Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 5 chapters and video availability01 · Read and understand
What you will learn
- Define volume as a count of equal cubes filling a solid.
- Explain your method and check what the result means in the stated situation.
Before you start
Multi-digit operations, equivalent fractions, decimal place value, and rectangular area.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A solid contains 2 layers, each with 3 rows of 4 unit cubes. What volume?
Why this math matters
Build a block model to connect visible layers to the space inside a solid. The worked example shows how to connect the situation, its mathematical representation, and a check on the result.
Set up the model
A useful answer starts with clear assumptions:
- Use the units, grouping rules, and reference whole stated in the question.
- Treat the supplied counts and measurements as exact within the classroom model, unless an estimate or a random outcome is requested.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Count space using unit cubes
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A solid contains 2 layers, each with 3 rows of 4 unit cubes. What volume?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the situation
One layer: 3 × 4 = 12 cubes
Count its rectangular array.
Connect the parts
Two layers: 2 × 12
Each layer has equal thickness and the same arrangement.
State and check the result
Volume = 24 cubic units
Cubes fill three-dimensional space without gaps or overlap.
The result
Volume = 24 cubic units
Cubes fill three-dimensional space without gaps or overlap.
Common mistakes to catch
- Volume uses cubic units rather than square units.
- A picture can hide cubes that must still be counted.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A solid has four layers of nine unit cubes. What volume?
Show a hint
Multiply layers by cubes per layer.
Reveal answer and explanation
36 cubic units
4 × 9 = 36.
Practice 2
Does counting only the visible top cubes give the whole volume?
Show a hint
Other layers may be hidden.
Reveal answer and explanation
No
Volume counts every filling cube, including interior and lower cubes.
Take the idea with you
Build a block model to connect visible layers to the space inside a solid.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Derive the box-volume formula
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