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Rate of Change & Slope

Lesson Plan

Rate of Change & Slope

Grade Levels

10th Grade, 8th Grade, 9th Grade

Course, Subject

Algebra I, Mathematics
Related Academic Standards
A1.2.2.1 A1.2.2.1
Describe, compute and/or use the rate of change (slope) of a line.
A1.2.2.1.1 A1.2.2.1.1
Identify, describe and/or use constant rates of change.
A1.2.2.1.2 A1.2.2.1.2
Apply the concept of linear rate of change (slope) to solve problems.
CC.2.2.HS.C.1 CC.2.2.HS.C.1
Use the concept and notation of functions to interpret and apply them in terms of their context.
CC.2.2.HS.C.3 CC.2.2.HS.C.3
Write functions or sequences that model relationships between two quantities.
Expand
  • Big Ideas
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    Data can be modeled and used to make inferences.
    Mathematical relations and functions can be modeled through multiple representations and analyzed to raise and answer questions.
    Mathematical relationships among numbers can be represented, compared, and communicated.
    Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations.
    Patterns exhibit relationships that can be extended, described, and generalized.
  • Concepts
    Analysis of one and two variable (univariate and bivariate) data
    Functions and multiple representations
    Equations and Inequalities
    Patterns, Relations, and Functions
  • Competencies
    Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation.
    Use algebraic properties and processes in mathematical situations and apply them to solve real world problems.
    Construct and compare linear, quadratic, and exponential models and solve problems.
    Create a function and/or sequence that model a relationship between two quantities.
    Create and/or analyze functions using multiple representations (graph, table, and equation).
    Create new functions from existing functions (transformations of graphs).
    Define, evaluate, and compare functions.
    Describe, compute, and/or use linear rate of change (slope).
    Understand and apply the Pythagorean Theorem.
    Use and/or identify algebraic properties.
    Use the concept and notation of function to interpret and apply them in terms of their context.
    Write and/or identify linear equations in various forms (slope-intercept, point-slope, standard, etc.).
    Write, solve, and/or graph compound inequalities.
    Write, solve, and/or graph linear equations and inequalities using various methods.
    Write, solve, and/or graph systems of linear equations and inequalities using various methods.

Rationale

Vocabulary

Rate of Change - a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

 

Slope - the measure of the steepness of a line.  [Rise/Run]

  • The steeper the line, the greater the slope.

  • Notation:  m stands for slope.

  • For any two points, the slope of the line connecting them can be determined by dividing how much the line rises vertically by how much it runs horizontally.

 

***Vocab and definitions included in the PowerPoint notes.***

 

 

 

Objectives

  • Find rates of change from tables
  • Find slope from a graph and ordered pairs

Lesson Essential Question(s)

How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How does the type of data influence the choice of display?
How is mathematics used to quantify, compare, represent, and model numbers?

Duration

Three 40-50 minute periods

Day 1:  Notes, introduction, and guided practice

Day 2:  Notes, independent practice, and review

Day 3:  Mini review and quiz

Materials

Teacher Materials: 

 

Student Materials:

  • Graphing Calculator
  • Keystone Algebra I Formula Sheet
  • Pencil
  • Notebook/Binder
  • Highlighter (optional)

 

Suggested Instructional Strategies

W: Post weekly lesson plans on teacher website.  Post daily agenda in classroom.
H: Bell ringers completed with a partner/small group
E: Exploratory,  notes, lecture, discussion, partner/group work, independent practice
R: Bell ringers, homework, discussion
E: Bell ringers, homework, discussion 
T: Teacher provided notes, hands-on learning (kinesthetic), lecture (auditory), scaffolding (visual)
O: Exploring, teacher examples, partner/group work, independent work 

Instructional Procedures

Day 1

  • Perimeter Chain Bell Ringer.docx  (can be completed with a partner)  
      • Provide students with disabilities concrete geometric shapes to allow them to manipulate the objects as necessary.
  • Review Bell Ringer as a whole class
  • Rate of Change and Slope Notes.pptx (cover slides 1-17)
      • Notes/Selected slides can be provided to students ahead of time (especially to students with IEPs).  In addition, you can customize the slide by deleting words/examples before printing so as to provide students with a guided notes handout to keep them engaged in the process.
  • Recommended to allow students to work with a partner during the "Your Turn" slides.
  • Worksheet 5.1.pdf -- Teacher guided practice (display on smart board/Promethean/overhead projector if possible)
  • Recommended to do the following problems in class:  #1-2, 4-5, 7-9, 13-14
  • Recommended to do the following problems as homework:  #3, 6, 10-12, 15 (start in class)
  • Start homework in class.
  • Closure:  Define rate of change in your own words.
 
 
 
 
Day 2
 
  • Bell Ringer Worksheet 5.1.pdf #23-25
  • Review Bell Ringer as a whole class
  • Review homework (display work & answers)
  • Discuss #16-19 (small group/partner then with whole class)
  • Whole class #20, Partner #21, Independent #22
  • Whole Class #31 & 33
  • Partner #32 & 34
  • Rate of Change and Slope Notes.pptx (slides 18-40)
      • Notes/Selected slides can be provided to students ahead of time (especially to students with IEPs).  In addition, you can customize the slide by deleting words/examples before printing so as to provide students with a guided notes handout to keep them engaged in the process.
  • Worksheet 5.1 Form K.pdf
  • Recommended to do the following problems in class:  #13-16
  • Recommended to assign "even" problems for homework:  #1-12 (start in class)
  • Closure:  What is the slope of a horizontal line? vertical line?
  • Quiz tomorrow
 
 
 
Day 3
 
  • Bell Ringer Worksheet 5.1 Form K.pdf #17, 23, 24
  • Review Bell Ringer as a whole class
  • Review homework (display work & answers)
  • Complete #18-20 (partner, if necessary)
  • Discuss #21-22
  • Last minute questions?
  • Quiz 5.1.pdf
  • Closure:  Name (at least) three ways rate of change and slope are used in real life.


 

Formative Assessment

Day 1:  Bell Ringer (Perimeter Chain Bell Ringer.docx)

Day 2:  Homework  (Worksheet 5.1.pdf #3, 6, 10-12, 15)

Day 3:  Quiz 5.1.pdf

Related Materials & Resources

For additional real-life application examples, please visit: 

http://www.algebra-class.com/rate-of-change.html

Author

Mallory Hafer (IU 11, IU 17)

Date Published

December 18, 2013
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