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
How many grams does one circle weigh?
3 circles weigh the same as 2 squares.
One square weighs 9 grams.
- A: 8
- B: 5
- C: 7
- D: 6 (the answer)
- E: 9
Why: 2 squares = 18 grams, so 3 circles = 18 grams. One circle = 18 ÷ 3 = 6.
Your turn
Your turn 1 of 3
How many grams does one circle weigh?
4 circles weigh the same as 2 squares.
One square weighs 8 grams.
Your turn 2 of 3
What is f(g(1))?
f(x) = 3x
g(x) = x + 3
Your turn 3 of 3
What is the smallest whole number n that works?
3n − 3 > 14
Keep practicing
Grown-ups: Connect it to budgeting: unknown cost, known total. Parent guide
Next lesson: Arguments and evidence