In this Grade 8 lesson from Illustrative Mathematics Chapter 4, students solve multi-step number puzzles by working backward and representing problems using verbal reasoning, diagrams, and linear equations such as 2x + 4 = 18. Students practice translating word problems into algebraic equations and compare solution strategies with partners. The lesson builds foundational skills for writing and solving increasingly complex linear equations throughout the chapter.
Section 1
Working Backwards Strategy for Two-Step Problems
To solve real-world problems involving two operations, work backwards from the final result by reversing each operation in opposite order: if the original operations were "multiply then add," work backwards by "subtract then divide."
Section 2
Strategy 2: Modeling Puzzles with Tape Diagrams
A tape diagram is a visual model that uses rectangular bars (tapes) to represent the parts and the whole in a word problem.
For a two-step problem, the diagram helps you see the relationship between the numbers and break the problem down into two smaller, manageable steps.
It helps you identify the knowns, the unknowns, and the operations needed to solve.
Section 3
Strategy 3, Part A: Translating Puzzle Language into Math
To solve number problems, translate key words from the sentence into mathematical operations.
Restate the problem in a single sentence to clarify the relationship between the numbers. Common key words include:
Section 4
Strategy 3, Part B: Connecting 'Working Backwards' to Solving Equations
To solve an equation:
Solving an equation is like unwrapping a gift. The variable is the gift inside, and the operations are the wrapping paper and box. To get to the gift, you must undo each layer in the reverse order it was applied.
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Section 1
Working Backwards Strategy for Two-Step Problems
To solve real-world problems involving two operations, work backwards from the final result by reversing each operation in opposite order: if the original operations were "multiply then add," work backwards by "subtract then divide."
Section 2
Strategy 2: Modeling Puzzles with Tape Diagrams
A tape diagram is a visual model that uses rectangular bars (tapes) to represent the parts and the whole in a word problem.
For a two-step problem, the diagram helps you see the relationship between the numbers and break the problem down into two smaller, manageable steps.
It helps you identify the knowns, the unknowns, and the operations needed to solve.
Section 3
Strategy 3, Part A: Translating Puzzle Language into Math
To solve number problems, translate key words from the sentence into mathematical operations.
Restate the problem in a single sentence to clarify the relationship between the numbers. Common key words include:
Section 4
Strategy 3, Part B: Connecting 'Working Backwards' to Solving Equations
To solve an equation:
Solving an equation is like unwrapping a gift. The variable is the gift inside, and the operations are the wrapping paper and box. To get to the gift, you must undo each layer in the reverse order it was applied.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter