1. ALGEBRA PATTERNS & ALGEBRAIC THINKING
Math Lecture Series
Mr. W. T. Burgess

2. BELL RINGER
Determine the number of skittles in the jar. Choose a representative from your class to come up to the stage.

3. Questions & Reflections
How did you determine the number of skittles in the jar? Discuss your thought process with a fellow student.
Did your partner use a different method than you to find the answer? If so, which method is most efficient? Explain.

4. Algebra Patterns
Let’s take a look at another pattern dealing with toothpicks.
Think of the different ways you will answer the questions that follow.

6. Findings
Each new shape has an additional column of toothpicks with as many toothpicks as the column it builds on and 3 more toothpicks – the perimeter increases by 4 toothpicks as the shape grows.
The first shape has a perimeter of 4 toothpicks, the second shape has a perimeter of 8 toothpicks, the third shape has perimeter of 12 toothpicks, and so on. The pattern is to add 4 toothpicks to the shape before it: 4, 8, 12, 16, 20, … .
Reflecting on this pattern shows that the fifth shape has 20 or 5 x 4 toothpicks for its perimeter, the perimeter of the tenth shape is 10 x 4 or 40 toothpicks, the perimeter of the twelfth shape is 12 x 4 or 48 toothpicks.

7. Developing A Rule
This multiplicative way of describing the pattern gives the result for each shape much more directly and can lead to a general statement – the perimeter of a shape is given by multiplying the shape number by 4.
Later, when the general shape can be named as the nth shape, the pattern can be expressed concisely as 4 x n (or 4n) where n is the shape number.

8. Finding the Number of Toothpicks
Now Calculate the number of toothpicks in each shape.
How many toothpicks in shape 5?
Develop a function rule.

9. ALGEBRA Language of Generalization
Describe Patterns
Describe Patterns Using Words & Graphs
Developing Symbols that express Generalizations
Language of Relationships between Quantities
Language used to solve problems.

10. We use patterns as a stimulus, through investigations to lead to understanding Algebraic Concepts.

11. Music & Math Connections
Patterns connect music and mathematics.
Musical pieces have repeating choruses and bars mimicking patterns.
In mathematics we use patterns to explain and predict the unknown.

12. EDU - RAP
ALL I WANT TO DO IS TEACH THE KIDS ALL ABOUT MATH!!!

13. ALL ABOUT MATH
Algebra Geometry Even Trigonometry Equations, Inequalities Graphing with Technology All I want to do is teach the kids all about math Addition, Subtraction, Divide & Multiply Circumference over Diameter, Pi

14. ALL ABOUT MATH
Systems of Equations Graphs of all Persuasions All I want to do is teach the kids all about math Functions Relations Transformations Patterns Fractals Tessellations

15. ALL ABOUT MATH
Bridge: It hearts me so bad to see what they don’t know, but if we can get them in the classroom we will help them grow.
Statistics, Calculus, College Algebra
U-shape graph is called Parabola
All I want to do is teach the kids all math

16. Importance of Developing Strong Algebraic Skills
Perform jobs or entering majors that require strong math skills.
Better control over your life without depending on others to complete tasks for you.
Make wise decisions financially and otherwise.
Understand ideas discussed in Chemistry, Physics, Economics, Business and Psychology.

17. Top Jobs Involving Mathematics
Engineers (Electrical, Civil, Computer, Mechanical)
Computer Scientist
Statistician
Business (Finance, Accountant, Administrators)
Pilot
Architects
Actuary
Medical Professionals (Doctors, Nursing, Pharmacist)