2nd Grade Math Pattern Worksheets Using Geometric Shapes

Let's solve each pattern step by step and determine which shape should replace the question mark in each row. The goal is to identify the repeating pattern and then choose the correct shape from the options on the right side of each row.

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🔹 Row 1:

Sequence: □ △ □ △ □ △ ?

Pattern: Alternating square (□) and triangle (△), starting with square.

So: □ △ □ △ □ △ → next should be □

✔ Answer: Square (□)
→ Already circled in the example.

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🔹 Row 2:

Sequence: △ △ □ ? △ △ □

We see: △ △ □ → then ? → then △ △ □

This suggests a repeating group of three: △ △ □

So after △ △ □, we expect △ △ □ again.

But the sequence is:
- Position 1: △
- 2: △
- 3: □
- 4: ?
- 5: △
- 6: △
- 7: □

So the pattern repeats every 3: [△ △ □] [△ △ □]

Thus, position 4 should be the first shape of the second group, which is △

✔ Answer: Triangle (△)

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🔹 Row 3:

Sequence: + ○ ♥ + ○ ♥ ?

Pattern: Repeats every 3: [+ ○ ♥]

So after + ○ ♥ comes another + ○ ♥ → so next should be +

✔ Answer: Plus sign (+)

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🔹 Row 4:

Sequence: ♥ ? △ ♥ △ △ ♥

Let’s look closely:

Position:
1: ♥
2: ?
3: △
4: ♥
5: △
6: △
7: ♥

Try grouping: Maybe a repeating pattern?

Look at positions 1–3: ♥ ? △
Then 4–6: ♥ △ △
Then 7: ♥

Hmm. Let’s try to find a repeating unit.

From position 4: ♥ △ △
And position 1: ♥ ? △

Wait — maybe the pattern is: ♥ △ △, but shifted?

Wait — look at positions 1, 4, 7: all are ♥ → so every 3rd one is ♥

Now positions 3, 5, 7: △, △, ♥ → not consistent.

Alternative idea: Try looking at groups of two?

Another approach: Look at the full sequence:

1: ♥
2: ?
3: △
4: ♥
5: △
6: △
7: ♥

Notice: positions 1, 4, 7 are all ♥ → every third position is ♥

So positions:
- 1: ♥
- 2: ?
- 3: △
- 4: ♥
- 5: △
- 6: △
- 7: ♥

So what about positions 2 and 5? Both are triangles? But 5 is △, so maybe 2 is also △?

But wait — position 3 is △, 5 is △, 6 is △ — too many triangles.

Alternatively, perhaps the pattern is:

Looking at positions 1–3: ♥ ? △
Then 4–6: ♥ △ △
Then 7: ♥

Maybe the pattern is ♥ △ △, but repeated?

But then first group would be ♥ ? △ → so ? must be △ to make it ♥ △ △

So if the pattern is: ♥ △ △, then:

- 1: ♥
- 2: △
- 3: △
- 4: ♥
- 5: △
- 6: △
- 7: ♥

That matches perfectly!

So the missing shape at position 2 is △

✔ Answer: Triangle (△)

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🔹 Row 5:

Sequence: ◆ (Crescent) □ ? (Crescent) □ ◆

So:
1: ◆
2: Crescent
3: □
4: ?
5: Crescent
6: □
7: ◆

Let’s write it clearly:
◆ → Crescent → □ → ? → Crescent → □ → ◆

Now look for repetition.

Try grouping:
- Positions 1–3: ◆ Crescent □
- Then 4–6: ? Crescent □
- Then 7: ◆

Wait — but position 7 is ◆, same as position 1.

Now look at positions 2, 5: both Crescent
Positions 3, 6: both □

So maybe the pattern is: ◆ Crescent □ → then repeat?

But then position 4 should be ◆ (to start the next cycle), but it's followed by Crescent and □.

So:
- 1: ◆
- 2: Crescent
- 3: □
- 4: ?
- 5: Crescent
- 6: □
- 7: ◆

If the pattern is ◆ Crescent □, then:
- 1: ◆
- 2: Crescent
- 3: □
- 4: ◆
- 5: Crescent
- 6: □
- 7: ◆

Perfect! So ? = ◆

✔ Answer: Diamond (◆)

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🔹 Row 6:

Sequence: Cylinder □ Cube Cylinder □ ? Cylinder

Shapes:
1: Cylinder
2: Square (□)
3: Cube
4: Cylinder
5: Square (□)
6: ?
7: Cylinder

Look at the pattern:
- 1: Cylinder
- 2: Square
- 3: Cube
- 4: Cylinder
- 5: Square
- 6: ?
- 7: Cylinder

So the pattern seems to be: Cylinder, Square, Cube, then repeats?

