Number sequences worksheet with exercises for identifying patterns and completing number sequences.
A worksheet titled "Number sequences" with instructions and exercises for finding missing numbers in number patterns, featuring sections for Ruby, Pearl, and Diamond levels, and a cartoon character illustration.
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Show Answer Key & Explanations
Step-by-step solution for: Print and digital resources for Primary, key stage 1 and 2 Maths
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Show Answer Key & Explanations
Step-by-step solution for: Print and digital resources for Primary, key stage 1 and 2 Maths
Absolutely! Let’s solve each part of the worksheet step by step, explaining the reasoning behind each answer.
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## Ruby Level
- Pattern: Each number increases by 25.
- 250 – 225 = 25
- 275 – 250 = 25
- So, next term: 375 + 25 = 400
✔ Answer: 400
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- Pattern: Adding 1,000 each time.
- 7,000 + 1,000 = 8,000
- 8,000 + 1,000 = 9,000
✔ Answers: 8,000; 9,000
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- Pattern: Adding 7 each time.
- 287 – 280 = 7
- 294 – 287 = 7
- So, 315 + 7 = 322
✔ Answer: 322
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- Look at differences:
- 936 – 927 = 9 → likely adding 9 each time.
- Check backward: 927 – 9 = 918 (missing first blank)
- 936 + 9 = 945 (second missing number)
✔ Answers: 918; 945
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- Pattern: Adding 10 each time.
- 700 – 690 = 10 → so before 690 is 690 – 10 = 680
- After 710: 710 + 10 = 720
✔ Answers: 680; 720
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- Pattern: Adding 6 each time.
- 246 + 6 = 252
✔ Answer: 252
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## Pearl Level
- Pattern: Adding 1,000 each time.
- 98,689 + 1,000 = 99,689
✔ Answer: 99,689
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- Pattern: Subtracting 10 each time.
- 2,974 – 10 = 2,964
✔ Answer: 2,964
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- Pattern: Subtracting 100 each time.
- 802 – 100 = 702
✔ Answer: 702
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- Look at difference between 6,889 and 6,989 = 100 → likely adding 100.
- So before 6,889: 6,889 – 100 = 6,789
- After 6,989: 6,989 + 100 = 7,089
✔ Answers: 6,789; 7,089
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- Pattern: Subtracting 1,000 each time.
- 14,678 – 1,000 = 13,678
- 13,678 – 1,000 = 12,678
✔ Answers: 13,678; 12,678
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- Difference between 129,078 and 139,078 = 10,000 → adding 10,000.
- So working backwards:
- 129,078 – 10,000 = 119,078
- 119,078 – 10,000 = 109,078
✔ Answers: 109,078; 119,078
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## Diamond Level
✘ No, I do not agree.
Explanation:
Only if you start with a number that ends in three zeros (like 1,000, 2,000, etc.) will every term end in three zeros. But if you start from, say, 500, then:
- 500 + 1,000 = 1,500 → ends in two zeros
- 1,500 + 1,000 = 2,500 → still ends in two zeros
So unless the starting number ends in 000, the terms won’t all end in three zeros.
✔ Answer: Disagree — only if you start with a multiple of 1,000 (ending in 000) will all terms end in three zeros.
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✔ Yes, I agree.
Explanation:
Let’s find the difference:
15,678 – 11,678 = 4,000
If they were consecutive terms in a sequence counting by 1,000, the difference would be exactly 1,000. But here it’s 4,000 — meaning there are three terms between them (e.g., 15,678 → 14,678 → 13,678 → 12,678 → 11,678). So they are not consecutive.
✔ Answer: Agree — the difference is 4,000, which means 3 terms lie between them if counting by 1,000.
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1,456, 1,556, 1,656, 1,756, 1,856
Is this correct?
✔ No, Sam is wrong.
Explanation:
Check the difference between terms:
- 1,556 – 1,456 = 100
- 1,656 – 1,556 = 100
- 1,756 – 1,656 = 100
- 1,856 – 1,756 = 100
So the actual step is +100, not +102.
✔ Answer: Disagree — the sequence increases by 100 each time, not 102.
---
## ✔ Final Summary of All Answers:
---
1. 400
2. 8,000; 9,000
3. 322
4. 918; 945
5. 680; 720
6. 252
---
1. 99,689
2. 2,964
3. 702
4. 6,789; 7,089
5. 13,678; 12,678
6. 109,078; 119,078
---
1. Disagree — Only works if starting number ends in 000.
2. Agree — Difference is 4,000, so not consecutive.
3. Disagree — Steps are +100, not +102.
---
Let me know if you’d like this formatted as a printable answer sheet! 😊
---
## Ruby Level
1. Sequence: 225, 250, 275, 300, 325, 350, 375, ___
- Pattern: Each number increases by 25.
- 250 – 225 = 25
- 275 – 250 = 25
- So, next term: 375 + 25 = 400
✔ Answer: 400
---
2. Sequence: 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, ___, ___
- Pattern: Adding 1,000 each time.
