Recognizing Patterns math worksheet for identifying and completing shape sequences.

Let’s go row by row and find the pattern in each. We’re looking for what shape comes next based on the sequence shown.

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Row 1:
Shapes: ▷ ◁ ✦ ▷ ◁ ✦ ▷ ___
Pattern: Triangle right, triangle left, star → repeats every 3 shapes.
After ▷ (right triangle), we had ◁ then ✦, then back to ▷, so after this ▷ should come ◁? Wait — let’s list positions:

1. ▷
2. ◁
3. ✦
4. ▷
5. ◁
6. ✦
7. ▷ ← this is position 7
So next (position 8) should be ◁? But wait — look at the answer choices on the right: they show three options per row. For Row 1, the options are: ✦ ▷

Wait — actually, looking again: The last shape given is ▷ (position 7). Since the pattern is repeating every 3: positions 1,4,7 = ▷; 2,5,8 = ; 3,6,9 = ✦. So position 8 should be ◁.

But hold on — maybe I miscounted. Let me write it clearly:

Sequence:
Pos 1: ▷
Pos 2: ◁
Pos 3: ✦
Pos 4: ▷
Pos 5: ◁
Pos 6: ✦
Pos 7: ▷ ← last one shown
Next should be Pos 8: ◁

✔ So first row answer: ◁

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Row 2:
Shapes: ◇ ■ ◇ ■ ◇ ■ ◇ ___
Pattern: diamond, square, repeat.
Positions:
1: ◇
2: ■
3: ◇
4: ■
5: ◇
6: ■
7: ◇ ← last shown
Next (pos 8): ■

Answer choices on right: ◇ ■ ◇ → so ■ is middle option.

✔ Second row answer: ■

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Row 3:
Shapes: ● ◇ ◆ ● ◇ ◆ ● ◇ ___
Pattern: circle, diamond, rhombus? Wait — let’s label:

Actually:
● = circle
◇ = diamond (square rotated)
◆ = filled diamond? Or same as ◇ but shaded? In image, looks like:

Looking carefully:
It goes: black circle, white diamond, gray diamond, black circle, white diamond, gray diamond, black circle, white diamond, ___

So pattern: [black circle], [white diamond], [gray diamond] — repeat every 3.

Positions:
1: ● (black circle)
2: ◇ (white diamond)
3: ◆ (gray diamond)
4: ●
5: ◇
6: ◆
7: ●
8: ◇
9: ? → should be ◆ (gray diamond)

Answer choices on right: ● ◇ ◆ → so third one is ◆

✔ Third row answer: ◆

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Row 4:
Shapes: ● ◆ ● ◆ ● ◆ ● ◇ ___
Wait — let’s list:

1: ● (circle)
2: ◆ (filled diamond)
3: ●
4: ◆
5: ●
6: ◆
7: ●
8: ◇ (white diamond?) ← different!
Then blank.

Hmm — up to position 7: alternating ● and ◆. Then position 8 is ◇ — which breaks the pattern? Or maybe new pattern?

Wait — perhaps it’s two patterns? Or mistake?

Wait — let’s count again from start:

Given: ● ◆ ● ◆ ● ◆ ● ◇ ___

That’s 8 shapes shown, need 9th.

From 1 to 7: ● ◆ ● ◆ ● ◆ ● → that’s 4 circles and 3 diamonds, alternating starting with circle.

Then 8th is ◇ — which is a different diamond? Maybe it’s signaling change?

Alternatively — maybe the pattern changed at position 8? But that seems odd.

Wait — perhaps I misread. Let me check the original problem layout.

Actually, looking back — in Row 4, the sequence is:

● ◆ ● ◆ ● ◆ ● ◇ ___

And answer choices on right: ● ◇ ◆

Perhaps the pattern is: groups of two? Or maybe it’s ● ◆ repeated, but then at position 8 it’s ◇, meaning the next should continue with something else?

Another idea: maybe it’s pairs: (● ◆), (● ◆), (● ◆), then (● ◇) — so next might be ◆? Because if the pair is changing from ◆ to ◇, maybe next is still ◆? Not clear.

Wait — let’s think differently. Maybe the pattern is based on color or fill?

In many such worksheets, sometimes the pattern alternates type and fill.

But here: positions 1,3,5,7: all ● (black circle)
Positions 2,4,6: all ◆ (filled diamond)
Position 8: ◇ (unfilled diamond) — so maybe now it switches to unfilled?

If so, then position 9 should be ●? But ● is already used.

Or perhaps the pattern is: circle, filled-diamond, circle, filled-diamond... until position 7 is circle, then position 8 is unfilled-diamond, so maybe position 9 is circle again? But that would break symmetry.

Wait — another approach: count how many of each before the break.

Up to position 7: 4 circles, 3 filled diamonds.

Position 8: unfilled diamond — so maybe now it’s switching to unfilled versions?

Then position 9 should be circle? But circle doesn’t have an unfilled version shown? All circles are black.

This is confusing.

Wait — let’s look at the answer choices for Row 4: ● ◇ ◆

Maybe the intended pattern is simpler: perhaps it’s alternating ● and ◆, but position 8 is a typo? Unlikely.

Alternative idea: maybe the pattern is “● ◆” repeating, but after three full cycles (positions 1-6), then position 7 is ●, position 8 is ◇ (which is like ◆ but empty), so perhaps the next is ◆ to complete a set? Not logical.

Wait — let’s consider that in some patterns, the last element introduces a variation.

