Mathematics — Logic and State Tracking · Forward-backward obstacle puzzle

Forward-Backward Walk Logic Puzzle

Track a moving character across numbered obstacles and develop repeatable forward/backward strategies without promising a hidden parity rule.

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📝 Description

Forward-Backward Walk Logic Puzzle is a motion and reasoning activity based on repeated forward and backward steps. Students analyze net displacement, step patterns, and time-based progress. It is useful for logical reasoning, arithmetic patterns, and introductory motion discussion.

📋 Instructions

Follow the step pattern, observe the movement, and use the solution cycle to understand net displacement and repeated-motion logic.

🎓 Learning Guide: Forward-Backward Walk Logic Puzzle

Learning focus: Track a moving character across numbered obstacles and develop repeatable forward/backward strategies without promising a hidden parity rule.

Mathematics — Logic and State Tracking Forward-backward obstacle puzzle

Learning objectives

Keep a written record of position after each move
Compare a tentative action with the stated move constraints
Explain why returning to an earlier state may be helpful or wasteful

Concepts and principles

A puzzle state can be described by current location and the moves still available.
A legal action changes the state according to a rule that must be taken from the displayed instructions.
Backtracking revisits previous states; detecting loops helps avoid cycling forever.

Examples and worked solutions

Independent teaching example (not verified as an in-game prompt): A separate number-line example starts at position 2, moves +4, then −3. Where does it end?: Worked solution: 2+4−3=3. Recording the intermediate position 6 helps verify the route.

Guided practice

Read the on-screen rules and inspect numbered stones before the first move
Record successive positions rather than relying on memory
Use any solution reveal only after testing and explaining your own route

Expected observations and explanations

Two move sequences can arrive at the same destination with different numbers of steps.
A route that looks visually shortest may violate the allowable-move rule.

Assessment questions and answers

What is the benefit of writing down visited states?: Answer: It prevents repeated unproductive cycles and helps trace mistakes.
Starting at 5, what is the result of moving back 2 then forward 4 on a number line?: Answer: 5−2+4=7.