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Investigate and Describe Patterns

Investigate and Describe Patterns. D efinitions. Algebra A method of expressing mathematical ideas that involves variables, constants, numerical coefficients, and mathematical operations. Variable Represents an unknown value, or a quantity that has a changing value

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Investigate and Describe Patterns

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  1. Investigate and Describe Patterns

  2. Definitions Algebra • A method of expressing mathematical ideas that involves variables, constants, numerical coefficients, and mathematical operations

  3. Variable • Represents an unknown value, or a quantity that has a changing value • Is usually represented by a letter

  4. Constant • A value that does not change • Represented by a number

  5. Numerical coefficient • The numeric factor in an algebraic term • For the algebraic term 4x, the numerical coefficient is 4, while in -3x2, the numerical coefficient is -3.

  6. Algebraic expression • A mathematical statement that usually includes: • One or more variables • One or more constants • At least one mathematical operation (+, -, x, ÷)

  7. Using Algebra Use algebra to express the table pattern mathematically. • Let the variable t represent the number of tables. • Write an algebraic expression for the number of guests who can be seated at a given number of tables, t.

  8. Write the expression

  9. Complete the sentence: To find the number of guests for each arrangement, you would

  10. Graph • Graph the data. • Describe the pattern formed by the points. • Should we join the points? Why or why not?

  11. Graph d) How many guests can be seated using • 8 tables? • 10 tables? • 50 tables?

  12. 4t + 2 • What is the meaning of the numerical coefficient in your algebraic expression? • What is the meaning of the constant in your algebraic expression?

  13. Expressing Number Patterns • A pattern using concrete materials or diagrams • A sequence of numbers • A sentence • A table • A graph • An algebraic expression

  14. Patterns in Diagrams • Describe the toothpick pattern in words. • Determine the number of toothpicks needed for the fifth and sixth diagram.

  15. c) Describe how to find the number of toothpicks if you know the number of squares. d) Write an algebraic expression to model the pattern, using the variable n to represent the number of squares.

  16. e) What are the meanings of the constant and the numerical coefficient in your expression? Where are these values represented in the diagrams? f) Determine the number of toothpicks in the 20th diagram.

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