Learn with Amar
Teaching video
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Browse grades and teaching videos01 · Read and understand
What you will learn
- Define a variable with its unit.
- Separate fixed and changing charges.
- Evaluate an expression by substitution.
Before you start
Multiply decimals and identify variables, coefficients, and constants.
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 delivery service charges $2.40 per parcel plus $1.20 per kilogram. Write a cost expression and evaluate it for a 3.5 kg parcel.
Why this math matters
A reusable expression describes many cases at once. Instead of solving each parcel separately, define an input and a rule. The fixed term and the variable term reveal how the total changes when the parcel mass changes.
Set up the model
A useful answer starts with clear assumptions:
- The fictional service charges continuously by exact mass, without bands or rounding up.
- The $2.40 fee applies once per parcel and no other charges apply.
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.
Write a parcel-cost rule before calculating
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional delivery service charges $2.40 per parcel plus $1.20 per kilogram. Write a cost expression and evaluate it for a 3.5 kg parcel.
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.
Name the variable
m = parcel mass in kilograms; C(m) = 2.40 + 1.20m
C is the numerical dollar cost. The coefficient 1.20 represents dollars per kilogram; the constant 2.40 represents the fixed charge.
Evaluate the changing part
1.20 × 3.5 = $4.20
Substitute the measured mass for m. Multiplying the rate by kilograms gives the mass-dependent charge.
Include the fixed part
C(3.5) = 2.40 + 4.20 = $6.60
The fixed fee is added once. It is not multiplied by the parcel's mass.
The result
The rule is C(m) = 2.40 + 1.20m, and a 3.5 kg parcel costs $6.60.
An extra kilogram adds $1.20, regardless of the starting mass. Doubling the mass does not double the full cost, because the fixed charge remains unchanged. This is linear but not direct variation.
Common mistakes to catch
- Writing 3.60m incorrectly multiplies the fixed charge by the mass.
- A variable's value must use the unit assumed by its coefficient; grams would need conversion first.
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
Use the rule to price a 5 kg parcel.
Show a hint
Substitute 5 for m, keeping the fixed fee.
Reveal answer and explanation
$8.40
2.40 + 1.20(5) = 2.40 + 6.00 = $8.40.
Practice 2
How much more does a 4 kg parcel cost than a 2 kg parcel under this rule?
Show a hint
Both parcels have the same fixed fee.
Reveal answer and explanation
$2.40 more
Their masses differ by 2 kg, giving 1.20(2) = $2.40 extra. Direct evaluation gives $7.20 − $4.80 = $2.40.
Take the idea with you
Write a rule for another fictional service. Explain which term changes and which stays fixed before substituting numbers.
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 an unknown mass with an inverse operation
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