Educational number pattern worksheet for children featuring a frog theme.

Let’s solve each row step by step. We’re looking for repeating or alternating patterns in the numbers.

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Row 1: 10, 11, 10, 11, __, __, __, __

Pattern: Alternating 10 and 11.
So next four should be: 10, 11, 10, 11

✔ Confirmed: It’s a simple A-B-A-B pattern.

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Row 2: 15, 18, __, __, 15, __, __, 18

We see 15, then 18, then two blanks, then 15 again, then two blanks, then 18.

This looks like a repeating group of 4 numbers: [15, 18, ?, ?] that repeats.

But we have:
Position 1: 15
Position 2: 18
Position 3: ?
Position 4: ?
Position 5: 15 → same as position 1
Position 6: ?
Position 7: ?
Position 8: 18 → same as position 2

So if positions 1 and 5 are both 15, and positions 2 and 8 are both 18, maybe the pattern is symmetric or has a cycle of 4?

Wait — let’s try assuming the full pattern is:
15, 18, X, Y, 15, 18, X, Y

But position 8 is 18, which would match position 2 — so if it’s repeating every 4, then:

Positions 1–4: 15, 18, X, Y
Positions 5–8: 15, 18, X, Y → but position 8 is given as 18, which matches position 2, not position 4.

That doesn’t fit unless Y = 18? But then position 4 would be 18, and position 8 is also 18 — possible.

Wait — look at positions:

Given:
Pos1: 15
Pos2: 18
Pos3: ?
Pos4: ?
Pos5: 15
Pos6: ?
Pos7: ?
Pos8: 18

If the pattern is 15, 18, A, B, 15, 18, A, B, then Pos8 should be B — but it’s given as 18. So B must be 18? Then Pos4 = 18, Pos8 = 18 — okay.

Then what about Pos3 and Pos7? They should be equal (both A).

But we don’t have more info. Maybe another approach.

What if the pattern is: 15, 18, 15, 18, 15, 18, 15, 18? But then Pos3 should be 15, Pos4=18, Pos5=15 (matches), Pos6=18, Pos7=15, Pos8=18 (matches). That works!

Check:

15, 18, 15, 18, 15, 18, 15, 18 → yes, alternates starting with 15.

But wait — original is: 15, 18, __, __, 15, __, __, 18

If we fill: 15, 18, 15, 18, 15, 18, 15, 18 → Pos7 would be 15, Pos8=18 — matches.

Perfect! So pattern is alternating 15 and 18.

So Row 2: 15, 18, 15, 18, 15, 18, 15, 18

Blanks: pos3=15, pos4=18, pos6=18, pos7=15

Wait — pos6 is after pos5=15, so should be 18; pos7 after 18 should be 15 — yes.

✔ Confirmed.

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Row 3: 12, 12, __, __, __, 12, __, __

Starts with two 12s, then three blanks, then a 12, then two blanks.

Maybe the pattern is groups of three? Or perhaps it's repeating “12, 12, X”?

Try: Suppose pattern is 12, 12, A, 12, 12, A, 12, 12 — but we have only one 12 at position 6.

Positions:

1:12
2:12
3:?
4:?
5:?
6:12
7:?
8:?

What if it’s 12, 12, X, 12, 12, X, 12, 12? Then pos6 should be X — but it’s 12. Doesn’t fit.

Another idea: Maybe it’s 12, 12, blank, blank, blank, 12, blank, blank — and the pattern is that every third number is something else? Not clear.

Wait — look at positions where 12 appears: pos1,2,6.

Difference between pos2 and pos6 is 4 steps. Maybe the pattern repeats every 4? Try grouping:

Group1: pos1-4: 12,12,?,?
Group2: pos5-8: ?,12,?,?

Not helpful.

Alternative: What if the pattern is 12, 12, A, B, C, 12, D, E — too many variables.

Wait — maybe it’s symmetric? Or perhaps the missing numbers are all the same?

Another thought: Maybe it’s 12, 12, 12, 12, 12, 12, 12, 12 — but why leave blanks? Probably not.

Look back at row 1 and 2 — they were alternating or simple repetition.

What if this is: 12, 12, X, X, X, 12, X, X — still vague.

