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 a × b?
a + b = 16
a − b = 2
- A: 63 (the answer)
- B: 73
- C: 71
- D: 16
- E: 52
Why: Add the two lines: 2a = 18, so a = 9. Then b = 7. a × b = 63.
Your turn
Your turn 1 of 3
What is the smallest whole number n that works?
4n − 8 > 19
Your turn 2 of 3
What is term number 24?
A pattern starts 4, 7, 10, 13, …
Your turn 3 of 3
what is 6x + 1?
If 2x + 1 = 15,
Keep practicing
Grown-ups: Connect it to budgeting: unknown cost, known total. Parent guide
Next lesson: Arguments and evidence