- 7,000 + 1,000 = 8,000
- 8,000 + 1,000 = 9,000
✔ Answers: 8,000; 9,000
---
3. Sequence: 280, 287, 294, 301, 308, 315, ___
- Pattern: Adding 7 each time.
- 287 – 280 = 7
- 294 – 287 = 7
- So, 315 + 7 = 322
✔ Answer: 322
---
4. Sequence: 909, ___, 927, 936, ___, 954, 963, 972
- Look at differences:
- 936 – 927 = 9 → likely adding 9 each time.
- Check backward: 927 – 9 = 918 (missing first blank)
- 936 + 9 = 945 (second missing number)
✔ Answers: 918; 945
---
5. Sequence: ___, 690, 700, 710, ___, 730, 740, 750
- Pattern: Adding 10 each time.
- 700 – 690 = 10 → so before 690 is 690 – 10 = 680
- After 710: 710 + 10 = 720
✔ Answers: 680; 720
---
6. Sequence: 240, 246, ___, 258, 264, 270, 276
- Pattern: Adding 6 each time.
- 246 + 6 = 252
✔ Answer: 252
---
## Pearl Level
1. Sequence: 95,689, 96,689, 97,689, 98,689, ___
- Pattern: Adding 1,000 each time.
- 98,689 + 1,000 = 99,689
✔ Answer: 99,689
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2. Sequence: 3,004, 2,994, 2,984, 2,974, ___
- Pattern: Subtracting 10 each time.
- 2,974 – 10 = 2,964
✔ Answer: 2,964
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3. Sequence: 1,102, 1,002, 902, 802, ___
- Pattern: Subtracting 100 each time.
- 802 – 100 = 702
✔ Answer: 702
---
4. Sequence: 6,689, ___, 6,889, 6,989, ___
- Look at difference between 6,889 and 6,989 = 100 → likely adding 100.
- So before 6,889: 6,889 – 100 = 6,789
- After 6,989: 6,989 + 100 = 7,089
✔ Answers: 6,789; 7,089
---
5. Sequence: 15,678, 14,678, ___, ___, 11,678
- Pattern: Subtracting 1,000 each time.
- 14,678 – 1,000 = 13,678
- 13,678 – 1,000 = 12,678
✔ Answers: 13,678; 12,678
---
6. Sequence: 99,078, ___, ___, 129,078, 139,078
- Difference between 129,078 and 139,078 = 10,000 → adding 10,000.
- So working backwards:
- 129,078 – 10,000 = 119,078
- 119,078 – 10,000 = 109,078
✔ Answers: 109,078; 119,078
---
## Diamond Level
1. Jake says: “If you count in steps of 1,000 from any number, each term in the number sequence will end in three zeros.” Do you agree?
✘ No, I do not agree.
Explanation:
Only if you start with a number that ends in three zeros (like 1,000, 2,000, etc.) will every term end in three zeros. But if you start from, say, 500, then:
- 500 + 1,000 = 1,500 → ends in two zeros
- 1,500 + 1,000 = 2,500 → still ends in two zeros
So unless the starting number ends in 000, the terms won’t all end in three zeros.
✔ Answer: Disagree — only if you start with a multiple of 1,000 (ending in 000) will all terms end in three zeros.
---
2. Two terms in a sequence are 15,678 and 11,678. These terms are not consecutive. Do you agree? Explain your thinking.
✔ Yes, I agree.
Explanation:
Let’s find the difference:
15,678 – 11,678 = 4,000
If they were consecutive terms in a sequence counting by 1,000, the difference would be exactly 1,000. But here it’s 4,000 — meaning there are three terms between them (e.g., 15,678 → 14,678 → 13,678 → 12,678 → 11,678). So they are not consecutive.
✔ Answer: Agree — the difference is 4,000, which means 3 terms lie between them if counting by 1,000.
---
3. Sam describes this sequence as counting in steps of 102:
1,456, 1,556, 1,656, 1,756, 1,856
Is this correct?
✔ No, Sam is wrong.
Explanation:
Check the difference between terms:
- 1,556 – 1,456 = 100
- 1,656 – 1,556 = 100
- 1,756 – 1,656 = 100
- 1,856 – 1,756 = 100
So the actual step is +100, not +102.
✔ Answer: Disagree — the sequence increases by 100 each time, not 102.
---
## ✔ Final Summary of All Answers:
---
Ruby
1. 400
2. 8,000; 9,000
3. 322
4. 918; 945
5. 680; 720
6. 252
---
Pearl
1. 99,689
2. 2,964
3. 702
4. 6,789; 7,089
5. 13,678; 12,678
6. 109,078; 119,078
---
Diamond
1. Disagree — Only works if starting number ends in 000.
2. Agree — Difference is 4,000, so not consecutive.
3. Disagree — Steps are +100, not +102.
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Let me know if you’d like this formatted as a printable answer sheet! 😊
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet year 3.
