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

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

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.

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.

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.

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.

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

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.

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

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.

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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.

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