01 · DISCOVER
Before you begin
Enter your name and school email to save your learning. You’ll explore Proportional Relationships in Tables and then practice 12 questions with feedback.
- I can explain the main math idea in my own words.
- I can use a model, calculation, or example to solve a related problem.
- I can check my answers and explain why a solution makes sense.
Essential question: How can we use rewriting expressions to reveal meaning to solve problems?
02 · LEARN & EXPLORE
Where this matters
Different but equivalent expressions can reveal total cost, unit cost, and how quantities change.
03 · LEARN & EXPLORE
Understand the mathematics
The expression 5(x + 2) means five groups containing x + 2 items. The equivalent expression 5x + 10 reveals x-items and ten additional items. Both give the same value.
Trace each operation and verify the result by checking the original problem.
Three equal groups of x + 2 can also be written 3x + 6.
04 · LEARN & EXPLORE
Model the first situation
A camp buys 6 kits with x pencils and 2 markers per kit. The grouped expression is 6(x + 2).
Think: Which operation or representation best shows this situation?
05 · LEARN & EXPLORE
Why this concept matters
Different but equivalent expressions can reveal total cost, unit cost, and how quantities change.
Use diagrams, number lines, tables, or algebraic representations where appropriate to explain why a procedure works.
06 · LEARN & EXPLORE
Understand a second strategy
The expanded expression 6x + 12 reveals six groups of pencils plus 12 markers. Both forms describe the same supplies.
Try it: Check the reasoning with your own numbers or a visual model.
07 · LEARN & EXPLORE
Apply your learning
Factor 8x + 24 as 8(x + 3). Factoring reveals eight equal groups containing x + 3.
Strategy reminder: Use the form that makes the situation easiest to interpret, and verify by substitution.
08 · LEARN & EXPLORE
Connect the idea
The form of an expression can highlight different features. Factored form can show repeated groups; expanded form can show separate parts.
Explain the idea in your own words and identify when you would use it.
INDEPENDENT PRACTICE · 1 OF 12
Which form best shows 20% of the total of a and b?
Choose the best answer, then study the feedback.
Twenty percent of a total means multiply the whole total by 0.2.
INDEPENDENT PRACTICE · 2 OF 12
Which is equivalent to 6x + 18?
Work independently and check that your answer makes sense.
Find the greatest common factor.
INDEPENDENT PRACTICE · 3 OF 12
Expand 4(x + 5).
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 4 OF 12
Factor 6x + 12.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 5 OF 12
Which equals 3x+9?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 6 OF 12
Simplify 2x+5x+4.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 7 OF 12
Expand 2(3a-4).
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 8 OF 12
Factor 8y-16.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 9 OF 12
Equivalent to 5(2x+1)?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 10 OF 12
Which shows a $3 ticket plus $2 fee for each of n people?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 11 OF 12
Simplify 7p-3p+2.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 12 OF 12
Factor 9x+18.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
RESULTS · REFLECT
Your Learning Pathway Results
Check your work and submit your first-attempt score to your teacher.