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Expression-transformation puzzle: match a starting expression to an equivalent target form via valid operations

Design · All designs
Evidence · no claims cited

Description

The core design pattern of FH2T is a transformation puzzle: "The program presents a starting expression and a mathematically equivalent target expression. Students manipulate the original expression to match the target form." Because moves must be "mathematically valid operations," students practice algebraic manipulation by direct interaction with notation rather than by answering discrete items. The pattern embeds practice of distribution, factoring, inverse operations, and order of operations inside the game's goal structure.

Design Implications

Context

Requirements

  • A starting expression paired with a mathematically equivalent target expression
  • An interface allowing students to drag and transform expressions using mathematically valid operations

Constraints

  • Applied in the article to algebraic expressions and equation solving for introductory prealgebra/algebra

Target Learners

  • Middle and high school students learning introductory prealgebra or algebra

Learning Goals

  • Fluency with algebraic manipulation operations, including distribution, factoring, inverse operations, and order of operations

Claims

Examples

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Key Sources

  • From Here to There (FH2T): Program Description and Evaluation Evidence. (2023). https://www.evidenceforlearning.org.au/the-toolkit/from-here-to-there/
Page metadata
Field Value
type design
id expression-transformation-target-matching-pattern
title Expression-transformation puzzle: match a starting expression to an equivalent target form via valid operations
description The core design pattern of FH2T is a transformation puzzle: "The program presents a starting expression and a mathematically equivalent target expression.
status review
generated by process:settle-candidates on 2026-10-07
trust unverified — no one has confirmed this page's content
sources 1 — from-here-to-there-fh2t-program-description-and-evaluation-evidence-2023

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