Can You Complete These Patterns? — Steemit - Free Printable

Let’s go row by row and find the pattern. We’ll look at what shapes repeat and in what order, then figure out which shape is missing (the ?).

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Row 1 (example):
Shapes: □ △ □ △ □ △ ? → Pattern is square, triangle, repeating. After △ comes □. So answer is □ — already circled.

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Row 2:
△ △ □ ? △ △ □
Look: Two triangles, one square, then ? , then two triangles, one square.
So the pattern is: △ △ □ | △ △ □
That means the ? should be the start of the next group → △

Wait — let’s check positions:

Position: 1=△, 2=△, 3=□, 4=?, 5=△, 6=△, 7=□
If it repeats every 3: positions 1-3 = △△□, positions 5-7 = △△□ → so position 4 should match position 1? No, that doesn’t fit.

Actually, maybe it’s grouped as: [△ △ □] [? △ △] [□] — no, that breaks.

Better way: Look at the full sequence:
△ △ □ ? △ △ □

Notice: The last three are △ △ □ — same as first three if we ignore the ?. So maybe the pattern is △ △ □ repeated. Then position 4 should be the start of the second group → which is △.

Yes! So ? = △

But wait — let’s count:

Group 1: pos1-3 → △ △ □
Group 2: pos4-6 → ? △ △ → to match group1, ? should be □? But then pos7 is □ — that would make group2: □ △ △ — not matching.

Alternative: Maybe it’s symmetric? Or alternating?

Try this: Write indices:

1: △
2: △
3: □
4: ?
5: △
6: △
7: □

Compare 1&5: both △
2&6: both △
3&7: both □
So 4 should match... what? There’s no pair for 4 yet. Unless the pattern is 3-shape repeat: △△□, then again △△□ — so position 4 should be △ (start of second group), position 5=△, 6=□? But position 6 is △, 7 is □ — that doesn’t fit.

Wait — position 5=△, 6=△, 7=□ → that’s a full group. So positions 5-7 = △△□. Then positions 1-3 = △△□. So position 4 must be the beginning of the middle part? That doesn’t work.

Perhaps it’s: △ △ □ △ △ □ — but there’s a ? in between. Total 7 items. If pattern is 3, then 7 mod 3 = 1, so maybe incomplete.

Another idea: Maybe the ? is where the pattern restarts? Let’s assume the pattern is “two triangles, one square” repeating.

So:
Positions 1-3: △ △ □
Positions 4-6: should be △ △ □ → but position 5 is △, 6 is △, 7 is □ → so position 4 should be △, position 5=△, 6=□? But position 6 is △, not □. Contradiction.

Wait — look again: the sequence is:
△ △ □ ? △ △ □

What if we split as:
First three: △ △ □
Last three: △ △ □
Then the middle one (?) is extra? But that doesn’t help.

Perhaps it’s a palindrome? Read forward and backward:

Forward: △ △ □ ? △ △ □
Backward: □ △ △ ? □ △ △ — not the same.

Let me try a different approach. Maybe the pattern is based on position modulo 3.

Pos 1: △
Pos 2: △
Pos 3: □
Pos 4: ?
Pos 5: △ → same as pos 2?
Pos 6: △ → same as pos 3? No, pos 3 is □.

This is tricky. Let’s skip and come back.

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Row 3:
+ ○ ♥ + ○ ♥ ?
Pattern: plus, circle, heart, repeat.
So after ♥ comes +. So ? = +

Check: positions 1-3: +○♥, 4-6: +○♥, so 7 should be + → yes.

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Row 4:
♥ ? △ ♥ △ △ ♥
Let’s list:
1: ♥
2: ?
3: △
4: ♥
5: △
6: △
7: ♥

Not obvious. Try grouping:
Maybe ♥ ? △ | ♥ △ △ | ♥ — doesn’t help.

Notice positions 1,4,7 are all ♥ → so every 3rd starting from 1 is ♥.

Then positions 3,5,6: △, △, △ — not consistent.

Position 3=△, 5=△, 6=△ — so maybe after position 2, it’s all △ except the ♥ at 4 and 7.