Wait — here’s an idea: Maybe the pattern is that the first two are 12, then three numbers, then 12, then two numbers — and those three and two are part of a sequence that mirrors or continues.

Perhaps it’s based on position modulo something.

Let me try assuming the pattern is 12, 12, A, B, C, 12, A, B — then pos6=12, pos7=A, pos8=B.

But we don’t know A,B,C.

Unless... what if A,B,C are such that the whole thing is palindromic? Let’s test:

Suppose the full row is: 12,12,X,Y,Z,12,X,Y — not symmetric.

Or: 12,12,A,B,C,12,B,A — then pos7=B, pos8=A.

Still arbitrary.

Wait — let’s count how many 12s are given: positions 1,2,6 — that’s three 12s.

Total 8 positions. If the pattern is to have 12 appear at positions 1,2,6,7,8? No.

Another approach: Look at the gaps.

From pos2 to pos6: 4 steps later, we have 12 again. So maybe every 4th position after start? Pos1, then pos5? But pos5 is blank, pos6 is 12.

Pos1=12, pos2=12, pos6=12 — differences: +4 from pos2 to pos6.

So perhaps pos6+4=pos10 — out of range.

Maybe the pattern is: two 12s, then three non-12s, then one 12, then two non-12s — but that seems forced.

Wait — let’s consider that in row 1 and 2, the patterns were very regular. Maybe this one is too.

What if it’s 12, 12, 12, 12, 12, 12, 12, 12? But then why blanks? Unlikely.

Perhaps it’s 12, 12, X, X, X, 12, X, X and X is always the same number? But what number?

No clue.

Let’s skip and come back.

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Row 4: __, 17, 14, __, __, 14, 20, 17

Given: pos2=17, pos3=14, pos6=14, pos7=20, pos8=17

Notice pos2=17, pos8=17 — symmetric?

Pos3=14, pos6=14 — also symmetric around center?

Center of 8 positions is between pos4 and pos5.

So pos1 and pos8 should be related, pos2 and pos7, pos3 and pos6, pos4 and pos5.

Given:

pos2=17, pos7=20 — not equal.

pos3=14, pos6=14 — equal.

pos8=17, so pos1 should be? If symmetric, pos1 should equal pos8=17? But pos2 is already 17.

Assume symmetry: pos1 = pos8 = 17
pos2 = pos7 → but pos2=17, pos7=20 — not equal. Contradiction.

Unless not mirror symmetry.

Another idea: Look at values: 17,14,...,14,20,17

From pos2 to pos3: 17 to 14 (down 3)
pos6 to pos7: 14 to 20 (up 6)
pos7 to pos8: 20 to 17 (down 3)

Not consistent.

What if the pattern is: A, 17, 14, B, C, 14, 20, 17

Notice that 17 appears at pos2 and pos8, 14 at pos3 and pos6.

So perhaps pos1 and pos7 are related? pos7=20, so pos1=?

Maybe the sequence is built as: start with some number, then 17,14, then some, then 14,20,17 — and the middle connects.

Another thought: Perhaps it's two interleaved sequences.

Odd positions: pos1,3,5,7: ?,14,?,20
Even positions: pos2,4,6,8: 17,?,14,17

Even positions: 17, ?, 14, 17 — so pos4 should be? If it's symmetric, pos4 should be 14? But pos6 is 14, pos2 and pos8 are 17 — so even positions: 17, X, 14, 17 — no obvious pattern.

Unless X is 14? Then 17,14,14,17 — possible.

Then odd positions: pos1,3,5,7: Y,14,Z,20

If we assume the whole thing is symmetric, then pos1=pos8=17, pos2=pos7=17 vs 20 — no.

Wait — pos8=17, pos2=17; pos6=14, pos3=14; pos7=20, so pos1 should be 20? Because pos1 and pos7 might correspond if we think of pairs.

Let’s pair them as (pos1,pos8), (pos2,pos7), (pos3,pos6), (pos4,pos5)

Given:
(pos2,pos7) = (17,20)
(pos3,pos6) = (14,14)
(pos8)=17, so (pos1,17) — if we want symmetry, pos1 should be 20 to match pos7=20? But pos7 is paired with pos2.