Check:
- 1: Cylinder
- 2: Square
- 3: Cube
- 4: Cylinder → yes, restarts
- 5: Square → yes
- 6: ? → should be Cube
- 7: Cylinder → yes

So missing shape is Cube

✔ Answer: Cube

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🔹 Row 7:

Sequence: Cube Cube ? Cylinder Cube Cube Cylinder

1: Cube
2: Cube
3: ?
4: Cylinder
5: Cube
6: Cube
7: Cylinder

So:
- 1–2: Cube Cube
- 3: ?
- 4: Cylinder
- 5–6: Cube Cube
- 7: Cylinder

Compare with earlier part:
After Cube Cube, comes ? and then Cylinder

Then later: Cube Cube → Cylinder

So likely the pattern is: Cube Cube Cylinder

So:
- 1: Cube
- 2: Cube
- 3: Cylinder → but wait, that would make 3: Cylinder, but then 4 is also Cylinder → conflict.

Wait — no: 3 is ?, 4 is Cylinder.

But 5–6: Cube Cube, 7: Cylinder

So the pattern might be: Cube Cube Cylinder, repeating.

So:
- 1: Cube
- 2: Cube
- 3: Cylinder → but 3 is ?, so should be Cylinder?
- 4: ??? — but 4 is Cylinder, so if 3 is Cylinder, then two Cylinders in a row?

But 4 is Cylinder, so if 3 is Cylinder, then we have Cylinder, Cylinder — but that breaks the pattern.

Wait — let’s list:
1: Cube
2: Cube
3: ?
4: Cylinder
5: Cube
6: Cube
7: Cylinder

So from 1–3: Cube Cube ?
Then 4: Cylinder
Then 5–7: Cube Cube Cylinder

Ah! So 5–7 is Cube Cube Cylinder, same as what we’d expect.

So 1–3 should be Cube Cube Cylinder, so ? = Cylinder

Then 4 is Cylinder — so now we have:
- 3: Cylinder
- 4: Cylinder

But that’s fine — maybe just two cylinders together?

Wait — but then the pattern is:
- Cube Cube Cylinder → (positions 1–3)
- Cylinder → (position 4)
- Cube Cube Cylinder → (positions 5–7)

So the whole thing is: [Cube Cube Cylinder] [Cylinder] [Cube Cube Cylinder]

But that doesn’t seem consistent.

Wait — maybe the pattern is: Cube Cube Cylinder, and it repeats?

But then:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cube → but 4 is Cylinder → contradiction

No.

Wait — maybe it's Cube Cube Cylinder, but only every 3 steps?

But 4 is Cylinder, and 7 is Cylinder — so maybe every 3rd shape is Cylinder?

Let’s check:
- 1: Cube
- 2: Cube
- 3: ?
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So positions 4 and 7 are Cylinder → every 3rd starting from 4?

But 3 is missing.

Wait — notice that 4 and 7 are both Cylinder → difference of 3 → so every 3rd shape from position 4?

But 1, 4, 7: 1 is Cube, 4 is Cylinder, 7 is Cylinder — not consistent.

Alternative idea: Look at positions 1–3: Cube Cube ?
Then 4: Cylinder
Then 5–7: Cube Cube Cylinder

So maybe the pattern is: Cube Cube Cylinder, but with a gap?

Wait — compare 1–3 and 5–7:

- 1: Cube
- 2: Cube
- 3: ?
- 5: Cube
- 6: Cube
- 7: Cylinder

So 5–7 is Cube Cube Cylinder → so likely 3 should be Cylinder to make 1–3: Cube Cube Cylinder

Then 4 is Cylinder — so we have:
- 3: Cylinder
- 4: Cylinder

So two cylinders in a row — acceptable.

Then the full sequence becomes:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

Now, is there a pattern?

