Two-Step Reasoning with Unknowns (Grades 6–7)
This pulls the pieces together: set up an equation from a situation, then solve it in two steps.
Understanding two-step reasoning with unknowns
Real problems often hide an equation — "I think of a number, multiply by 2 and add 7 to get 15." Writing that as 2n + 7 = 15 and solving (undo +7, then ÷2) gives n = 4. The skill is turning words into an equation, then using inverse operations to solve.
Seeing it in action
Worked example
"Twice a number plus 7 is 15." Find the number.
Write it: 2n + 7 = 15.
Solve: 2n = 15 − 7 = 8, so n = 8 ÷ 2 = 4. (Check: 2·4 + 7 = 15 ✓.)
Translate the words, then solve backward.
A common mistake, and the fix
Undoing the steps in the order they happened.
For “twice a number plus 7 is 15”, dividing first gives 15 ÷ 2 = 7.5 and then 7.5 − 7 = 0.5, which is wrong. Undo the last step first: 15 − 7 = 8, then 8 ÷ 2 = 4, and check: 2 × 4 + 7 = 15.
Try a few
"3 times a number minus 1 is 14."
"A number divided by 2, plus 4, is 9."
"5 more than 4 times a number is 25."
Function Foundry
A calm pre-algebra game for function machines, inverse operations, and solving for an unknown.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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