Complete the patterns by drawing the correct shape in each empty box.

Let's solve each pattern in the "Patterns and Sequences Worksheet" step by step. We need to identify the repeating sequence in each row and fill in the missing shapes.

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Row 1:

Shapes:
□ □ ○ □ □ ○ □ □

Pattern:
The sequence is □, □, ○, repeating.

- Positions:
1: □
2: □
3: ○
4: □
5: □
6: ○
7: □
8: □

✔ So, the last two boxes should be □, □

> Answer: □ □

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Row 2:

Shapes:
△ △ △ ✕ △ ✕ △ ✕

Pattern:
We see:
- First three: △, △, △
- Then a ✕ (plus)
- Then △, then ✕, then △, then ✕

Wait — let’s look carefully:

Positions:
1: △
2: △
3: △
4: ✕
5: △
6: ?
7: ?
8: ✕

After position 4, it goes: △, ?, ?, ✕

But notice: from position 5 onward: △, ?, ?, ✕ — and we know that at position 8 is ✕.

So maybe the pattern is alternating between △ and ✕? But not exactly.

Wait — perhaps the pattern is three △s followed by one ✕, then repeats?

But after the first three △s and one ✕, we have:
- Position 5: △
- Position 6: ?
- Position 7: ?
- Position 8: ✕

That doesn't fit a 3-1 cycle.

Alternative idea: Maybe it's △, △, △, ✕, then △, ✕, △, ✕?

No, inconsistent.

Wait — look again:

1: △
2: △
3: △
4: ✕
5: △
6: ?
7: ?
8: ✕

Now check if it's △, △, △, ✕, then △, ✕, △, ✕ — but that would make positions 5–8: △, ✕, △, ✕ → which matches what we have!

So the full pattern might be:

△ △ △ ✕ △ ✕ △ ✕

But wait — that’s only 8 items. Is this a repeating pattern?

Alternatively, could it be △, △, △, ✕, then △, ✕, △, ✕ — but that’s not repeating.

Wait — another idea: Perhaps the pattern is △, △, △, ✕, and then it changes?

But then position 5 is △, which fits, but position 6 should be △ if continuing the first pattern, but then position 7 would be △, and position 8 would be ✕ — but that would be △ △ △ ✕ again.

But we already had △ △ △ ✕ at positions 1–4, so maybe it's repeating every 4?

Then:
- 1–4: △ △ △ ✕
- 5–8: △ △ △ ✕

But position 5 is △ → OK
Position 6 should be △ → so far so good
Position 7 should be △ → OK
Position 8 should be ✕ → YES! Given

So the pattern is △ △ △ ✕, repeating every 4.

Thus:
- 1: △
- 2: △
- 3: △
- 4: ✕
- 5: △
- 6: △
- 7: △
- 8: ✕

But wait — in the image, position 5 is △, position 6 is blank, position 7 is blank, position 8 is ✕.

So yes — if the pattern is △ △ △ ✕, then:
- 6: △
- 7: △

✔ So △, △

> Answer: △ △

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Row 3:

Shapes:
☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆

Wait — no, let's read:

Given:
1: ☆
2: ⬤ (pentagon)
3: ○
4: ☆
5: ⬤
6: ?
7: ☆
8: ?

Sequence:
1: ☆
2: ⬤
3: ○
4: ☆
5: ⬤
6: ?
7: ☆
8: ?

So:
- 1: ☆
- 2: ⬤
- 3: ○
- 4: ☆
- 5: ⬤
- 6: ?
- 7: ☆
- 8: ?

Look at positions 1–3: ☆, ⬤, ○
Then 4–6: ☆, ⬤, ? → so likely the same pattern

So pattern: ☆, ⬤, ○, repeating every 3.

Check:
- 1: ☆
- 2: ⬤
- 3: ○
- 4: ☆ (start of next cycle)
- 5: ⬤
- 6: ○ → should be ○
- 7: ☆ (next cycle)
- 8: ⬤ → should be ⬤

But wait — position 7 is ☆, so position 8 should be ⬤.

So:
- 6: ○
- 8: ⬤

But position 7 is already ☆, so 8 must be ⬤.

Yes.

