Learn with Amar
Teaching video
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Grade 6 chapters and video availability01 · Read and understand
What you will learn
- Calculate and compare unit rates with clear units.
- 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 fictional shop offers 6 notebooks for $15 or 4 identical notebooks for $11. Which has lower cost per notebook?
Why this math matters
Compare offers or motion models using rates expressed per the same unit. 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.
Compare rates per one unit
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional shop offers 6 notebooks for $15 or 4 identical notebooks for $11. Which has lower cost per notebook?
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
$15 ÷ 6 = $2.50 per notebook
Divide total cost by the first pack's item count.
Connect the parts
$11 ÷ 4 = $2.75 per notebook
Use the same cost-per-item unit for the second pack.
State and check the result
The six-pack has the lower unit price
The saving is $0.25 per notebook, although its total price is larger.
The result
The six-pack has the lower unit price
The saving is $0.25 per notebook, although its total price is larger.
Common mistakes to catch
- Keep the denominator quantity clear.
- A lower total cost need not mean a lower unit cost.
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 cyclist covers 36 km in 3 hours at a constant model speed. What unit rate?
Show a hint
Divide distance by time.
Reveal answer and explanation
12 km/h
36/3 = 12 kilometres for each hour.
Practice 2
Why cannot $2 per pen be directly compared with 3 pens per dollar as numbers 2 and 3?
Show a hint
The units are reversed.
Reveal answer and explanation
They measure reciprocal rates
Convert both to the same unit before deciding which purchase rate is better.
Take the idea with you
Compare offers or motion models using rates expressed per the same unit.
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: Find a percentage of a quantity
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