Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

Let’s solve each row one by one. We’re looking for repeating patterns — like a sequence that repeats over and over.

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Row 1:
_ △ _ △ △ _ ⬠ △

Let’s look at the known shapes: positions 2,4,5,7,8 are given.

Try to find a repeating unit. Let’s test if it’s “△ △ ⬠” or something else.

Wait — let’s write positions:

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

Hmm… maybe the pattern is: △ △ ⬠ — but then position 2 is △, 4 is △, 5 is △ — doesn’t fit.

Alternative idea: Maybe the full pattern is 3 shapes long? Let’s try grouping in threes:

Group 1: pos1-3 → ? △ ?
Group 2: pos4-6 → △ △ ?
Group 3: pos7-9 → ⬠ △ ?

That doesn’t help yet.

Wait — what if we assume the pattern is “△ △ ⬠” and see where it fits?

If pattern = [△, △, ⬠], then:

Positions 4,5,6 should be △, △, ⬠ → but pos6 is blank, pos7 is ⬠ — so maybe pos6 is ⬠? Then pos7 would start next group: △, △, ⬠ — but pos7 is ⬠, not △. Doesn’t match.

Another approach: Look at the end: pos7=⬠, pos8=△ — maybe the pattern ends with ⬠ △? And before that?

Look at pos4=△, pos5=△ — so maybe “△ △ ⬠” is the pattern, and it starts at pos4?

Then pos4=△, pos5=△, pos6=⬠ → that works.

Then pos7 should start new pattern: △, △, ⬠ — but pos7 is ⬠ — no.

Wait — what if the pattern is “△ ⬠ △”? Let’s test:

Pos2=△, pos3=?, pos4=△ → if pattern is △ ⬠ △, then pos3 should be ⬠.

Then pos4=△ (start of next), pos5=△ — but should be ⬠ — no.

This is tricky. Let’s try a different row first and come back.

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Row 2:
△ _ _ _ △ ⬠ ⬠ △

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

Notice: pos5=△, pos6=⬠, pos7=⬠, pos8=△ — that looks like “△ ⬠ △” — but that’s 4 items.

What if the pattern is “△ ⬠ ⬠”? Then:

Pos1=△ → start
Pos2=⬠
Pos3=⬠
Pos4=△ (next pattern)
Pos5=△ — wait, should be ⬠ — no.

But pos5=△, pos6=⬠, pos7=⬠ — that’s “△ ⬠ ⬠” — then pos8=△ — which could be start of next.

So pattern might be “△ ⬠ ” repeating.

Then:

Pos1: △ (start)
Pos2: ⬠
Pos3: ⬠
Pos4: △ (start of next)
Pos5: △ — but should be ⬠ — conflict.

Unless... maybe the pattern is “△ ⬠ ⬠ △” — 4 items?

Then:

Pos1-4: △ ? ? ?
Pos5-8: △ ⬠ △

So pos5-8 matches “△ ⬠ ⬠ △”

Then pos1-4 should also be “△ ⬠ ⬠ △”

So pos1=△ (given)
pos2=⬠
pos3=⬠
pos4=△

Yes! That fits.

So Row 2 answer: ⬠, , △

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Back to Row 1:

_ △ _ △ △ _ ⬠ △

We have 8 positions. Let’s assume pattern length 3 or 4.

Try pattern length 3: suppose pattern is A B C, repeating.

Pos2=B=△
Pos4=A=△
Pos5=B=△
Pos7=C=⬠
Pos8=A=△

From pos4=A=△, pos5=B=△, pos6=C=?
Then pos7 should be A=△ — but it’s ⬠ — contradiction.

Try pattern length 4: A B C D

Pos1=A=?
Pos2=B=△
Pos3=C=?
Pos4=D=△
Pos5=A=△
Pos6=B=?
Pos7=C=⬠
Pos8=D=△

Now check consistency:

From pos5=A=△, pos6=B=?, pos7=C=⬠, pos8=D=△ → so pattern is △ ? ⬠ △

But pos2=B=△, pos4=D=△ — so B=△, D=△

Then from pos5=A=△, pos6=B=△ (since B=△), pos7=C=⬠, pos8=D=△ — yes!

So pattern is: A=△, B=△, C=⬠, D=△ → so “△ △ ⬠ △”

Check pos1=A=△
pos2=B=△ (matches given)
pos3=C=⬠
pos4=D=△ (matches given)
pos5=A=△ (matches)
pos6=B=△
pos7=C=⬠ (matches)
pos8=D=△ (matches)

Perfect!

