Milestone map
Milestone map
3 milestones
Work with variables, expressions, and order of operations
2–3 weeks (20 min/day)
Evaluate algebraic expressions by substituting values for variables, simplify expressions by combining like terms, and apply the order of operations (PEMDAS/BODMAS) correctly. A parent or teacher gives 10 expression problems (at least 3 requiring order-of-operations with parentheses and exponents) and checks the solutions.
Proof required
Submit a photo of 10 completed expression problems — evaluation with substitution (at least 3), combining like terms (at least 3), and order of operations (at least 4, including parentheses and exponents) — with working shown and a parent or teacher note confirming answers.
What gets checked
- Substitution problems show the value written in place of the variable before calculating
- Like terms correctly identified and combined (2x + 5x = 7x, not 7x²)
- Order of operations applied in correct sequence: parentheses first, then exponents, then multiplication/division left to right, then addition/subtraction left to right
Common mistakes
- Performing addition before multiplication — order of operations errors are the most common pre-algebra mistake; write out each step in sequence to catch these
- Combining unlike terms (3x + 2y = 5xy) — variables must match for terms to be combined
Powstik Guide
Worked problems on expressions and order of operations.
Steps
- Write out each step in order.
- Combine like terms.
- Substitute a number for each variable.
- Check one answer a second way.
Template
Problem: Step-by-step working: Answer:
What gets sent back
- Answers only, no working.
- Fewer problems than required.
- An adult did the work.
Resources
Foundationstart here
Depthgo deeper
Masteryfor the dedicated
What a verifier looks for
- Check the substitution step is written explicitly — '2x + 3 when x = 4' should show '2(4) + 3 = 11', not just '11'
- Ask the student to explain the order of operations for a mixed expression — they should state the sequence correctly
- Look for like-term errors: 3a + 2b cannot be combined; 3a + 5a = 8a
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Solve equations and inequalities
2 weeks (20 min/day)
Solve one-step and two-step equations by performing inverse operations, and graph simple inequalities on a number line. A parent or teacher gives 10 problems: 5 equations (at least 3 two-step), 3 inequalities with graphing, and 2 word problems requiring setting up and solving an equation.
Proof required
Submit a photo of 10 completed problems — 5 equations with inverse operations shown, 3 inequalities with number-line graphs drawn, and 2 word problems showing the equation set up before solving — with a parent or teacher note confirming the answers.
What gets checked
- Inverse operations shown step-by-step — not just the answer
- Inequalities graphed correctly (open circle for < and >, closed circle for ≤ and ≥, arrow in the right direction)
- Word problems show the equation written before any calculation
Common mistakes
- Guessing equation solutions by substitution rather than solving algebraically — the goal is to show the inverse operation method, not to test whether an answer works
- Forgetting to flip the inequality sign when dividing or multiplying by a negative number — this is a critical rule that gets missed even by students who otherwise understand inequalities
Powstik Guide
Solved equations and inequalities with every step shown.
Steps
- Undo operations in reverse order.
- Keep both sides balanced.
- Flip the sign if you divide by a negative.
- Substitute back to check.
Template
Equation/inequality: Steps: Solution: Check:
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 that inverse operations are written step-by-step, not skipped
- For inequalities: verify the circle is correct (open or closed) and the arrow points the right direction
- For word problems: confirm the equation is written before the solving begins
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Pass Pre-Algebra assessment at 80%
3–5 days (review and practice of weak areas)
Reach 80% mastery on the Khan Academy Pre-Algebra course. A teacher-graded pre-algebra test at 80% or above is also accepted. This is the level gate for Level 8 (Algebra I).
Proof required
Submit a screenshot of your Khan Academy Pre-Algebra course showing 80%+ in the course mastery meter (or a teacher-graded pre-algebra test scoring 80%+). Your name must be visible.
What gets checked
- 80%+ on the full Pre-Algebra course (expressions, equations, AND inequalities)
- Student's name visible on submission
- If teacher-graded: test covers both expressions/equations and inequalities
Common mistakes
- Completing equations but skipping the inequalities unit — both are required for the Algebra I prerequisite
- Submitting a unit mastery score rather than the full course mastery percentage
Powstik Guide
Proof of 80% mastery on Pre-Algebra.
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: Pre-Algebra 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
What a verifier looks for
- Confirm 80%+ on the full course, not just a single unit
- If teacher-graded: test should include both equations and inequalities
- Name visible on submission
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