2nd Grade Math Geometric Shapes Pattern Worksheets

Let's solve each pattern step by step. The goal is to identify the repeating sequence of shapes and then draw the next shapes in the blank boxes to continue the pattern.

---

1)

Pattern: □ △ □□ △ □ △ □□ △
→ Repeating group: □ △ □□ △

Break it down:
- Group 1: □ △ □□ △
- Group 2: □ △ □□ △

So, next should be: □ △ □□ △

But since only three boxes are given, we need to fill the next three shapes after the last △.

After △ (end of group), next is □, then △, then □□ → but wait, let’s count:

Sequence:
1. □
2. △
3. □□ (two squares)
4. △
5. □
6. △
7. □□
8. △
9. ? → Should be □
10. ? → Then △
11. ? → Then □□

So, next three: □, △, □□

✔ Answer: □, △, □□

---

2)

Pattern: □ ∞ □△ □ ∞ □△
→ Repeating unit: □ ∞ □△

So:
- Group 1: □ ∞ □△
- Group 2: □ ∞ □△
- Next group: □ ∞ □△

So, next three: □, ∞, □△

✔ Answer: □, ∞, □△

---

3)

Pattern: ▷ ▷▷ ▷▷▷ ▷▷▷▷
→ Number of triangles increases by one each time:
- 1 triangle → 2 → 3 → 4

Next: 5 triangles

So, draw: ▷▷▷▷▷

✔ Answer: ▷▷▷▷▷

---

4)

Pattern: △ ○○ △ △ ○○ △
Wait — let’s list carefully:

Given:
1. △
2. ○○ (two circles)
3. △
4. △
5. ○○
6. △
7. △
8. ○○
9. △

Wait — that doesn’t look right. Let's recheck:

Actually, the image shows:

△ ○○ △ △ ○○ △ △ ○○ △

Wait — maybe it's grouped as:

- △ ○○ △
- △ ○○ △
- △ ○○ △

But first group: △ ○○ △
Second: △ ○○ △
Third: △ ○○ △

Yes! So repeating unit: △ ○○ △

So next three: △, ○○, △

✔ Answer: △, ○○, △

---

5)

Pattern: △ □ ○ □ △ □
Wait — let’s list them:

1. △
2. □
3. ○
4. □
5. △
6. □
7. ?

Wait — no, looking at the image:

It says:
△ □ ○ □ △ □

Wait — perhaps:

1. △
2. □
3. ○
4. □
5. △
6. □

That’s not a clear repeat.

Wait — actually, the image shows:

△ □ ○ □ △ □

No — better to look at the full sequence:

Looking closely:
△, □, ○, □, △, □

Wait — this seems like two parts.

Wait — perhaps it's:

△, □, ○, □, △, □ → Not matching.

Wait — let's re-express:

From the worksheet:
△ □ ○ □ △ □

But the next box is after □.

Wait — perhaps there’s a typo? Or maybe it’s:

Look again:
It says:
△ □ ○ □ △ □

Then blank boxes.

But if we look at positions:

1. △
2. □
3. ○
4. □
5. △
6. □

Now, does this repeat?

Wait — maybe the pattern is: △ □ ○ □, then repeats?

But after that, we have △ □ — which could be start of next cycle.

Wait — perhaps the pattern is: △ □ ○ □ → then △ □ — incomplete.

Wait — let’s try another approach.

Maybe it's alternating between triangle and square, with circle inserted?

Wait — let's check the actual image description.

Alternatively, perhaps the pattern is:

Group: △ □ ○ □
Then △ □ → so maybe missing ○ □?

Wait — maybe it's △ □ ○ □, then △ □ ○ □, etc.

But we have: △ □ ○ □ △ □

So far:
1. △
2. □
3. ○
4. □
5. △
6. □

So from 1–4: △ □ ○ □
Then 5–6: △ □ — so maybe next is ○ □?

But that would make the pattern: △ □ ○ □, △ □ ○ □, ...

So after △ □, next is ○ □

So next three: ○, □, ○? No — only three boxes.

Wait — after position 6 (□), next should be ○, then □, then ○?

