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PREPARING FOR THE Common core standards: CCSS ALGEBRA

PREPARING FOR THE Common core standards: CCSS ALGEBRA. Presented SUMMER 2011 BY judith t. brendel , NJPSA/FEA SUPERVISOR OF MATHEMATICS & ART PASCACK VALLEY REGIONAL H.S. DISTRICT. Be Pro-active Prepare for the change. Timeline: implementation & assessment What’s different?

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PREPARING FOR THE Common core standards: CCSS ALGEBRA

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  1. PREPARING FOR THE Common core standards: CCSS ALGEBRA Presented SUMMER 2011 BY judith t. brendel, NJPSA/FEA SUPERVISOR OF MATHEMATICS & ART PASCACK VALLEY REGIONAL H.S. DISTRICT

  2. Be Pro-activePrepare for the change • Timeline: implementation & assessment • What’s different? • Transition Phase - Today’s Reality: • Pre-Algebra LAST YEAR (gr. 7 - 8) vs CCSS • Algebra THIS YEAR (gr. 8 – 9) • Mathematical Practices • Plan: Curriculum, Pacing, Assessments • Resources: Textbook alignment +++

  3. TIMELINE • Curriculum Assessments • 2011-12 K-2 CCSI • 2012-13 3-5, HS New NJASK, HSPA • 2013-14 6-8 New NJASK, HSPA • 2014- K?-Alg. NEW* • from • Algebra-EOC test to quarterly benchmarks for all students 3-12 (transition) NJASK, HSPA, SAT 2012-13 HS CCSI NJASK, HSPA, SAT 3-5 CCSI 2013-14 6-8 CCSI NJASK, HSPA

  4. assessment • Measure standards that are rigorous, globally competitive, and consistent across the states. • New Jersey’s choice • The assessment consortium PARCC (Partnership for Assessment of Readiness for College and Careers) • New assessments will replace current state NCLB tests in 2014-2015.

  5. What does this mean to you? • TRANSITION YEAR(S) • CONTENT • CCSS Skills not mastered in PreAlgebra • Grade-8: NJASK8 standards not in CCSS • Grade-9: HSPA/SAT content not in CCSS • PROCESS • Conceptual understanding of content • Applying skills in real-world situations • New vocabulary

  6. OLD EXPECTATIONS Find ‘F’ when ‘S’ = 81 VERMONT: F = 4 ( S – 65 ) + 10 • (The speeding fine in Vermont is $4 for every mile per hour over the 65 mph limit plus $10 handling fee.) • (Maximum speeding fine in Ct. is $350) CONNECTICUT: F = 10 (S-55) + 40 What is the fine for driving 72 mph?

  7. New expectations • Describe the speeding fine in words. • In Connecticut at what speed does it no longer matter? • At 80 mph how much better off would you be in VT than in CT? • Use a graph to show this difference.

  8. TRANSITION PHASE: “Mathematics Grade-8” (pre-algebra) • FOCUS: 3 CRITICAL AREAS p.52- • 1- Formulate and reason about expressions & equations • 2- Grasp the concept of function and using functions to describe relationships • 3- Analyze 2 and 3-dimensional space/figures (distance, angle, similarity, congruence; understand and apply the Pythagorean Theorem.)

  9. TRANSITION PHASE: 5 DOMAINS • Mathematics Grade-8 Overview (p.53)(pre-algebra) • The Number System • Expressions and Equations • Functions • Geometry • Statistics and Probability

  10. Expressions • Price plus 6% sales tax • Perimeter: p + .06p or p(1.06) L L + w + L + w L + L + w + w 2(L) + 2(w) 2(L + w) W W L

  11. CREATE EQUATIONS • CREATE * REPRESENT * REARRANGE • Create equations in 2 or more variables to represent relationships: • A line going through (2,5) (-3,8) • 2. Create an inequality: • The car and insurance payments cannot exceed 8% of her income. • 3. RearrangeOhm’s law: • V = IR to highlight resistance R

  12. Reason with equations • Explain each step in solving a simple equation. • 8x + 2(x-6) = 16 – 3(x-2) • 8x + 2x – 12 = 16– 3x +6 • 10x - 12 = 22 – 3x • 13x - 12 = 22 • 13x = 34

  13. Solve (Pre-Algebra) • EQUATIONS in one variable (w/coefficients represented by letters) • ab + c = d Solve for b. • SYSTEMS 8.EE8.a.b.c. (p.55) • Does the line through (2,6) and (3,5) intersect with the line going through points (4,8)and(2,4)? EXPLAIN or model how you know!

