Daily Math Review Worksheets - Math Buzz (Level E) - Free Printable

Let’s solve each part of the worksheet step by step.

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Part 1: Partition the L-shaped figure into two rectangular prisms (Prism A and Prism B) and find total volume.

We are given an L-shaped 3D figure with these dimensions:

- Total height on right side: 20 mm
- Bottom width: 18 mm
- Left vertical part height: 5 mm, depth: 3 mm
- Top horizontal part: extends 4 mm wide, 3 mm deep, and goes up to 20 mm tall
- The “notch” in the middle: from left, it starts at 13 mm along the bottom, so the top part overhangs 18 - 13 = 5 mm? Wait — let’s look again.

Actually, looking at the diagram description:

The shape can be split vertically or horizontally. Let’s split it vertically into two parts:

→ Prism A: The bottom-left rectangle that sticks out.
Dimensions:
- Length = 13 mm (along bottom)
- Width = 3 mm (depth)
- Height = 5 mm

Wait — but then the right part would be taller. Alternatively, split horizontally?

Better approach: Split into two rectangles stacked or side-by-side.

Looking at standard way to split L-shape:

Option 1: Split vertically into left block and right block.

Left block (Prism A):
- Width (front to back) = 3 mm
- Depth (left to right) = 13 mm
- Height = 5 mm → Volume = 13 × 3 × 5

Right block (Prism B):
This is the tall part on the right. Its width (left to right) is 18 - 13 = 5 mm? But wait — the top part says 4 mm wide. Hmm.

Wait — re-examining labels:

From the diagram:

- The full base is 18 mm long.
- From left, there's a segment labeled 13 mm — that’s the length of the lower front part.
- Then above that, on the right, there’s a vertical column that is 4 mm wide (top label), 3 mm deep, and 20 mm tall.
- Also, the left protrusion is 5 mm high and 3 mm deep.

So better split:

→ Prism A: The bottom horizontal slab that covers the entire 18 mm length, but only 5 mm high? No — because the right part goes up to 20 mm.

Alternative correct split:

Split into:

Prism A: The large vertical prism on the right.
- Dimensions: width = 4 mm (given at top), depth = 3 mm, height = 20 mm → Volume = 4 × 3 × 20

Prism B: The smaller horizontal prism attached to the left bottom.
But its length? The total base is 18 mm, and the right prism takes 4 mm? Not necessarily aligned.

Wait — actually, looking at the drawing logic:

The L-shape has:

- A vertical tower on the right: 4 mm (width) × 3 mm (depth) × 20 mm (height)
- Attached to its left, at the bottom, a horizontal arm: which extends leftward for some distance.

The bottom total length is 18 mm. The vertical tower is 4 mm wide, so the horizontal arm must extend 18 - 4 = 14 mm to the left? But the diagram shows a label "13 mm" on the bottom of the horizontal part.

Also, the horizontal part is 5 mm high and 3 mm deep.

And between them, there’s a notch — meaning the horizontal part doesn’t go all the way under the tower? Actually, no — they share the same depth (3 mm).

Let me define:

Assume we split as:

Prism A: The bottom rectangular prism that spans the entire 18 mm length, but only 5 mm high, and 3 mm deep.

Then Prism B: The additional part on top of the right section, which is (20 - 5) = 15 mm high, 4 mm wide, 3 mm deep.

Check if this fits:

Total height on right: 5 + 15 = 20 mm ✔️
Width of top part: 4 mm ✔️
Bottom length: 18 mm ✔️
Depth: 3 mm everywhere ✔️
Left part height: 5 mm ✔️
Label “13 mm” — maybe that’s the length of the bottom part excluding the tower? If tower is 4 mm wide, then 18 - 4 = 14 mm, but label says 13 mm. Contradiction?

Wait — perhaps the 13 mm is the length of the horizontal arm *before* the tower starts. So:

Horizontal arm: 13 mm long, 3 mm deep, 5 mm high → Prism A

Vertical tower: sits on top of the last part of the horizontal arm? Or next to it?

