Curriculum / Math / 9th Grade / Unit 3: Linear Expressions & Single-Variable Equations/Inequalities / Lesson 4
Math
Unit 3
9th Grade
Lesson 4 of 12
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Lesson Notes
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Solve equations with a variable in the denominator.
The core standards covered in this lesson
F.IF.A.1 — Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
The foundational standards covered in this lesson
8.EE.C.7.B — Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
A common misconception can arise from students treating terms in the numerator or denominator separately instead of as grouped expressions when operating. Ensure students use parentheses around expressions in the numerator or denominator of an expression when solving to minimize this misconception.
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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
Solve for $$x$$, if possible.
a. $$\frac{x}{4}=5$$
b. $$\frac{x}{\frac{1}{2}}=6$$
c. $$\frac{x}{0}=10$$
Solve both of the equations below.
$${10=\frac{x-2}{5}}$$
$${10=\frac{5}{x-2}}$$, where $${x\neq2}$$
Identify any domain restrictions and solve the equation below.
$${\frac{3}{x}=\frac{2}{x+2}}$$
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
Solve for $$x$$.
$$\frac{x-2}{x-9}=2$$
Algebra I > Module 1 > Topic C > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Write an equation that would have the restriction $${x\neq-3}$$.
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
Solve for a variable in an equation or formula.
Topic A: Properties and Solutions of Single-Variable Linear Expressions and Equations
Identify properties of operations that result in equivalent linear expressions.
Standards
A.REI.A.1A.SSE.A.1A.SSE.A.2
Use properties of equations to analyze and write equivalent equations.
A.REI.A.1
Solve single-variable linear equations using properties of equality.
A.REI.A.1A.REI.B.3
A.REI.B.3F.IF.A.1
A.CED.A.4
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Topic B: Modeling with Single-Variable Linear Equations
Write equations using defined variables to represent a contextual situation.
A.CED.A.2A.CED.A.4F.BF.A.1F.IF.B.5N.Q.A.1
Define variables; write and solve equations to represent a contextual situation.
A.CED.A.1A.CED.A.2A.CED.A.4F.BF.A.1F.IF.B.5N.Q.A.1
Write and solve equations to represent contextual situations where estimations and unit conversions are required.
2 days
Model a contextual situation and make an informed decision based on the model.
Topic C: Properties and Solutions of Single-Variable Linear Inequalities
Solve unbounded single-variable inequalities in contextual and non-contextual situations.
A.CED.A.3A.REI.A.1A.REI.B.3A.SSE.B.3
Write and graph compound single-variable inequalities to describe the solution to contextual and non-contextual situations.
A.CED.A.3A.REI.B.3
Solve and graph compound inequalities where algebraic manipulation is necessary in contextual and non-contextual situations.
A.CED.A.3A.REI.A.1A.REI.B.3
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