Curriculum  /  Math  /  9th Grade  /  Unit 3: Linear Expressions & Single-Variable Equations/Inequalities  /  Lesson 6

Linear Expressions & Single-Variable Equations/Inequalities

Lesson 6

Math

Unit 3

9th Grade

Lesson 6 of 12

Objective

Write equations using defined variables to represent a contextual situation.

Common Core Standards

Core Standards

  • F.BF.A.1 — Write a function that describes a relationship between two quantities 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.
  • A.CED.A.2 — Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • 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.
  • N.Q.A.1 — Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
  • F.IF.B.5 — Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 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.

Foundational Standards

  • 8.F.B.4

Criteria for Success

  1. Define units associated with variables. 
  2. Write simple expressions and equations to model contextual situations. 
  3. Use known quantities to try the algebraic model developed and determine reasonability of the model.
  4. Assign domain restrictions based on context and algebraic relationships. 
  5. Rearrange the equation used to model a relationship to highlight a quantity of interest. 
  6. Use nested expressions to describe a larger model.

Tips for Teachers

  • This lesson only contains one anchor problem so that a performance task from Mathematics Vision Project (listed under Problem Set Guidance, first bullet) can be addressed fully. 
  • This lesson is the first in a series of five lessons on defining variables, modeling a contextual situation, and applying the model to specific situations.
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Anchor Problems

25-30 minutes

Below is a formula that describes a quantity related to getting to a destination via walking and riding the bus. 

$${S_{b}}$$ represents the average speed of the bus. 
$${D_{b}}$$ represents the distance you travel on the bus. 
$${D_{w}}$$ represents the distance you walk to your final destination. 
$${S_{w}}$$ represents the average speed you walk 
$$h$$ represents the amount of time you wait for the bus. 

 

What does the variable $$R$$ mean in the formula below?

$${D_{b}}={S_{b}}\left ( R-\frac{{D_{w}}}{{S_{w}}}-h \right )$$

Guiding Questions

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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.

Target Task

5-10 minutes

Here is a parallelogram. 

  1. Which of these are correct expressions for the area of this parallelogram? 

$${{ab}}$$        $$\frac{1}{2}{{ab}}$$        $${{ah}}$$        $$\frac{1}{2}{{ah}}$$        $${{2a+2b}}$$        $${{2(a+b)}}$$        $${{ab}}h$$

  1. Which of these are correct expressions for the perimeter of the parallelogram? 

 

$${{ab}}$$        $$\frac{1}{2}{{ab}}$$        $${{ah}}$$        $$\frac{1}{2}{{ah}}$$        $${{2a+2b}}$$        $${{2(a+b)}}$$        $${{ab}}h$$

 

  1. Here is a trapezoid. It is made up of two triangles, each with height $$h$$. 

Write a formula, using the area of each triangle, that describes the area of the trapezoid. 

References

Inside Mathematics Performance Assessment Tasks Grades 3-High School Expressions

Expressions of the Performance Assessment Tasks created by the by the Mathematics Assessment Resource Service (MARS) of the Shell Centre for Mathematical Education, University of Nottingham, England are made available by Inside Mathematics under a license from Shell Centre Publications. Accessed Sept. 12, 2017, 4:46 p.m..

Additional Practice

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.

  • Mathematics Vision Project: Secondary Mathematics One Module 4: Equations & Inequalities — Lesson 4.2, Elvira's Equations, Questions #1-10 (This section should be done in its entirety and in order.)

Next

Define variables; write and solve equations to represent a contextual situation.

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Properties and Solutions of Single-Variable Linear Expressions and Equations

Topic B: Modeling with Single-Variable Linear Equations

Topic C: Properties and Solutions of Single-Variable Linear Inequalities

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