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Mathematics · Grade 8

Functions and Multiple Representations

Learners define a function as a rule that gives each input exactly one output and test relations given as pairs, tables, graphs and descriptions. They find and interpret the rate of change and initial value of linear functions, compare functions shown in different representations, tell linear from nonlinear functions, and read and describe qualitative graphs.

  • 5 lessons
  • About 100 minutes
  • Functions and representations check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, draw a graph, match pairs, type a number and put in order
See plans Included with Family, Teacher and School plans. Open in PlayOwl

What learners will discover

  • Decide whether a relation is a function (each input has exactly one output) from ordered pairs, tables, graphs and descriptions.
  • Find the rate of change and initial value of a linear function from a description, two input-output pairs, a table or a graph, and interpret them in context.
  • Compare the rates of change, initial values and outputs of two functions represented in different ways.
  • Distinguish linear from nonlinear functions using tables, equations and graphs, and give examples of nonlinear functions.
  • Describe how quantities change from a qualitative graph and match graphs to situations (increasing, decreasing, constant, faster or slower).

Lessons

  1. What makes a function? 8 steps5 practiceabout 20 min
  2. Rate of change and initial value 9 steps4 practiceabout 22 min
  3. Comparing functions in different representations 8 steps5 practiceabout 20 min
  4. Linear or nonlinear? 7 steps4 practiceabout 18 min
  5. Qualitative graphs 8 steps5 practiceabout 20 min
  6. Functions and representations check 11 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Algebra BalanceKeep the scale level and the equation true, step by step.
  • Function FactoryFeed the machine, crack its rule and predict what comes out.

More 8th grade math

Guide for grown-ups