Standard pairing for 8 elements: (1,8), (2,7), (3,6), (4,5)

So:
(1,8): (?,17)
(2,7): (17,20)
(3,6): (14,14)
(4,5): (?,?)

For symmetry, each pair should be equal? But (2,7) is 17 and 20 — not equal.

Unless it's not equality, but a function.

Notice that in (2,7): 17 and 20 — difference of 3.
In (3,6): 14 and 14 — difference 0.
In (1,8): ? and 17 — if we assume the difference is decreasing or something.

Another idea: Perhaps the sum of each pair is constant.

(2,7): 17+20=37
(3,6): 14+14=28 — not same.

Product? Unlikely.

Let’s look at the values: 17,14, then later 14,20,17 — so perhaps the beginning is reverse of the end.

End: pos6=14, pos7=20, pos8=17
Beginning: pos1=?, pos2=17, pos3=14

If we reverse the last three: 17,20,14 — compare to first three: ?,17,14 — so if pos1=17, then first three: 17,17,14 — not matching 17,20,14.

If pos1=20, then 20,17,14 — and last three are 14,20,17 — which is almost reverse: reverse of 14,20,17 is 17,20,14 — not 20,17,14.

Close but not quite.

20,17,14 vs 14,20,17 — not the same.

Perhaps it's a cycle: 17,14, then something, then 14,20,17 — and the something is 20,17 or something.

Let’s try to assume that the pattern is: A,17,14,B,C,14,20,17

And suppose that B and C are 20 and 17 or something.

Notice that from pos3=14 to pos6=14, there are two numbers in between: pos4 and pos5.

From pos2=17 to pos7=20, etc.

Another approach: Let's list what we have:

Pos: 1 2 3 4 5 6 7 8
Val: ? 17 14 ? ? 14 20 17

Let me denote unknowns as W,X,Y for pos1,4,5.

So: W,17,14,X,Y,14,20,17

Now, look at pos3=14, pos6=14 — same value, 3 apart.

Pos2=17, pos8=17 — 6 apart.

Pos7=20.

Perhaps the sequence has a period of 4 or 6.

Try period 4: positions 1-4 and 5-8 should be similar.

Pos1=W, pos2=17, pos3=14, pos4=X
Pos5=Y, pos6=14, pos7=20, pos8=17

Compare: pos2=17, pos8=17 — good.
pos3=14, pos6=14 — good.
pos4=X, pos7=20 — so if period 4, X should equal 20?
pos1=W, pos5=Y — should be equal if period 4.

So assume X=20, and W=Y.

Then the row is: W,17,14,20, W,14,20,17

Now, is there a relation between W and other numbers? Not yet.

But we have pos5=W, pos6=14, pos7=20, pos8=17 — which is the same as pos1=W, pos2=17, pos3=14, pos4=20 — so yes, it repeats every 4: [W,17,14,20], [W,14,20,17] — wait, not the same because second group has pos6=14, pos7=20, pos8=17, but pos5=W, so [W,14,20,17] while first is [W,17,14,20] — different order.

Unless W is chosen so that it fits.

Perhaps W is 20? Let's try W=20.

Then row: 20,17,14,20,20,14,20,17

Check: pos1=20, pos2=17, pos3=14, pos4=20, pos5=20, pos6=14, pos7=20, pos8=17

Is there a pattern? 20,17,14,20, then 20,14,20,17 — not obvious.

Notice that pos4=20, pos5=20 — two 20s together.

Pos1=20, pos4=20, pos5=20, pos7=20 — many 20s.

But let's see if it makes sense with the given.

We have pos6=14, pos7=20, pos8=17 — matches.

Pos2=17, pos3=14 — matches.

Pos4 and pos5 are both 20 in this case.

But is there a better choice?

Another idea: Perhaps the pattern is that the number before 14 is 17, and after 14 is 20 or something.

In pos2-3: 17,14
In pos6-7: 14,20 — not the same.

Let's calculate differences:

From pos2 to pos3: 17 to 14 = -3
Pos3 to pos4: 14 to X
Pos4 to pos5: X to Y
Pos5 to pos6: Y to 14
Pos6 to pos7: 14 to 20 = +6
Pos7 to pos8: 20 to 17 = -3

Oh! Pos2 to pos3: -3, pos7 to pos8: -3 — same change.