Actually, looking at typical such problems, the 13 mm is likely the length of the bottom-left extension, and the tower is adjacent to it on the right, making total length 13 + something.

But total bottom is labeled 18 mm. So if left part is 13 mm, then right part (tower base) is 18 - 13 = 5 mm? But top of tower is labeled 4 mm. Inconsistency?

Perhaps the 4 mm is the width of the tower, and it’s centered or offset? This is confusing.

Alternative interpretation based on common textbook problems:

Often, the L-shape is made of:

- One prism: 18 mm (length) × 3 mm (depth) × 5 mm (height) → bottom layer
- Second prism: sitting on top of the right end, size: 4 mm (width) × 3 mm (depth) × (20 - 5) = 15 mm (height)

Then total length: the bottom is 18 mm, the top prism is 4 mm wide, placed at the right end, so it overlaps the last 4 mm of the bottom prism.

In that case, the “13 mm” label might refer to the part of the bottom prism that does NOT have anything on top — i.e., 18 - 4 = 14 mm? Still not 13.

Wait — maybe the 13 mm is a red herring or mislabeled? Or perhaps I need to use the numbers as given without assuming alignment.

Let’s read the diagram carefully as described:

Labels present:

- On the very bottom: “18 mm” — total length
- On the left vertical face of the lower part: “5 mm” height, “3 mm” depth
- On the horizontal top surface of the lower part: “13 mm” — this is probably the length of that lower horizontal piece
- On the upper vertical part: “15 mm” — this is likely the height from the top of the lower part to the top of the whole thing? Because 5 + 15 = 20, and total height is 20 mm.
- At the very top: “4 mm” — width of the upper part
- Right side: “20 mm” — total height
- Upper part also has “3 mm” depth (same as lower)

So, here’s the correct partition:

Prism A: The lower horizontal prism
- Length = 13 mm (as labeled on its top surface)
- Width (depth) = 3 mm
- Height = 5 mm
→ Volume A = 13 × 3 × 5

Prism B: The upper vertical prism
- It sits on top of the right part of Prism A? But how much does it overlap?

Actually, since the total length is 18 mm, and Prism A is 13 mm long, then Prism B must start after that? But then the total length wouldn't be 18 unless Prism B extends further.

Perhaps Prism B is positioned such that its base is within the 18 mm.

Another idea: The 13 mm is the length of the lower part extending left, and the upper part is 4 mm wide and sits on the right, so the distance from left end to start of upper part is 18 - 4 = 14 mm, but labeled 13 mm — close but not exact.

Perhaps it's a typo, or perhaps the 13 mm includes something else.

Let’s calculate using the most logical split that uses all given numbers consistently.

Notice: The upper part has height 15 mm (labeled on its side), and total height is 20 mm, so the lower part is 5 mm — matches.

The upper part is 4 mm wide, 3 mm deep, 15 mm high? But 15 mm is labeled on the side of the upper part, which might be its height.

If upper part height is 15 mm, and lower is 5 mm, total 20 mm — good.

Now, where is the upper part located? It should be sitting on the lower part.

The lower part has length 13 mm (labeled), but total base is 18 mm, so there is an additional 5 mm on the right that is part of the lower part but not labeled separately? That could be.

So:

Prism A: Lower prism covering full 18 mm length? But then why label 13 mm?

Perhaps the 13 mm is the length of the lower part that is only 5 mm high, and the remaining 5 mm (18-13=5) is the base of the upper prism, which is 4 mm wide — still not matching.

I think there's a mistake in my initial assumption.

Let me try this:

Split the L-shape into two prisms:

- Prism A: The big vertical one on the right: dimensions 4 mm (width) × 3 mm (depth) × 20 mm (height) → Volume = 4*3*20 = 240

- Prism B: The small horizontal one on the left bottom: but what are its dimensions? It must connect to the big one.

The total length is 18 mm. If the big prism is 4 mm wide, then the small one must be 18 - 4 = 14 mm long? But labeled 13 mm.

Unless the 13 mm is measured differently.

Perhaps the 13 mm is the length of the small prism, and the big prism is attached to its right, so total length is 13 + 4 = 17 mm, but labeled 18 mm — off by 1.

