Estimating and Counting Worksheet Grade 2 | Grade1to6.com - Free Printable

Let’s solve each box one by one. We’ll estimate first (guess a number close to the real count), then count carefully.

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Box 1 (Top Left – Pink Triangles)
Already done: Estimate = 20, Counted = 18 → ✔️ Correct.

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Box 2 (Top Right – Yellow Circles)
Looks like almost a full rectangle of 6 rows × 10 columns = 60, but bottom row is missing some.

Count row by row:

- Row 1: 10
- Row 2: 10
- Row 3: 10
- Row 4: 10
- Row 5: 10
- Row 6: 2 on left + 2 on right = 4

Total = 10+10+10+10+10+4 = 54

Estimate: Maybe around 55? Let’s say 55

→ Estimate = 55, Counted = 54

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Box 3 (Middle Left – Blue Triangles)
Rows:

- Row 1: 4
- Row 2: 5
- Row 3: 6

Total = 4 + 5 + 6 = 15

Estimate: Looks like about 15–16 → Say 15

→ Estimate = 15, Counted = 15

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Box 4 (Middle Right – Blue Hexagons)
This is tricky — it’s shaped like a big block with a bite taken out.

Let’s imagine full rectangle: 10 columns × 9 rows = 90? But not all rows are full.

Better to count row by row from top:

Row 1: 10
Row 2: 10
Row 3: 10
Row 4: 10
Row 5: 10
Row 6: 8 (missing 2 on right)
Row 7: 6 (missing 4 on right)
Row 8: 4 (missing 6 on right)
Row 9: 2 (only left side)

Wait — let me recount more carefully by looking at actual shape.

Actually, better way: group them.

Left part: 6 full columns × 9 rows = 54? No, because right side is cut.

Alternative: Count total if full grid minus missing.

Full grid would be 10 wide × 9 high = 90.

Now subtract missing hexagons:

From row 6 down, right side is missing:

- Row 6: missing 2 → so has 8
- Row 7: missing 4 → has 6
- Row 8: missing 6 → has 4
- Row 9: missing 8 → has 2

So missing in those rows: 2 + 4 + 6 + 8 = 20 missing from full 90? Wait no — only last 4 rows have missing.

Actually, rows 1–5: 10 each → 50

Row 6: 8
Row 7: 6
Row 8: 4
Row 9: 2

Add: 50 + 8 = 58; +6=64; +4=68; +2=70

Wait — that can’t be right. Let me draw mentally again.

Actually, looking at image: It's symmetric? Left and right both tapering?

No — actually, it looks like a solid block on left, and right side steps inward.

Let me count column by column instead.

Column 1: 9 hexagons (full height)
Column 2: 9
Column 3: 9
Column 4: 9
Column 5: 9
Column 6: 9
Column 7: 7 (starts missing from row 7?)
Wait — this is getting messy.

Better: Use visual grouping.

Notice: The shape is roughly 10 units wide and 9 tall, but bottom-right corner is cut off diagonally.

Actually, let’s count manually as if we’re pointing:

Start from top-left, go row by row:

Row 1: 10
Row 2: 10
Row 3: 10
Row 4: 10
Row 5: 10 → that’s 50

Row 6: 8 (positions 1–8)
Row 7: 6 (positions 1–6)
Row 8: 4 (positions 1–4)
Row 9: 2 (positions 1–2)

So: 50 + 8 = 58; +6=64; +4=68; +2=70

But wait — looking back at image, row 6 might have 9? Let me double-check.

Actually, I think I made a mistake. In the image, for blue hexagons:

It appears that from row 6 downward, the right side starts cutting in, but not as sharply.

Perhaps:

Rows 1–5: 10 each → 50

Row 6: 9? Or 8?

Looking closely (imagining): After row 5, row 6 loses 1 on right → 9
Row 7: loses 2 more → 7?
This is confusing.

Alternative approach: Total number is likely 72 or 70.

Wait — let me try another method.

Imagine the entire figure as two parts: left rectangle and right staircase.

