Working Backwards Word Problems Worksheet

Lesson Overview

About this worksheet

Working backwards is a problem-solving STRATEGY rather than a single computation skill. Students learn to start at the FINAL result and undo each step using the inverse operation, then list the original steps in reverse order to find the unknown starting amount. The skill is foundational for pre-algebra: ‘find x’ problems are nothing more than working backwards from an equation.

The reference box at the top of page 1 covers the strategy in three layers. First, the one-sentence definition: start at the FINAL result and UNDO each step using INVERSE operations. Second, the two inverse PAIRS (addition undoes subtraction; multiplication undoes division). Third, the procedural rule: list the steps in original order, then REVERSE the order and apply the inverse of each step. A worked example – Tina thought of a number, added 6, got 10 – shows the undo subtraction 10 – 6 = 4. The (10, 6) operand pair does NOT appear in any assessed item.

Section A on page 1 has 6 single-step items in a single-column layout – each reverses ONE operation. Two items undo addition or subtraction (gave-stickers-away, spent-on-lunch), one undoes halving (lost half its marbles), one undoes tripling (a tripled batch), one undoes a subtraction-of-cost (paid for tickets), and one undoes doubling (a doubled score). The variety locks in the inverse-pair table the reference introduces.

Section B on page 2 has 4 multi-step problems with work boxes. Item 7 is the classic ‘thought of a number’ problem (added 9, doubled, got 32 – undo division then undo addition). Item 8 reverses a halving and a subsequent subtraction (sold half, then 14 more, with 36 left). Item 9 is a fraction-of-allowance reversal (1/3 on snacks then 8 dollars on a book, 12 left). Item 10 reverses a subsequent halving and earlier earning (earned 18, then spent half, with 22 left). Page 3 is a complete answer key with each undo step shown in order.

How to Use This Lesson

Project the page 1 reference box and read the strategy out loud: start at the FINAL result and undo each step using INVERSE operations.

Read the two inverse pairs aloud (addition undoes subtraction; multiplication undoes division) and have students give one example of each.

Walk through the worked example (Tina thought of a number, added 6, got 10 – undo by subtracting: 10 – 6 = 4).

Work Section A item 1 (Maya gave 7 stickers away, has 12 now) together; show 12 + 7 = 19 stickers to start.

Walk through Section A item 3 (jar lost half, has 18 now) to anchor ‘undo half by multiplying by 2’.

Assign the rest of Section A independently; remind students to ask ‘what operation was done, and what is its inverse?’ before computing.

Read Section B item 7 (Sam thought of a number, added 9, doubled, got 32) together; show the two-step undo in REVERSE order – undo doubling first (32 / 2 = 16), then undo addition (16 – 9 = 7).

Walk through Section B item 9 (one-third on snacks, then 8 dollars on a book, 12 left) since fractions-of-amount reversal is the most often-missed type.

Use Section B item 10 (Lana earned 18, then spent half, 22 left) as a closing whole-class problem.

Use the answer key on page 3 for self-check or aide spot-check.

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