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Title: Linear Equations Sub-topic/Focus: Investigating Linear equations and solutions Grade level: 8 FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? CCLS standards: 8.EE.C.7.A Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.C.7.B Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? CCLS Mathematical practice standards: FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Focus How can we determine the solutions for an equation by inspection? FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Objectives Students will be able to solve algebraic equations to determine the number of solutions an equation has by: • using the distributive property of multiplication over addition/subtraction. • Combining/grouping like terms using opposite operation or additive inverse, to solve the equations. FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Material: Computer and Projector, Smart Board Chart Paper and Markers Index Cards FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Strategies: • • • • • Grouping(small group) Investigation Voicing(specifically targeting Ells) Differentiation(students that are still struggling with solving one- and two step equations will continue to work on that topic) Individual attention where necessary FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? “Do Now: Select one question to complete” FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? “ Fluency Drill” Evaluate the following using a strategy of your choice. Prepare to share your strategy with the class. , 15 –(−10) −8 + −15 FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Complete the equations and write the solution in the column labeled solution Equation 1 Equation 2 4(x – 3) = 4(x− 8) -3(x – 3) = -3(x− 8) 3x + 2 − 5 = 3x − 3 -2x + 2 − 5 = -2x − 3 3(𝑥 − 5) = 2(𝑥 − 5) Solution 4(𝑥 − 5) = 3(𝑥 − 5) FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Equations Conjecture 4(x – 3) = 4(x− 8) Working: 2x – 8 = x - 3 -x -x x – 8 = -3 +8 +8 x= 5 The equation has no solution: when the variables have the same coefficient. 3(x -5) = 3(x + 8) Working: 3x -15 =3x +24 -3x -3x -15 = 24 (not true) The equitation has no solution: when the coefficient of the variables are the same value on either side of the equation, the equations have no solution, therefore: a =b Graph 7x +14 -3x = The equation has many FOCUS: HOWsolution(real CAN WEDETERMINE THE number SOLUTIONS FOR AN EQUATION BY INSPECTION? 4x+14 Solve the equations below and state the type of solution each equation has. 1. 4𝑥 – 3𝑥 + 7 = 2𝑥 – 9 + 3 2. 8𝑥 – 4𝑥 – 5 = 4𝑥 + 8 – 13 3. 7𝑥 – 4𝑥 = 3𝑥 − 3 FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Ready Guided Practice Review the example on guided practice. All students :Complete question 11 Select either 9 or 10. FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Summarize: Teacher Share Review Questions: 1. How can I tell the type of solution an equation will have. Explain using examples. 2. What steps do I need to take in order to simplify or evaluate and equation. Explain using examples. FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Homework Write an equation whose solution results in one of three following: 1. No solution 2. Many/Infinitely Many Solution 3. Exactly one solution FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Exit Slip Write an equation that would have one of the following solution: 1. No solution 2. Many Solution 3. One solution FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Accommodations and Adaptations UDL Accommodations: -Provide information in multiple formats and media -Provide multiple pathways for students’ action, expression -Provide multiple ways to engage students UBD Adaptations -Shift to direct instruction as needed -Reframe problems using familiar context as needed - Read instructions & problems aloud to ESL students as well as help them using pictures and individual attention during the guided practice, and tiered task. -Maximize impact using technology FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION? Teacher Reflection FOCUS: HOW CAN WEDETERMINE THE SOLUTIONS FOR AN EQUATION BY INSPECTION?