Unknowns and balances
Strategy card
Algebraic reasoning is about structure: what stays equal and what changes.
- Step 1: Name the unknown and write the relationship.
- Step 2: Isolate it with inverse operations, in reverse order.
- Step 3: For patterns, generalize: write the nth term.
- Step 4: Substitute back to check.
Tip: Check by substitution and by estimating size.
Worked example
What is x?
x : y = 3 : 8
x + y = 33
- A: 24
- B: 8
- C: 9 (the answer)
- D: 11
- E: 7
Why: There are 11 equal parts worth 33 ÷ 11 = 3 each. x is 3 parts = 9.
Your turn
Your turn 1 of 3
What is x?
x : y = 2 : 3
x + y = 20
Your turn 2 of 3
What is f(5)?
f(x) = 3x² − 4
Your turn 3 of 3
What is f(g(4))?
f(x) = 4x
g(x) = x + 4
Keep practicing
Grown-ups: Connect it to budgeting: unknown cost, known total. Parent guide
Next lesson: Arguments and evidence