Assume the pattern is: ♥, X, △, then repeat? But position 4 is ♥, 5=△, 6=△ — not matching.

Another idea: Perhaps it’s two interleaved patterns.

Odd positions: 1=♥, 3=△, 5=△, 7=♥ → not clear.

Even positions: 2=?, 4=♥, 6=△

Still messy.

Let’s look at the whole thing: ♥ ? △ ♥ △ △ ♥

What if the pattern is "heart, something, triangle" but then it changes.

Notice that from position 4 to 7: ♥ △ △ ♥ — which looks like a new pattern.

Perhaps the ? is meant to complete a triplet with 1 and 3: ♥ ? △ — and later we have ♥ △ △ — not the same.

Wait — compare to row 2, maybe I made a mistake there.

Let me try row 2 again with fresh eyes.

Row 2: △ △ □ ? △ △ □

Suppose the pattern is groups of 3: [△△□] [???] [△△□] — but there are only 7 items, so middle group has only one item: the ?.

That doesn't work.

Total items: 7. If pattern length is 3, then 7 = 2*3 +1, so perhaps the first 6 are two full groups, and the 7th is start of third.

But positions 1-3: △△□
Positions 4-6: ? △ △ — to be a group, it should be △△□, so ? should be △, and position 6 should be □, but it's △ — contradiction.

Unless the pattern is not fixed length.

Another thought: Maybe it's alternating based on even/odd or something.

Let's list the shapes in order and see the sequence:

Index: 1 2 3 4 5 6 7
Shape: △ △ □ ? △ △ □

Notice that shape at 1 = shape at 5 = △
Shape at 2 = shape at 6 = △
Shape at 3 = shape at 7 = □
So shape at 4 should be... what? There's no corresponding position. Unless the pattern is symmetric around center.

Center is position 4. So if symmetric, position 3 should equal position 5, but 3=□, 5=△ — not equal.

Position 2 and 6 are both △, good. Position 1 and 7: 1=△, 7=□ — not equal.

Not symmetric.

Perhaps the ? is △, and the pattern is simply "two triangles, one square" but with an extra triangle in the middle or something.

Let's count how many of each:

Triangles: positions 1,2,5,6 — that's 4 triangles
Squares: 3,7 — 2 squares
? is unknown.

If the pattern is supposed to have equal groups, perhaps ? is a square, then we have 4 triangles and 3 squares — not balanced.

I recall that in such worksheets, often the pattern repeats every few items. Let's assume the pattern length is 3 for row 2.

So the sequence should be periodic with period 3: s1,s2,s3,s1,s2,s3,s1,...

So s1=△, s2=△, s3=□, then s4=s1=△, s5=s2=△, s6=s3=□, s7=s1=△

But in the given, s5=△ (good), s6=△ (but should be □), s7=□ (should be △) — doesn't match.

Given s6=△, s7=□, while expected s6=□, s7=△ — so it's swapped.

Perhaps the pattern is s1,s2,s3 = △,△,□, then s4,s5,s6 = △,△,□, but s6 is given as △, not □.

Unless there's a typo, but probably not.

Another idea: Maybe the ? is not part of the main pattern, but let's look at the options on the right. For row 2, the choices are: □ and △ (since the right column for row 2 shows □ and △).

In the image, for each row, the right side has possible answers. For row 2, it's □ and △.

From the sequence, if we put ? = △, then the sequence is △ △ □ △ △ △ □ — which has four triangles in a row almost, not nice.

If ? = □, then △ △ □ □ △ △ □ — still not great.

Perhaps the pattern is "triangle, triangle, square" but the fourth item is the start of a new pattern or something.

Let's move to row 5 and come back.

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Row 5:
◇ ☐ ? ☐ ◇
Wait, the shapes are: diamond, crescent, square, ?, crescent, square, diamond

List:
1: ◇
2: ☾ (crescent)
3: □
4: ?
5: ☾
6: □
7: ◇

Now, notice:
1: ◇
7: ◇ — same
2: ☾
5: ☾ — same
3: □
6: □ — same
So 4 should be the center, and perhaps it should be the same as itself, but what is it?

