Curriculum / Math / 11th Grade / Unit 1: Linear Functions and Applications / Lesson 3
Math
Unit 1
11th Grade
Lesson 3 of 13
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Lesson Notes
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Solve for a desired quantity in a linear function.
The core standards covered in this lesson
A.CED.A.1 — Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A.CED.A.4 — Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
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
This lesson teaches skills similar to what students learned in Algebra 1; however, because of the relationship to inverse functions, use this skill as a way to review concepts and understand the topic conceptually before applying notation and the definition of inverse functions more formally in the next lesson.
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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
The equation below is the equation of a line in the $${ xy- }$$ plane, and $$t$$ is a constant. If the slope of the line is $${-2}$$, what is the value of $$t$$?
$$tx + 8y = -4Â $$
Alex is working on a budget after getting a new job.
There are two ways to Alex can think about modeling this situation:
Below is the equation that shows the total amount she has budgeted herself based on the amount each meal costs and the amount of times she goes out.
$$(c \cdot x)+ (\frac{1}{2}c)(\frac{1}{4}x)+20=170$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Anton writes a model that describes the number of tacos his friends eat as a function of the cost of the total tacos. Below is a graph of the model.Â
Anton writes a second model that describes the total cost of the tacos as a function of the number of tacos his friends eat. Below is a graph of the model.Â
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.
Next
Find the inverse of a contextual situation graphically and describe the meaning of the function and its inverse.
Topic A: Features of Linear Functions
Identify features of linear functions from equations, verbal descriptions, tables, and graphs.
Standards
A.SSE.A.1.AF.IF.B.4F.IF.C.9
Write linear functions that represent contextual situations.
F.IF.A.2F.IF.B.4F.IF.B.5
A.CED.A.1A.CED.A.4
F.BF.B.4.AF.BF.B.4.C
Find the inverse of contextual and non-contextual situations algebraically.
F.BF.B.4.AF.BF.B.4.BF.BF.B.4.C
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Topic B: Systems of Functions and Constraints
Write a system of functions for contextual situations and solve algebraically. Describe the solutions in context of the problem.
A.CED.A.2A.REI.C.6F.IF.B.5
Describe the number of solutions of a system of equations. Verify algebraically.
A.REI.C.6A.REI.D.11
Solve a system of three equations in three variables.
A.REI.C.6
Identify the solution to a system of an absolute value equation and a linear function algebraically and graphically.
A.REI.D.11
Graph and identify solutions to systems of linear inequalities.
A.CED.A.3A.REI.D.12F.IF.B.5
Write systems of linear inequalities from a contextual situation.
A.CED.A.3A.REI.D.12
Topic C: Piecewise Functions
Write and evaluate piecewise functions from graphs. Graph piecewise functions from algebraic representations.
A.CED.A.2F.IF.C.7.B
Write piecewise functions from contextual situations.
A.CED.A.2A.CED.A.3F.IF.B.4F.IF.C.7.B
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