit inequalities, including cases with more than one valid answer.

Day 7

Use a short mixed unseen set without chapter headings, then correct the first wrong step.

Frequently asked questions

Are number patterns a P3 MOE syllabus topic?

Yes. Number patterns are listed in the P3 whole-number content, alongside numbers to 10,000 and place value.

Are these exact sequences on a 2027 paper?

No. They are original examples; each school sets its own assessment questions and scope.

What should a child do first?

Find the difference between adjacent known terms, then verify that the same rule works throughout.

Why do sequences cross thousands?

Because a repeated change can require place-value regrouping, just like ordinary addition or subtraction.

Is a missing digit always unique?

No. An inequality can allow several values. Check all conditions and state all valid digits.

Should a P3 child learn algebraic nth-term formulas?

Not as a compulsory requirement for these P3 whole-number objectives. Use accessible arithmetic reasoning first.

How do I check a missing middle term?

Apply the proposed step from the previous term to the blank and from the blank to the next.

What if a child knows the rule but writes the wrong number?

Inspect place-value regrouping and copying separately from pattern understanding.

How much daily practice is appropriate?

A short mixed set with explanations and independent checking is often more informative than many identical questions.

Do P3 schools all test the same term’s topics?

No. Use the actual school’s assessment notice.

Can number patterns be taught with money?

Yes, through fictional regular savings or repeated counts, while keeping values within the child’s current skills.

What should follow this topic?

Connect patterns to four-digit calculations, word-problem relationships and independent inverse checks.

MOE syllabus and further reading

Editorial note, 13 November 2026: All sequence examples are original and are not official school examination questions or claims about a future national Primary 3 paper.