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
Powstik Guide
Worked ratio and unit-rate problems.
Steps
- Write each ratio three ways.
- Find equivalent ratios.
- Work out a price or speed per one unit.
- Compare two unit rates.
Template
Ratio (a:b, a to b, a/b): Equivalent ratios: Unit rate: Which is the better deal and why:
What gets sent back
- Answers only, no working.
- Fewer problems than required.
- An adult did the work.
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
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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
Powstik Guide
Solved proportion and percentage problems.
Steps
- Set up a proportion with the unknown.
- Cross-multiply to solve.
- Turn percentages into fractions and back.
- Check your answer makes sense.
Template
Problem: Proportion: Working: Answer:
What gets sent back
- Answers only, no working.
- Fewer problems than required.
- An adult did the work.
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
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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
Powstik Guide
Proof of 80% mastery on 6th Grade Math.
Steps
- Work through each unit in order.
- Redo any unit below 80%.
- Screenshot the course page with your name.
- Or sit a teacher-graded test instead.
Template
Course: 6th Grade Math Units and mastery %: - Name visible: yes / no Or: test score __% (marked by ______)
What gets sent back
- Below 80%.
- No name on the screenshot.
- Self-marked test.
Resources
Foundationstart here
Depthgo deeper
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
You'll sign in first, then come straight back here.
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