Working Backwards Strategy for Real-World Problems
The working backwards strategy for real-world problems is a Grade 7 problem-solving approach in Big Ideas Math, Course 2. Instead of solving forward from given information, this strategy starts from the known final result and applies inverse operations in reverse order to find the initial value. For example: a number is multiplied by 3, then 7 is subtracted, giving 14. Working backwards: 14 + 7 = 21, then 21 ÷ 3 = 7. This is particularly useful in percent chain problems, multi-step consumer math, and situations where only the end result is given. The key is identifying each operation in the forward process and reversing it in opposite order.
Key Concepts
When solving real world problems, work backwards from the final result to set up a two step equation. If the final value is $y$ and the operations performed were: multiply by $a$, then add $b$, the equation becomes $ax + b = y$.
Common Questions
What is the working backwards problem-solving strategy?
Start with the final known result and apply inverse operations in reverse order to find the starting value or unknown quantity.
A number is multiplied by 3 then reduced by 7 to give 14. What is the number?
Work backwards: 14 + 7 = 21 (undo the subtraction), then 21 ÷ 3 = 7 (undo the multiplication). The original number is 7.
When is working backwards more efficient than solving forward?
When you know the final result but the starting value is unknown and multiple operations were applied in sequence—especially in percent and money problems.
What are the inverse operations used when working backwards?
Addition reverses subtraction, subtraction reverses addition, multiplication reverses division, and division reverses multiplication.
How does this strategy apply to percent problems in Grade 7?
If a price after a 20% increase is $72, work backwards: $72 ÷ 1.20 = $60. The original price was $60.
How is working backwards related to solving equations?
Both use inverse operations to isolate unknowns. Working backwards applies this informally in sequential steps; solving equations formalizes it with algebraic notation.