✔ So:
- 6: ○
- 8: ⬤

> Answer: ○, ⬤

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Row 4:

Shapes:
1: ❤️
2: ❤️
3: ✕
4: ✕
5: ?
6: ?
7: ✕
8: ✕

So:
- 1: ❤️
- 2: ❤️
- 3: ✕
- 4: ✕
- 5: ?
- 6: ?
- 7: ✕
- 8: ✕

Pattern: Two hearts, then two crosses → repeated?

So: ❤️ ❤️ ✕ ✕, repeat

Then:
- 5: ❤️
- 6: ❤️
- 7: ✕
- 8: ✕

Matches!

So:
- 5: ❤️
- 6: ❤️

✔ Answer: ❤️ ❤️

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Row 5:

Shapes:
1: ?
2: □
3: ◆ (diamond)
4: ?
5: ⬤ (hexagon)
6: □
7: ◆
8: ⭐ (star)

Let’s list:
1: ?
2: □
3: ◆
4: ?
5: ⬤
6: □
7: ◆
8: ⭐

Now observe positions 2–4: □, ◆, ?
Then 5–7: ⬤, □, ◆
Then 8: ⭐

Wait — maybe look for a repeating group.

From position 2: □
3: ◆
4: ?
5: ⬤
6: □
7: ◆
8: ⭐

Notice that:
- 2: □
- 6: □ → every 4 steps?
- 3: ◆
- 7: ◆ → also every 4 steps

So possibly a 4-step pattern?

Let’s try to see:

Assume the pattern starts at position 1.

But we don’t have pos 1.

But look at:
- 2: □
- 3: ◆
- 4: ?
- 5: ⬤
- 6: □
- 7: ◆
- 8: ⭐

Wait — from 2 to 6: □ → □ → 4 apart
3 to 7: ◆ → ◆ → 4 apart

So perhaps the pattern repeats every 4?

But 5 is ⬤, 6 is □, 7 is ◆, 8 is ⭐

So maybe the sequence is:

Let’s suppose the pattern is: A, B, C, D, then repeats.

But we don’t know A.

But look at positions 2–5: □, ◆, ?, ⬤
Then 6–8: □, ◆, ⭐

Wait — 6: □, 7: ◆, 8: ⭐

But 2: □, 3: ◆, so maybe 4: ⬤, 5: ⭐?

But 5 is given as ⬤ (hexagon), not ⭐.

Wait — position 5 is ⬤ (hexagon), position 8 is ⭐ (star).

Maybe not.

Alternative idea: Look at the known values.

Let’s write all:

Pos: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
Shape: ? | □ | ◆ | ? | ⬤ | □ | ◆ | ⭐

Now look at positions 2, 6: both □
3, 7: both ◆
So maybe every 4 positions, same shape?

So:
- Pos 2: □ → pos 6: □ → pos 10: □
- Pos 3: ◆ → pos 7: ◆ → pos 11: ◆

So pattern might be periodic with period 4.

So:
- Pos 1: ?
- Pos 2: □
- Pos 3: ◆
- Pos 4: ?
- Pos 5: ⬤
- Pos 6: □
- Pos 7: ◆
- Pos 8: ⭐

Now, if the pattern repeats every 4, then:
- Pos 1 = Pos 5 = ⬤
- Pos 2 = Pos 6 = □
- Pos 3 = Pos 7 = ◆
- Pos 4 = Pos 8 = ⭐

So:
- Pos 1: ⬤
- Pos 4: ⭐

And we are asked to fill in pos 1 and pos 4.

So:
- 1: ⬤ (hexagon)
- 4: ⭐ (star)

✔ Answer: ⬤, ⭐

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Row 6:

Shapes:
1: ○
2: ☆
3: ?
4: ○
5: ☆
6: ☆
7: ○
8: ?

List:
1: ○
2: ☆
3: ?
4: ○
5: ☆
6: ☆
7: ○
8: ?

Look at:
- 1: ○
- 4: ○ → every 3?
- 7: ○ → yes, every 3

So ○ appears at 1, 4, 7 → so every 3rd box

Similarly:
- 2: ☆
- 5: ☆
- 8: ? → so probably ☆

So:
- 2: ☆
- 5: ☆
- 8: ☆ → yes

Now 3: ?
6: ☆

So what about position 3?

Look at 3, 6, 9... but we only have up to 8.

But 6 is ☆, 3 is ?

Also, 1: ○, 2: ☆, 3: ?, then 4: ○, 5: ☆, 6: ☆

Wait — 6 is ☆, but 3 is ?

