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* *Reflection: High Quality Task
Solve systems of linear functions by graphing - TWO lines on the same graph?!? - Section 2: Play of the Day

I like using the SILVER question (see the resource section of this reflection for the question and a sample of student work) to push the use of structure (MP7) right away in the beginning of this unit. I ask students to create (not choose) a line that will have one solution, no solutions, and infinite solutions with a given line, which reinforces the idea that in any system, there are three possibilities for intersection, and that the only thing that matters when trying to determine which is the case is the rate of change of each line. I think this implants and embeds an important conceptual understanding right at the outset of this unit, which lives on throughout the unit, before we get into the deep algebra of substitution and elimination.

*High Quality Task: Making note of structure with systems of linear equations*

# Solve systems of linear functions by graphing - TWO lines on the same graph?!?

Lesson 1 of 19

## Objective: SWBAT solve systems of linear equations by graphing.

*75 minutes*

#### Warm-up

*10 min*

Each day, students complete a warm-up that spirals older material in with content from the previous lesson. Warm-up problems sometimes extend content that students have encountered before to more unfamiliar contexts.

For a video narrative about how I structure each lesson, and how the warm-up fits in, click here.

Today, to save time for a longer Play of the Day, we are reviewing HW as our warm-up.

*expand content*

#### Homework

*15 min*

HW60 Solve systems of linear functions by graphing includes problems related to this lesson, as well as spiraled review. I also give the kids the answers to the problems.

Sometimes, the HW file is a take-home assessment.

*expand content*

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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: Solve systems of linear functions by graphing - TWO lines on the same graph?!?
- LESSON 2: Solve systems of linear equations by graphing - with some real-life applications
- LESSON 3: SUB! How can we use the properties of algebra to figure out the intersection of two lines WITHOUT graphing? (Day 1 of 3)
- LESSON 4: SUB! How can we use the properties of algebra to figure out the intersection of two lines WITHOUT graphing? (Day 2 of 3)
- LESSON 5: SUB! How can we use the properties of algebra to figure out the intersection of two lines WITHOUT graphing? (Day 3 of 3)
- LESSON 6: Assessment #9
- LESSON 7: Elimination 1 - add or subtract only
- LESSON 8: Elimination 2 - add or subtract only
- LESSON 9: Elimination 3 - multiply one equation only
- LESSON 10: Elimination 4 - multiply one equation only
- LESSON 11: Elimination 5 - mulitply both equations
- LESSON 12: Choose the best method to solve systems of equations
- LESSON 13: Real-life Systems 1
- LESSON 14: Real-life Systems 2
- LESSON 15: Real-life Systems 3 - Easy Price
- LESSON 16: Real-life Systems 4 - Sum Plus One Other
- LESSON 17: Real-life Systems 5 - Price-Sum Plus One Other
- LESSON 18: Mixed Review of Systems of Equations
- LESSON 19: Assessment #10 - Systems Unit Assessment