Pos6 to pos7: +6

Perhaps pos3 to pos4 is +6? 14 to 20? Then X=20

Then pos4 to pos5: 20 to Y
Pos5 to pos6: Y to 14

If we assume pos4 to pos5 is -3, then Y=17, then pos5 to pos6: 17 to 14 = -3 — good.

Then pos1 to pos2: W to 17 — if we assume the same as pos7 to pos8 which is -3, but pos7 to pos8 is 20 to 17 = -3, so pos1 to pos2 should be +3 or something? Let's see the direction.

From pos1 to pos2: if it's like pos7 to pos8, but pos7 to pos8 is decrease, pos1 to pos2 could be increase or decrease.

Assume the changes are symmetric or repeating.

List the changes between consecutive positions:

Between 1-2: ?
2-3: 17 to 14 = -3
3-4: 14 to X
4-5: X to Y
5-6: Y to 14
6-7: 14 to 20 = +6
7-8: 20 to 17 = -3

We have two -3 changes: at 2-3 and 7-8.

Also, 6-7 is +6.

Perhaps 3-4 is +6? So X = 14 +6 = 20

Then 4-5: 20 to Y
5-6: Y to 14

If 5-6 is -3, then Y = 17, and 4-5: 20 to 17 = -3 — good.

Then 1-2: W to 17 — if we want another -3, then W = 20, because 20 to 17 = -3.

Perfect!

So changes:
1-2: 20 to 17 = -3
2-3: 17 to 14 = -3
3-4: 14 to 20 = +6
4-5: 20 to 17 = -3
5-6: 17 to 14 = -3
6-7: 14 to 20 = +6
7-8: 20 to 17 = -3

The changes are: -3, -3, +6, -3, -3, +6, -3

Not perfectly periodic, but notice that after the first two -3, we have +6, then two -3, then +6, then -3.

But it works with the given numbers.

So pos1=20, pos4=20, pos5=17

Row: 20,17,14,20,17,14,20,17

Check given: pos2=17, pos3=14, pos6=14, pos7=20, pos8=17 — all match.

Yes! And pos1=20, pos4=20, pos5=17.

So for Row 4: blanks are pos1=20, pos4=20, pos5=17

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Row 5: __, __, __, 13, 16, 13, 16, __

Given: pos4=13, pos5=16, pos6=13, pos7=16, pos8=?

Clearly, from pos4 to pos7: 13,16,13,16 — alternating.

So likely the pattern is alternating 13 and 16 throughout.

Then pos3 should be 16 (since pos4=13, so before it should be 16 if alternating backwards)

Pos2=13, pos1=16

Pos8: after pos7=16, should be 13

So row: 16,13,16,13,16,13,16,13

Check: pos4=13, pos5=16, pos6=13, pos7=16 — matches.

Pos8=13

Blanks: pos1=16, pos2=13, pos3=16, pos8=13

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Row 6: 18, 11, 12, __, __, __, 18, __

Given: pos1=18, pos2=11, pos3=12, pos7=18, pos8=?

Look at pos1=18, pos7=18 — 6 apart.

Pos2=11, pos3=12

Perhaps the pattern repeats every 6? But 8 positions.

Maybe it's symmetric: pos1 and pos7 are both 18, so perhaps pos2 and pos6 are related, pos3 and pos5, pos4 and pos4.

Assume symmetry around center between pos4 and pos5.

So pos1=pos7=18
pos2=pos6
pos3=pos5
pos4=pos4

Given pos2=11, so pos6=11
pos3=12, so pos5=12
pos7=18, matches pos1.

Then pos4 is unknown, pos8 is unknown.

But pos8 should correspond to pos0 — not exist.

For 8 positions, symmetry would be pos1 with pos8, pos2 with pos7, etc., but earlier we saw pos2=11, pos7=18 — not equal.

With pos1 and pos7 both 18, perhaps it's not full symmetry.

Another idea: Perhaps the sequence is 18,11,12, then repeat or something.

From pos1 to pos3: 18,11,12
Then pos7=18, so perhaps pos4,5,6 are 11,12,18 or something.

Assume that the pattern is groups of three: [18,11,12], [A,B,C], [18,D,E] but only up to pos8.

Pos7=18, so perhaps the third group starts with 18.

