Foundations and Pre-Calculus 10.6 . . . Relations and Functions . . .
Outcome: FP 10.6 Expand and apply understanding of relations and functions including:
 relating data, graphs and situations
 analyzing and interpreting
 distinguishing between relations and functions
Indicators: see curriculum guide, page 25
Enduring Understandings :
Students will understand that…
 Relations are a foundation for all mathematics.
 A relation expresses the relationship between the term of a pattern and its term number and can be used to represent situations and to solve problems.
 A function is a special type of relation for which each element of the first set is associated with a unique element of the second set.
Students will know :
Stage 1 – Desired Results
 Relations can be expressed in a variety of ways.
 All functions are relations, but not all relations are functions.
 Restrictions are placed on relations.
Essential Questions :
 What is a relation?
 What is a function?
 How do we determine whether or not a relation is a function?
 Why is it necessary to determine acceptable values for a situation?
 Which kinds of situations cannot be represented on a graph?
 What methods can be used to represent relations?
 When is it not appropriate to join the points on a graph?
Students will do :
 Explain relationships between relations and functions.
 Determine whether or not data represents a function.
 Graph data and list restrictions on domain and range.
 Determine the domain, range and restrictions of a graph, a set of ordered pairs or a table of values.
 Provide and explain situations represented by given graphs.
 Sketch a graph to represent a given situation.
Stage 2 – Assessment Evidence
Performance Tasks:
(will be used as part of summative evaluation for unit)
 Representing Relations and Properties of
Functions
Summative
 performance task
 unit exam
Formative (Pre-assessment, Self, …) :
 Homework/self-evaluation
 Assess Your Understanding textbook activities
 Entrance pass - day 2
 L to J quizzes (square root)
 Group presentation – day 1
 Journal entry – day 4, day 8
 Frayer model – day 4

Stage 3 – Learning Plan
Learning Activities:
Note: textbook referenced in Pearson’s Foundations and Pre-calculus Mathematics 10
Day 1 (5.1) Representing Relations (pages 256-263)
 Make Connections and Construct Understandings (pages 256-258)
 Explore and discuss examples 1, 2 3 on pages 259 – 261.
 Discuss the Ideas on page 261.
 Give a formal definition of a relation.
Will there still be time for this??
 Have students work in small groups (ideal size = 4; leader, materials manager, recorder, reporter) to create a relation that they can describe in words. Instruct them to work together to produce two different visual representations of the relation.
 Groups present their relations to the class.
 Summarize/closure.
Day 2
 Use entrance pass question: “What is a relation and how can it be displayed?”
 Review yesterday’s concept.
 Give assignment from textbook, page 261, #1  14, selecting questions appropriate to specific group of students.
Day 3 (5.2) Properties of Functions (pages 264-273)
 Begin by discussing last day’s assignment and addressing any difficulties presented by students.
 Make Connections and Construct Understanding pages 264-265.
 Explore and discuss examples 1, 2, 3 on pages 266-269.
 Discuss the Ideas on page 270.
 Give assignment from textbook, page 272, #4  23, choosing an appropriate number of questions for group.
Day 4
 Journal entry: Critique the statement: “Relations and functions are the same thing”.
 Discuss Frayer Model for a function, page 274.
 Assess Your Understanding activity, page 275.
Day 5 (5.3) Interpreting and Sketching Graphs (pages 276-283)
 Make Connections and Construct Understanding activity, pages 276-277.
 Explore and discuss examples 1, 2, 3 on pages 278 – 280.
 Discuss the Ideas on page 281.
 Assignment: textbook, pages 281-283, #3  18, choosing a number of questions appropriate to the specific group.
Day 6 (5.4) Graphing Data (Math Lab)
 Make Connections, page 284.
 Construct Understanding, page 285, parts A, B, C.
 Assess Your Understanding activity, page 286

Day 12
 Unit exam
Day 7 (5.5) Graphs of Relations and Functions (pages 287-297)
 Make Connections, page 287.
 Construct Understanding activity, pages 288-289.
 Explore and discuss examples 1, 2, 3, 4, pages 290 – 293.
 Discuss the Ideas, page 293.
Day 8 (5.5) Graphs of Relations and Functions (pages 287-297) continued . . .
 Journal: Reflect, page 297.
 Assignment: textbook, pages 294  297, #4  24, choosing an amount appropriate to specific group.
Day 9
 As a review/summary activity, the group will be given 10 minutes to create and display a concept map for the unit. The teacher will then refer the students to Checkpoint 2 on page 298 and have them add any concepts they have missed.
 Assign Assess Your Understanding, page 299.
Days 10 and 11
 Individual Performance Task: Representing Relations and Properties of Functions (see handouts)