# HS Algebra - PowerPoint PPT Presentation

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HS Algebra

## HS Algebra

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##### Presentation Transcript

1. “Teachers are thus free to provide students with whatever tools and knowledge their professional judgment and experience identify as most helpful for meeting the goals set out in the Standards.” ~ Introduction to the CCSS HS Algebra February 2013

2. Outcomes • Align the regional/district Algebra course to the PARCC framework • Create tape diagrams and double number lines to solve application problems • Explain the information we have, need and will make do with

3. PARCC Resources • Progressions • http://ime.math.arizona.edu/progressions/ • Illustrative Mathematics • http://illustrativemathematics.org/ • Common Core Tools • http://commoncoretools.wordpress.com/ • Quality Review Rubrics • http://www.achieve.org/files/TriState-Mathematics-Quality-RubricFINAL-May2012.pdf • Achieve the Core • http://www.achievethecore.org/

4. PARCC Components • Key Advances from the Previous Grade • Discussion of Mathematical Practices in Relation to Course Content • Fluency Recommendations • Pathway Summary Tables • Assessment Limits Tables

6. Math Practice Meditation  • Imagine your best students… consider how they showed each of these qualities… Perseverance Reason abstractly and quant. Construct and critique Model Use tools strategically Precision Use structure Find and express repeated reasoning

7. Look For’s in a CCLS Lesson • Fluency Task (~10 mins) • Modeling • Concept Building • Application • Debrief • Pair Sharing • Exit Ticket (Daily formative assessment)

8. Module Sources

9. Construct

10. Assessment

11. Content Gap Instruction • Multiplication • Division Strategies • Algebraic Understanding • Fractions • Number Sense & Place Value

12. Quiz 1 • What teaching materials will likely be available? • Is State Ed is making and providing all of the math materials teachers need? • What are important documents to help build our HS curriculum?

13. Math Modules

14. Fluency

15. Required Fluencies

16. Multiplication Facts Gene Jordan’s work but I got the Idea from Gina King’s article:www.nctm.org teaching children mathematics • King, Fluency with Basic Addition, September 2011 p. 83

17. Addition Facts Gina King’s article:www.nctm.org teaching children mathematics • King, Fluency with Basic Addition, September 2011 p. 83

18. Fluency Example • Finger Counting • 1,2,3, sit on 10 • High 5

19. Fluency

20. Math Sprints

21. Conceptual Modeling

22. Conceptual • Concrete Pictorial  Abstract • Moving both ways • Draw a picture of 4+4+4 • Show your thinking • Explain, defend and critique the reasoning of others

23. Concrete Model  Equation X + 3 = 5

24. Tape Diagram Problems Tape diagrams are best used to model ratios when the two quantities have the same units.

25. Tape Diagrams: Q1 • 1. David and Jason have marbles in a ratio of 2:3. Together, they have a total of 35 marbles. How many marbles does each boy have?

26. Tape Diagrams : Q2 • 2. The ratio of boys to girls in the class is 5:7. There are 36 children in the class. How many more girls than boys are there in the class?

27. Tape Diagrams Q3: Comparing 3 items Lisa, Megan and Mary were paid \$120 for babysitting in a ratio of 2: 3: 5. How much less did Lisa make than Mary?

28. Tape Diagrams Q4: Different Ratios The ratio of Patrick’s M & M’s to Evan’s is 2: 1 and the ratio of Evan’s M & M’s to Michael’s is 4: 5. Find the ratio of Patrick’s M & M’s to Michael’s.

29. Tape Diagrams Q5: Changing Ratios The ratio of Abby’s money to Daniel’s is 2: 9. Daniel has \$45. If Daniel gives Abby \$15, what will be the new ratio of Abby’s money to Daniel’s?

30. Double Number Line Double number line diagrams are best used when the quantities have different units. Double number line diagrams can help make visible that there are many, even infinitely many, pairs of numbers in the same ratio—including those with rational number entries. As in tables, unit rates (R) appear in the pair (R, 1).

31. Double Number Line:Finding average rate • It took Megan 2 hours to complete 3 pages of math homework. Assuming she works at a constant rate, if she works for 8 hours, how many pages of math homework will she complete? What is the average rate at which she works?

32. Identify properties of the RDW modeling technique for application problems • Read (2x) • Draw a model • Write an equation or number sentence • Write and answer statement • Unit • Object • Context

33. Use RDW to solve Problem

34. Modeling Challenge • 2 boxes of salt and a box of sugar cost \$6.60. A box of salt is \$1.20 less than a box of sugar. What is the cost of a box of sugar? Salt Salt \$6.60 3 parts = \$6.60- \$1.20 Sugar 3 parts = \$5.40 1 part = \$5.40 ÷ 3 = \$1.80 \$1.20+\$1.80= \$3.00 \$1.20

35. Challenging Problems Mika Said: “Four more girls jumped rope than played soccer.” Chaska Said: “For every girl that played soccer, two girls jumped rope.” • The students in Mr. Hill’s class played games at recess. • 6 boys played soccer • 4 girls played soccer • 2 boys jumped rope • 8 girls jumped rope • 1) Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did. • 2)Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did. • 3) Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did. Mr Hill Said: “Mika compared girls by looking at the difference and Chaska compared the girls using a ratio”

36. Challenging Problems • Compare these fractions: Which one is bigger than the other? Why? and

37. Application

38. Application • The beginning of the year is characterized by establishing routines that encourage hard, intelligent work through guided practice rather than exploration. • Slower and deeper • Use the Read-Draw-Write (RDW) steps

39. Application

41. High School Functions A--‐REI.4. Solvequadraticequationsinonevariable.

42. High School Illustrative Sample Item Seeing Structure in a Quadratic Equation A--‐REI.4. Solvequadraticequationsinonevariable.

43. High School Illustrative Sample Item Seeing Structure in a Quadratic Equation A--‐SSE, SeeingStructureinExpressions