Learn with Amar
Teaching video
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Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Model a constant percentage increase applied to the current amount.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
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 simulated population starts at 200 and increases by 10% after each round. Find the amount after three rounds.
Why this math matters
Compare additive increases with compounded proportional growth using explicit time steps. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
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.
Turn repeated percentage growth into a multiplier
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A simulated population starts at 200 and increases by 10% after each round. Find the amount after three rounds.
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 conditions
Each round multiplies by 1.10
The next amount is the current whole plus ten percent of that current whole.
Develop the calculation
P(n)=200(1.10)ⁿ
Three rounds apply the multiplier three times.
Check and interpret
P(3)=266.2 model units
A continuous classroom model can produce a fractional value; actual indivisible populations need a counting interpretation.
The result
P(3)=266.2 model units
A continuous classroom model can produce a fractional value; actual indivisible populations need a counting interpretation.
Common mistakes to catch
- Apply the percentage to the current amount at each step.
- A model's fractional outputs may need contextual interpretation.
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 quantity doubles each hour from an initial 5. What is it after four hours?
Show a hint
Use four factors of two.
Reveal answer and explanation
80
5·2⁴=80.
Practice 2
Is three rounds of 10% growth exactly 30% total growth?
Show a hint
Later increases use larger bases.
Reveal answer and explanation
No; it is 33.1%
1.1³=1.331, so the increase is 0.331 of the original amount.
Take the idea with you
Compare additive increases with compounded proportional growth using explicit time steps.
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: Model a constant fraction remaining
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