But 3 and 6 are both multiples of 3.

But 3: ?, 6: ☆ → different?

But earlier we saw ○ at 1,4,7 → so maybe positions 1,4,7 are ○

Then positions 2,5,8: ☆

So:
- 2: ☆
- 5: ☆
- 8: ☆ → so 8 is ☆

Now what about 3 and 6?

We have:
- 3: ?
- 6: ☆

But 6 is not part of the 2,5,8 pattern — 6 is multiple of 3.

But 3 and 6 are both divisible by 3.

But 3 is ?, 6 is ☆

But 1,4,7: ○ → positions ≡1 mod 3

2,5,8: ☆ → positions ≡2 mod 3

Then 3,6: positions ≡0 mod 3 → what shape?

We have:
- 3: ?
- 6: ☆

But 6 is ☆, so 3 should be ☆ too? But 3 is not filled.

Wait — 6 is ☆, so if pattern is based on modulo 3:

- Pos 1: ○ (mod 1)
- Pos 2: ☆ (mod 2)
- Pos 3: ? (mod 0)
- Pos 4: ○ (mod 1)
- Pos 5: ☆ (mod 2)
- Pos 6: ☆ (mod 0) ← but this is ☆, while pos 3 is ?

But if pos 3 is also ☆, then all mod 0 positions are ☆?

But then why is pos 6 ☆?

But pos 3 is unknown.

But look — 6 is ☆, so maybe all mod 0 positions are ☆?

Then pos 3: ☆

But then what about pos 3?

Wait — but pos 3 is blank, pos 6 is ☆.

So if pattern is:
- mod 1: ○
- mod 2: ☆
- mod 0: ☆

Then:
- pos 3: ☆
- pos 6: ☆
- pos 9: ☆

But pos 1: ○ (mod 1)
pos 2: ☆ (mod 2)
pos 3: ☆ (mod 0)
pos 4: ○ (mod 1)
pos 5: ☆ (mod 2)
pos 6: ☆ (mod 0)
pos 7: ○ (mod 1)
pos 8: ? → mod 2 → ☆

So:
- pos 3: ☆
- pos 8: ☆

But wait — is there a conflict?

But pos 6 is ☆, and pos 3 is ?, so if we assume mod 0 → ☆, then pos 3 = ☆

And pos 8 = ☆

But let’s check if this makes sense.

So sequence:
1: ○ (mod 1)
2: ☆ (mod 2)
3: ☆ (mod 0)
4: ○ (mod 1)
5: ☆ (mod 2)
6: ☆ (mod 0)
7: ○ (mod 1)
8: ☆ (mod 2)

Yes — consistent.

So:
- pos 3: ☆
- pos 8: ☆

But wait — pos 6 is ☆, which is fine.

Is there any contradiction?

But look: pos 3 is ☆, pos 6 is ☆ — both mod 0 → same shape.

But is there another possibility?

Wait — maybe the pattern is ○, ☆, ☆, repeating?

Try:

Group of 3: ○, ☆, ☆

Then:
- 1: ○
- 2: ☆
- 3: ☆
- 4: ○
- 5: ☆
- 6: ☆
- 7: ○
- 8: ☆

Perfect match!

Yes!

So the pattern is ○, ☆, ☆, repeating.

So:
- 1: ○
- 2: ☆
- 3: ☆
- 4: ○
- 5: ☆
- 6: ☆
- 7: ○
- 8: ☆

So:
- 3: ☆
- 8: ☆

✔ Answer: ☆, ☆

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Final Answers:

| Row | Missing Shapes |
|-----|----------------|
| 1 | □, □ |
| 2 | △, △ |
| 3 | ○, ⬤ |
| 4 | ❤️, ❤️ |
| 5 | ⬤, ⭐ |
| 6 | ☆, ☆ |

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Summary of Completed Patterns:

1. □ □ ○ □ □ ○ □ □
2. △ △ △ ✕ △ △ △ ✕
3. ☆ ⬤ ○ ☆ ⬤ ○ ☆ ⬤
4. ❤️ ❤️ ✕ ✕ ❤️ ❤️ ✕ ✕
5. ⬤ □ ◆ ⭐ ⬤ □ ◆ ⭐
6. ○ ☆ ☆ ○ ☆ ☆ ○ ☆

✔ All patterns completed!