Grouping:
- 1–3: Cube Cube Cylinder
- 4: Cylinder
- 5–7: Cube Cube Cylinder

Still odd.

Wait — maybe the pattern is Cube Cube Cylinder, and it repeats every 3:

So:
- 1: Cube
- 2: Cube
- 3: Cylinder → but in the image, 3 is ?, so if we assume 3 = Cylinder, then 4 should be Cube — but 4 is Cylinder → conflict.

No.

Wait — maybe the pattern is Cube Cube Cylinder, but the sequence is:
- 1: Cube
- 2: Cube
- 3: ?
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So from 4 to 7: Cylinder, Cube, Cube, Cylinder → that’s not matching.

Wait — perhaps the pattern is Cube, Cube, Cylinder, and it starts over at position 4?

But position 4 is Cylinder, so if pattern starts at 4: Cylinder, then next should be Cube, Cube, Cylinder...

But 4: Cylinder
5: Cube → ok
6: Cube → ok
7: Cylinder → ok

So pattern starting at 4: Cylinder, Cube, Cube, Cylinder — but that’s not the same as before.

But 1–3: Cube, Cube, ?

So maybe 1–3 is Cube, Cube, Cylinder → so ? = Cylinder

Then 4: Cylinder → so now we have Cylinder, Cylinder — possible.

Then 5–7: Cube, Cube, Cylinder — matches.

So the full pattern is:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So the pattern is: Cube Cube Cylinder, then Cylinder, then Cube Cube Cylinder — but that’s not consistent.

Wait — maybe the pattern is Cube Cube Cylinder, and it repeats every 3, but with overlap?

Alternatively, perhaps it's Cube Cube Cylinder repeated, but shifted.

Wait — let’s suppose the pattern is Cube Cube Cylinder, then Cylinder, then Cube Cube Cylinder

But that doesn’t help.

Wait — look at the shapes on the right: options are: □, Cylinder, Cube

But the missing shape is at position 3.

Given that positions 5 and 6 are Cube, Cube, and 7 is Cylinder → so 5–7 is Cube Cube Cylinder

Similarly, positions 1 and 2 are Cube, Cube → so likely 3 should be Cylinder

Then 4 is Cylinder — so two Cylinders in a row — acceptable.

So even though it looks odd, the most logical choice is that the pattern is Cube Cube Cylinder, repeated.

But then 4 should be Cube — but it’s Cylinder → contradiction.

Wait — unless the pattern is Cube Cube Cylinder, but only every 3 steps?

But 1: Cube, 2: Cube, 3: ? → so ? = Cylinder

Then 4: Cylinder — okay

5: Cube, 6: Cube, 7: Cylinder — perfect

So the sequence is:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So the pattern is: Cube Cube Cylinder, then Cylinder, then Cube Cube Cylinder

But why the extra Cylinder?

Wait — maybe the pattern is Cube Cube Cylinder, and it’s repeated, but the first one is cut off?

No — better idea: Perhaps the pattern is Cube Cube Cylinder, and it repeats every 3, but the sequence has a mistake?

Wait — no, look at the options on the right: they are: □, Cylinder, Cube

But the missing shape is at position 3.

Given that positions 1 and 2 are both Cubes, and 5 and 6 are both Cubes, and 7 is Cylinder, and 4 is Cylinder, it's likely that the pattern is Cube Cube Cylinder, and it repeats.

But then:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cube → but 4 is Cylinder → conflict

So impossible.

Wait — unless the pattern is Cube Cube Cylinder, but the sequence is:
- 1: Cube
- 2: Cube
- 3: ?
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So maybe the pattern is: Cube Cube, then Cylinder, then Cube Cube, then Cylinder

So:
- 1: Cube
- 2: Cube
- 3: ? → but this is the end of first pair
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So the pattern is: Cube Cube Cylinder, then Cube Cube Cylinder

But then:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cube → but 4 is Cylinder → no

Wait — unless the pattern is Cube Cube, then Cylinder, then Cube Cube, then Cylinder

So:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cube → but 4 is Cylinder → no

Wait — perhaps the pattern is: Cube Cube, then Cylinder, then Cube Cube, then Cylinder

But then:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cube → but 4 is Cylinder → contradiction

Unless the pattern is Cube Cube Cylinder, and it starts at position 1:
- 1: Cube
- 2: Cube
- 3: Cylinder → so ? = Cylinder
- 4: Cube → but 4 is Cylinder → no

Wait — unless the pattern is Cube, Cube, Cylinder, and it repeats every 3, but the sequence is:

1: Cube
2: Cube
3: Cylinder
4: Cube
5: Cube
6: Cylinder
7: Cube

But in the image, 7 is Cylinder — so not matching.

