Curriculum / Math / 9th Grade / Unit 4: Linear Equations, Inequalities and Systems / Lesson 10
Math
Unit 4
9th Grade
Lesson 10 of 14
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Lesson Notes
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Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.
The core standards covered in this lesson
A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
A.REI.D.12 — Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
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
25-30 minutes
Some treasure has been buried at a point $${(x,y)}$$ on the grid, where $$x$$ and $$y$$ are whole numbers.
Here are three clues to help you find the treasure: Clue 1: $$x> 2$$ Clue 2: $$x+y< 8$$ Clue 3: $$2y-x\geq 0$$
Which of the following points could be a possible location for the treasure?
$${(3,2) }$$ $${(2,3)}$$ $${(5,3)}$$ $${(3,5)}$$ $${(4,3)}$$ $${(5,2)}$$
Representing Inequalities Graphically from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Oct. 20, 2017, 4:36 p.m..
Write a system of linear inequalities that only has the region named as part of the solution set.
Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She is only allowed to work 13 hours per week. She wants to make at least $65. Write and graph a system of inequalities to represent this situation.
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
Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can hold at most eight people. Additionally, each boat can only carry 1,200 pounds of people and gear for safety reasons. Assume an average an adult weighs 150 pounds and a child weighs 75 pounds. Also assume each group will require 200 pounds of gear plus 10 pounds of gear per person.
Fishing Adventures 3, accessed on Oct. 19, 2017, 3:49 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.
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.
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Solve linear systems of equations of two variables by substitution.
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.
Standards
A.REI.D.10A.SSE.B.3
Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.
A.SSE.B.3F.IF.B.4F.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.6F.IF.C.7.AF.IF.C.9F.LE.A.1.A
Identify inverse functions graphically and from a table of values in contextual and non-contextual situations.
F.BF.B.4.AF.IF.A.1F.IF.A.2F.IF.B.5
Find inverse functions algebraically, and model inverse functions from contextual situations.
A.CED.A.4F.BF.B.4.AF.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.3A.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.3A.REI.D.11
A.CED.A.3A.REI.C.5A.REI.C.6N.Q.A.2
Identify solutions to systems of equations algebraically using elimination. Write systems of equations.
A.REI.C.5
Identify solutions to systems of equations using any method. Write systems of equations.
A.REI.A.1A.REI.C.6A.SSE.B.3
Identify solutions to systems of equations with three variables.
A.REI.C.6
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