Patterns and Sequences Maths Worksheet - Free Printable

Let's solve the "Patterns & Sequences" worksheet step by step. We'll analyze each pattern and determine the next three shapes or colors in each group.

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Part A: Complete the pattern by drawing the next 3 shapes in each group

We need to identify the repeating pattern in each row and extend it.

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#### 1. □ △ □ △ □
- Pattern: Square, Triangle, Square, Triangle, Square
- Alternating: □ △ (repeat)
- Next 3: △ □ △

✔ Answer: △ □ △

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#### 2. △ □ □ △ □ □ △ □ □
- Pattern: Triangle, Square, Square → repeats
- Sequence: △ □ □ | △ □ □ | △ □ □
- Next 3: △ □ □

✔ Answer: △ □ □

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#### 3. △ ○ ○ △ ○ ○ △ ○ ○
- Pattern: Triangle, Circle, Circle → repeats
- Same as above: △ ○ ○ | △ ○ ○ | △ ○ ○
- Next 3: △ ○ ○

✔ Answer: △ ○ ○

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#### 4. □ □ □ ○ ○ ○ □ □ □ ○ ○ ○
- Pattern: Three squares, then three circles → repeats
- Group: □□□ ○○○ | □□□ ○○○
- Next 3: □ □ □

✔ Answer: □ □ □

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#### 5. □ □ □ □ □ □ □ □ □
- All squares → no variation
- Pattern: Repeating square
- Next 3: □ □ □

✔ Answer: □ □ □

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#### 6. □ △ ◇ □ △ ◇ □ △ ◇
- Pattern: Square, Triangle, Diamond → repeats
- Sequence: □ △ ◇ | □ △ ◇ | □ △ ◇
- Next 3: □ △ ◇

✔ Answer: □ △ ◇

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#### 7. ★ ☆ ○ ☆ ★ ☆ ○ ☆ ★ ☆ ○ ☆
- Let's look closely:
- ★ ☆ ○ ☆ | ★ ☆ ○ ☆ | ★ ☆ ○ ☆
- Pattern: ★ ☆ ○ ☆ → repeats every 4 shapes
- So after the last ☆, next should be: ★ ☆ ○

✔ Answer: ★ ☆ ○

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#### 8. ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
- All triangles → constant
- Next 3: ▲ ▲ ▲

✔ Answer: ▲ ▲ ▲

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#### 9. □ □ □ □ □ □ □ □ □
- All squares again → same as #5
- Next 3: □ □ □

✔ Answer: □ □ □

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Part B: Create a colour pattern by colouring the shapes

Now we are to color the shapes based on a pattern. Since this is text-based, I’ll describe the coloring pattern for each row.

Assume we can use two colors, e.g., Red and Blue, or any two colors — but the pattern must be consistent.

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#### 1. △ △ △ △ △ △ △ △ △
- All triangles → color them in a repeating pattern.
- Example: Red, Blue, Red, Blue, ...
- But since they're all the same shape, you can create a color pattern like:
- R B R B R B R B R
- Or alternating: R B R B R B R B R

✔ Pattern idea: Alternate colors: Red, Blue, Red, Blue, ...

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#### 2. □ □ □ □ □ □ □ □ □
- All squares → same as above
- Color alternately: R B R B R B R B R

✔ Pattern: Alternating colors

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#### 3. ○ ○ ○ ○ ○ ○ ○ ○ ○
- All circles → again, alternate colors
- R B R B R B R B R

✔ Pattern: Alternating

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#### 4. □ □ □ □ □ □ □ □ □
- All squares → repeat the same alternating pattern
- R B R B R B R B R

✔ Pattern: Alternating

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#### 5. ★ ★ ★ ★ ★ ★ ★ ★ ★
- All stars → same
- R B R B R B R B R

✔ Pattern: Alternating

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✔ Summary of Answers:

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Part A – Next 3 Shapes:

| No. | Pattern | Next 3 Shapes |
|-----|--------|----------------|
| 1 | □ △ □ △ □ | △ □ △ |
| 2 | △ □ □ △ □ □ △ □ □ | △ □ □ |
| 3 | △ ○ ○ △ ○ ○ △ ○ ○ | △ ○ ○ |
| 4 | □ □ □ ○ ○ ○ □ □ □ ○ ○ ○ | □ □ □ |
| 5 | □ □ □ □ □ □ □ □ □ | □ □ □ |
| 6 | □ △ ◇ □ △ ◇ □ △ ◇ | □ △ ◇ |
| 7 | ★ ☆ ○ ☆ ★ ☆ ○ ☆ ★ ☆ ○ ☆ | ★ ☆ ○ |
| 8 | ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ | ▲ ▲ ▲ |
| 9 | □ □ □ □ □ □ □ □ □ | □ □ □ |

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Part B – Colour Patterns (Example):

For all rows, you can use an alternating color pattern, such as:

- Red, Blue, Red, Blue, ...
(or any two colors)

So for each row of 9 shapes:
- Color 1st: Red
- 2nd: Blue
- 3rd: Red
- 4th: Blue
- etc.

This creates a clear, repeating color pattern.

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🔍 Explanation of How to Solve These:

1. Look for repetition: Identify the smallest unit that repeats.
2. Check position: Are shapes alternating? Grouped?
3. Predict next: Use the identified pattern to draw or color the next items.
4. For coloring: Choose a rule (e.g., alternate colors) and apply it consistently.

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Let me know if you'd like a visual version or help with coloring instructions!