This document provides an overview of a teacher's training, philosophy on teaching algebra, units taught, and results from implementing a functions-based approach to teaching algebra. The teacher has taken several courses related to curriculum, instruction, and assessment. Their philosophy is to use a functions-based approach to help students make their own associations and build patterns, using visualization and context to give meaning to algebra. Units covered include families of functions, linear, absolute value, systems, exponential, quadratic, polynomial, and radical functions. Test results showed students scored higher using the functions-based approach, particularly co-taught students. The teacher reflects on personal and professional growth from implementing this approach.

1. Emily Alderman
Jessica Markstrom
Noah Salter
Sarah Tarchala

2. History/Training
 Algebra for All
 Year 1
 Year 2
 Master’s Work
 Curriculum, Instruction, and Assessment
 MAT – Master of Arts in Teaching
 Online PD last year
 EMATHS – Implementing Algebra Units
 Project PRIME

3. Philosophy
 What is a Functions Based Approach?
 Content
 Instruction
 Reasons for Using a Functions Based Approach
 We remember Algebra longer when make and use our own associations
 Pattern Building makes learning simpler, faster, understandable
 Graphing Calculator and effects of engagement
 Use of visualization first and symbolic second
 Function implementation module and early activities prime the brain
for algebra that follows
 Enriched learning environment
 Contextual situations (represented as functions) help give
meaning to the algebra
Laughbaum, E.D. Why Use a Function Approach when Teaching Algebra. Texas Mathematics
Teacher, 53(1), 10 - 16

4. Units
1) Family of Functions
2) Linear Functions and Equations
3) Absolute Value Functions and Linear Inequalities
4) Systems of Linear Equations and Inequalities
5) Exponential Functions
6) Quadratic Functions and Quadratic Equations
7) Polynomial Functions
8) Radical Functions and Equations
9) Bi-variate Data and Mathematical Modeling

5. Unit 5 – Exponential Functions
Lesson Type of Lesson
Let’s Make a Deal with Your Parents Investigation
Pay It Forward Investigation
Bee Gone? Investigation
Transformations with Online Graphing Investigation/Notes
Calculator
Quiz: Exponential Growth and Assessment
Decay/Transformations of Exponential
Functions
HW: Which Family of Functions is it?

6. Unit 5 – Exponential Functions
Lesson Type of Lesson
Properties of Exponents Notes
Practice with Properties of Exponents Group Work
Properties of Exponents Notes/Group Work
Properties of Exponents Practice: Fraternal Twins Group Work
Quiz: Properties of Exponents Assessment
HW: Pre-Scientific Notation
Scientific Notation Notes/Investigation
Exponential Growth and Decay with Percentages
HW: Finish investigation
Percent Increase and Decrease Notes/Group Work
Review Group Work/Individual Practice
Unit 5 Test: Exponential Functions Assessment

7. Unit 5 – Exponential Functions
**Exponential Activity Assessment somewhere in unit? (did
not do but would like to)
Exponential Activities that we have:
 Pay it Forward Video clip
 One Grain of Rice Book
 Alice and Wonderland Video Clip or Book
 Make a Deal with your Teacher
 Paper Folding Mythbusters Video Clip
 M&M Hands on with M&Ms
 Lily’s Mussels
 USA Today- Population Uses Census Data
 Bee Gone

8. Student Work
Homework

9. Video Reflections
 What are the different ways students are asked to
record information?
 What are some methods used to keep all students
engaged?
 What percentage of students involved in the board
activity in the co-taught class do you think are
students with special needs?
 Can you see any examples that demonstrate students’
comfort level with math conversations?

15. 1st Semester Results
PLC/Function Based
Algebra 1 PLC Functions Based
 Students scores were higher  Students scores were higher
by at least 5% on 9 out of 50 by at least 5% on 13 out of 50
questions questions
 Co-taught students scores  Co-taught students scores
were higher by at least 5% on were higher by at least 5% on
13 out of 50 questions 24 out of 50 questions

16. Comparisons
PLC Function Based
 Solving absolute value  Graphing linear functions.
equations.  Horizontal and vertical lines.
 Solving a linear equation with  Writing an equation for a
a fraction. linear situation in real-life.
 Proportion to solve  Correlation of scatter plots.
contextual problem.  Simplify an expression using
order of operations.

17. Things that were not explicitly
addressed but did comparably…
 Unit rate
 Ordering numbers from least to greatest
 Perfect squares
 Finding the length of a square mirror if the area is given
 Giving coordinates of a point

18. Michigan Algebra 1 Assessment
Content 2010 – 2011 2011 – 2012 Change
Follow Pattern in Table 72 78 + 6%
Relationship in table 73 60 - 7%
Which family of function? 55 46 - 9%
Follow Pattern in Table- Linear 17 48 + 31%
Write Equation Perpendicular 50 48 - 2%
through a point
Graphing Linear Equations 50 71 + 21%
Which function is it? 82 95 + 13%
Horizontal/Vertical Linear and 58 76 + 18%
Parallel
Correlation Strength 50 80 + 30%
Graph Linear Equations 75 86 + 11%
Scatterplots-modeling 33 54 + 21%
Correlation – interpreting the 25 58 + 33%
situation

19. Functions Based and the CCSS Math Practices

20. Personal/Professional Reflections
 Personal Growth
 Professional Growth
 Challenges
 Beliefs

21. Questions?

22. Next Steps