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÷ and Conquer!

÷ and Conquer!. Supporting your child through middle school math Susan Bycoff & Nat Vaughn. Pre-Algebra Skills. I. Working with Integers II. Order of Operations III. Solving Equations. Why do we study math?. Why do we study math?. Why do we study math?.

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÷ and Conquer!

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  1. ÷ and Conquer! Supporting your child through middle school math Susan Bycoff & Nat Vaughn

  2. Pre-Algebra Skills I. Working with Integers II. Order of Operations III. Solving Equations

  3. Why do we study math?

  4. Why do we study math?

  5. Why do we study math?

  6. Algebra…dealing with variability (or not)

  7. Expressions An expression is a collection of numbers, variables and operators that represent a value. (NO verb) 2x 55 + 120 2(-4) 6(3 - y) -3a² -12

  8. Anatomy of an Equation

  9. Equations An equation links two expressions together to show a balance of values. (HAS a math verb) 2x = –12 3x + 5 = 17 6(3 – y) = 20 –3a² = –12

  10. Expressions vs. Equations NO verb We evaluateexpressions The value of an expression can often change. Directions: Simplify Evaluate Find the value of: Has a verb: = (isequal to) We solveequations The solution to equations are static…never change. Directions: Solve Find the solution to:

  11. I. Working with Integers Addition & Subtraction Multiplication & Division a. 4 + 5 b. –1 + – 4 c. 8 – 6 d. 2 – 7 a. 7 x –2 b. –8 x –6 c. d. –(–10)

  12. II. Working with Integers • Addition & Subtraction • Positive + Positive: Add answer is + • Negative + Negative: Add answer is – • Positive + Negative: Subtract and keep the sign of the # furthest from zero. • Multiplication & Division • Positive * Positive = Positive • Negative * Negative = Positive • Positive * Negative = Negative

  13. Models for Operations with Integers Number Line Chips

  14. What type of number are we dealing with? 4 + 2 –3 + 5 –3 + –1 4 – 6 –2 – 5

  15. Operations with Integers There is no subtraction!

  16. Examples of Operations with Integers 5 – 3 ………………………....5 + – 3 –4 – 2………………………–4 + – 2 4 – 3 – 10………………….. 4 + – 3 + – 10 15 – 10 – 2 + 5 – 6 ….… 15 + – 10 + – 2 + 5 + – 6

  17. II. Order of Operations iPEMDAS Inside Parentheses Exponents Multiplication or Division whichever comes first left to right Addition or Subtraction whichever comes first left to right. 2(5 – 8) + 27/3²

  18. Examples of Order of Operations 1. 5 – 4(2) 2. 4 + 30/5(3) 3. 2(5 – 8) + 27/3²

  19. III. Solving Equations 2x + 5 = 15 Simplifying uses PEMDAS Solving uses the reverse (SADMEP)

  20. III. Solving Equations • Steps to Solving Equations EQUATION? DISTRIBUTE COMBINE LIKE TERMS SIMPLIFY BALANCE = SOLVE SOLVE ANSWER = SOLUTIONS

  21. Working Tips Highlighters and different colored pens Boxing in answers…think inside the box! Post-it notes Different types of paper…lined, blank, colored, etc.

  22. Questions? Please feel free to email me with questions or suggestions for future workshops. Thank you! sbycoff@medfield.mec.edu

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