Printable math worksheet for children to identify and continue growing and repeating patterns using shapes and symbols.

Let's solve each pattern step by step and determine the next shape or figure in each sequence.

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Pattern 1:

Sequence: □ ⭐ □ ⭐ □

- This is a repeating pattern: square, star, square, star, square...
- The pattern alternates between a blue square and a red star.
- The last shape is a square, so the next one should be a star.

✔ Next shape: 🌟 (Red Star)

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Pattern 2:

Sequence:
- First: Green rectangle with 1 purple square on the right
- Second: Green rectangle with 2 purple squares on the right
- Third: Green rectangle with 3 purple squares on the right

- The number of purple squares increases by 1 each time.
- So this is a growing pattern where the number of purple squares grows by 1.

✔ Next shape: Green rectangle with 4 purple squares on the right.

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Pattern 3:

Sequence: ○ ◻ ◻ ○ ◻

- Shapes: Circle, parallelogram, parallelogram, circle, parallelogram
- Let's list them:
1. Circle
2. Parallelogram
3. Parallelogram
4. Circle
5. Parallelogram

Looking at the pattern:
- It seems to repeat every three shapes? Let's check:
- Positions: 1 (○), 2 (◻), 3 (◻), 4 (○), 5 (◻)
- From position 1 to 4: both are circles → suggests a repeating cycle of ○ ◻ ◻

So the pattern is: ○ ◻ ◻ repeating.

- After ○ ◻ ◻ ○ ◻, the next should be ◻ (parallelogram) to complete the second cycle.

✔ Next shape: ◻ (Pink Parallelogram)

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Pattern 4:

Sequence:
- 1st: 1 blue dot
- 2nd: 3 blue dots arranged in a triangle (like a small pyramid)
- 3rd: 6 blue dots arranged in a larger triangle

This looks like triangular numbers:

- 1 = 1
- 3 = 1 + 2
- 6 = 1 + 2 + 3

So the pattern is increasing triangular numbers:
1, 3, 6, ...

Next: 10 dots (1+2+3+4)

The arrangement will be a triangle with 4 rows:
- Row 1: 1 dot
- Row 2: 2 dots
- Row 3: 3 dots
- Row 4: 4 dots

✔ Next shape: A triangle made of 10 blue dots (in a triangular formation with 4 rows).

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Pattern 5:

Sequence:
1. Red rectangle
2. Blue pentagon
3. Red rectangle
4. Red rectangle
5. Blue pentagon

Wait — let's list it carefully:

- 1: 🔴 (rectangle)
- 2: 🔵 (pentagon)
- 3: 🔴 (rectangle)
- 4: 🔴 (rectangle)
- 5: 🔵 (pentagon)

Now look closely:

Is there a repeating pattern?

Let’s see if it's alternating or growing.

But notice:
- Positions: 1 (🔴), 2 (🔵), 3 (🔴), 4 (🔴), 5 (🔵)

Hmm… maybe not obvious.

Wait — could it be that the red rectangles are appearing in groups?

Let’s try grouping:

- Group 1: 🔴 🔵 → then 🔴 🔴 🔵

Wait — perhaps the pattern is alternating pairs?

Try another idea:

Maybe it's a repeating pair: 🔴 🔵, but then it breaks.

Alternatively, look at positions:

- 1: 🔴
- 2: 🔵
- 3: 🔴
- 4: 🔴
- 5: 🔵

No clear repetition yet.

Wait — what if we consider the positions of the blue pentagons?

They appear at positions 2 and 5 → difference of 3.

And red rectangles at 1, 3, 4.

Not helpful.

Wait — maybe it's two red rectangles followed by one blue pentagon, but the first one is just one red.

Let’s re-express:

- 1: 🔴
- 2: 🔵
- 3: 🔴
- 4: 🔴
- 5: 🔵

So after the first 🔴, it goes 🔵, 🔴, 🔴, 🔵

That suggests: 🔴 🔵 🔴 🔴 🔵

Now, if we assume the pattern is: 🔴 🔵 🔴 🔴 🔵, then the next might be 🔴?

But wait — maybe the pattern is alternating between red and blue, but with increasing reds?

Wait — think differently.

What if it's a repeating pattern of two shapes?

Try: 🔴 🔵, 🔴 🔵 → but no, because third is 🔴, fourth is 🔴 — so not matching.

Wait — look again:

Position: 1 → 🔴
2 → 🔵
3 → 🔴
4 → 🔴
5 → 🔵

Could the pattern be: 🔴, 🔵, 🔴, 🔴, 🔵, 🔴, 🔴, 🔴, 🔵... ?

That would be increasing number of reds before a blue.

Let’s test:

- First blue at pos 2 → preceded by 1 red
- Second blue at pos 5 → preceded by 2 reds (pos 3 and 4)
- Then next blue should be preceded by 3 reds?

So after pos 5 (🔵), we need three red rectangles.

So the next shape should be 🔴

Then next: 🔴
Then next: 🔴
Then next: 🔵

So the pattern is: (n reds), 🔵, where n increases by 1 each time.

- First group: 1 🔴, then 🔵 (at pos 2)
- Second group: 2 🔴, then 🔵 (at pos 5)
- Third group: 3 🔴, then 🔵

But wait — in the sequence:
- Pos 1: 🔴 (first red)
- Pos 2: 🔵 (blue) → ends first group
- Pos 3: 🔴 (second red)
- Pos 4: 🔴 (third red)
- Pos 5: 🔵 (blue) → ends second group

So the first group has 1 red + 1 blue
Second group has 2 reds + 1 blue

So the pattern is: (n reds), 1 blue, where n increases by 1 each time.

So far:
- Group 1: 1 🔴, 1 🔵 → positions 1–2
- Group 2: 2 🔴, 1 🔵 → positions 3–5

Now, Group 3 should have 3 🔴, then 🔵

We are at position 5 (last is 🔵), so next should be 🔴

Then next: 🔴
Then next: 🔴
Then next: 🔵

So the next shape (after pos 5) is the first of the 3 reds in the third group.

✔ Next shape: 🔴 (Red Rectangle)

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✔ Final Answers:

1. Red Star (⭐)
2. Green rectangle with 4 purple squares
3. Pink Parallelogram (◻)
4. Triangle of 10 blue dots (arranged in 4 rows: 1+2+3+4)
5. Red Rectangle (🔴)

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Summary of Answers:

| Problem | Next Shape |
|--------|------------|
| 1 | 🌟 (Red Star) |
| 2 | Green rectangle with 4 purple squares |
| 3 | ◻ (Pink Parallelogram) |
| 4 | Triangle of 10 blue dots |
| 5 | 🔴 (Red Rectangle) |

You can now draw these accordingly in the blank spaces on the worksheet!