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# Fractional coefficients

Lesson 4 of 16

## Objective: SWBAT solve equations with fractional coefficients.

## Big Idea: Get kids to play matchmaker by matching up fractional coefficients with their perfect match... another fraction with whom they become 1. :)

*75 minutes*

#### Warm-up

*10 min*

Each day, students complete a warm-up that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.

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#### Play of the Day

*40 min*

In this lesson, I walk kids through some basic equations, and show them that they are essentially creating 1's for coefficients. For example, 3x = 84. When you divide by 3 on both sides, you are creating a 1 (3 over 3).

We can apply this thinking to fractional coefficients. How can we create “1” with a fractional coefficient? (We need to multiply by the multiplicative inverse.) I use an analogy that the kids love… matchmaker. Make a perfect match – reciprocals are perfect matches, because when multiplied, they yield 1.

Then, we extend this to negative fractional coefficients as well… how can you create a POSITIVE 1 (a positive relationship with no yelling and arguing)… by using a negative number as the multiplicative inverse.

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#### Huddle

*10 min*

In the huddle in this lesson, we review a bunch of examples where kids make the perfect matches… and I tell the same joke over and over again until it sticks. J The kids generally love it, and also understand the concept of multiplicative inverse.

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#### Homework

*15 min*

The homework includes questions related to this lesson, as well as spiraled review. I also provide answers to the problems on page 2.

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- UNIT 1: FLUENCIES AND THE LANGUAGE OF ALGEBRA
- UNIT 2: SOLVING LINEAR EQUATIONS
- UNIT 3: INTRODUCTION TO FUNCTIONS
- UNIT 4: INTERPRETING AND COMPARING LINEAR FUNCTIONS
- UNIT 5: SYSTEMS OF LINEAR EQUATIONS
- UNIT 6: EXPONENTS AND SCIENTIFIC NOTATION
- UNIT 7: PARALLEL LINES, TRANSVERSALS, AND TRIANGLES
- UNIT 8: CONGRUENCE AND SIMILARITY THROUGH TRANSFORMATIONS
- UNIT 9: PATTERNS OF ASSOCIATION IN BIVARIATE DATA
- UNIT 10: SLOPE REVISITED
- UNIT 11: VOLUME OF CYLINDERS, CONES, AND SPHERES
- UNIT 12: POLYNOMIALS AND FACTORING
- UNIT 13: QUADRATIC FUNCTIONS

- LESSON 1: Introduction to solving equations
- LESSON 2: Solving Equations- Distributive Property
- LESSON 3: Collect like terms first
- LESSON 4: Fractional coefficients
- LESSON 5: Variables on both sides (Day 1 of 2)
- LESSON 6: Variables on both sides (Day 2 of 2)
- LESSON 7: Assessment #2
- LESSON 8: Understand one, infinite, or no solutions (Part 1 of 2)
- LESSON 9: Understand one, infinite, or no solutions (Part 2 of 2)
- LESSON 10: Apply algebra to solve problems (Part 1 of 2)
- LESSON 11: Apply algebra to solve problems (Part 2 of 2)
- LESSON 12: Assessment #3
- LESSON 13: Equations with mixed numbers and fractions
- LESSON 14: Solve for a given variable (Part 1 of 2)
- LESSON 15: Solve for a given variable (Part 2 of 2)
- LESSON 16: Assessment #4