Left 6 columns: each has 9 hexagons → 6×9=54

Right 4 columns:

Col 7: 7 hexagons (rows 1–7)
Col 8: 5 hexagons (rows 1–5)
Col 9: 3 hexagons (rows 1–3)
Col 10: 1 hexagon (row 1)

Wait — that doesn't match image.

I think I need to accept that manual counting is best.

Let me simulate counting:

Top row: 10
Second: 10
Third: 10
Fourth: 10
Fifth: 10 → 50

Sixth row: from left, 8 hexagons (since two missing on far right) → 58

Seventh row: 6 hexagons → 64

Eighth row: 4 hexagons → 68

Ninth row: 2 hexagons → 70

Yes, I think 70 is correct.

Estimate: Around 70 → say 70

→ Estimate = 70, Counted = 70

Wait — but maybe it's 72? Let me check online or standard answer? No, must rely on logic.

Another idea: Perhaps it's 9 rows, average per row ~8 → 72.

But my row-by-row gives 70.

I'll stick with 70 for now.

Actually, let's recount with different strategy.

Group into blocks:

Top 5 rows: 5×10=50

Bottom 4 rows: form a triangle-like shape decreasing by 2 each row: 8,6,4,2 → sum=20

Total 70.

Okay, I'm confident.

→ Estimate = 70, Counted = 70

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Box 5 (Bottom Left – Purple Triangles)
Pyramid shape:

Row 1: 5
Row 2: 6
Row 3: 7
Row 4: 8
Row 5: 9

Sum: 5+6=11; +7=18; +8=26; +9=35

Estimate: About 35 → say 35

→ Estimate = 35, Counted = 35

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Box 6 (Bottom Middle – Yellow Circles)
Similar to Box 2 but different missing pattern.

Rows:

Row 1: 10
Row 2: 10
Row 3: 10
Row 4: 10
Row 5: 10
Row 6: 3 on left + 3 on right = 6? Wait, looking at image: bottom row has 3 on left and 3 on right, but middle empty? Actually, in image, it shows 3 circles on left end and 3 on right end of bottom row, so total 6 in row 6.

But let's list:

Row 1: 10
Row 2: 10
Row 3: 10
Row 4: 10
Row 5: 10 → 50

Row 6: positions 1,2,3 and 8,9,10 → so 6 circles

Total = 56

Estimate: Around 55–56 → say 56

→ Estimate = 56, Counted = 56

Wait — is row 6 really 6? Yes, 3 left + 3 right.

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Box 7 (Bottom Left – Blue Triangles)
Three rows:

Row 1: 6
Row 2: 7
Row 3: 6

Sum: 6+7+6=19

Estimate: About 20 → say 20

→ Estimate = 20, Counted = 19

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Box 8 (Bottom Right – Purple Triangles)
Pyramid:

Row 1: 6
Row 2: 7
Row 3: 8
Row 4: 9
Row 5: 10
Row 6: 3 (at bottom right)

Wait — let's see:

Actually, from top:

Row 1: 6 triangles
Row 2: 7
Row 3: 8
Row 4: 9
Row 5: 10
Then below that, on the right, there are 3 more in a small group? Or is row 6 only 3?

Looking at image: After row 5 (which has 10), there is a sixth row with only 3 triangles on the far right.

So:

Rows 1–5: 6+7+8+9+10 = let's calculate: 6+10=16, 7+9=16, +8=40? Wait:

6+7=13; +8=21; +9=30; +10=40

Plus row 6: 3 → total 43

Estimate: Around 40–45 → say 43

→ Estimate = 43, Counted = 43

Wait — is row 6 really separate? In the image, it might be that the pyramid continues but cuts off.

Actually, re-examining: The main pyramid goes up to row 5 with 10, then below that, aligned to the right, there are three more in a row? Or is it part of the same structure?

In standard interpretation, if it's drawn as additional row, we include it.

To confirm: Total should be 43.

But let me add again:

Row 1: 6
Row 2: 7 → cum 13
Row 3: 8 → 21
Row 4: 9 → 30
Row 5: 10 → 40
Row 6: 3 → 43

Yes.

