Number Patterns worksheet with sequences to complete, featuring whole numbers and fractions.
A worksheet titled "Number Patterns" with exercises to complete numerical sequences, including whole numbers and fractions, from T. Smith Publishing.
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Show Answer Key & Explanations
Step-by-step solution for: Finding Number Patterns Worksheet for 1st - 3rd Grade | Pattern ...
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Show Answer Key & Explanations
Step-by-step solution for: Finding Number Patterns Worksheet for 1st - 3rd Grade | Pattern ...
Explanation:
Let’s go through each number pattern one by one. The goal is to find the rule (like adding a certain number each time, or multiplying, or alternating) and fill in the missing numbers.
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1. 0, 2, 4, __, 8, 10, __, 14, __, __, 20
Look at the differences:
2 − 0 = 2
4 − 2 = 2
So it's +2 each time.
Next: 4 + 2 = 6
Then: 10 + 2 = 12
14 + 2 = 16
16 + 2 = 18
✔ So: 6, 12, 16, 18
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2. 1, __, 3, __, 5, 6, 7, __, 9, 10, __
Check: 1 → ? → 3 → ? → 5 → 6 → 7 → ? → 9 → 10 → ?
From 5 to 6 to 7: +1 each
From 7 to 9: skip 8? Wait — maybe it's just counting up from 1, but some blanks are missing. Let’s list positions:
1, ?, 3, ?, 5, 6, 7, ?, 9, 10, ?
If it’s natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Yes! So blanks are:
2nd = 2, 4th = 4, 8th = 8, 11th = 11
✔ So: 2, 4, 8, 11
---
3. 0, __, 6, 9, 12, __, 18, __, 24, __, 30
Differences:
6 − ? = ?
But 6 → 9 = +3
9 → 12 = +3
12 → ? → 18 → so likely +3 again: 12 + 3 = 15
18 + 3 = 21
24 + 3 = 27
Now what about first blank? 0 → ? → 6
If +3 each: 0, 3, 6, 9,... Yes!
✔ So: 3, 15, 21, 27
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4. 10, 20, 30, __, 50, 60, __, 80, 90, __, 110
Clearly multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110
✔ So: 40, 70, 100
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5. 5, __, 15, __, 25, 30, 35, __, 45, 50, 55
Look: 5 → ? → 15 → ? → 25 → 30 → 35 → ? → 45...
From 25 to 30 = +5
30 to 35 = +5
35 to 45 = +10? Hmm — maybe two patterns?
Wait: Try listing expected if +5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
Yes! That fits perfectly.
So blanks: 10, 20, 40
✔ So: 10, 20, 40
---
6. 6, __, 10, 12, 14, 16, __, 20, 22, __, 26
Differences:
10 − ? = ?
But 10 → 12 = +2
12 → 14 = +2
14 → 16 = +2
So likely +2 throughout.
Then: 6 → ? → 10 ⇒ ? = 8
16 → ? → 20 ⇒ ? = 18
22 → ? → 26 ⇒ ? = 24
✔ So: 8, 18, 24
---
7. 100, 90, __, 70, 60, __, 40, __, 20, 10, 0
Decreasing by 10:
100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0
✔ So: 80, 50, 30
---
8. 4, 8, 12, __, 20, __, 28, 32, 36, 40, __
+4 each time:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
✔ So: 16, 24, 44
---
9. __, 11, 10, 9, __, 7, __, 5, 4, 3, __
Going down: 11 → 10 → 9 → ? → 7 → ? → 5 → 4 → 3 → ?
Looks like decreasing by 1 each step.
So before 11: 12
After 9: 8
After 7: 6
After 3: 2
✔ So: 12, 8, 6, 2
---
10. 20, 40, 60, 80, 100, 120, __, 160, __, 200
+20 each time:
20, 40, 60, 80, 100, 120, 140, 160, 180, 200
✔ So: 140, 180
---
Now the thinking cap part:
A. .5, 1, 1.5, __, 2.5, 3, 3.5, 4, 4.5, __, 5.5
This increases by 0.5 each time.
1.5 + 0.5 = 2
4.5 + 0.5 = 5
✔ So: 2, 5
B. 1/2, 1, 1 1/2, 2, __, 3, 3 1/2, 4, 4 1/2, __
Same as above: +1/2 each time.
2 + 1/2 = 2 1/2
4 1/2 + 1/2 = 5
✔ So: 2 1/2, 5
Now compile all answers in order:
1. 6, 12, 16, 18
2. 2, 4, 8, 11
3. 3, 15, 21, 27
4. 40, 70, 100
5. 10, 20, 40
6. 8, 18, 24
7. 80, 50, 30
8. 16, 24, 44
9. 12, 8, 6, 2
10. 140, 180
A. 2, 5
B. 2 1/2, 5
Let me double-check a few tricky ones:
- #9: __, 11, 10, 9, __, 7, __, 5, 4, 3, __
Sequence: 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2 → yes, correct.
- #7: 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0 → correct.
- B: 1/2 = 0.5, then 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5 → yes.
All consistent.