  14. Sample 8.ee (pre-algebra) • Work with radicals and integer exponents. • Know and apply the properties of integer exponents to generate equivalent numerical expressions. • For example, • 32 x 3-5 = 3-3 = 1/33 = 1/27

  15. GRADE-8 (PRE-ALGEBRA) Overview (p.53) • Number Sense • Expressions & Equations • Functions • Geometry • Statistics & Probability • ALGEBRA Overview (p.57) • Seeing Structure in Expressions • Arithmetic w/Polynomials & Rational Expressions • Creating Equations • Reasoning w/Equations & Inequalities

  16. Use the CCSS Grade-8 PRE-ALGEBRA STANDARDS • Middle School – think grade-7 students • HS – think grade-8 students • Highlight what was not experienced by last year’s pre-algebra students.

  17. Discuss pre-algebra

  18. Use the CCSS ALGEBRA STANDARDS • Middle School – think grade-8 students • HS – think grade-9 students • Low-level Algebra class • Middle-level Algebra class

  19. SET UP FORMAT MIDDLE-SCHOOL ALGEBRA HIGH SCHOOL ALGEBRA

  20. WHERE: Algebra? • HIGH SCHOOL • SELECT √ content for each level of Algebra • TRANSFER topics to appropriate course • ADD CCSS not completed gr.8 and HSPA MIDDLE SCHOOL SELECT √ content to be included from CCSS Alg. TRANSFER topics to learn on own ADD CCSS skills not completed grade-7 NJASK-8 content, format, vocabulary

  21. Format Algebra sTANDARDS: • DOMAIN: A-SSE Seeing Structure in Expressions • CLUSTER: Interpret the structure of expressions • STANDARD: • Interpret expressions that represent a quantity in terms of its context. • Interpret parts of an expression (terms, factors, coefficients) • Interpret complicated expressions by viewing one or more of their parts as a single entity. Interpret P(1+r)nas the product of Pand a factornot depending on P.

  22. Algebra (NEW CONTENT) • QUADRATIC EQUATIONS in one variable • -completing the square • x2 + 6x -9 = x2 + 6x + (3x)2-9 –(3x)2

  23. Discuss algebra

  24. Reasoning & SENSE MAKING

  25. PROBLEM-SOLVING activity • What is the perimeter of this shape? • (long bars represent ‘x’, squares are 1 x 1) • WORK ALONE; SHARE STRATEGIES with your GROUP Why is this a good REASONING & SENSE MAKING task?

  26. OVERARCHING MATHematical PRACTICES • 1. Make sense of problems and persevere in solving them. • 2. Reason abstractly and quantitatively. • 3. Construct viable arguments and critique the reasoning of others. • 4. Model with mathematics. • 5. Use appropriate tools strategically. • 6. Attend to precision • 7. Look for and make use of structure. • 8. Look for and express regularity in repeated reasoning.

  27. AS THE CROW FLIES • STUDENT ACTIVITY SHEET • (Beginning Algebra) NCTM • Suppose that the city in which you live has a system of evenly spaced perpendicular streets forming square city blocks. The map below shows your school; your house, which is located two blocks west and five blocks north of the school; and your best friend’s house, which is located eight blocks east and one block south of the school. • See questions 1-5 on pages 20-21

  28. MAXIMIZING AREA • BEGINNING ALGEBRA (p.30-31) • Question 1. What happens to the perimeter and area when you begin with a rectangle, cut a strip off the rectangle, and rearrange this piece to form a new figure as shown? • See also Questions 2-5.

  29. Sharing W/OTHERSBEYOND THE TEXTBOOK • PORTFOLIOS (Basic Algebra samples) • PROJECTS • - Restaurant (modified for collab. Algebra) • - Cell Phone (any level Algebra) • - Probability and Genetics (Gr. 9 aligns w/Biology) • PRACTICE (vocabulary and form of Algebra EOC test) • EOC PACKETS: Algebra by chapter • TEST: Sample ALG EOC 14 example test(JBS) • TEST: Official sample ALG EOC TEST (ACHIEVE)

  30. And we continue … • http://www.pascack.k12.nj.us [curriculum instruction] [ mathematics]; can also link to [staff] • http://www.nctm.org/ • Judith T. Brendel jbrendel@pascack.k12nj.us

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