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 multiplying & dividing rational numbers to solve problems?
02 · LEARN & EXPLORE
Where this matters
Negative numbers and fractions help us express repeated changes, rates, and shared quantities.
03 · LEARN & EXPLORE
Understand the mathematics
Multiply magnitudes first, then apply sign rules. (-4)(3) = -12 because opposite signs produce a negative result. (-18) ÷ (-3) = 6 because equal signs produce a positive quotient.
Trace each operation and verify the result by checking the original problem.
Check the signs before calculating the magnitude.
04 · LEARN & EXPLORE
Model the first situation
A loss of $3 each day for four days is (−3) × 4 = −12. Repeated negative changes lead to a negative total.
Think: Which operation or representation best shows this situation?
05 · LEARN & EXPLORE
Why this concept matters
Negative numbers and fractions help us express repeated changes, rates, and shared quantities.
Use diagrams, number lines, tables, or algebraic representations where appropriate to explain why a procedure works.
06 · LEARN & EXPLORE
Understand a second strategy
When multiplying two negative values, the product is positive. For example, (−6) × (−2) = 12. Divide signs the same way.
Try it: Check the reasoning with your own numbers or a visual model.
07 · LEARN & EXPLORE
Apply your learning
Compute (−3/4) × 8 = −6: multiply numerators, divide by the denominator, and assign the negative sign.
Strategy reminder: First find the magnitude, then determine the sign. A zero factor always produces zero.
08 · LEARN & EXPLORE
Connect the idea
Same signs give a positive product or quotient; different signs give a negative one. Division by a fraction can be rewritten as multiplication by its reciprocal.
Explain the idea in your own words and identify when you would use it.
INDEPENDENT PRACTICE · 1 OF 12
What is (-35) ÷ 7?
Choose the best answer, then study the feedback.
Different signs give a negative quotient.
INDEPENDENT PRACTICE · 2 OF 12
What is (-3/4) ÷ (1/2)?
Work independently and check that your answer makes sense.
Multiply by the reciprocal 2/1.
INDEPENDENT PRACTICE · 3 OF 12
(-3)(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 · 4 OF 12
(-5)(-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 · 5 OF 12
24 ÷ (-6) = ?
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
(-30) ÷ (-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 · 7 OF 12
(-2.5)(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
1/2 × (-3/4) = ?
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 · 9 OF 12
(-6) ÷ 3/2 = ?
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 · 10 OF 12
(-0.6) ÷ (-0.2) = ?
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 · 11 OF 12
(-7)(0) = ?
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
A debt changes by -$4 each day for 5 days. Total change?
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.