So maybe [18,11,12], [X,Y,Z], [18,W,V] but we have only pos8.

Positions 4,5,6 are blank, pos7=18, pos8=?

If the second group is the same as first, then pos4=18, pos5=11, pos6=12, then pos7=18 (start of third group), pos8=11

Then row: 18,11,12,18,11,12,18,11

Check given: pos1=18, pos2=11, pos3=12, pos7=18 — matches.

Pos8=11

Blanks: pos4=18, pos5=11, pos6=12, pos8=11

But pos8 is blank, and we have it as 11.

Is there any contradiction? pos7=18, which is start of new group, so pos8 should be 11 — yes.

Could be.

Perhaps it's a different pattern, but this fits.

Another possibility: maybe it's 18,11,12, then 13,14,15 or something, but no indication.

With the given, the repeating group of three seems plausible.

So I'll go with that.

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Now back to Row 3: 12,12,__,__,__,12,__,__

Earlier I was stuck.

Given: pos1=12, pos2=12, pos6=12

Perhaps similar to row 6, but with 12.

In row 6, we had pos1=18, pos7=18, and assumed repeating every 3: [18,11,12]

Here, pos1=12, pos2=12, pos6=12 — not the same spacing.

Pos1 and pos2 are both 12, then pos6 is 12.

Difference of 4 from pos2 to pos6.

Perhaps the pattern is that every 4th position after pos2 is 12? Pos2, then pos6, then pos10 — out of range.

Maybe the sequence is 12,12, then three numbers, then 12, then two numbers, and the three numbers are the same as the last two plus something.

Another idea: Perhaps it's 12,12, X, Y, Z, 12, X, Y — then pos6=12, pos7=X, pos8=Y

But what are X,Y,Z?

If we assume that the "three numbers" are fixed, but no clue.

Notice that in row 1,2,4,5,6, the patterns were either alternating or repeating blocks.

For row 3, perhaps it's all 12s except some positions, but unlikely.

Let's try to apply the same logic as row 4 or others.

Suppose we assume that pos3,4,5 are the same as pos7,8, and something.

Pos6=12, so perhaps pos3=12? But then why blank.

Another thought: In row 3, the given 12s are at 1,2,6 — perhaps 6 is the start of a repeat.

So from pos6 onwards: 12, __, __ — and before that pos1-5: 12,12,__,__,__

If the pattern from pos6 is the same as from pos1, then pos6=12 (like pos1), pos7=12 (like pos2), pos8= ? (like pos3)

But pos2 is 12, so pos7 should be 12, but it's blank, and we can set it.

Then pos3 should equal pos8.

But what is pos3? Unknown.

Perhaps the first two are 12,12, then the next three are A,B,C, then 12, then A,B — so pos6=12, pos7=A, pos8=B

Then the row is: 12,12,A,B,C,12,A,B

Now, is there a constraint? Not really, but perhaps A,B,C are specific.

Maybe A,B,C are 12,12,12 — then it's all 12s.

Or perhaps from context, but no.

Let's look at the frog or something — but the instruction says not to describe image.

Perhaps in such puzzles, the pattern is often simple.

Another idea: Perhaps the number of 12s increases or something.

Let's count the positions: 8 positions.

Given three 12s at 1,2,6.

If we assume that the pattern is that positions 1,2,6,7,8 are 12, then pos3,4,5 are not.

But what are they? No information.

Perhaps it's a typo or I missed something.

Let's try to see if there's a mathematical pattern.

Suppose the value at position n is f(n).

For example, f(1)=12, f(2)=12, f(6)=12.

f(n) = 12 for n=1,2,6.

Perhaps f(n) = 12 when n mod 4 = 1 or 2 or 2, but 6 mod 4 =2, so n≡1 or 2 mod 4.

Then for n=3,4,5,7,8: n=3≡3, n=40, n=5≡1, n=7≡3, n=8≡0

n=5≡1, so should be 12, but pos5 is blank, and if it's 12, then ok, but pos6 is already 12, and n=6≡2, also 12.

n=11, n=2≡2, n=5≡1, n=6≡2, n=9≡1, etc.

For n=3≡3, n=4≡0, n=73, n=8≡0 — these should not be 12.

But what are they? Still unknown.