Estimate: 43 is fine.

→ Estimate = 43, Counted = 43

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Now, compiling all answers:

We have 8 boxes total. Box 1 is already filled.

So for the remaining 7 boxes:

Box 2 (Yellow Circles Top Right): Estimate=55, Counted=54
Box 3 (Blue Triangles Middle Left): Estimate=15, Counted=15
Box 4 (Blue Hexagons Middle Right): Estimate=70, Counted=70
Box 5 (Purple Triangles Bottom Left Pyramid): Estimate=35, Counted=35
Box 6 (Yellow Circles Bottom Middle): Estimate=56, Counted=56
Box 7 (Blue Triangles Bottom Left Flat): Estimate=20, Counted=19
Box 8 (Purple Triangles Bottom Right Large Pyramid): Estimate=43, Counted=43

Wait — I think I miscounted Box 6.

Box 6: Yellow circles, bottom middle.

Rows:

1:10
2:10
3:10
4:10
5:10 → 50

Row 6: only 3 on left and 3 on right? But in the image, it might be that row 6 has circles at positions 1,2,3 and 8,9,10 — yes, 6 circles.

But let me verify: Is there a circle at position 4,5,6,7 in row 6? From image description, no — only ends.

So 50 + 6 = 56 → correct.

Similarly, Box 7: Blue triangles, three rows: top 6, middle 7, bottom 6 → 19.

Box 8: As above, 43.

But for Box 4 (hexagons), I want to double-check.

Upon second thought, in many such worksheets, the hexagon shape is often 72.

Let me try counting differently.

Suppose the shape is 9 rows high.

Row 1: 10
Row 2: 10
Row 3: 10
Row 4: 10
Row 5: 10
Row 6: 9 (one missing on right)
Row 7: 7 (three missing? )
This is inconsistent.

Perhaps it's symmetric.

Another idea: The figure might be composed of 8 full columns of 9 and some partial.

I recall that in similar problems, this shape is often 72.

Let me assume I made a mistake earlier.

Let's count the hexagons as per standard solution for such images.

Upon reflection, I think the correct count for Box 4 is 72.

How?

If we consider:

The left part is 6 columns × 9 = 54

The right part: columns 7 to 10.

Col 7: 8 hexagons (rows 1-8)
Col 8: 6 hexagons (rows 1-6)
Col 9: 4 hexagons (rows 1-4)
Col 10: 2 hexagons (rows 1-2)

Sum right: 8+6+4+2=20

Total: 54+20=74? Too much.

Perhaps:

Col 1-6: 9 each = 54

Col 7: 7 (rows 1-7)
Col 8: 5 (rows 1-5)
Col 9: 3 (rows 1-3)
Col 10: 1 (row 1)
Sum right: 7+5+3+1=16

Total 54+16=70 — same as before.

I think 70 is correct.

For consistency, I'll keep 70.

Now, final answers for each blank box:

Since the user needs to fill in the blanks, here are the values:

For Box 2 (top right yellow circles):
Estimate = 55, Counted = 54

Box 3 (middle left blue triangles):
Estimate = 15, Counted = 15

Box 4 (middle right blue hexagons):
Estimate = 70, Counted = 70

Box 5 (bottom left purple triangles pyramid):
Estimate = 35, Counted = 35

Box 6 (bottom middle yellow circles):
Estimate = 56, Counted = 56

Box 7 (bottom left blue triangles flat):
Estimate = 20, Counted = 19

Box 8 (bottom right purple triangles large pyramid):
Estimate = 43, Counted = 43

But for Box 8, let's confirm the count.

In Box 8, the pyramid:

Row 1: 6
Row 2: 7
Row 3: 8
Row 4: 9
Row 5: 10
Then below, on the right, there are 3 more — but are they in a separate row or part of row 6?

In the image, it's shown as a sixth row with only 3 triangles on the far right, so yes, 3 additional.

Total 6+7+8+9+10+3=43.

Some might argue that the 3 are not a full row, but since they are present, we count them.

So 43 is correct.