This is frustrating.

Another approach: Use the fact that the shape can be seen as a large rectangle minus a missing part, but the problem asks to partition into two prisms, so addition is required.

Let’s look at the labels again as per user's image description:

"Portition the shape into frism A and frism 8." — probably "prism A and prism B"

Dimensions given:

- Overall: bottom 18 mm, right side 20 mm
- Left protrusion: 5 mm high, 3 mm deep
- On the bottom of the left protrusion: 13 mm (length)
- On the top of the right tower: 4 mm (width), 3 mm (depth)
- On the side of the right tower: 15 mm — this is likely the height of the tower above the base level, so total height 5 + 15 = 20 mm

So, the right tower is 15 mm high above the 5 mm base, so its total height is 20 mm, but when calculating volume, if we take the tower as separate, its height is 15 mm if we consider the base as separate.

Yes! That's it.

Correct partition:

Prism A: The bottom layer that is 5 mm high, spanning the entire 18 mm length, and 3 mm deep.
- Volume A = 18 × 3 × 5

Prism B: The additional part on top of the right section, which is 4 mm wide, 3 mm deep, and 15 mm high (since 20 - 5 = 15)
- Volume B = 4 × 3 × 15

Then total volume = A + B

But is the bottom layer really 18 mm long? Yes, because the total base is 18 mm, and the tower sits on top of the right part of it, so the bottom layer is continuous.

The "13 mm" label might be indicating the length of the part that is only 5 mm high and has nothing on top, but for volume calculation, we don't need it if we take the full bottom layer.

However, the problem says "partition the shape", and if we take the bottom layer as 18x3x5, and the top as 4x3x15, then the top part is sitting on the last 4 mm of the bottom layer, so the first 14 mm of the bottom layer are exposed, but the label says 13 mm — still discrepancy.

Perhaps the 13 mm is the length of the bottom layer that is not covered by the top prism, so if top prism is 4 mm wide, then bottom layer is 13 + 4 = 17 mm, but labeled 18 mm.

I think there might be a typo in the problem or in my reading.

Let's assume that the "13 mm" is the length of the horizontal arm, and the vertical tower is 4 mm wide, and they are adjacent, so total length is 13 + 4 = 17 mm, but the diagram says 18 mm — perhaps the 18 mm includes a 1 mm overlap or something.

To resolve this, let's use the numbers as given for the prisms based on the labels provided for each part.

From the diagram:

- For the lower left part: it has length 13 mm, depth 3 mm, height 5 mm → this is Prism A
- For the upper right part: it has width 4 mm, depth 3 mm, and height 15 mm (since 20 - 5 = 15, and 15 is labeled on its side) → this is Prism B

Then, how do they connect? The lower part is 13 mm long, the upper part is 4 mm wide, so if they are placed end to end, total length is 17 mm, but the diagram shows 18 mm for the base. Perhaps the 18 mm is the maximum extent, and there is a 1 mm gap or something, but that doesn't make sense.

Maybe the 18 mm is the length of the bottom of the lower prism, and the upper prism is set back or forward.

Another idea: perhaps the 13 mm is not the length of the lower prism, but the distance from the left to the start of the upper prism.

Let's calculate the volume using the two prisms as defined by their own dimensions, ignoring the total 18 mm for a moment.

Prism A: 13 mm × 3 mm × 5 mm = 195 cubic mm

Prism B: 4 mm × 3 mm × 15 mm = 180 cubic mm

Total volume = 195 + 180 = 375 cubic mm

Now, check if this makes sense with the total dimensions.

The combined shape would have:

- At the bottom: from left, 13 mm of 5 mm height, then 4 mm of 20 mm height (since the upper prism adds 15 mm on top of the 5 mm base? No, if Prism B is 15 mm high, and it's sitting on the ground, then its total height is 15 mm, but the diagram says the right side is 20 mm, so it must be that Prism B is sitting on top of a 5 mm base.

In that case, for Prism B, if it's 15 mm high, and it's on top of the 5 mm base, then the base under it must be included in Prism A.

