Learn with Amar
Teaching video
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Grade 6 chapters and video availability01 · Read and understand
What you will learn
- Extend prism volume to positive fractional dimensions.
- Explain your method and check what the result means in the stated situation.
Before you start
Fraction and decimal operations, whole-number factors, measurement units, and reading simple tables.
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 rectangular prism is 3/2 m by 2/3 m by 5/4 m. Find its volume.
Why this math matters
Use fractional dimensions without rounding away exact geometric relationships. 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.
Use fractional edges in a volume model
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A rectangular prism is 3/2 m by 2/3 m by 5/4 m. Find its 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
Base area = (3/2)(2/3) = 1 m²
The first two perpendicular dimensions produce a square-unit area.
Connect the parts
V = base area × height
The constant cross-section is repeated through the height.
State and check the result
V = 1 × 5/4 = 1¼ m³
Fractional edges still use the same three-dimensional multiplication rule.
The result
V = 1 × 5/4 = 1¼ m³
Fractional edges still use the same three-dimensional multiplication rule.
Common mistakes to catch
- Do not apply only one length scale factor to volume.
- All input edge lengths must use compatible units.
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
Find volume of a cube whose edges are 1/2 m.
Show a hint
Multiply three halves.
Reveal answer and explanation
1/8 m³
(1/2)³ = 1/8.
Practice 2
If all edges double, how does volume change?
Show a hint
Each of three factors doubles.
Reveal answer and explanation
It becomes 8 times as large
2 × 2 × 2 = 8 is the volume scale factor.
Take the idea with you
Use fractional dimensions without rounding away exact geometric relationships.
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: Ask a question that expects variation
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