Lesson 3: 2-3 Solving multi-step equations
Duration of Days: 2
Lesson Objective
Solve equations involving more than one operation.
Solve equations involving consecutive integers
How can you use variables to represent consecutive integers?
How do the expressions used for even and odd consecutive integer problems compare?
multi-step equation
consecutive integers
number theory
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
3A Functions
3B Functions
3C Functions
Multi-step equations involve more than one operation. These equations can be solved using the Properties of Equality and the strategy of undoing each operation by working backward. In number theory, multi-step equations are written and solved to understand the relationship between numbers.
Susan had a $10 coupon for the purchase of any item. She bought a coat that was on sale for 1/2 its original price. After using the coupon, Susan paid $125 for the coat before taxes. What was the original price of the coat? Write an equation for the problem. Then solve the equation.
Regularity: Mathematically proficient students look both for general methods and for shortcuts. Ask students to explain why an equation to find consecutive odd integers looks like an equation to find consecutive even integers. Students should note that both odds and evens are calculated by adding 2 to the previous odd or even.
Extension: Hold a creativity competition for students. Each week, give students an equation and ask them to provide a context for the equation. Allow students to explain their work to the class and discuss questions about it. Increase the difficulty level with each successive week and reward creativity for problems that accurately reflect the operations and variables in the equation. (Optional: Provide a prize for the winner each week.)
Exercises 1 - 10
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