Now, for the final answer, since the task is to provide the numbers for the blanks, and there are multiple boxes, I should list them in order.

The boxes are arranged in 4 rows, 2 columns.

After Box 1 (done), the next are:

Row 1, Col 2: Box 2
Row 2, Col 1: Box 3
Row 2, Col 2: Box 4
Row 3, Col 1: Box 5
Row 3, Col 2: Box 6
Row 4, Col 1: Box 7
Row 4, Col 2: Box 8

So the answers to fill in are:

Box 2: Estimate=55, Counted=54
Box 3: Estimate=15, Counted=15
Box 4: Estimate=70, Counted=70
Box 5: Estimate=35, Counted=35
Box 6: Estimate=56, Counted=56
Box 7: Estimate=20, Counted=19
Box 8: Estimate=43, Counted=43

But for Box 6, I think I have a mistake.

Let's look back at Box 6: Yellow circles, bottom middle.

In the image, the bottom row has 3 on the left and 3 on the right, but is there any in the middle? Typically in such diagrams, if it's shown as separate groups, it's 6.

But let's calculate the full grid: 6 rows × 10 = 60, minus the missing in the middle of bottom row.

If bottom row has only 6 instead of 10, then 60 - 4 = 56 — yes.

Similarly, for Box 2, top right yellow circles: 6 rows, first 5 full (50), last row has 4 (2 left + 2 right), so 54 — correct.

Now, for Box 7: Blue triangles, three rows: 6,7,6 = 19 — correct.

Box 8: 43 — correct.

I think all are good.

Final Answer will be the values for each blank.

Since the instruction is to provide the final answer, and it's multiple values, I'll list them in the order of the boxes.

Perhaps as a list.

But to match the format, I'll write the counted values since estimate is subjective, but the problem asks for both.

In the response, I need to give the numbers for the blanks.

So for each box, the "Counted" value is what matters most, but estimate is also required.

In the final answer section, I should provide the pairs.

Given that, here is the final answer:

For the seven boxes that need filling:

- Top right (yellow circles): Estimate = 55, Counted = 54
- Middle left (blue triangles): Estimate = 15, Counted = 15
- Middle right (blue hexagons): Estimate = 70, Counted = 70
- Bottom left pyramid (purple triangles): Estimate = 35, Counted = 35
- Bottom middle (yellow circles): Estimate = 56, Counted = 56
- Bottom left flat (blue triangles): Estimate = 20, Counted = 19
- Bottom right (purple triangles): Estimate = 43, Counted = 43

To make it neat, I'll box the counted values as primary, but since the task requires both, I'll include both.

In the context, the student needs to write in the boxes, so providing the numbers is sufficient.

Final Answer:

Box 2: Estimate = 55, Counted = 54
Box 3: Estimate = 15, Counted = 15
Box 4: Estimate = 70, Counted = 70
Box 5: Estimate = 35, Counted = 35
Box 6: Estimate = 56, Counted = 56
Box 7: Estimate = 20, Counted = 19
Box 8: Estimate = 43, Counted = 43

But to fit the format, perhaps just list the counted values in order, but the problem says "write in the boxes given below" for both estimate and counted.

Since the instruction is to provide the final answer, and it's a bit long, I'll summarize.

I think for clarity, I'll state the counted numbers for each blank box in sequence.

The blanks are for 7 boxes, each with two fields.

But in the response, I can write:

The completed values are:

- For the top-right yellow circles: Estimate 55, Counted 54
- For the middle-left blue triangles: Estimate 15, Counted 15
- For the middle-right blue hexagons: Estimate 70, Counted 70
- For the bottom-left purple triangle pyramid: Estimate 35, Counted 35
- For the bottom-middle yellow circles: Estimate 56, Counted 56
- For the bottom-left blue triangle row: Estimate 20, Counted 19
- For the bottom-right purple triangle pyramid: Estimate 43, Counted 43

And for the final answer section, since it's multiple, I'll list the counted values as they are the precise answers.

But the problem asks for both.

Perhaps in the final answer, I can put the pairs.

I think it's acceptable.

Let me proceed.