The pattern might be symmetric: position 1=7, 2=5, 3=6, so 4 is middle, no pair.

But what should it be? In a symmetric pattern, the middle can be anything, but here we need to choose from options.

Options for row 5: ☾, ◇, □ (from the right column)

Since 1,7 are ◇; 2,5 are ☾; 3,6 are □; then 4 could be any, but likely it should complete the symmetry or be the "missing" one.

Notice that the sequence is: ◇ ☾ □ ? ☾ □ ◇

If we assume it's palindromic, then reading forward and backward should be the same.

Forward: 1◇,2☾,3□,4?,5☾,6□,7◇
Backward: 7◇,6□,5☾,4?,3□,2☾,1◇ — so for it to be palindrome, position 4 must be such that it matches itself, which it does, but the values at 3 and 5 are □ and ☾, which are different, so not palindrome unless ? is chosen to make it work, but 3 and 5 are fixed.

Position 3 is □, position 5 is ☾ — different, so not symmetric.

Another idea: Perhaps the pattern is repeating every 3, but shifted.

Let's see the sequence without ?: ◇ ☾ □ ? ☾ □ ◇

Suppose the pattern is ◇ ☾ □ repeating.

Then positions 1-3: ◇ ☾ □
Positions 4-6: should be ◇ ☾ □, but position 5 is ☾, 6 is □, so position 4 should be ◇
Then position 7 should be ☾, but it's ◇ — not match.

If pattern is 4 items, etc.

Notice that positions 2,5 are both ☾; positions 3,6 are both □; positions 1,7 are both ◇; so position 4 is alone. What is common? Perhaps position 4 should be the same as position 1 or something.

Maybe the ? is ◇, then the sequence is ◇ ☾ □ ◇ ☾ □ ◇ — which is almost repeating every 3, but position 7 is ◇, while if repeating, position 7 should be the first of the third group, which is ◇, good, but position 4 is ◇, which is start of second group, position 5=☾, 6=□, perfect!

Let's check:

If ? = ◇, then:
1: ◇
2: ☾
3: □
4: ◇
5: ☾
6: □
7: ◇

Now, groups: 1-3: ◇☾□, 4-6: ◇☾□, and 7: ◇ — which is the start of the next group. But since there are 7 items, it's two full groups and one extra.

But position 7 is ◇, which matches position 1 and 4, so it's consistent with the pattern starting over.

Moreover, in the sequence, after position 6 (□), position 7 is ◇, which is correct for the next group.

So for row 5, ? = ◇

And the options include ◇, so good.

Now back to row 2.

Row 2: △ △ □ ? △ △ □

With the same logic, if we assume the pattern is △ △ □ repeating, then:

Positions 1-3: △△□
Positions 4-6: should be △△□, so ? = △ (position 4), position 5=△, position 6=□ — but in the given, position 6 is △, not □. Problem.

Unless the given has a mistake, but probably not.

Perhaps for row 2, the pattern is different.

Let's list the shapes: A A B ? A A B

Where A=△, B=□

So A A B ? A A B

This looks like it might be symmetric if ? is B, then A A B B A A B — not symmetric.

If ? is A, then A A B A A A B — not good.

Another idea: Perhaps the ? is the shape that makes the number of each shape equal or something.

Count: currently, without ?: triangles at 1,2,5,6 — 4 triangles; squares at 3,7 — 2 squares.

If ? is square, then 4 triangles, 3 squares.

If ? is triangle, 5 triangles, 2 squares.

Not helpful.

Let's look at the right-side options for row 2: it shows □ and △, as per the image description.

Perhaps in the context, for row 2, the pattern is "two triangles, one square" but the fourth item is the beginning of the next, so ? = △, and then position 5=△, 6=△ — but that would be three triangles, then 7=□, so not consistent.

Unless the pattern is not strict.

Let's try row 6.

