Repeating Patterns Worksheets - 15 Worksheets Library - Free Printable

Let's solve each pattern step by step and extend it based on the repeating sequence.

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1. Pattern: △ ▽ △ ▽ △

- Sequence: Triangle, Inverted Triangle, Triangle, Inverted Triangle, Triangle
- This is an alternating pattern: △ ▽ repeats.
- The last shape is △, so the next should be ▽, then △, then ▽.
- Extension: ▽ △ ▽

✔ Answer: ▽ △ ▽

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2. Pattern: □ ○ □ ○ □

- Sequence: Square, Circle, Square, Circle, Square
- Alternating pattern: □ ○ repeats.
- Last shape is □, so next should be ○, then □, then ○.
- Extension: ○ □ ○

✔ Answer: ○ □ ○

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3. Pattern: ↑ → ↓ ← ↑

- Sequence: Up, Right, Down, Left, Up
- This looks like a cycle of 4 directions: ↑ → ↓ ←, then back to ↑.
- So the full cycle is: ↑ → ↓ ← ↑ (5 shapes)
- The pattern repeats every 4 steps: ↑ → ↓ ←
- Since the last shape is ↑, the next in the cycle would be →, then ↓, then ←.
- Extension: → ↓ ←

✔ Answer: → ↓ ←

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4. Pattern: • •• ••• • ••

- Shapes: Single dot, two dots, three dots, single dot, two dots
- Counting the number of dots:
- 1, 2, 3, 1, 2
- Pattern: 1, 2, 3, then repeats from 1, 2
- So next should be: 3, then 1, then 2
- But we need only 3 more entries.
- After "• •" (which is 2 dots), the next is 3 dots: •••
- Then 1 dot: •
- Then 2 dots: ••
- Extension: ••• • ••

✔ Answer: ••• • ••

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5. Pattern: △ ○ □ △ ○

- Sequence: Triangle, Circle, Square, Triangle, Circle
- Looks like: △ ○ □, then △ ○ — so maybe the base pattern is △ ○ □?
- But it starts over with △ ○ after □.
- Let's check:
Position: 1:△, 2:○, 3:□, 4:△, 5:○
So: △ ○ □ △ ○ — this suggests that the pattern might be △ ○ □ repeating.
- But after □, it goes back to △, which fits the repeat.
- However, the 5th shape is ○, so the pattern is likely: △ ○ □, repeated.
- So far: △ ○ □ △ ○ → missing one more for a full repeat.
- Next should be: □, then △, then ○
- But we only need 3 more shapes.
- After △ ○ comes □
- Then △
- Then ○
- So: □ △ ○

✔ Answer: □ △ ○

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6. Pattern: □ □ ◆ ◆ □

- Sequence: Square, Square, Diamond, Diamond, Square
- So: □ □ ◆ ◆ □
- Looks like a pattern of two squares, two diamonds, then one square again?
- But wait: let’s see if it's repeating in blocks.
- Maybe: □ □ ◆ ◆, then □ — but not yet complete.
- Could it be a larger repeating unit?
- Let’s assume the pattern is □ □ ◆ ◆, and then repeats.
- But the last shape is □, which breaks the symmetry.
- Alternatively, could it be: □ □ ◆ ◆ □ □ ◆ ◆...?
- But we have: □ □ ◆ ◆ □ — so next should be □ (to make another pair), then ◆, then ◆.
- But that would be: □ □ ◆ ◆ □ □ ◆ ◆...
- So after □, we expect □, then ◆, then ◆.
- But the pattern ends at □, so next is: □, ◆, ◆

Wait — let’s re-express:

Sequence:
1: □
2: □
3: ◆
4: ◆
5: □

So it seems like: (□ □) (◆ ◆) (□) — but not symmetric.

But perhaps the pattern is: □ □ ◆ ◆, and then it starts over?

But the fifth is □ — so maybe the pattern is: □ □ ◆ ◆, and then the next □ is the beginning of a new cycle?

That doesn’t fit.

Alternatively, think of it as: □ □ ◆ ◆ □, and now we’re at the start of a new cycle?

But that’s just guessing.

Wait — look again:

It could be: □ □ ◆ ◆, then □, and now we expect the next part of the pattern.

But what if the pattern is □ □ ◆ ◆, and then it restarts? But the fifth shape is □, which is the first of the pair.

So maybe the pattern is: □ □ ◆ ◆, and it repeats.

So positions:
1: □
2: □
3: ◆
4: ◆
5: □ ← this is the first of the next block

Then:
6: □
7: ◆
8: ◆

So the extension is: □ ◆ ◆

✔ Answer: □ ◆ ◆

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✔ Final Answers:

1. ▽ △ ▽
2. ○ □ ○
3. → ↓ ←
4. ••• • ••
5. □ △ ○
6. □ ◆ ◆

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✔ Completed Worksheet:

```
Repeating Patterns
Look at the pattern and extend the pattern.

△ ▽ △ ▽ △ → ▽ △ ▽
□ ○ □ ○ □ → ○ □ ○
↑ → ↓ ← ↑ → → ↓ ←
• •• ••• • •• → ••• • ••
△ ○ □ △ ○ → □ △ ○
□ □ ◆ ◆ □ → □ ◆ ◆
```

Let me know if you'd like this formatted as a printable answer sheet!