So, if Prism A is the entire bottom layer of 5 mm height, then its length should be the full 18 mm, and Prism B is on top of the right 4 mm of it.

Then Volume A = 18 × 3 × 5 = 270

Volume B = 4 × 3 × 15 = 180

Total = 450

But then what is the 13 mm for? Perhaps it's the length of the part that is only 5 mm high, so 18 - 4 = 14 mm, but labeled 13 mm — still off.

Perhaps the 13 mm is a distractor, or perhaps I need to use it.

Let's look at the answer format: it asks for Prism A: _ x _ x _ = _, Prism B: _ x _ x _ = _, Volume = _

So I need to fill in the blanks.

Given that, and to match the labels, let's assume:

Prism A: the lower horizontal part with dimensions 13 mm (length) × 3 mm (depth) × 5 mm (height)

Prism B: the upper vertical part with dimensions 4 mm (width) × 3 mm (depth) × 15 mm (height) — and we ignore the total 18 mm for the partition, or assume that the 18 mm is the overall footprint, but for the prisms, we use the given local dimensions.

Then volume A = 13 * 3 * 5 = 195

Volume B = 4 * 3 * 15 = 180

Total = 375

And the 18 mm might be the sum 13 + 5, but 5 is not given; or 13 + 4 = 17, close to 18.

Perhaps the 18 mm is incorrect, or the 13 mm is for something else.

Another possibility: the 13 mm is the length of the bottom of the lower prism, and the upper prism is 4 mm wide, but they overlap by 1 mm, so total length 13 + 4 - 1 = 16, not 18.

I think for the sake of progressing, I'll go with the most reasonable partition using the labeled dimensions for each prism.

So:

Prism A: 13 mm × 3 mm × 5 mm = 195 mm³

Prism B: 4 mm × 3 mm × 15 mm = 180 mm³

Volume: 195 + 180 = 375 mm³

And for the total length, perhaps the 18 mm is the distance from left to right including both, but with the upper prism starting at 13 mm from left, so from 13 to 17 mm (4 mm wide), and the 18 mm might be a mistake, or perhaps it's 17 mm labeled as 18.

Maybe the 18 mm is the length of the bottom of the lower prism, and the 13 mm is the length of the top of the lower prism or something.

Let's calculate the volume another way to verify.

Imagine the shape as a large rectangular prism minus a missing part.

Large prism: 18 mm (L) × 3 mm (W) × 20 mm (H) = 1080 mm³

Missing part: on the top left, a rectangle that is (18 - 4) = 14 mm long, 3 mm wide, and (20 - 5) = 15 mm high? No, because the missing part is only where there is no material.

Actually, the missing part is a rectangular prism that is cut out from the top left.

From the L-shape, the missing part is: length = 18 - 4 = 14 mm? But the lower part is only 5 mm high, so the missing part is from y=5 to y=20, and x=0 to x=14 mm, z=0 to 3 mm.

So missing volume = 14 × 3 × 15 = 630 mm³

Then actual volume = large - missing = 1080 - 630 = 450 mm³

Oh! So 450 mm³.

And this matches if we take:

Prism A: bottom layer 18×3×5 = 270

Prism B: top right 4×3×15 = 180

Sum 450

And the "13 mm" label might be the length of the part that is only 5 mm high and has no top, which would be 18 - 4 = 14 mm, but labeled 13 mm — perhaps a typo, or perhaps it's 14 mm and written as 13.

Maybe in the diagram, the 13 mm is measured from the left to the beginning of the upper prism, but the upper prism is 5 mm wide, not 4 mm.

The top is labeled 4 mm, so likely 4 mm.

Perhaps the 13 mm is for the depth or something else.

Given that the subtraction method gives 450, and it's consistent with the total dimensions, I think the intended partition is:

Prism A: 18 mm × 3 mm × 5 mm = 270 mm³

Prism B: 4 mm × 3 mm × 15 mm = 180 mm³

Volume: 450 mm³

And the "13 mm" might be a red herring or mislabeled; perhaps it's the length of the lower part before the upper part, but in reality, for the volume, we need the full bottom.

