Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 6 chapters and video availability01 · Read and understand
What you will learn
- Scale both entries of a ratio by a common factor.
- 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 model paint mix uses 2 measures blue for 5 measures white. How much blue accompanies 20 measures white?
Why this math matters
Organize consistent recipes or mixtures in a ratio table before scaling them. 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.
Build a table of equivalent ratios
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A model paint mix uses 2 measures blue for 5 measures white. How much blue accompanies 20 measures white?
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
5 × 4 = 20
The white amount is scaled by four.
Connect the parts
2 × 4 = 8
Apply the same multiplier to blue.
State and check the result
8 blue : 20 white = 2:5
Equal scaling preserves the mixture ratio.
The result
8 blue : 20 white = 2:5
Equal scaling preserves the mixture ratio.
Common mistakes to catch
- Adding the same amount to ratio entries generally changes the ratio.
- Use the same positive scale factor for both physical amounts.
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
At the same ratio, how much white accompanies 6 blue?
Show a hint
Blue is three times two.
Reveal answer and explanation
15 measures
5 × 3 = 15.
Practice 2
Does adding three to both ratio entries preserve 2:5?
Show a hint
Compare 5:8 with the original fraction.
Reveal answer and explanation
No
2/5 differs from 5/8; equivalent ratios multiply or divide both entries equally.
Take the idea with you
Organize consistent recipes or mixtures in a ratio table before scaling them.
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: Compare rates per one unit
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