Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 4
Math
Unit 6
8th Grade
Lesson 4 of 11
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Solve real-world and mathematical problems by graphing systems of linear equations.
The core standards covered in this lesson
8.EE.C.8.C — 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.
The foundational standards covered in this lesson
8.F.B.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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
You and a friend are reading the same book over the summer. You have already read 35 pages of the book, and you set a goal to read 15 pages each day. Your friend has only read 15 pages so far but sets a goal to read 20 pages each day.
a. Write a system of linear equations to represent the situation and graph both lines on the coordinate plane below.
b. After how many days will you both be on the same page?
c. Who will have read more pages after 10 days? Explain how you got your answer.
One line passes through points (0, 2) and (4, 6). Another line passes through points (-3, 2) and (1, 6). Will the two lines intersect at a single point? If so, where? Use the coordinate plane if needed.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Two companies offer a subscription service for listening to and downloading music by the month. The company Musik charges $5 a month for unlimited listening plus a $0.50 fee for every album that you download. The company Waves charges $8 a month for unlimited listening plus a $0.25 fee for every album that you download.
a. Write and graph a system of linear equations to determine which company offers the better monthly deal based on the number of albums you download a month. Label your graph.
b. How many albums would you need to download for the costs to be the same?
c. How many albums could you download per month for Musik to be the better deal?
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 3
Lesson 5
Topic A: Analyze & Solve Systems of Equations Graphically
Define a system of linear equations and its solution.
8.EE.C.8.A
Solve systems of linear equations by graphing.
8.EE.C.8.A 8.EE.C.8.B
Classify systems of linear equations as having a unique solution, no solutions, or infinite solutions.
8.EE.C.8.C
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Topic B: Analyze & Solve Systems of Equations Algebraically
Solve systems of linear equations using substitution when one equation is already solved for a variable.
8.EE.C.8.B
Solve systems of linear equations using substitution by first solving an equation for a variable.
Solve real-world and mathematical problems using linear systems and substitution.
Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.
Solve systems of linear equations using elimination (linear combinations) by first creating a zero pair.
Solve real-world and mathematical problems using systems and any method of solution.
8.EE.C.8.B 8.EE.C.8.C
Model and solve real-world problems using systems of equations.
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