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 number goes in the box?
4 × □ + 9 = 41
- A: 7
- B: 9
- C: 11
- D: 8 (the answer)
- E: 10
Why: Undo the steps: 41 − 9 = 32, then 32 ÷ 4 = 8.
Your turn
Your turn 1 of 3
How many grams does one circle weigh?
3 circles weigh the same as 2 squares.
One square weighs 6 grams.
Your turn 2 of 3
What number goes in the box?
6 × □ + 3 = 15
Your turn 3 of 3
What is f(3)?
f(x) = 4x² − 5
Keep practicing
Grown-ups: Connect it to budgeting: unknown cost, known total. Parent guide
Next lesson: Arguments and evidence