Curriculum / Math / 9th Grade / Unit 4: Linear Equations, Inequalities and Systems / Lesson 13
Math
Unit 4
9th Grade
Lesson 13 of 14
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Identify solutions to systems of equations using any method. Write systems of equations.
The core standards covered in this lesson
A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A.REI.C.6 — Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A.SSE.B.3 — Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
The foundational standards covered in this lesson
8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Which strategy would you use to solve each of the following problems? Justify your answer. (You do not need to solve them.)
Greg wants to buy a new car. He looks at two different models. Car A costs $40,000, and he estimates it will cost $2,000 per year for gas and maintenance. Car B costs $60,000, and he estimates it will cost about $1,000 per year for gas and maintenance. Under what circumstances would it make sense for Greg to buy Car A? Under what circumstances would it make sense for Greg to buy Car B? Justify your answer.
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
The basketball team sold t-shirts for a fundraiser. They sold a total of 23 items and made a profit of $246. They made a profit of $10 for every t-shirt they sold and $12 for every hat they sold.
Determine the number of t-shirts and the number of hats the basketball team sold.Â
Item #3334 from Smarter Balanced Assessments' Sample Items is made available by Smarter Balanced Assessment Consortium. © The Regents of the University of California – Smarter Balanced Assessment Consortium. Accessed Oct. 19, 2017, 4:18 p.m..
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 12
Lesson 14
Topic A: Properties and Solutions of Two-Variable Linear Equations and Inverse Functions
Identify the solutions and features of a linear equation and when two linear equations have the same solutions.
A.REI.D.10 A.SSE.B.3
Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.
A.SSE.B.3 F.IF.B.4 F.IF.C.7.A
Determine if a function is linear based on the rate of change of points in the function presented graphically and in a table of values.
F.IF.B.6 F.IF.C.7.A F.IF.C.9 F.LE.A.1.A
Identify inverse functions graphically and from a table of values in contextual and non-contextual situations.
F.BF.B.4.A F.IF.A.1 F.IF.A.2 F.IF.B.5
Find inverse functions algebraically, and model inverse functions from contextual situations.
A.CED.A.4 F.BF.B.4.A F.IF.B.6
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Topic B: Properties and Solutions of Two-Variable Linear Inequalities
Describe the solutions and features of a linear inequality. Graph linear inequalities.
A.REI.D.12
Write linear inequalities from graphs.
A.CED.A.3 A.REI.D.12
Write linear inequalities from contextual situations.
A.CED.A.3
Topic C: Systems of Equations and Inequalities
Solve a system of linear equations graphically.
A.CED.A.3 A.REI.D.11
Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.
Solve linear systems of equations of two variables by substitution.
A.CED.A.3 A.REI.C.5 A.REI.C.6 N.Q.A.2
Identify solutions to systems of equations algebraically using elimination. Write systems of equations.
A.REI.C.5
A.REI.A.1 A.REI.C.6 A.SSE.B.3
Identify solutions to systems of equations with three variables.
A.REI.C.6
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