Row 6:
Cylinder, cube, rectangular prism, cylinder, cube, ?, cylinder

Shapes:
1: cyl
2: cube
3: rect
4: cyl
5: cube
6: ?
7: cyl

Pattern: cyl, cube, rect, then cyl, cube, ?, cyl

So likely, the pattern is cyl, cube, rect repeating.

So positions 1-3: cyl,cube,rect
Positions 4-6: should be cyl,cube,rect, so ? = rect
Then position 7 should be cyl, which it is — perfect.

So for row 6, ? = rectangular prism (which is the box with lines, like a 3D rectangle)

Options for row 6: rect, cyl, cube — so rect is available.

Good.

Now row 7:
Cube, cube, ?, cylinder, cube, cube, cylinder

Shapes:
1: cube
2: cube
3: ?
4: cyl
5: cube
6: cube
7: cyl

Pattern: cube, cube, ?, cyl, cube, cube, cyl

Notice that positions 1,2: cube,cube; 5,6: cube,cube; positions 4,7: cyl,cyl

So perhaps positions 3 and ? should be related.

If the pattern is "two cubes, one something, then cylinder" but not clear.

Groups: 1-3: cube,cube,? ; 4-7: cyl,cube,cube,cyl — not matching.

Symmetric: position 1=5=cube, 2=6=cube, 4=7=cyl, so position 3 should equal position ? but position 3 is ?, position 4 is cyl, not paired.

Position 3 and position 4 are adjacent.

Assume the pattern is repeating every 4 or something.

Notice that from position 4 to 7: cyl, cube, cube, cyl — which is symmetric.

Positions 1 to 3: cube, cube, ? — if we want symmetry with 5 to 7: cube, cube, cyl — so ? should be cyl.

Then the sequence is: cube, cube, cyl, cyl, cube, cube, cyl

Now, is there a pattern? It could be two groups: first three: cube,cube,cyl; last four: cyl,cube,cube,cyl — not the same.

But if ? = cyl, then positions 3 and 4 are both cyl, and positions 1,2,5,6 are cubes, 7 is cyl.

Not obvious, but let's see the options.

Options for row 7: rect, cyl, cube — so cyl is available.

Perhaps the pattern is "cube, cube, cylinder" but then position 4 is cyl, which would be start of next, but position 4 is cyl, 5=cube, 6=cube, 7=cyl — so if pattern is cube,cube,cyl, then positions 1-3: cube,cube,cyl (if ?=cyl), positions 4-6: cyl,cube,cube — not matching, position 7=cyl should be start of next.

If pattern is 3 items: s1,s2,s3 = cube,cube,cyl, then s4=s1=cube, but s4=cyl — not match.

Another idea: Perhaps it's "two cubes, then a cylinder" but with overlap or something.

Let's consider that positions 1,2,5,6 are cubes; positions 4,7 are cylinders; so position 3 should be cylinder to make it balanced or something.

Or perhaps the ? is cylinder, and the sequence is designed to have cylinders at 3,4,7 or something.

Let's calculate the difference.

I recall that in some patterns, the missing item is the one that completes a set.

For example, in row 7, if we have cube, cube, ?, and later cube, cube, cyl, so perhaps ? should be cyl to match the later part.

Moreover, in the sequence, after two cubes, it's often a cylinder, as in positions 5,6 are cubes, 7 is cyl, so similarly, positions 1,2 are cubes, so 3 should be cyl.

Then position 4 is cyl, which might be separate.

So ? = cylinder

And options include cyl, so ok.

Now row 8:
◇ ◇ + ◇ ? ◇ ◇

Shapes:
1: ◇
2: ◇
3: +
4: ◇
5: ?
6: ◇
7: ◇

Pattern: diamond, diamond, plus, diamond, ?, diamond, diamond

Notice that positions 1,2,4,6,7 are diamonds; position 3 is plus; position 5 is ?

If the pattern is mostly diamonds with a plus in between, perhaps the plus is at position 3, and another at position 5? But position 5 is ?.

Options for row 8: ◇ and +

If ? = +, then we have diamonds at 1,2,4,6,7 and plus at 3,5 — so two pluses.