Since the problem asks to partition, and the bottom is continuous, this makes sense.

Moreover, in many textbooks, they split the L-shape into the base and the stem.

So I'll go with that.

So:

Prism A: 18 x 3 x 5 = 270

Prism B: 4 x 3 x 15 = 180

Volume = 450

Now, for the other parts.

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Part 2: Evaluate expressions for x=8, y=20

First expression: (12x - 3y) + 6

Plug in x=8, y=20:

12*8 = 96

3*20 = 60

96 - 60 = 36

36 + 6 = 42

Second expression: 160 + (4x + 2y)

4*8 = 32

2*20 = 40

32 + 40 = 72

160 + 72 = 232

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Part 3: Multiply 3.5 × 8.3

Calculate:

3.5 × 8.3

First, 35 × 83 = ?

30×83 = 2490

5×83 = 415

Sum 2490 + 415 = 2905

Since 3.5 has one decimal, 8.3 has one decimal, total two decimals, so 29.05

Or: 3.5 × 8 = 28, 3.5 × 0.3 = 1.05, total 29.05

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Part 4: Divide by powers of 10

Recall: dividing by 10^n moves decimal point n places left.

For 54.7 ÷ 10^1 = 54.7 ÷ 10 = 5.47

54.7 ÷ 10^2 = 54.7 ÷ 100 = 0.547

54.7 ÷ 10^3 = 54.7 ÷ 1000 = 0.0547

Similarly for 36.98:

36.98 ÷ 10^1 = 3.698

36.98 ÷ 10^2 = 0.3698

36.98 ÷ 10^3 = 0.03698

Note: 10^1 = 10, 10^2 = 100, 10^3 = 1000

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Now, to summarize all answers.

For the volume part, despite the confusion, I believe the intended answer is 450 mm³ with Prism A as 18x3x5 and Prism B as 4x3x15.

Perhaps the "13 mm" is the length of the lower part that is visible, but in 3D, the bottom is 18 mm.

Maybe the 13 mm is for the depth, but it's labeled on the length.

I think for accuracy, I'll box the answers as per calculation.

Final Answer:

Prism A: 18 x 3 x 5 = 270
Prism B: 4 x 3 x 15 = 180
Volume = 450 cubic mm

(12x - 3y) + 6 = 42
160 + (4x + 2y) = 232

3.5 × 8.3 = 29.05

54.7 10¹ = 5.47
54.7 ÷ 10² = 0.547
54.7 ÷ 10³ = 0.0547
36.98 ÷ 10¹ = 3.698
36.98 ÷ 10² = 0.3698
36.98 ÷ 10³ = 0.03698

But to confirm the volume, let's see if there's another way.

Suppose Prism A is the left part: 13 mm (L) × 3 mm (D) × 5 mm (H) = 195

Prism B is the right part: which includes the bottom and top. The right part has width 4 mm, depth 3 mm, height 20 mm, but then it would include the bottom 5 mm, so if we add Prism A and this, we double-count the bottom right corner.

So that's wrong.

If Prism B is only the top part: 4x3x15 = 180, and Prism A is the entire bottom: 18x3x5 = 270, sum 450, and no double-counting because the top part is additional.

And the 13 mm might be the length of the bottom that is not under the top prism, which is 18 - 4 = 14 mm, but labeled 13 — perhaps it's a typo, and it's 14 mm.

Maybe in the diagram, the 13 mm is measured from the left to the inner edge, but anyway, 450 is consistent with the subtraction method.

So I'll stick with that.

Final Answer:

Prism A: 18 × 3 × 5 = 270
Prism B: 4 × 3 × 15 = 180
Volume = 450 cubic mm

(12x - 3y) + 6 = 42
160 + (4x + 2y) = 232

3.5 × 8.3 = 29.05

54.7 ÷ 10¹ = 5.47
54.7 10² = 0.547
54.7 ÷ 10³ = 0.0547
36.98 ÷ 10¹ = 3.698
36.98 ÷ 10² = 0.3698
36.98 ÷ 10³ = 0.03698