Write the distributed expression. Activating Prior Knowledge – Notes Tie to LO M4:LSN7 Classifying Solutions to Linear Equations.

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Presentation transcript:

Write the distributed expression. Activating Prior Knowledge – Notes Tie to LO M4:LSN7 Classifying Solutions to Linear Equations

Learning Objective Today, we will classify solutions to linear equations. CFU

M4:LSN2 Linear and Non-Linear Expressions in x CFU Concept Development Review – Notes #1 & 2 1. Constants are fixed numbers. 2. When a term is the product of a constant(s) and a power of x, the constant is called a coefficient.

M4:LSN7 Classifying Solutions to Linear Equations CFU Concept Development – Pair Share unique solution

M4:LSN7 Classifying Solutions to Linear Equations CFU Concept Development – Pair Share no solution

M4:LSN7 Classifying Solutions to Linear Equations CFU Concept Development – Pair Share infinitely many solutions

M4:LSN7 CFU Concept Development – Notes #3 Solve the following equations – we will review in about 5 minutes. 7x – 3 = 7x + 5 7x – 3 = 5x + 5 Classifying Solutions to Linear Equations 7x – 3 = x

M4:LSN7 CFU Concept Development – Look at Notes #3 Classifying Solutions to Linear Equations 7x – 3 = 5x + 57x – 3 = 7x + 57x – 3 = x 7x – 3 = 5x x 2x – 3 = x = 8 ÷2 x = 4 What does x = 4 mean for the equation 7x – 3 = 5x + 5 ? How many solutions make this equation true?

M4:LSN7 CFU Concept Development – Look at Notes #3 Classifying Solutions to Linear Equations 7x – 3 = 5x + 57x – 3 = 7x + 57x – 3 = x 7x – 3 = 5x + 5 What do you notice about the coefficients in the equation? What do you notice about the constants in the equation?

M4:LSN7 CFU Concept Development – Look at Notes #3 Classifying Solutions to Linear Equations 7x – 3 = 5x + 57x – 3 = 7x + 57x – 3 = x 7x – 3 = 7x x – 3 = 5 Does -3 = 5? What does this mean about the equation 7x – 3 = 7x + 5 ?

M4:LSN7 CFU Concept Development – Look at Notes #3 Classifying Solutions to Linear Equations 7x – 3 = 5x + 57x – 3 = 7x + 57x – 3 = x 7x – 3 = 7x + 5 What do you notice about the coefficients in the equation? What do you notice about the constants in the equation?

M4:LSN7 CFU Concept Development – Look at Notes #3 Classifying Solutions to Linear Equations 7x – 3 = 5x + 57x – 3 = 7x + 57x – 3 = x -7x – 3 = -3 What value makes 7x – 3 = x true? Does -3 = -3? 7x – 3 = x 7x – 3 = 7x - 3 What do you notice about this equation?

M4:LSN7 CFU Concept Development – Look at Notes #3 Classifying Solutions to Linear Equations 7x – 3 = 5x + 57x – 3 = 7x + 57x – 3 = x What do you notice about the coefficients in the equation? What do you notice about the constants in the equation?

M4:LSN7 CFU Concept Development – Notes #4 Classifying Solutions to Linear Equations What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? 3x + 4 = 8x - 96x + 5 = 8 + 6x10x – 4 = x -4x – 5 = 6 – 11x12 – 15x = -2 – 15x-2x + 5 = -2x x = 9x + 7 Generalize about the equations – unique solution, no solution, or infinitely many solutions. **2 minutes **

M4:LSN7 CFU Skill Development/Guided Practice – Notes #5 Classifying Solutions to Linear Equations What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary.

Concept Development – Whiteboard Complete the following equation so that it doesn’t have a solution. Classifying Solutions to Linear Equations M4:LSN7 CFU 3x + 1 = ___________

M4:LSN7 CFU Skill Development/Guided Practice – Notes #6 Classifying Solutions to Linear Equations 8 – 9x = 15x x What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. 8 – 9x = 18x + 7

Concept Development – Whiteboard Complete the following equation so that it has infinitely many solutions. Classifying Solutions to Linear Equations M4:LSN7 CFU 3x + 1 = ___________

M4:LSN7 CFU Skill Development/Guided Practice – Notes #7 Classifying Solutions to Linear Equations 5(x + 9) = 5x + 45 What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. 5x + 45 = 5x + 45

Concept Development – Whiteboard Complete the following equation so that it has only one solution. Classifying Solutions to Linear Equations M4:LSN7 CFU 3x + 1 = ___________

M4:LSN7 CFU Skill Development/Guided Practice – Notes #8 Classifying Solutions to Linear Equations -3x + 32 – 7x = -2(5x + 10) What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. -10x + 32 = -10x - 20

1. What did we learn today? Closure – Complete at the end of notes 2. Why is this important to you? 3. How can you tell if an equation has infinitely many solutions? CFU