Perhaps: the first six are strict alternation: ● ◆ ● ◆ ● ◆

Then position 7: ● (same as before)

Position 8: ◇ — which is different from ◆ — so maybe now the diamond changes to unfilled, and the circle stays?

Then position 9 should be ●? But that would make it ● ◇ ● — which isn't symmetric.

Another thought: maybe the pattern is grouped as:

(● ◆) (● ◆) (● ◆) (● ◇) — so the fourth group has ◇ instead of ◆, so perhaps the next group starts with ●? But we only need one more shape.

I think I made a mistake earlier. Let me recount the shapes in Row 4 as presented:

The user's image shows for Row 4:

Left side: ● ◆ ● ◆ ● ◆ ● ◇ ___ → that’s 8 shapes, need 9th.

Right side options: ● ◇ ◆

Now, notice: from position 1 to 6: perfect alternation of ● and ◆.

Position 7: ● — which continues the circle part.

Position 8: ◇ — which is a diamond but not filled — so perhaps the "diamond" type is changing from filled to unfilled.

If that’s the case, then the pattern might be: circle, [diamond-type], circle, [diamond-type], etc., where diamond-type was filled for first three times, now becomes unfilled.

So position 9 should be circle? But circle is always filled — no unfilled circle shown.

Unless... position 9 is ◆? To go back? That doesn’t fit.

Wait — perhaps the pattern is not about fill, but about the sequence being interrupted.

Let’s try a different angle: maybe it’s two interleaved sequences.

Odd positions: 1,3,5,7: all ● — so position 9 (odd) should also be ●.

Even positions: 2,4,6: ◆, position 8: ◇ — so even positions are changing from ◆ to ◇.

If that’s the case, then position 9 is odd, so should be ●.

And ● is one of the answer choices.

Also, in the answer choices for Row 4: ● ◇ ◆ — so ● is first option.

Moreover, if we assume that the circle sequence is constant on odd positions, then yes.

So position 9: ●

✔ Fourth row answer: ●

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Row 5:
Shapes: ▲ ▼ ▲ ▼ ▲ ▼ ▲ ___
Pattern: up-triangle, down-triangle, repeat.

Positions:
1: ▲
2: ▼
3: ▲
4: ▼
5: ▲
6: ▼
7: ▲ ← last shown
Next (pos 8): ▼

Answer choices on right: ▲ ▼ ● → so ▼ is middle.

✔ Fifth row answer: ▼

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Row 6:
Shapes: ◇ ● ◆ ◇ ● ◆ ◇ ● ___
Pattern: diamond, circle, filled-diamond, repeat every 3.

List:

1: ◇ (white diamond)
2: ● (circle)
3: ◆ (filled diamond)
4: ◇
5: ●
6: ◆
7: ◇
8: ●
9: ? → should be ◆

Answer choices on right: ◇ ● ◆ → so third is ◆

✔ Sixth row answer: ◆

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Row 7:
Shapes: ★ ☆ ★ ☆ ★ ☆ ★ ___
Pattern: star, hollow-star, repeat.

Positions:
1: ★
2: ☆
3: ★
4: ☆
5: ★
6: ☆
7: ★ ← last shown
Next (pos 8): ☆

Answer choices on right: ★ ☆ ■ → so ☆ is middle.

✔ Seventh row answer: ☆

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Row 8:
Shapes: ▼ △ ▽ ▼ △ ▽ ▼ △ ___
Wait — let’s identify:

First shape: ▼ (down-pointing triangle)
Second: △ (up-pointing triangle)
Third: (another down-pointing? Or same as first?) — in image, probably ▼ and ▽ are same? No, likely:

Actually, in standard notation:

▼ = downward triangle
△ = upward triangle
▽ = also downward? Or perhaps it's a different orientation.

Looking at the sequence: ▼ △ ▽ ▼ △ ▽ ▼ △ ___

Assume:

Position 1: ▼ (down)
Position 2: △ (up)
Position 3: ▽ (down, but maybe same as ▼?) — if ▼ and ▽ are both down, then why two symbols?

Perhaps it's a cycle of three distinct shapes: down, up, down-alt? But that seems messy.

Another idea: maybe it's ▼, △, then ▽ is a variant, but let's see the repetition.

From 1 to 6: ▼ △ ▼ △ ▽ — so repeats every 3: [▼, △, ▽]

Then position 7: ▼
Position 8: △
Position 9: ? → should be ▽

Answer choices on right: ▼ △ ▽ → so third is ▽

✔ Eighth row answer: ▽

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Now, compiling all answers:

Row 1: ◁
Row 2: ■
Row 3: ◆
Row 4: ●
Row 5: ▼
Row 6: ◆
Row 7: ☆
Row 8: ▽

But the question says: "Circle the shape that comes next." and for each row, there are three options on the right. We need to select which one matches our prediction.

Since the user didn't specify to list them, but to solve the problem, and the problem is to circle the correct next shape for each row, I think we need to provide the sequence of correct choices.

However, in the context, since it's a worksheet with multiple rows, and the instruction is to circle the shape that comes next for each, the final answer should be the list of correct shapes for each row, in order.

But to match the format, perhaps just state the answers per row.

Since the assistant is to provide the final answer, and it's a multi-part problem, I'll list them.

Final Answer:
Row 1: ◁
Row 2: ■
Row 3: ◆
Row 4: ●
Row 5: ▼
Row 6: ◆
Row 7: ☆
Row 8: ▽

To box it neatly:

◁, ■, ◆, ●, ▼, ◆, ☆, ▽