Mathematics • Year 7 • Unit 2 • Lesson 12
One-Step Add/Subtract in the Real World
Translate everyday situations — saving, baking, walking, temperature — into one-step equations, then solve and check.
1. Word problems
For each: choose a letter for the unknown, write a one-step equation (+ or − only), solve, then write a short sentence answering the question. Always check your answer.
1.1 — Flour in the bowl. A recipe needs 250 g of flour. After tipping some flour into the bowl, the chef adds another 75 g and the bowl now contains exactly 250 g.
(a) Let f be the amount of flour (in grams) already in the bowl. Write an equation.
(b) Solve to find f.
(c) Write one sentence answering: how much flour was in the bowl to start with? 3 marks
1.2 — Saving up for a game. Liam wants to buy a $90 video game. He already has some money saved, and after birthday cash of $35, he has exactly $90.
(a) Let s be Liam's original savings. Write an equation.
(b) Solve for s and check. 2 marks
1.3 — Lost pencils. Ava had a tin of pencils. She lent 8 to a friend and now has 17 pencils.
(a) Let p be the number of pencils she had originally. Write an equation.
(b) Solve and write the answer in a sentence. 2 marks
1.4 — Cool morning. The temperature in Sydney rose by 6.5 °C between 6 a.m. and noon and reached 19.2 °C at noon.
(a) Let t be the temperature at 6 a.m. (in °C). Write an equation.
(b) Solve to find t and check your answer. 2 marks
1.5 — Step counter. Maya wants to walk 10 000 steps today. By lunchtime she has walked some steps and still needs another 3650 steps to hit her goal.
(a) Let n be the number of steps she has walked by lunchtime. Write an equation.
(b) Solve and write the answer in a sentence. 2 marks
2. Explain your thinking
This question is about communication, not just symbols. Use full sentences. 4 marks
2.1 A classmate writes: "For x + 6 = 14, just take 6 off the x to get x = 14." In your own words, explain (i) why this method is wrong even though they got the right answer, (ii) what the balance-scales picture tells us must happen, (iii) why "doing it to both sides" is the rule, and (iv) what could go wrong if you only changed one side.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Flour in the bowl
(a) Equation: f + 75 = 250.
(b) Subtract 75 from both sides: f = 250 − 75 = 175. Check: 175 + 75 = 250 ✓.
(c) The bowl contained 175 g of flour to start with.
1.2 — Saving up for a game
(a) Equation: s + 35 = 90.
(b) Subtract 35: s = 90 − 35 = $55. Check: 55 + 35 = 90 ✓.
1.3 — Lost pencils
(a) Equation: p − 8 = 17.
(b) Add 8: p = 17 + 8 = 25. Ava had 25 pencils to start with.
1.4 — Cool morning
(a) Equation: t + 6.5 = 19.2.
(b) Subtract 6.5: t = 19.2 − 6.5 = 12.7 °C. Check: 12.7 + 6.5 = 19.2 ✓.
1.5 — Step counter
(a) Equation: n + 3650 = 10 000.
(b) Subtract 3650: n = 10 000 − 3650 = 6350. Maya has walked 6350 steps by lunchtime.
2.1 — Explain your thinking (sample response)
(i) "Take 6 off the x" only describes half the move — they ignored the RHS. They got the right number by luck because they subtracted 6 from the RHS in their head without writing it down. The method is incomplete.
(ii) The equation is a set of balance scales. The left pan has x + 6 and the right pan has 14. Removing 6 from the LEFT only would tip the scales, making them unequal.
(iii) The rule "do it to both sides" is the only way to keep the scales balanced — and therefore the only way to keep the equation true.
(iv) If you only changed one side, the new equation would NOT be equivalent to the original. For example, "x + 6 = 14" becomes "x = 14" if you only change the left side, which is wrong. You always have to mirror the move on the other side.
Marking: 1 for spotting the missing step; 1 for the balance picture; 1 for explaining the both-sides rule; 1 for a clear example of what goes wrong.