Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 11
Math
Unit 6
8th Grade
Lesson 11 of 11
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Lesson Notes
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Model and solve real-world problems using systems of 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.EE.C.7 — Solve linear equations in one variable.
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
There is only one Anchor Problem for this lesson, which will likely take up a large portion of class. This problem is a great opportunity for students to collaborate with one another and to create visual presentations of their work and strategy to share with others.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Ivan’s furnace has quit working during the coldest part of the year, and he is eager to get it fixed. He decides to call some mechanics and furnace specialists to see what it might cost him to have the furnace fixed. Since he is unsure of the parts he needs, he decides to compare the costs based only on service fees and labor costs. Shown below are the price estimates for labor that were given to him by three different companies. Each company has given the same time estimate for fixing the furnace.
For which time intervals should Ivan choose Company A, Company B, or Company C? Support your decision with sound reasoning and representations. Consider including equations, tables, and graphs.
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Fixing the Furnace, accessed on March 21, 2018, 8:12 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
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
5-10 minutes
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
$${3x+6y-9=0}$$
$${x=y}$$
$${1.25x=1.25y}$$
$${9.9=6x+8y}$$
$${9x=2.5y-8.8}$$
$${11x-2y=1.5}$$
$${11x-2y=2.5}$$
Simultaneous Linear Equations Mini-Assessment by is made available by Achieve the Core under the CC0 1.0 license. Accessed March 21, 2018, 8:17 p.m..
Kim has a small container and a large container as shown.
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?
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.
Topic A: Analyze & Solve Systems of Equations Graphically
Define a system of linear equations and its solution.
Standards
8.EE.C.8.A
Solve systems of linear equations by graphing.
8.EE.C.8.A8.EE.C.8.B
Classify systems of linear equations as having a unique solution, no solutions, or infinite solutions.
Solve real-world and mathematical problems by graphing systems of linear equations.
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.B8.EE.C.8.C
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