4th Grade Resources - Page 36 - ActivInspire Flipcharts, Smart ... - Free Printable

Let's solve each pattern step by step and explain the reasoning behind each.

---

1. 35, ____, 55, 65, 75, 85, 95

Pattern:
Look at the numbers:
- From 55 to 65 → +10
- 65 to 75 → +10
- So it's increasing by 10 each time.

Now go backward from 35:
- 35 + 10 = 45

✔ Answer: 45

---

2. 10, 25, 40, ____, 70, 85

Pattern:
- 10 to 25 → +15
- 25 to 40 → +15
- So adding 15 each time.

Next:
- 40 + 15 = 55

Check: 55 + 15 = 70 ✔

✔ Answer: 55

---

3. 25, ____, 75, 100

Pattern:
From 25 to 75 is +50, but there’s one blank in between.
So two steps from 25 to 75 → must be equal increases.

Let’s suppose the increase is constant:
- Let x be the missing number.
- Then: 25 → x → 75 → 100

From 75 to 100 → +25
So likely increasing by +25 each time.

Then:
- 25 + 25 = 50
- 50 + 25 = 75
- 75 + 25 = 100 ✔

✔ Answer: 50

---

4. 7, 14, 21, ____, 35, 42, 49

Pattern:
- 7 to 14 → +7
- 14 to 21 → +7
- So adding 7 each time.

Next:
- 21 + 7 = 28

Check: 28 + 7 = 35 ✔

✔ Answer: 28

---

5. 100, 90, 80, ____, 60, 50, 40

Pattern:
Decreasing by 10 each time:
- 100 → 90 → 80 → ? → 60 → 50 → 40

So:
- 80 - 10 = 70

✔ Answer: 70

---

6. 1, 3, 6, 10, ____, 21, 28, 36

This looks like triangular numbers.

Let’s check the differences:
- 3 - 1 = 2
- 6 - 3 = 3
- 10 - 6 = 4
- So next difference should be 5 → 10 + 5 = 15

Check next: 15 + 6 = 21 ✔
Then 21 + 7 = 28 ✔
28 + 8 = 36 ✔

✔ Answer: 15

---

7. 23, 26, ____, 32, 35, 38

Pattern:
- 23 to 26 → +3
- Then next should be +3 again → 26 + 3 = 29

Check: 29 + 3 = 32 ✔
32 + 3 = 35 ✔
35 + 3 = 38 ✔

✔ Answer: 29

---

8. 24, 20, 16, ____, 8, 4

Pattern:
- 24 → 20 → -4
- 20 → 16 → -4
- So subtracting 4 each time.

Next:
- 16 - 4 = 12

Check: 12 - 4 = 8 ✔
8 - 4 = 4 ✔

✔ Answer: 12

---

9. 2, 4, 6, ____, 10, 12, 14

Pattern:
Even numbers increasing by 2:
- 2, 4, 6, ?, 10, 12, 14

So:
- 6 + 2 = 8

✔ Answer: 8

---

10. 8, 16, 24, 32, ____, 48, 56

Pattern:
- 8 → 16 → +8
- 16 → 24 → +8
- 24 → 32 → +8
- So add 8 each time.

Next:
- 32 + 8 = 40

Check: 40 + 8 = 48 ✔
48 + 8 = 56 ✔

✔ Answer: 40

---

✔ Final Answers:

1. 45
2. 55
3. 50
4. 28
5. 70
6. 15
7. 29
8. 12
9. 8
10. 40

Let me know if you'd like a visual explanation or chart!