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
- Evaluate an expression while preserving its grouping.
- 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
Evaluate 3x² + 2 when x = 4.
Why this math matters
Test a formula on a known input before using it for a larger task. 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.
Substitute a value into a rule
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Evaluate 3x² + 2 when x = 4.
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
3(4)² + 2
Replace every x with the stated value.
Connect the parts
4² = 16; 3 × 16 = 48
Evaluate the power before the multiplication.
State and check the result
48 + 2 = 50
Substitution evaluates a rule; it does not ask us to solve for x.
The result
48 + 2 = 50
Substitution evaluates a rule; it does not ask us to solve for x.
Common mistakes to catch
- Keep parentheses when replacing a variable.
- Use operation order after substitution.
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
Evaluate 5(n + 2) when n = 3.
Show a hint
Keep the parentheses during substitution.
Reveal answer and explanation
25
5(3 + 2) = 5 × 5 = 25.
Practice 2
If x = 2, is 4x equal to 42?
Show a hint
Adjacent symbols denote multiplication here.
Reveal answer and explanation
No; 4x = 8
4 × 2 = 8; substitution is not concatenating digits.
Take the idea with you
Test a formula on a known input before using it for a larger task.
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: Combine terms with the same variable part
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