Perhaps for those, it's a different number, say 13 or something, but no basis.

Another approach: Perhaps the pattern is that the first two are 12, then the next three are the same as the last three minus the first or something.

Let's give up and assume that the pattern is repeating "12,12,12" but shifted.

Notice that in row 6, we had a repeating block of 3: [18,11,12]

Here, perhaps [12,12,X] repeating.

Then for 8 positions: pos1=12, pos2=12, pos3=X, pos4=12, pos5=12, pos6=X, pos7=12, pos8=12

But given pos6=12, so X=12, then all are 12.

Then the row is all 12s.

And the blanks are all 12.

That could be it. Perhaps it's trivial.

In that case, for Row 3: all blanks are 12.

Let me verify with the given: pos1=12, pos2=12, pos6=12 — if all are 12, it satisfies.

And it's simple.

Probably that's intended, as other rows have variations, but this might be uniform.

So I'll go with that.

---

Summary of all rows:

Row 1: 10,11,10,11, 10,11,10,11

Row 2: 15,18, 15,18, 15, 18,15, 18 → so blanks: pos3=15, pos4=18, pos6=18, pos7=15

Row 3: 12,12, 12,12,12, 12, 12,12 → all blanks are 12

Row 4: 20,17,14,20,17,14,20,17 → blanks: pos1=20, pos4=20, pos5=17

Row 5: 16,13,16,13,16,13,16,13 → blanks: pos1=16, pos2=13, pos3=16, pos8=13

Row 6: 18,11,12,18,11,12,18,11 → blanks: pos4=18, pos5=11, pos6=12, pos8=11

Now, to write the final answer, we need to fill in the blanks for each row.

The task is to fill in the blank squares, so for each row, list the numbers for the blanks in order.

Since the user will fill the squares, we provide the sequence of numbers for the blanks in each row.

For clarity, I'll list the completed rows or just the missing parts.

But the instruction is to provide the final answer, probably the filled-in numbers for the blanks.

Since it's a worksheet, likely they want the numbers to put in the empty boxes.

So for each row, the values for the blank positions in left-to-right order.

Let's do that.

Row 1: blanks at positions 5,6,7,8 → values: 10,11,10,11

Row 2: blanks at positions 3,4,6,7 → values: 15,18,18,15

Row 3: blanks at positions 3,4,5,7,8 → values: 12,12,12,12,12

Row 4: blanks at positions 1,4,5 → values: 20,20,17

Row 5: blanks at positions 1,2,3,8 → values: 16,13,16,13

Row 6: blanks at positions 4,5,6,8 → values: 18,11,12,11

Now, to present the final answer, perhaps list them row by row.

Since the problem says "fill in the blank squares", and there are multiple rows, we should specify for each row what goes in the blanks.

But in the response, we can list the completed sequences or just the missing numbers.

I think listing the missing numbers in order for each row is fine.

To be precise, let's write the full row for each, but since the question is to complete the patterns, providing the numbers for the blanks is sufficient.

Final Answer format: probably a list or grid.

Since it's text, I'll write:

For Row 1: 10, 11, 10, 11
For Row 2: 15, 18, 18, 15
For Row 3: 12, 12, 12, 12, 12
For Row 4: 20, 20, 17
For Row 5: 16, 13, 16, 13
For Row 6: 18, 11, 12, 11

But to make it clear, perhaps specify the positions, but I think for the student, they can match the blanks.

Since the blanks are in order, we can just list the numbers to fill in sequentially for each row.

So for each row, the sequence of numbers to put in the empty boxes from left to right.

Yes.

Now, double-check Row 3: if all are 12, is that acceptable? Given that pos1,2,6 are 12, and if we fill all blanks with 12, it works, and it's simple. Other interpretations were complicated, so likely correct.

Similarly, others seem solid.

So Final Answer:

Row 1 blanks: 10, 11, 10, 11
Row 2 blanks: 15, 18, 18, 15
Row 3 blanks: 12, 12, 12, 12, 12
Row 4 blanks: 20, 20, 17
Row 5 blanks: 16, 13, 16, 13
Row 6 blanks: 18, 11, 12, 11

To box it, perhaps write as a list.

Since the problem might expect the filled grid, but I think this is fine.

I'll write it clearly.