If ? = ◇, then all are diamonds except position 3 is plus.

Which is more likely? Probably the pattern is "diamond, diamond, plus" repeating, but let's see.

Positions 1-3: ◇◇+
Positions 4-6: ◇ ? ◇ — to match, ? should be +, then position 7 should be ◇, which it is.

So if ? = +, then 4-6: ◇ + ◇, but the first group is ◇◇+, not the same.

Unless the pattern is not fixed.

Notice that position 3 is +, and if position 5 is also +, then it's symmetric: positions 1,2,4,6,7 are ◇, positions 3 and 5 are +.

And the sequence is symmetric around position 4: pos1=7=◇, pos2=6=◇, pos3=5=+, pos4=◇ — yes! Perfect symmetry.

So ? = +

Good.

Row 9:
♥ ? ♥ ◇ ♥ ♥ ♥

Shapes:
1: ♥
2: ?
3: ♥
4: ◇
5: ♥
6: ♥
7: ♥

Options: ◇ and ♥

If ? = ♥, then all are hearts except position 4 is diamond.

If ? = ◇, then positions 2 and 4 are diamonds.

Pattern: perhaps "heart, something, heart, diamond, heart, heart, heart"

Not clear.

Symmetry: pos1=3=5=6=7=♥, pos4=◇, so pos2 should be ?

If symmetric around center (pos4), then pos3 should equal pos5, both ♥, good; pos2 should equal pos6, both should be the same; pos6 is ♥, so pos2 should be ♥.

Pos1 should equal pos7, both ♥, good.

So ? = ♥

Then the sequence is all hearts except position 4 is diamond.

Makes sense.

Row 10:
? ◇ △ 😊 ◇ △ 😊

Shapes:
1: ?
2: ◇
3: △
4: 😊
5: ◇
6: △
7: 😊

Options: ◇, △, 😊

Clearly, positions 2-4: ◇ △ 😊
Positions 5-7: ◇ △ 😊
So position 1 should be the start of the first group, which is ◇? But position 2 is already ◇.

If the pattern is ◇ △ 😊 repeating, then position 1 should be the last of the previous group or something.

Positions 2,3,4: ◇△😊
Positions 5,6,7: ◇△😊
So position 1 is extra. What should it be? If the pattern started earlier, position 1 might be 😊, since before ◇ would be 😊 if repeating.

For example, if the sequence is ... 😊 ◇ △ 😊 ◇ △ 😊, then position 1 is 😊.

And options include 😊.

So ? = 😊

Now back to row 2 and row 4.

First, row 4: ♥ ? △ ♥ △ △ ♥

We have:
1: ♥
2: ?
3: △
4: ♥
5: △
6: △
7: ♥

Options for row 4: ♥ and △ (from the right column)

Let's try to find a pattern.

Notice that positions 1,4,7 are all ♥ — so every 3rd starting from 1 is ♥.

Then positions 3,5,6 are △ — so perhaps position 2 should be △ to continue.

If ? = △, then sequence: ♥ △ △ ♥ △ △ ♥

Now, this looks like "heart, triangle, triangle" repeating.

Positions 1-3: ♥△△
Positions 4-6: ♥△△
Position 7: ♥ — start of next group.

Perfect! And position 7 is ♥, which matches.

So for row 4, ? = △

Now row 2: △ △ □ ? △ △ □

With the same logic, if we assume "two triangles, one square" repeating, then:

Positions 1-3: △△□
Positions 4-6: should be △△□, so ? = △ (position 4), position 5=△, position 6=□ — but in given, position 6 is △, not □.

However, in the given, position 6 is △, position 7 is □.

So if we take positions 4-6 as ? △ △, and position 7 is □, then if ? = □, we have □ △ △ □ — not good.

Perhaps the pattern is "triangle, triangle, square" but the fourth item is square, then fifth and sixth are triangle, triangle, seventh is square — so it's like the pattern is shifted.

Let's write the sequence with ? = □: △ △ □ □ △ △ □

Then it's two triangles, two squares, two triangles, one square — not nice.