Wait — in the image:
- 7: Cylinder

So 7 is Cylinder.

So if the pattern is Cube Cube Cylinder, then:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cube
- 5: Cube
- 6: Cylinder
- 7: Cube

But in image, 7 is Cylinder — so not matching.

Wait — perhaps the pattern is Cube, Cube, Cylinder, and it repeats, but the sequence is:
- 1: Cube
- 2: Cube
- 3: ?
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So maybe the pattern is: Cube Cube Cylinder, but shifted?

Wait — look at positions 4–7: Cylinder, Cube, Cube, Cylinder — that’s not helpful.

Wait — perhaps the pattern is Cube Cube Cylinder, and it appears twice: once at 1–3, once at 5–7.

So:
- 1: Cube
- 2: Cube
- 3: Cylinder → so ? = Cylinder
- 4: ? → but 4 is Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So if 3 is Cylinder, and 4 is Cylinder, and 5–7 is Cube Cube Cylinder, then it's possible that the pattern is Cube Cube Cylinder, and the cylinder at position 4 is just a continuation or error.

But more likely, the pattern is Cube Cube Cylinder, and it repeats every 3, but the sequence is:

1: Cube
2: Cube
3: Cylinder
4: Cube
5: Cube
6: Cylinder
7: Cube

But in the image, 7 is Cylinder — so not matching.

Wait — perhaps I misread.

Let me recheck the image:

Row 7:
- 1: Cube
- 2: Cube
- 3: ?
- 4: Cylinder
- 5: Cube
- 6: Cube
- 7: Cylinder

So 5–7: Cube, Cube, Cylinder — that's Cube Cube Cylinder

1–2: Cube, Cube — so likely 3 should be Cylinder to complete the first group.

Then 4 is Cylinder — so now we have:
- 3: Cylinder
- 4: Cylinder

So two Cylinders — possible.

Then 5–7: Cube, Cube, Cylinder — matches.

So the pattern is: Cube Cube Cylinder, then Cylinder, then Cube Cube Cylinder

But that's not elegant.

Wait — perhaps the pattern is Cube Cube Cylinder, and it repeats every 3, but the sequence is:
- 1: Cube
- 2: Cube
- 3: Cylinder
- 4: Cube
- 5: Cube
- 6: Cylinder
- 7: Cube

But in the image, 7 is Cylinder — so no.

Wait — unless the pattern is Cube Cube Cylinder, and it starts at position 4?

But position 4 is Cylinder, so can't start.

Perhaps the pattern is Cube, Cube, Cylinder, and it's not continuous.

Given that positions 1–2 are Cube, Cube, and 5–6 are Cube, Cube, and 7 is Cylinder, and 4 is Cylinder, the most logical conclusion is that the pattern is Cube Cube Cylinder, and it occurs at positions 1–3 and 5–7.

So:
- 1: Cube
- 2: Cube
- 3: Cylinder → so ? = Cylinder
- 4: Cylinder (extra)
- 5: Cube
- 6: Cube
- 7: Cylinder

So the missing shape is Cylinder

✔ Answer: Cylinder

Even though it's a bit messy, it fits best.

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🔹 Row 8:

Sequence: ◆ ◆ + ◆ ? ◆ ◆

1: ◆
2: ◆
3: +
4: ◆
5: ?
6: ◆
7: ◆

Look at positions:
- 1: ◆
- 2: ◆
- 3: +
- 4: ◆
- 5: ?
- 6: ◆
- 7: ◆

So pattern might be: ◆ ◆ + ◆ ◆ + ◆ ◆

But then 5 should be +, and 6: ◆, 7: ◆

Yes!

