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Understanding Algebraic Expressions and Mathematical Language

This lesson focuses on the fundamental concepts of algebraic expressions, covering variables, coefficients, and mathematical operations. Students will learn how to identify and interpret different components, such as terms and factors, within expressions. The importance of mathematical language is emphasized, giving students the tools to solve problems, such as calculating travel time and understanding operations like addition and subtraction. Included are worksheets for practice, ensuring comprehension through engaging exercises that reinforce key skills.

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Understanding Algebraic Expressions and Mathematical Language

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Presentation Transcript

  1. Warm up • How long does a car traveling at 70 mph take to travel 88 miles, in hours? • How many terms are in the expression: 36x + 27xy – 18y – 9? • 5 word prediction. Guess the meanings of the following words: Variable, expression, base, constant, & factor. 1.257 hours 4

  2. Skills Check No notes

  3. EQ CCCA Unit 1 • Why is it important to understand the “language” of mathematics?

  4. Definitions Identifying Parts

  5. Algebraic Expression • Can have variables, numbers, addition, subtraction, multiplication, division, parenthesis, square roots, exponents… • Examples:

  6. Variable • Symbols or letters used to represent an unknown • Examples: 

  7. Term • How many items are being added, subtracted, divided • Examples: 3 4

  8. Like Terms • Same variable raised to the same power • Examples:

  9. Coefficient • The number in front of a variable • Examples: 123 9 1

  10. Exponent • The number “up in the air” next to a base • The number of times you multiply something times itself • Examples: 3 12 4

  11. Base • What the exponent “sits on” • The part that has been raised to a power • Examples: 2 x y

  12. Constant • A number that has no variable • It can be positive or negative • Examples: -42 5 -8

  13. Factors • Items that are being multiplied together • Can be numbers, variables, parenthesis • Examples: 1 and 6…. Or 2 and 3 9 and x and y (x + 2) and (y – 3) 3 and (z – 9)

  14. Order of Operations • Simplify inside parenthesis • Take care of exponents • In order from left to right, multiplication or division • In order from left to right, addition or subtraction • Examples: -18

  15. Translations

  16. ADDITION • Sum • Plus • Add • More Than • Increased • Together

  17. SUBTRACTION • Difference • Minus • Decreased • Less Than (swaps the order) • Take away

  18. DIVISION • Quotient • Half • Divide by

  19. MULTIPLICATION • Product • Twice • Double • Triple • Times

  20. EXPONENTS • Square • Cubed • To the power of • Raised to a power

  21. Translate The sum of a number and 10 x + 10

  22. Translate The product of 9 and x squared 9x2

  23. Translate 9 less than g to the fourth power g4 – 9

  24. Translate 8 + 3x Eight increased by three times x

  25. Translate 5x3 - 14 Fourteen less than five times x cubed

  26. Practice Worksheet Tapas and Tennis

  27. HOMEWORK WORKSHEET Writing an Expression Worksheet

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