1. Welcome to Math 112 Class #3 9/15/16 Please turn in HW #2 (staple all pages together). Make sure your name and “HW #2” is on the top!

2. Warm-up:

3. Tonight’s Agenda  Warm-up: Order of Operations  Return HW #1 and Quiz #1  Test #1  The Centauri Challenge  Fractions Adding and subtracting fractions Reducing fractions to lowest terms  Area  Writing expressions for area  Start Group task

4. Just for today, no matter where I am going, or what I am doing, or who I am doing it with, it is my intention to focus on the positive. Lucy MacDonald

5. Last week’s focus: Math practice #1 Make sense of problems and persevere in solving them.

6. Persevere Continue in a course of action even in the face of difficulty or with little or no prospect of success

7. Test #1

8. Reminders about test-taking:  All cell phones, iPods, and other electronic devices must be shut off and put away.  Only the exam, pen or pencils and erasers and a non- graphing calculator are allowed on the desk. All other items must be on the floor or under your seat.  Scrap paper will be provided.  No one will be allowed to leave the room until finished with the exam. This includes no visits to the restroom during an exam.  No talking is allowed during the exam.  When you have finished the exam, please turn in the exam and all scratch paper.  After the exam, if you go outside – please stand AWAY from the room so you don’t disturb students still working!

9. The Centauri Challenge

10. PQRSSQR --------  RQ  Any 2 letters can be switched (PQ = QP)  If ending is 2 same letters, replace 2 letters with Q (RSS = RQ)  If beginning is 2 same letters, add S in front (PPR = SPPR)  If start and finish is same letter, put an R in place of all the middle letters (PQRSP = PRP)

11. Tonight’s focus: Math practice #4 Model with mathematics

12. Fractions Reducing fractions to lowest terms Adding and subtracting fractions

13. Simplifying Fractions using the greatest common factor(GCF)

14. Factor A number that divides evenly into another number. The factors of 6 are ____ and _____ or _____ and _____

15. Common Factor When two numbers have the same factor. For example: 6 = 2 x 3 and 8 = 2 x 4 The common factor is _____

16. Greatest Common Factor  The greatest common factor is the largest factor between two numbers. 12 = 1, 2, 3, 4, 6, 12 18 = 1, 2, 3, 6, 9, 18 GCF = 6

17. What is the Greatest Common Factor? 8 = 1, 2, 4, 8 12 = 1, 2, 3, 4, 6, 12 GCF = 4

18. What is the Greatest Common Factor? 6 = 1, 2, 3, 6 18 = 1, 2, 3, 6, 9, 15 GCF = 6

19. Simplest Form  When the only common factor of the numerator and denominator is 1, the fraction is in simplest form, or it is reduced to lowest terms. 3 4 3 4 ÷ 1 1 =

20. How to Simply a Fraction  Find the greatest common factor of the numerator and the denominator and divide both by that number.

21. Simplifying a Fraction: 12 18 2 3 ÷ 6 6 =

22. Simplify: 9 21 3 7 ÷ 3 3 =

23. Simplify: 12 20 3 5 ÷ 4 4 =

24. Simplify: 10 15 2 3 ÷ 5 5 =

25. Simplify: 10 16 5 8 ÷ 2 2 =

26. Simplify: 12 16 3 4 ÷ 4 4 =

27. Simplify: 3 12 1 4 ÷ 3 3 =

28. Simplify: 2 4 1 2 ÷ 2 2 =

29. 6 9 2 3 ÷ 3 3 =

30. Adding or Subtracting Fractions Always reduce the answer to lowest terms

31. Find each sum or difference:

32. Writing Expressions for Area

33. Writing Expressions P-33 3 4 5 Write an expression to represent the total area of this diagram

34. Write an expression for the diagram below: ½ 5

35. 5 5 5

36. Compound Area Diagrams P-36 4 5 1 2 1 2 5 4 Area A Area C 2 1 4 5 Area B Which compound area diagram represents the expression: 5 + 4 x 2?

37. Write at least two different expressions for the diagram below: 6 2 6 2

38. Area Task This will be completed in groups and will count as a quiz grade!

39. Area Task – Materials needed for each group:  One envelope  Colored markers (save the elastic please!)  Glue stick  Your poster paper from last week

40. Matching Cards P-40 1.Take turns at matching pairs of cards that you think belong together. For each Area card there are at least two Expressions cards. 2.Each time you do this, explain your thinking clearly and carefully. Your partners should either explain that reasoning again in their own words or challenge the reasons you gave. 3.If your team thinks there is no suitable card that matches, write one of your own on a blank card. 4.Once agreed, place the matched cards onto the poster paper. DO NOT GLUE THEM YET!!! Your whole team needs to be able to agree on and to be able to explain the placement of every card!

41. Sharing Work P-41 1.Compare your work with another team. Check to see which matches are different from your own. 2.If there are differences, ask for an explanation. If you still don’t agree, explain your own thinking. 3.Return to your own poster, review your own matches and make any necessary changes. Glue the pieces when you are sure of your answers.

42. HW #3  Worksheet: Area task (revisited)  Extra practice booklet