But that breaks the rhythm.

Wait — maybe the pattern is △ □ ○ □, repeated.

So:
- First: △ □ ○ □
- Second: △ □ ○ □
- Third: △ □ ○ □

We have: △ □ ○ □ △ □ → so far: first group complete, second group started: △ □

So next: ○, □, △? But that would be too long.

Wait — no, the third group starts with △, but we already have △ at position 5.

Wait — position 5: △ — that’s the start of second group.

Position 6: □ — that’s second shape of second group.

So second group: △ □ → needs ○ □

So next two: ○, □

But we have three boxes to fill.

So after □ (position 6), next: ○, □, and then △?

Wait — but that would make the third group start.

But the pattern is four-shape repeat: △ □ ○ □

So:
- Group 1: △ □ ○ □
- Group 2: △ □ ○ □
- Group 3: △ □ ○ □

So after △ □ ○ □ △ □ → next should be: ○, □, △? No — wait.

After △ □ (start of group 2), we need ○ □ to finish group 2.

But we already have △ □ at positions 5 and 6.

So group 2: positions 5 and 6: △ □ — so we need ○, □ to complete group 2.

But then group 3 starts: △

But we have three boxes.

So:

Box 1: ○
Box 2: □
Box 3: △

But that’s not consistent.

Wait — maybe the pattern is △ □ ○ □, repeated.

So full sequence:
1. △
2. □
3. ○
4. □
5. △
6. □
7. ○
8. □
9. △
10. □
...

So after position 6 (□), next is: ○, □, △

But we have three boxes after position 6.

So:
First blank: ○
Second: □
Third: △

But that makes the pattern: △ □ ○ □ △ □ ○ □ △

Yes — that works.

But is there a mistake?

Wait — let’s write it out:

1. △
2. □
3. ○
4. □
5. △
6. □
7. ○
8. □
9. △

But the worksheet shows: △ □ ○ □ △ □ ___ ___ ___

So after □ (pos 6), next three: ○, □, △

But then the next group would be △ □ ○ □, etc.

So yes.

✔ Answer: ○, □, △

Wait — but that makes the sequence: △ □ ○ □ △ □ ○ □ △ — which is fine.

But is the pattern really △ □ ○ □?

Yes — it repeats every 4 shapes.

So answer: ○, □, △

Wait — but that’s not correct because after □ (pos 6), next is ○ (pos 7), then □ (pos 8), then △ (pos 9).

So for the three blanks: pos 7, 8, 9 → ○, □, △

✔ Yes.

Answer: ○, □, △

---

6)

Pattern: ○ ○ □ △ ○ ○ □
So:
1. ○
2. ○
3. □
4. △
5. ○
6. ○
7. □

Then blank boxes.

So likely: repeating group: ○ ○ □ △

Check:
- Group 1: ○ ○ □ △
- Group 2: ○ ○ □ △

But we have: ○ ○ □ △ ○ ○ □ — so far: first group complete, second group: ○ ○ □

So missing: △

So next three: △, ○, ○

Because next group starts with ○ ○ □ △

So after □ (pos 7), next is △, then ○, then ○

✔ Answer: △, ○, ○

---

7)

Pattern: ♡ ♡ ♡ □ ♡ ♡ ♡
So:
1. ♡
2. ♡
3. ♡
4. □
5. ♡
6. ♡
7. ♡

So pattern: ♡ ♡ ♡ □ repeated?

Group 1: ♡ ♡ ♡ □
Group 2: ♡ ♡ ♡

So next should be: □, then ♡, ♡

But we have three boxes.

After ♡ (pos 7), next is: □, ♡, ♡

So:
Box 1: □
Box 2: ♡
Box 3: ♡

✔ Answer: □, ♡, ♡

---

8)

Pattern: △ △ △ △ △ △
Wait — looks like shaded and unshaded triangles.

Let’s see:

1. Gray triangle (filled)
2. White triangle (unfilled)
3. White triangle
4. Gray triangle
5. White triangle
6. White triangle

Wait — no, the image shows:

- Gray △
- White △
- White △
- Gray △
- White △
- White △

So:
1. Gray
2. White
3. White
4. Gray
5. White
6. White

So pattern: Gray, White, White, then repeat?