With ? = △: △ △ □ △ △ △ □ — three triangles in a row.

But notice that in row 4, we had a similar issue initially, but it worked out.

Another idea: Perhaps for row 2, the pattern is based on the sum or something, but unlikely.

Let's count the number of triangles and squares.

Without ?: triangles at 1,2,5,6 — 4; squares at 3,7 — 2.

If ? = △, then 5 triangles, 2 squares.

If ? = □, then 4 triangles, 3 squares.

In other rows, the counts are balanced in groups.

Perhaps the ? is the shape that makes the sequence have a certain property.

Let's look at the right-side options for row 2: in the image, for row 2, the choices are □ and △, and typically in such worksheets, the answer is one of them.

Now, comparing to row 4, which was similar, we resolved it by assuming the pattern repeats every 3.

For row 2, if we force the pattern to be △△□ repeating, then position 4 should be △, position 5=△, position 6=□, but position 6 is given as △, which is a problem.

Unless there's a mistake in my reading.

Let me double-check the user's description or the image.

The user said: "Circle a shape from the right side, to complete the pattern."

And for row 2: "△ △ □ ? △ △ □"

And right side has □ and △.

Perhaps in this case, the pattern is not strictly repeating, but the ? is △ because it's the most frequent or something.

Another thought: In the sequence △ △ □ ? △ △ □, if we remove the ?, we have two instances of "△ △ □" but with a gap.

Positions 1-3 and 5-7 are both "△ △ □", so position 4 is in between, and it should be the same as position 1 or something.

Position 1 is △, so ? = △.

Then the sequence is △ △ □ △ △ △ □, which has "△ △ □" at start, then "△ △ △ □" at end, not identical, but perhaps acceptable.

Maybe the pattern is that after every two triangles, there is a square, but here after positions 1-2 (two triangles), position 3 is square; after positions 5-6 (two triangles), position 7 is square; so position 4 is after position 3 (square), so it should be the start of the next pair, which is triangle.

So ? = △

I think that's the best we can do.

So for row 2, ? = △

Now let's summarize all answers:

Row 1: example, done.

Row 2: ? = △

Row 3: ? = + (plus)

Row 4: ? = △ (triangle)

Row 5: ? = ◇ (diamond)

Row 6: ? = rectangular prism (the 3D box)

Row 7: ? = cylinder

Row 8: ? = + (plus)

Row 9: ? = ♥ (heart)

Row 10: ? = 😊 (smiley)

Now, to confirm, let's list them:

- Row 2: triangle

- Row 3: plus sign

- Row 4: triangle

- Row 5: diamond

- Row 6: rectangular prism (sometimes called cuboid)

- Row 7: cylinder

- Row 8: plus sign

- Row 9: heart

- Row 10: smiley face

In the right-side options, for each row, the correct choice should be among them.

For example, row 6 options include the rectangular prism, etc.

So I think this is correct.

Final Answer:

For each row, the missing shape is:

Row 2: Triangle
Row 3: Plus sign
Row 4: Triangle
Row 5: Diamond
Row 6: Rectangular prism
Row 7: Cylinder
Row 8: Plus sign
Row 9: Heart
Row 10: Smiley face

But since the question is to solve the problem, and it's multiple rows, perhaps list them in order.

The user might expect the answers for each ?.

Since the worksheet has 9 problems (rows 2 to 10), we provide the answer for each.

In the response, we can list them.

But the Final Answer should be concise.

Perhaps: The missing shapes are: triangle, plus, triangle, diamond, rectangular prism, cylinder, plus, heart, smiley.

To be precise, let's specify by row.

Since the instruction is to provide the final answer after reasoning, and it's a single response, I'll list them.

Note: In row 6, the rectangular prism is the shape that looks like a 3D rectangle, often drawn with lines.

Similarly, others are clear.

So:

Final Answer:
Row 2: Triangle
Row 3: Plus sign
Row 4: Triangle
Row 5: Diamond
Row 6: Rectangular prism
Row 7: Cylinder
Row 8: Plus sign
Row 9: Heart
Row 10: Smiley face