Final Answer:
1. 6, 12, 16, 18
2. 2, 4, 8, 11
3. 3, 15, 21, 27
4. 40, 70, 100
5. 10, 20, 40
6. 8, 18, 24
7. 80, 50, 30
8. 16, 24, 44
9. 12, 8, 6, 2
10. 140, 180
A. 2, 5
B. 2 1/2, 5
Let’s go through each number pattern one by one. The goal is to find the rule (like adding a certain number each time, or multiplying, or alternating) and fill in the missing numbers.
---
1. 0, 2, 4, __, 8, 10, __, 14, __, __, 20
Look at the differences:
2 − 0 = 2
4 − 2 = 2
So it's +2 each time.
Next: 4 + 2 = 6
Then: 10 + 2 = 12
14 + 2 = 16
16 + 2 = 18
✔ So: 6, 12, 16, 18
---
2. 1, __, 3, __, 5, 6, 7, __, 9, 10, __
Check: 1 → ? → 3 → ? → 5 → 6 → 7 → ? → 9 → 10 → ?
From 5 to 6 to 7: +1 each
From 7 to 9: skip 8? Wait — maybe it's just counting up from 1, but some blanks are missing. Let’s list positions:
1, ?, 3, ?, 5, 6, 7, ?, 9, 10, ?
If it’s natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Yes! So blanks are:
2nd = 2, 4th = 4, 8th = 8, 11th = 11
✔ So: 2, 4, 8, 11
---
3. 0, __, 6, 9, 12, __, 18, __, 24, __, 30
Differences:
6 − ? = ?
But 6 → 9 = +3
9 → 12 = +3
12 → ? → 18 → so likely +3 again: 12 + 3 = 15
18 + 3 = 21
24 + 3 = 27
Now what about first blank? 0 → ? → 6
If +3 each: 0, 3, 6, 9,... Yes!
✔ So: 3, 15, 21, 27
---
4. 10, 20, 30, __, 50, 60, __, 80, 90, __, 110
Clearly multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110
✔ So: 40, 70, 100
---
5. 5, __, 15, __, 25, 30, 35, __, 45, 50, 55
Look: 5 → ? → 15 → ? → 25 → 30 → 35 → ? → 45...
From 25 to 30 = +5
30 to 35 = +5
35 to 45 = +10? Hmm — maybe two patterns?
Wait: Try listing expected if +5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
Yes! That fits perfectly.
So blanks: 10, 20, 40
✔ So: 10, 20, 40
---
6. 6, __, 10, 12, 14, 16, __, 20, 22, __, 26
Differences:
10 − ? = ?
But 10 → 12 = +2
12 → 14 = +2
14 → 16 = +2
So likely +2 throughout.
Then: 6 → ? → 10 ⇒ ? = 8
16 → ? → 20 ⇒ ? = 18
22 → ? → 26 ⇒ ? = 24
✔ So: 8, 18, 24
---
7. 100, 90, __, 70, 60, __, 40, __, 20, 10, 0
Decreasing by 10:
100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0
✔ So: 80, 50, 30
---
8. 4, 8, 12, __, 20, __, 28, 32, 36, 40, __
+4 each time:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
✔ So: 16, 24, 44
---
9. __, 11, 10, 9, __, 7, __, 5, 4, 3, __
Going down: 11 → 10 → 9 → ? → 7 → ? → 5 → 4 → 3 → ?
Looks like decreasing by 1 each step.
So before 11: 12
After 9: 8
After 7: 6
After 3: 2
✔ So: 12, 8, 6, 2
---
10. 20, 40, 60, 80, 100, 120, __, 160, __, 200
+20 each time:
20, 40, 60, 80, 100, 120, 140, 160, 180, 200
✔ So: 140, 180
---
Now the thinking cap part:
A. .5, 1, 1.5, __, 2.5, 3, 3.5, 4, 4.5, __, 5.5
This increases by 0.5 each time.
1.5 + 0.5 = 2
4.5 + 0.5 = 5
✔ So: 2, 5
B. 1/2, 1, 1 1/2, 2, __, 3, 3 1/2, 4, 4 1/2, __
Same as above: +1/2 each time.
2 + 1/2 = 2 1/2
4 1/2 + 1/2 = 5
✔ So: 2 1/2, 5
Now compile all answers in order:
1. 6, 12, 16, 18
2. 2, 4, 8, 11
3. 3, 15, 21, 27
4. 40, 70, 100
5. 10, 20, 40
6. 8, 18, 24
7. 80, 50, 30
8. 16, 24, 44
9. 12, 8, 6, 2
10. 140, 180
A. 2, 5
B. 2 1/2, 5
Let me double-check a few tricky ones:
- #9: __, 11, 10, 9, __, 7, __, 5, 4, 3, __
Sequence: 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2 → yes, correct.
- #7: 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0 → correct.
- B: 1/2 = 0.5, then 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5 → yes.
All consistent.
Final Answer:
1. 6, 12, 16, 18
2. 2, 4, 8, 11
3. 3, 15, 21, 27
4. 40, 70, 100
5. 10, 20, 40
6. 8, 18, 24
7. 80, 50, 30
8. 16, 24, 44
9. 12, 8, 6, 2
10. 140, 180
A. 2, 5
B. 2 1/2, 5
Parent Tip: Review the logic above to help your child master the concept of pattern worksheet for third.
