One-Step Equations with Variables
Warm-up
Show the balance: left side has X + 5; right side has 14. The balance is level: X + 5 = 14. To find X: remove 5 from both sides. X = 9. Verify: 9 + 5 = 14. True. The balance model makes the algebraic manipulation physical and intuitive.
Explore
Equation card sort and solve: 16 cards covering all four operations and all three unknown positions (start, change, result). Students sort by operation, solve each, verify each. Partner check: swap and re-verify your partner's work. Discuss any discrepancies.
Formalize
Word problem translation: three community members share a prize equally. Each receives 750. Verify: 750/3 = 250. Correct. Practise the translation step as a distinct skill before the full solve.
One-Step Equations with Variables
Multi-context practice: one equation from each of (1) measurement context, (2) financial context, (3) natural world context, (4) sports context. Students recognize that equations appear everywhere, not just in mathematics textbooks.
Practice
Students solve 8 equations (2 per operation), write equations for 4 word problems, and verify all 12 answers. Exit ticket: solve and verify X/5 = 8.
Exit ticket
Students solve 8 equations (2 per operation), write equations for 4 word problems, and verify all 12 answers. Exit ticket: solve and verify X/5 = 8.
Step 1: Stage it on the balance: left pan holds three identical mystery bags (each hiding n) plus 4 loose cubes; right pan holds 19 cubes. Level.
Step 2: Remove 4 loose cubes from BOTH pans (legality: identical removals keep balance): 3 bags = 15 cubes.
Step 3: Share the 15 cubes equally among the 3 bags: each bag = 5. So n = 5.
Step 4: Write the symbolic diary of what your hands did: 3n + 4 = 19 → subtract 4 both sides → 3n = 15 → divide both sides by 3 → n = 5. The algebra IS the balance-moves, recorded.
Step 5: Substitute: 3(5) + 4 = 19 ✓.
The order question students ask: "why remove the 4 first, not divide by 3 first?" Try dividing first on the balance: you'd have to split the loose 4 into thirds — messy but legal (n + 4/3 …). Undoing in REVERSE order of operations keeps the numbers whole. Reverse-order undo: the rule with a reason.
The story: Sam buys 4 packs of cards and 3 loose cards, 27 cards total. Cards per pack?
Step 1: Write the candidate equations on the board (harvested from real student work): (a) 4p + 3 = 27, (b) 4p = 27 + 3, (c) 4(p + 3) = 27, (d) p = 27 − 4 − 3.
Step 2: Audit each against the STORY, not against the answer: (a) four packs of p, plus 3 loose, totalling 27 ✓ THE story. (b) says the packs alone beat the total by 3 — a different store. (c) says each pack contains p + 3 — no. (d) says one pack is 27 minus 4 minus 3 = 20?! — keyword salad.
Step 3: Solve the survivor: 4p + 3 = 27 → 4p = 24 → p = 6.
Step 4: Verify IN the story: 4 packs of 6 is 24, plus 3 loose = 27 ✓.
The assessment secret shared with students: writing the equation is worth more than solving it — because solvers with wrong equations get confidently wrong answers, and the world is full of those.
The riddle: a box weighs as much as 3 bricks. A brick weighs 2 kg. Later: a crate balances a box plus 4 bricks. What does the crate weigh?
Step 1: Solve the box first — substitute what's known: box = 3 bricks = 3 × 2 = 6 kg.
Step 2: Now the crate: crate = box + 4 bricks = 6 + 4 × 2 = 14 kg.
Step 3: Rewrite the chain symbolically to see what happened: b = 2; x = 3b = 6; c = x + 4b = 6 + 8 = 14. Each equation FED the next — substitution is using a solved mystery to crack the next one.
Step 4: The reversal that stretches: "a crate weighs 14 kg and balances a box plus 4 bricks; a box is 3 bricks; find the BRICK." Now the chain runs backwards: 3b + 4b = 14 → 7b = 14 → b = 2. Combining the bricks (3b + 4b = 7b) before dividing is the new move — like terms, met in the wild.
Exit: write your own two-object riddle where solving one unlocks the other, and trade with a neighbour.