# Ms. Minner's Classroom

A Louisville Middle School Classroom

A system of equations includes two or more equations that each involve the same set of two variables. In this module, we will study systems of equations involving two linear equations containing the variables (unknowns) x and y. The solution to a system of equations will be the values that satisfy both equations. These values are written as an ordered pair or point. When graphed, the solution to the system is represented by the point of intersection. Systems of equations can be solved graphically or algebraically. In this module, we will focus on how to solve systems of equations by graphing.

The point of intersection is the solution.

### Monday, February 5

Shortened class due to awards assembly
Plans carried over from last week

Common Core Standards and Extended Standards
8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
8.F. 3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s squared giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Student Objectives
I can identify functions using sets of ordered pairs, tables, mappings, and graphs.
I can identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.
I can distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.
I can analyze and interpret graphs.

Bellwork
Students will complete Math Minute 67.

Lesson (Functions Review)
1. Go over homework.
2. Review key ideas
3. Trashketball-functions review

4. Independent practice: functions review packet and IXL module 6 to-do list

Closing
Summarize key ideas with a venn diagram: linear functions vs. non-linear functions

Homework
The functions review worksheet and the IXL module 6 to-do list are due tomorrow. The unit test over functions is tomorrow.

### Tuesday, February 6

Plans carried over from last week

Common Core Standards and Extended Standards
8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
8.F. 3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s squared giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Student Objectives
I can identify functions using sets of ordered pairs, tables, mappings, and graphs.
I can identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.
I can distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.
I can analyze and interpret graphs.

Bellwork
Students will complete Math Minute 68.

Lesson (Functions Test)
1. XtraMath challenge
2. Collect IXL module 6 to-do list
3. Review key ideas
4. Functions test

5. Math vocabulary: bingo, Quizlet Live or Pictionary (student choice-majority rules)
6. Independent practice: Just for You IXL To-Do List

Closing

Homework
Work on the “Just for You IXL To-Do List.”

### Wednesday, February 7

Common Core Standards and Extended Standards
8.EE.8a: Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.8b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
8.EE.8c: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Student Objectives
I can solve a pair of linear equations graphically.
Given a linear equation in standard form, I can write it in slope-intercept form.

Bellwork
Students will complete Math Minute 69.
Video: Trolls & Tolls

Lesson (Introduction to Systems of Equations/Solving Systems Graphically)
1. Math vocabulary warm-up: Pictionary
2. Display a graphed line, a linear equation and a completed x-y chart for the equation. Ask essential question: “What does each point on the line represent?” Answer: a solution that makes the equation/function true
4, Modeling/demonstration/discovery: systems of equations with yarn
3. Review graphing lines in slope-intercept form:

4. Journal entry, demonstration, and guided practice: system of equations-definition and examples

5. Cooperative practice: solving systems wack-a-mole activity from TPT
6. Independent practice and individual/small group remediation: solving systems by graphing worksheet, quiz and test corrections, pass back papers & organize binders

Closing
Exit ticket:

Homework
There will be a quiz on Friday.

### Thursday, February 8

Common Core Standards and Extended Standards
8.EE.8a: Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.8b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
8.EE.8c: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Student Objectives
I can solve a pair of linear equations graphically.
Given a linear equation in standard form, I can write it in slope-intercept form.

Bellwork
Students will complete Math Minute 70.

Lesson (Solving Systems by Graphing)
1. Introduce math vocabulary assignment in Schoology.
2. Review: “What is the solution to a system of equations?” Answer-an ordered pair, the point of intersection
3. Systems of equations “hot seat” game in teams
4. Review and blended learning: Khan Academy-solving systems by graphing
5. Guided practice: solving systems by graphing worksheet
6. Cooperative practice: solving systems maze from TPT
7. Independent practice & individual/small group remediation: solving systems by graphing worksheet, make-up work

Closing
IXL AA.2

Homework
Complete the remaining items on the solving systems by graphing worksheet. Tomorrow, there will also be a quiz over solving systems graphically.

Like equations, systems of equations can have special solutions. A system of linear equations that both have the same slope will have no solutions. They are parallel lines and never intersect. Lines that are identical will overlap and will have infinite solutions. Lines that intersect at one point have one solution. Systems of equations can have one solution, no solutions, or infinite solutions.

### Friday, February 9

Common Core Standards and Extended Standards
8.EE.8a: Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.8b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
8.EE.8c: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Student Objectives
I can solve a pair of linear equations graphically.
Given a graphed system of equations, I can identify the solution and/or the number of solutions (one, none, or infinite) for the system.
Given a multiple choice question, I can solve a pair of linear equations by substitution.
I can analyze real-world scenarios involving systems of equations and answer related questions.

Bellwork
Students will complete Math Minute 71.

Lesson (Solving Systems by Graphing Quiz/Special Solutions)
1. Math vocabulary warm-up: Pictionary
2. Go over homework.
3. Quiz: solving systems quiz one (identify # of solutions and solutions given graphs)-link to quiz in Schoology
4. Reinforce big ideas: parallel lines=no solution, point of intersection=one solution, overlapping lines=infinite solutions, solution=(x, y) that makes both equations true
5. Guided notes review:

6. Review and guided practice: slope-intercept form and graphing lines given an equation in slope-intercept form

7. Independent practice: graphing systems of equations whack-a-mole

Closing
IXL AA.2 Solve a system of equations by graphing

Homework
Finish the graphing systems practice sheet you selected: whack-a-mole.