So:
- 1: ◆
- 2: ◆
- 3: +
- 4: ◆
- 5: +
- 6: ◆
- 7: ◆

So ? = +

✔ Answer: Plus sign (+)

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🔹 Row 9:

Sequence: ♥ ? ♥ ◆ ♥ ♥ ♥

1: ♥
2: ?
3: ♥
4: ◆
5: ♥
6: ♥
7: ♥

So:
- 1: ♥
- 2: ?
- 3: ♥
- 4: ◆
- 5: ♥
- 6: ♥
- 7: ♥

Look at positions 5–7: ♥ ♥ ♥ — three hearts

Position 4: ◆

Position 3: ♥

Position 1: ♥

So maybe the pattern is: ♥ ? ♥ ◆ ♥ ♥ ♥

Could it be that the pattern is ♥ ♥ ♥, but with a ◆ inserted?

Wait — positions 5–7: ♥ ♥ ♥

Positions 1–3: ♥ ? ♥

So if 1–3 is ♥ ♥ ♥, then ? = ♥

Then 4: ◆

5–7: ♥ ♥ ♥

So the sequence is:
- 1: ♥
- 2: ♥
- 3: ♥
- 4: ◆
- 5: ♥
- 6: ♥
- 7: ♥

But in the image, position 3 is ♥ — yes, so if ? = ♥, then 2 is ♥, so 1–3: ♥ ♥ ♥

Then 4: ◆ — break
Then 5–7: ♥ ♥ ♥

So the pattern might be: Heart Heart Heart, then Crescent, then Heart Heart Heart

But that's not a repeating pattern.

Wait — maybe the pattern is Heart, Heart, Heart, but with a diamond in between?

Alternatively, look at the options on the right: ◆, ♥

So ? could be ◆ or ♥

But if ? = ◆, then sequence: ♥ ◆ ♥ ◆ ♥ ♥ ♥ — not clear.

If ? = ♥, then: ♥ ♥ ♥ ◆ ♥ ♥ ♥ — so two groups of three hearts separated by a diamond.

That makes sense.

So the pattern is: Three hearts, then diamond, then three hearts

So ? = ♥

✔ Answer: Heart (♥)

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🔹 Row 10:

Sequence: ? ◆ △ ☺ ◆ △ ☺

So:
1: ?
2: ◆
3: △
4: ☺
5: ◆
6: △
7: ☺

Look at 2–4: ◆ △ ☺
5–7: ◆ △ ☺

So pattern: ◆ △ ☺ repeats

So the sequence is:
- 1: ?
- 2: ◆
- 3: △
- 4: ☺
- 5: ◆
- 6: △
- 7: ☺

So the pattern starts at position 2: ◆ △ ☺, then repeats at 5.

So position 1 is before that — what should it be?

If the pattern is ◆ △ ☺, and it starts at 2, then position 1 is the beginning.

But what came before?

Wait — maybe the pattern is ◆ △ ☺, and it repeats every 3.

So:
- 2: ◆
- 3: △
- 4: ☺
- 5: ◆
- 6: △
- 7: ☺

So positions 2–7 follow the pattern.

Then position 1 is before — could be anything?

But the pattern should continue.

If the pattern is ◆ △ ☺, then before 2, it should be the previous cycle.

So position 1 should be the last shape of the previous cycle — which is ☺

So sequence: ☺ ◆ △ ☺ ◆ △ ☺

Yes! That works.

So ? = ☺

✔ Answer: Smiley face (☺)

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✔ Final Answers:

| Row | Missing Shape | Reason |
|-----|---------------|--------|
| 1 | □ | Alternating □ △ |
| 2 | △ | Pattern: △ △ □ |
| 3 | + | Pattern: + ○ ♥ |
| 4 | △ | Pattern: ♥ △ △ |
| 5 | ◆ | Pattern: ◆ Crescent □ |
| 6 | Cube | Pattern: Cylinder □ Cube |
| 7 | Cylinder | Pattern: Cube Cube Cylinder |
| 8 | + | Pattern: ◆ ◆ + |
| 9 | ♥ | Pattern: ♥ ♥ ♥, then ◆, then ♥ ♥ ♥ |
| 10 | ☺ | Pattern: ◆ △ ☺ |

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📌 Summary of Answers:

- Row 1: Square
- Row 2: Triangle
- Row 3: Plus sign
- Row 4: Triangle
- Row 5: Diamond
- Row 6: Cube
- Row 7: Cylinder
- Row 8: Plus sign
- Row 9: Heart
- Row 10: Smiley face

You should circle these shapes from the right-hand side choices.