Group 1: Gray, White, White
Group 2: Gray, White, White

Yes!

So after 6th (White), next: Gray, White, White

✔ Answer: Gray △, White △, White △

---

9)

Pattern: Octagons with different lines inside.

Each octagon has a line drawn in a certain way.

Let’s analyze:

1. Octagon with diagonal from bottom-left to top-right
2. Octagon with diagonal from top-left to bottom-right
3. Octagon with vertical line
4. Octagon with horizontal line
5. Octagon with diagonal from top-right to bottom-left
6. Octagon with diagonal from bottom-right to top-left

Wait — let’s list:

1. ↘ (bottom-left to top-right)
2. ↙ (top-left to bottom-right)
3. | (vertical)
4. — (horizontal)
5. ↖ (top-right to bottom-left)
6. ↗ (bottom-right to top-left)

Wait — that’s all directions?

Wait — maybe it's rotating diagonals?

Wait — actually, the pattern might be:

Each octagon has a line going through it, and the direction changes.

But look: after 6th, it’s just plain octagons.

Wait — the pattern is:

1. Line from bottom-left to top-right (↗)
2. Line from top-left to bottom-right (↘)
3. Vertical line (|)
4. Horizontal line (—)
5. Line from top-right to bottom-left (↖)
6. Line from bottom-right to top-left (↙)

Wait — now we have all possible lines?

Wait — maybe it's cycling through all 4 diagonals and 2 axes?

Wait — but there are 6 shapes.

Wait — perhaps it's a rotation: each line is rotated 45 degrees?

But octagon has 8 sides.

Alternatively, perhaps the pattern is:

- Diagonal 1: ↘
- Diagonal 2: ↙
- Vertical
- Horizontal
- Diagonal 3: ↖
- Diagonal 4: ↗

So all four diagonals and two axes — total 6.

Then next should be back to ↘?

But the next ones are empty octagons.

Wait — the worksheet shows:

After 6th, it’s: octagon, octagon, octagon

But the 7th, 8th, 9th are blank.

Wait — but the pattern may be that the line rotates.

Wait — perhaps the pattern is repeating every 4?

But 6 shapes shown.

Wait — maybe it’s:
1. ↘
2. ↙
3. |
4. —
5. ↖
6. ↗

Then next: ↘, ↙, |

So next three: ↘, ↙, |

But the shapes are blank — so we need to draw the lines.

So:

1st blank: ↘ (bottom-left to top-right)
2nd: ↙ (top-left to bottom-right)
3rd: | (vertical)

✔ Answer: Draw lines: ↘, ↙, |

---

10)

Pattern: L-shapes

1. L-shape pointing right-bottom
2. L-shape pointing left-bottom
3. L-shape pointing up-right
4. L-shape pointing down-left
5. L-shape pointing right-bottom

Wait — let’s describe:

1. L: right and down
2. L: left and down
3. L: up and right
4. L: down and left
5. L: right and down

So sequence:
1. ↘ (right-down)
2. ↙ (left-down)
3. ↗ (up-right)
4. ↖ (down-left)
5. ↘ (right-down)

So pattern: ↘, ↙, ↗, ↖, ↘

So it might be rotating?

Wait — after ↖ (4), next is ↘ (5)

So maybe it’s a cycle: ↘, ↙, ↗, ↖, then ↘ again?

So next: ↙, ↗, ↖

So:

6. ↙
7. ↗
8. ↖

✔ Answer: L-shapes pointing: left-down, up-right, down-left

---

✔ Final Answers:

1) □, △, □□
2) □, ∞, □△
3) ▷▷▷▷▷
4) △, ○○, △
5) ○, □, △
6) △, ○, ○
7) □, ♡, ♡
8) Gray△, White△, White△
9) ↘, ↙, |
10) ↙, ↗, ↖

---

> Note: For drawing, you would sketch the shapes accordingly. Since this is text-based, I've described the shapes using symbols or directions.

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