Milestone map
Milestone map
3 milestones
Solve linear equations and graph lines
4 weeks (30 min/day)
Solve multi-step linear equations (including those with variables on both sides), understand slope and y-intercept, write equations in slope-intercept form (y = mx + b), and graph a line given its equation. A parent or teacher gives 10 problems covering these skills and checks the working and graphs.
Proof required
Submit a photo of 10 completed problems: multi-step linear equations with variables on both sides (at least 4), graphed lines from equation form (at least 4 with slope and y-intercept labelled), and slope-from-two-points calculation (at least 2) — with working shown and a parent or teacher note confirming answers.
What gets checked
- Variables collected on one side before solving — step-by-step working shown
- Graphs include labelled axes, plotted y-intercept, and correct slope direction
- Slope calculated correctly from two points: (y₂−y₁)/(x₂−x₁)
Common mistakes
- Moving terms without changing sign — '3x + 5 = 11, so 3x = 11 + 5' is the classic error; reinforce that moving across the equals sign means applying the inverse operation to both sides
- Plotting the y-intercept correctly but drawing the slope in the wrong direction — slope is rise over run (positive slope goes up-right, negative slope goes down-right)
Resources
Foundationstart here
Depthgo deeper
Masteryfor the dedicated
What a verifier looks for
- Check that 'variables on both sides' problems show the step of moving one variable term across the equals sign
- For graphs: confirm slope direction is correct (rise/run) and y-intercept is on the y-axis
- Ask the student to state the equation of a line from a graph — they should read the y-intercept and count the slope
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Factor polynomials and solve quadratics
3–4 weeks (30 min/day)
Factor trinomials of the form x² + bx + c, factor by finding the greatest common factor (GCF), and solve quadratic equations by factoring and using the quadratic formula. A parent or teacher gives 8 problems (at least 4 factoring and 4 solving quadratics using two methods) and checks the working.
Proof required
Submit a photo of 8 completed problems: GCF factoring (at least 2), trinomial factoring (at least 2), and solving quadratics (at least 4 using both factoring and the quadratic formula at least once) — with full working shown and a parent or teacher note confirming answers.
What gets checked
- Factoring shown as the reverse of FOIL — (x + a)(x + b) checked by expanding
- Quadratic formula applied correctly: x = (−b ± √(b²−4ac)) / 2a
- Both factoring and formula methods used — at least one problem solved by each method
Common mistakes
- Factoring by trial and error without checking — always verify by expanding the factored form back; (x + 3)(x + 4) = x² + 7x + 12 should match the original
- Forgetting the ± in the quadratic formula — this gives only one root when two exist
Resources
Foundationstart here
Depthgo deeper
Masteryfor the dedicated
What a verifier looks for
- Ask the student to verify their factoring by expanding — (x + 3)(x + 4) should give x² + 7x + 12
- Check the quadratic formula is written out before substituting — error-prone when applied from memory only
- Both methods (factoring and formula) must appear in the submission
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Pass Algebra 1 assessment at 80%
3–5 days (final review across all units)
Reach 80% mastery on the Khan Academy Algebra 1 course. A teacher-graded Algebra 1 exam at 80% or above is also accepted. This is the capstone of the Math Mastery Progression path — completing Algebra 1 prepares the student for Geometry and Algebra 2 at the high school level.
Proof required
Submit a screenshot of your Khan Academy Algebra 1 course showing 80%+ in the course mastery meter (or a teacher-graded Algebra 1 test scoring 80%+). Your name must be visible.
What gets checked
- 80%+ on the full Algebra 1 course — linear equations, graphing, systems, AND polynomials/quadratics
- Student's name visible on submission
- If teacher-graded: test covers both linear and quadratic content
Common mistakes
- Completing the linear equations section but skipping polynomials and quadratics — all Algebra 1 units are required for the 80% course mastery
- Submitting a unit score rather than the full course mastery percentage
Resources
Foundationstart here
Masteryfor the dedicated
What a verifier looks for
- Confirm 80%+ on the full course mastery meter — not just linear equations
- If teacher-graded: test must include both linear and quadratic content
- Name visible on submission
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