Geometric Patterns Homework Worksheet for Grade 3, featuring pattern recognition exercises with shapes and arrows.

Let's solve each of the three geometric pattern problems step by step.

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Problem 1:

Pattern:
★ ○ △ ◯ ★ ○ △ ◯ ★ ○ ...

The sequence is:
Star, Circle, Triangle, Cloud, then repeats.

So the core pattern (repeating unit) is:
★ ○ △ ◯ → 4 shapes.

We want to find the 15th figure.

To find which shape is in position 15, divide 15 by the length of the repeating cycle (which is 4):

$$
15 \div 4 = 3 \text{ remainder } 3
$$

This means:
- The pattern repeats 3 full times (covering 12 figures),
- Then we go 3 more steps into the next cycle.

So the 15th figure corresponds to the 3rd shape in the core pattern.

Core pattern positions:
1. ★ (Star)
2. ○ (Circle)
3. △ (Triangle)
4. ◯ (Cloud)

So the 15th figure is a Triangle.

✔ Answer: d. Triangle

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Problem 2:

Pattern:
☆ ☆ □ ☆ ☆ □ ☆ ☆ □ ☆ ...

Core pattern: ☆ ☆ □ → repeats every 3 shapes.

We are asked: What are the next three shapes after the current ones?

Current sequence shown ends with:
... ☆ ☆ □ ☆

Let’s list them in order:

1. ☆
2. ☆
3. □
4. ☆
5. ☆
6. □
7. ☆
8. ☆
9. □
10. ☆

So far: 10 shapes.

Next three should continue the pattern:
After ☆ (10th), the pattern continues as:
11. ☆
12. □
13. ☆

Wait — let's check the cycle again:

Cycle: ☆ ☆ □ → repeats

So after the 10th shape (☆), the next should be:
- 11th: ☆ (first in cycle)
- 12th: ☆ (second in cycle)
- 13th: □ (third in cycle)

But wait! Let's double-check the given pattern:

Given:
☆ ☆ □ ☆ ☆ □ ☆ ☆ □ ☆

Positions:
1. ☆
2. ☆
3. □
4. ☆
5. ☆
6. □
7. ☆
8. ☆
9. □
10. ☆

Yes — so the 10th is ☆, and the next should follow the pattern:
→ 11th: ☆
→ 12th: □
→ 13th: ☆

But look at the options:

a. ☆ ☆ ☆
b. ☆ ☆ □
c. □ ☆ ☆
d. □ ☆ ☆

Wait — we just said the next three should be: ☆, ☆, □

That matches option b: ☆ ☆ □

But let's verify:

After 10th (☆), the next three are:
- 11th: ☆ (start of new cycle)
- 12th: ☆
- 13th: □

Yes → ☆ ☆ □

✔ Answer: b. ☆ ☆ □

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Problem 3:

Pattern:
→ ↓ ← → ↓ ← ...

Each shape is a square with an arrow inside.

List the arrows:
1. → (right)
2. ↓ (down)
3. ← (left)
4. → (right)
5. ↓ (down)
6. ← (left)

So the pattern is: → ↓ ← → ↓ ← ...

Repeats every 3 shapes: → ↓ ←

We need the 11th shape.

Divide 11 by 3:

$$
11 \div 3 = 3 \text{ remainder } 2
$$

So it's the 2nd shape in the cycle.

Cycle:
1. →
2. ↓
3. ←

So the 11th shape is ↓ (down)

Now look at the choices:

a. ↓ (down) → correct
b. ↑ (up) → no
c. → (right) → no
d. ← (left) → no

✔ Answer: a. ↓

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✔ Final Answers:

1. d. Triangle
2. b. ☆ ☆ □
3. a. ↓

Let me know if you'd like this explained visually or in a different format!