Learn with Amar
Teaching video
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Grade 6 chapters and video availability01 · Read and understand
What you will learn
- Translate a repeating cost and fixed cost into an expression.
- 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 craft kit costs $4 plus $2 for each extra sheet. Write its cost for n extra sheets.
Why this math matters
Define a variable and its units before building a rule for a changing total. 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.
Represent a changing quantity with a variable
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional craft kit costs $4 plus $2 for each extra sheet. Write its cost for n extra sheets.
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
Extra-sheet cost = 2n
Two dollars repeats once for every extra sheet.
Connect the parts
Add one fixed $4
The base kit cost does not repeat.
State and check the result
C = 4 + 2n dollars
The context restricts n to whole numbers zero or greater.
The result
C = 4 + 2n dollars
The context restricts n to whole numbers zero or greater.
Common mistakes to catch
- Parentheses determine which costs repeat.
- A variable's contextual inputs may be more restricted than all real numbers.
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
Write the total length of k ribbons, each 3 m, plus a separate 5 m ribbon.
Show a hint
Separate the repeated and fixed lengths.
Reveal answer and explanation
3k + 5 metres
Each of k ribbons contributes three metres, then five is added once.
Practice 2
Does 2(n + 4) describe the kit?
Show a hint
Expand the repeated group.
Reveal answer and explanation
No; it equals 2n + 8
It doubles the fixed four-dollar amount as well as the sheet count.
Take the idea with you
Define a variable and its units before building a rule for a changing total.
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: Substitute a value into a rule
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