Unit 8 Algebra and Functions

Unit 8 Course Outcomes EP210-1 Explain the central mathematical concepts of arithmetic, pre-algebra, and geometry EP210-3 Identify developmentally appropriate grade level strategies for mathematics instruction

By the end of Unit 8, you should be able to: Explain the fundamental concepts of algebra (the use of patterns and equations with variables to express these patterns) Apply algebraic thinking to problem-solving Identify relationships that are considered functions and note some relevant personal examples

Reminders for the week Complete Readings Respond to the discussion thread under Discussion – Do your best to give a thoughtful response, in the 100-word range – Please continue to respond to each other’s posts to keep a meaningful discussion going Either attend Seminar OR complete Seminar Option 2 – See rubric in the syllabus for grading guidelines for both options Unit 8 Project – See the rubrics in the syllabus for grading guidelines. Final Project: You should already be working on a first draft of your final paper. Now is the time to reread and revise and make sure you have covered everything in the directions and rubric!

Unit 8 Project In Chapter 15, you read about the five different ways a function might be presented: – Context – Tables – Use of words (“is a function of”) – Graphing – Equations Create an example of a function and pick three ways to represent it. Consider how each of these different representations might appeal to different kinds or ages of students. Explain the factors that might affect why some of these representations might work better than others for particular students. Your project should be approximately two (2) typed pages. This does not include the title page and the reference page.

Algebraic Reasoning Involves forming generalizations from experiences with number and computation, formalizing these ideas with the use of a meaningful symbol system, and exploring the concepts of pattern and functions.

Patterns can be recognized, extended, and generalized.

Functions are relationships or rules that uniquely associate members of one set with members of another set. Functional relationships can be represented in real-world contexts.

Generalization in Number and Operations Variables in Equations Variables Used as an Unknown Value

Growing Patterns – A First Look at Functions Extend and Explain Predict How Many

Function Concepts and Representation Function: Rule that uniquely defines how the first (independent) variable affects the second (dependent) variable

Function Concepts and Representation Five ways to interpret or represent a function 1. Contextual Representations Context Hot dogs

Function Concepts and Representation Five ways to interpret or represent a function 2. Table Representations of Functions Hot Dogs Profit

Function Concepts and Representation Five ways to interpret or represent a function 3. Language Expressions for Functions “Profit is a function of the number of hot dogs sold.”

Function Concepts and Representation Five ways to interpret or represent a function 4. Graphical Representations of Functions

Function Concepts and Representation Five ways to interpret or represent a function 5. Equations to Represent Functions Y=mX+b

Function Concepts and Representation Developing Function Concepts in the Classroom Connect Different Representations

Explorations With Functional Relationships Relationships found in the Real World

Literature Connections Pattern Pluckrose Anno’s Mysterious Multiplying Jar Anno & Anno Anno’s Magic Seeds Anno

Questions Are there any questions/confusion about the lesson topics? What is your comfort level of these topics?

Your preparation and support of the ideas of your classmates is noted and appreciated! “Mathematics is a science of pattern and order.” -Everybody Counts Mathematical Sciences Educational Board, 1989

References Walle, J. A. (2007). Elementary and Middle School Mathematics. Boston: Pearson Education, Inc.