## SolveEquations&InequalitiesUsingReciprocal_ExitTicket.docx - Section 4: Exit Ticket

*SolveEquations&InequalitiesUsingReciprocal_ExitTicket.docx*

*SolveEquations&InequalitiesUsingReciprocal_ExitTicket.docx*

# Equation and Inequality Reteach - Fraction Coefficients

Lesson 15 of 20

## Objective: SWBAT solve equations and inequalities with fraction coefficients by multiplying by the reciprocal

## Big Idea: My students can solve two-step equations with integers but not fraction coefficients. This is a lesson designed to strengthen fluency solving equations and inequalities with fraction coefficients.

*50 minutes*

#### Introduction

*10 min*

I will begin with the essential question: How can we solve equations and inequalities with fraction coefficients?

In order to make sure students understand the question, we will review the terms coefficient and reciprocal. I will ask students to think to themselves the meaning of the two terms. I will then call on some students for an answer. The definition of coefficient is given in the resource.

This is a direct instruction lesson designed specifically to strengthen students' ability to solve equations and inequalities with fraction coefficients. Fluency of this sort is how I partially interpret mathematical practice 8 (**MP8)**. I will give little to no attention on the meaning of solutions (though the distinction between the solution of an inequality and an equation is an important concept for the students to understand).

The method for solving the problems in the lesson are given in two steps:

1) Undo any addition or subtraction

2) Multiply both sides by the reciprocal of the coefficient

I will then present an example. What I write I will expect the students to write. Each example comes with a check for understanding problem.

*expand content*

#### Guided Problem Solving

*15 min*

Students may now work in pairs or trios on this set of 6 problems. The first 4 problems can be solved in one-step, the last 2 problems in two steps.

Though I said I would spend little time discussing the meaning of solutions, I may discuss it a bit with GP4 - an inequality with a negative coefficient. We may evaluate potential solutions to the inequality by substituting in simple values for d. Solutions like + 2, +4, +6, etc. This serves as reminder to students of why the sign must be flipped.

The last two problems may require close attention as they require two-steps. You may want to stop students after the 4th problem in order to go over a two-step equation or inequality. I have seen that most of my students understand the order of inverse operations to solve equations and inequalities so I am not expecting this to cause any difficulties.

*expand content*

#### Independent Problem Solving

*20 min*

Students will now work on 8 problems independently. There are 4 one-step problems and 4 two-step problems. If students are stuck, I will guide them back to the steps given in the notes. As students are working, I will be on the lookout for proper use of the reciprocal. If I see an error, I may stop and ask the students a few questions: 1) What is the coefficient in the problem? ; 2) What is the reciprocal of the coefficient? 3) How do we solve an equation or inequality like this?

*expand content*

#### Exit Ticket

*5 min*

Before beginning the exit ticket, we will review the two-steps for solving equations and inequalities with fraction coefficients. Every student should know them by now! It might be worth cold calling students for a minute or so with a question: What is the first step? What is second step?

There are 5 questions on the exit ticket. They match the difficulty of the problems solved in the lesson. A successful exit ticket will have at least 4 correct answers.

*expand content*

This is a perfect lesson for my students. They were able to solve 2 step equations but the fractional coefficients were killing them! Thank you for the awesome lesson!

| 3 years ago | Reply##### Similar Lessons

Environment: Suburban

###### Solving Equations by Flow Chart - Working Backwards

*Favorites(8)*

*Resources(7)*

Environment: Suburban

Environment: Urban

- LESSON 1: Simplifying Linear Expressions by Combining Like Terms
- LESSON 2: Expand Algebraic Expressions Using the Distributive Property
- LESSON 3: Factor Algebraic Expressions Using the Distributive Property
- LESSON 4: Linear Expressions and Word Problems
- LESSON 5: Solving Addition and Subtraction Equations Using Models
- LESSON 6: Solve Addition and Subtraction Equations using Inverse Operations
- LESSON 7: Solve One-Step Equations Using Inverse Operations
- LESSON 8: Diagrams of Two-Step Equations
- LESSON 9: Speeding Tickets
- LESSON 10: Translate Verbal Statements to Inequalities
- LESSON 11: Graph Inequalities on a Number Line
- LESSON 12: Solve Inequalities Using Addition and Subtraction
- LESSON 13: Solve Inequalities Using Multiplication and Division
- LESSON 14: Solve Two-Step Equations Using Inverse Operations
- LESSON 15: Equation and Inequality Reteach - Fraction Coefficients
- LESSON 16: Algebraic Expressions and Equations for Shape Patterns
- LESSON 17: Simplify Expressions Containing Fractions by Combining Like Terms
- LESSON 18: Simplify Rational Number Expressions Using the Distributive Property
- LESSON 19: Writing Algebraic Expressions to Solve Perimeter Problems
- LESSON 20: An Introduction To Programming in SCRATCH