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Ratios & Proportional Reasoning

8 weeks · 3 milestones

Understand and apply ratios, rates, percentages, and proportional relationships in real-world contexts (Grades 5–6). Proof: 80%+ on Khan Academy Grade 6 Math or Ratios & Proportional Relationships unit mastery meter (screenshot with name visible), or teacher-graded test at 80%+.

Milestone map

Milestone map

3 milestones

Understand ratios and unit rates

2 weeks (20 min/day)

Write ratios three ways (3:4, 3/4, '3 to 4'), find unit rates (price per item, speed in km/h), and identify proportional relationships in tables and graphs. A parent or teacher gives 10 ratio and rate problems from a worksheet and checks both the setup and the answer.

Proof required

Submit a photo of 10 completed ratio and rate problems (at least 5 involving unit rates like price-per-item or speed) with work shown and a parent or teacher note confirming the answers.

What gets checked

  • Ratios written in all three forms at least once
  • Unit rate calculated correctly (division used to isolate 'per 1' unit)
  • 8 of 10 problems correct with working shown

Common mistakes

  • Confusing ratios with fractions — a ratio compares two quantities (3 apples to 4 oranges) while a fraction represents part of a whole; treating them identically causes errors in proportionality problems
  • Forgetting to divide to find the unit rate — 'price per item' requires dividing total by quantity, not multiplying

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

  • Ask 'what does 5:2 mean?' — the student should explain it as comparing 5 of one thing to 2 of another, not as a fraction
  • Check that unit rate problems show division in the working (total ÷ quantity = per-unit)
  • 8 of 10 correct with working shown is the bar

Solve proportional relationships and percentages

2 weeks (20 min/day)

Set up and solve proportions using cross-multiplication, calculate percentages of quantities (what is 30% of 80?), and find the original quantity from a percentage (60 is 75% of what?). A parent or teacher gives 10 mixed problems covering proportions and percentage calculations.

Proof required

Submit a photo of 10 completed problems covering proportions and percentages (at least 4 proportion problems using cross-multiplication and at least 4 percentage problems) with working shown and a parent or teacher note confirming answers.

What gets checked

  • Cross-multiplication set up correctly for proportion problems
  • Percentage problems show the decimal or fraction conversion step
  • 8 of 10 correct with working shown

Common mistakes

  • Setting up the proportion in the wrong order (mixing up which quantities go in the same position) — label each position of the proportion before cross-multiplying
  • Converting percentages incorrectly — 30% is 0.30 or 30/100, not 3 or 300; this error cascades through all subsequent calculations

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

  • Check cross-multiplication setup — ratios should be equal when cross products are equal
  • Verify percentage problems show the conversion step (% → decimal or fraction) before the multiplication
  • Ask the student to explain 'what does 25% mean?' — should say 25 out of 100, or 0.25

Pass 6th Grade Math assessment at 80%

2–3 days (review)

Reach 80% mastery on the Khan Academy 6th Grade Math course. A teacher-graded test covering ratios, unit rates, proportions, and percentages at 80% or above is also accepted. This is the level gate for Level 6 (Geometry and Measurement) or Level 7 (Pre-Algebra).

Proof required

Submit a screenshot of your Khan Academy 6th Grade Math course showing 80%+ in the course mastery meter (or a teacher-graded test on ratios, proportions, and percentages scoring 80%+). Your name must be visible.

What gets checked

  • 80%+ on the full 6th grade course or specifically on the ratios, rates, and percentages units
  • Both ratio/proportion and percentage sections covered
  • Student's name visible

Common mistakes

  • Completing the number system units but not the ratio/proportion units — submit the full course mastery, not a partial unit
  • Stopping at 70% and submitting — the 80% threshold exists because 6th grade proportional reasoning is foundational for all of pre-algebra

Resources

Foundationstart here

What a verifier looks for

  • Confirm 80%+ on the full course summary — not just the ratios unit
  • If teacher-graded: ensure the test covers both proportions and percentage problems
  • Name visible on submission

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