So Row 1: pos1=△, pos3=⬠, pos6=△

Answer: △, ⬠, △

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Row 3:
☆ _ _ _ ☆ ☆ △ ☆

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

Look at pos5-8: ☆ ☆ △ ☆

Maybe pattern is “☆ ☆ △” — then pos5=☆, pos6=☆, pos7=△, pos8 should be ☆ — but if pattern is 3, pos8 would be start of next: ☆ — yes!

So pattern: ☆ ☆ △

Then:

Pos1: ☆ (start)
Pos2: ☆
Pos3: △
Pos4: ☆ (start of next)
Pos5: ☆ (should be second ☆) — yes
Pos6: △ — but given is ☆ — conflict.

pos6 is ☆, but if pattern is ☆ ☆ △, then after pos4=☆ (first), pos5=☆ (second), pos6=△ — but actual pos6=☆ — no.

Alternative: pattern “☆ ☆ △ ☆” — 4 items?

Pos1-4: ☆ ? ? ?
Pos5-8: ☆ ☆ △ ☆

So pos5-8 = ☆ ☆ △ ☆

Then pos1-4 should be same: ☆ ☆ △ ☆

So pos1=☆ (given)
pos2=☆
pos3=△
pos4=☆

Check: pos5=☆ (matches), pos6=☆ (matches), pos7=△ (matches), pos8=☆ (matches)

Yes!

So Row 3: ☆, △, ☆

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Row 4:
⬡ ⬢ ⬢ ⬡ _ _ _

Given: pos1=⬡, pos2=⬢, pos3=⬢, pos4=⬡, pos5=⬡

Look at pos1-3: ⬡ ⬢ ⬢
pos4-6: ⬡ ⬡ ? — not matching.

Perhaps pattern is “⬡ ⬢” — then pos1=⬡, pos2=⬢, pos3=⬢ — good.

pos4 should be start of next: ⬡ — yes (given)
pos5=⬢ — but given is ⬡ — conflict.

pos5 is ⬡, not ⬢.

Another idea: maybe “⬡ ⬢ ⬢ ⬡” — 4 items?

Pos1-4: ⬡ ⬢ ⬢ ⬡ — matches given.

Then pos5-8: should be same: ⬡ ⬢ ⬢

But pos5= (given) — good
pos6=⬢
pos7=⬢
pos8=⬡

Yes! Fits.

So Row 4: ⬢, , ⬡

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Row 5:
⬡ _ _ ⬡ ⬡ △ _

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

Look at pos4-6: ⬡ ⬡ — three pentagons.

pos7=△ — different.

Perhaps pattern includes △.

Notice pos1=⬡, pos4=⬡, pos5=⬡, pos6=⬡ — many ⬡.

Maybe the pattern is “⬡ ⬡ ⬡ △” — 4 items.

Then:

Pos1-4: ⬡ ? ? — if pattern is ⬡ ⬡ △, then pos1=⬡, pos2=⬡, pos3=⬡, pos4=△ — but pos4 is ⬡, not △ — no.

Alternative: look at end: pos6=⬡, pos7=△, pos8=?

And pos4=⬡, pos5=⬡, pos6=⬡ — so perhaps “⬡ ⬡ ⬡ △” starting at pos4?

pos4=⬡, pos5=⬡, pos6=⬡, pos7=△ — yes!

Then pos8 should be start of next pattern: ⬡

Now, what about pos1-3? Should be same pattern: ⬡ ⬡ ⬡ △ — but pos4 is already used as first of this group.

If pattern starts at pos4, then pos1-3 must be previous instance.

So pos1=⬡ (given) — should be first of pattern? But pattern is 4 items: ⬡ ⬡ △

Then pos1=⬡, pos2=⬡, pos3=⬡, pos4=△ — but pos4 is ⬡, not △ — conflict.

Unless the pattern is shifted.

Another idea: perhaps the pattern is “⬡ △” but that doesn't fit.

Let’s list all:

Pos1: ⬡
Pos2: ?
Pos3: ?
Pos4: ⬡
Pos5: ⬡
Pos6: ⬡
Pos7: △
Pos8: ?

Notice that from pos4 to pos7: ⬡ ⬡ ⬡ △ — that’s four items.

If this is the pattern, then pos8 should be start of next: ⬡

Now, what about pos1-3? They should be the same as pos4-7 but shifted? Or perhaps the pattern started earlier.

Assume the pattern is “⬡ ⬡ △” and it repeats every 4.

Then positions modulo 4:

Pos1: index 1 → should be first item: ⬡ — matches
Pos2: index 2 → second item: ⬡
Pos3: index 3 → third item: ⬡
Pos4: index 4 → fourth item: △ — but given is ⬡ — conflict.

Not working.

Perhaps the pattern is “⬡ △” — 3 items.

Pos1=⬡, pos2=⬡, pos3=△
Pos4=⬡, pos5=⬡, pos6=△ — but pos6 is ⬡, not △ — no.

Wait — look at pos7=△, and pos8=?

And pos6=⬡, pos5=⬡, pos4=⬡ — so maybe the △ comes after three ⬡s.

So pattern: three ⬡s then one △.

So “⬡ ⬡ △”

Then:

The last △ is at pos7, so pos4,5,6,7: ⬡ ⬡ △ — perfect.

Then pos8 should be start of next: ⬡

Now, pos1,2,3 should be the previous set: ⬡ ⬡ ⬡

Because pos1=⬡ (given), so pos2=⬡, pos3=⬡

Then pos4=⬡ (start of next group) — yes.

So Row 5: pos2=⬡, pos3=⬡, pos8=⬡

Answer: ⬡, , ⬡

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Row 6:
□ △ △ _ _ △ _ □

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

Look at pos1=□, pos8=□ — symmetric?

Pos2=△, pos3=△, pos6=△

Perhaps pattern is “□ △ △” — then pos1=□, pos2=△, pos3=△ — good.

Pos4 should be □ (start of next)
Pos5=△
Pos6=△ — matches given pos6=△
Pos7=□
Pos8=△ — but given is □ — conflict.

pos8 is □, not △.

If pattern is “□ △ △”, then pos7 should be □ (if pos4=□, pos5=△, pos6=△, pos7=□, pos8=△) — but pos8 is □, not △.

Not matching.

Another idea: perhaps “□ △ △ □” — 4 items.

Pos1-4: □ △ △ ?
Pos5-8: ? △ ? □

If pattern is “□ △ △ □”, then:

Pos1=□, pos2=△, pos3=△, pos4=□
Pos5=□, pos6=△, pos7=△, pos8=□

Check given: pos6=△ — matches, pos8=□ — matches.

pos4 is blank, should be □
pos5 is blank, should be □
pos7 is blank, should be △

Yes! Fits.

So Row 6: pos4=□, pos5=□, pos7=△

Answer: □, □, △

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Row 7:
○ ⬢ _ _ _ ⬢ ○

Positions:
1: ○
2: ⬢
3: ?
4: ?
5: ?
6: ⬢
7: ⬢
8: ○

Look at pos6=⬢, pos7=⬢, pos8=○

And pos1=○, pos2=⬢

Perhaps pattern is “○ ⬢ ” — 3 items.

Then:

Pos1=○, pos2=⬢, pos3=⬢
Pos4=○, pos5=⬢, pos6=⬢
Pos7=○, pos8=⬢ — but pos7 is ⬢, pos8 is ○ — conflict.

pos7=⬢, pos8=○ — so if pattern is “○ ⬢ ⬢”, then pos7 should be ○ — no.

Alternative: pattern “○ ⬢ ⬢ ○” — 4 items.

Pos1-4: ○ ⬢ ? ?
Pos5-8: ? ⬢ ⬢ ○

If pattern is “○ ⬢ ⬢ ○”, then:

Pos1=○, pos2=⬢, pos3=⬢, pos4=○
Pos5=○, pos6=⬢, pos7=⬢, pos8=○

Check given: pos6=⬢ — matches, pos7=⬢ — matches, pos8=○ — matches.

pos3 should be ⬢, pos4=○, pos5=○

Yes!

So Row 7: ⬢, ○, ○

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Row 8:
□ _ _ _ □ □ ○ □

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

Look at pos5=□, pos6=□, pos7=○, pos8=□

And pos1=□

Perhaps pattern is “□ □ ○” — 3 items.

Then:

Pos1=□, pos2=□, pos3=○
Pos4=□, pos5=□, pos6=○ — but pos6 is □, not ○ — no.

Pattern “□ □ ○ □” — 4 items.

Pos1-4: □ ? ? ?
Pos5-8: □ □ ○ □

So pos5-8 = □ □ ○ □

Then pos1-4 should be same: □ □ ○ □

So pos1=□ (given)
pos2=□
pos3=○
pos4=□

Check: pos5=□ (matches), pos6=□ (matches), pos7=○ (matches), pos8=□ (matches)

Yes!

So Row 8: □, ○, □

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Now summarize all answers:

Row 1: △, ⬠, △
Row 2: ⬠, , △
Row 3: ☆, △, ☆
Row 4: ⬢, ⬢, ⬡
Row 5: ⬡, , ⬡
Row 6: □, □, △
Row 7: ⬢, ○, ○
Row 8: □, ○, □

Final Answer:
Row 1: △, ⬠, △
Row 2: ⬠, ⬠, △
Row 3: ☆, △, ☆
Row 4: ⬢, ⬢, ⬡
Row 5: ⬡, ⬡, ⬡
Row 6: □, □, △
Row 7: ⬢, ○, ○
Row 8: □, ○, □