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-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 +++

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, SAT2012-13 HS CCSI NJASK, HSPA, SAT

3-5 CCSI2013-14 6-8 CCSI NJASK, HSPA

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.

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

OLD EXPECTATIONS

(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?

Find ‘F’ when ‘S’ = 81VERMONT: F = 4 ( S – 65 ) + 10

NEW EXPECTATIONS

1. Describe the speeding fine in words.

2. In Connecticut at what speed does it no longer matter?

3. At 80 mph how much better off would you be in VT than in CT?

4. Use a graph to show this difference.

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.)

TRANSITION PHASE: “Mathematics Grade-8” (pre-algebra)

TRANSITION PHASE: 5 DOMAINS

Mathematics Grade-8 Overview (p.53)(pre-algebra)

1. The Number System

2. Expressions and Equations

3. Functions

4. Geometry

5. Statistics and Probability

EXPRESSIONS

Price plus 6% sales tax

Perimeter:L

WW

L

p + .06p or p(1.06)

L + w + L + wL + L + w + w 2(L) + 2(w) 2(L + w)

CREATE EQUATIONS

CREATE * REPRESENT * REARRANGE

1. 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. Rearrange Ohm’s law:

V = IR to highlight resistance R

REASON WITH EQUATIONS

Explain each step in solving a simple equation.

8x + 2(x-6) = 16 – 3(x-2)

1. 8x + 2x – 12 = 16 – 3x +6

2. 10x - 12 = 22 – 3x

3. 13x - 12 = 22

4. 13x = 34

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!

SAMPLE 8.EE (PRE-ALGEBRA)

Work with radicals and integer exponents.

1. 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

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

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.

DISCUSS PRE-ALGEBRA

Use the CCSS ALGEBRA STANDARDS

Middle School – think grade-8 students

HS – think grade-9 students

Low-level Algebra class

Middle-level Algebra class

SET UP FORMAT

Algebra8

Geom9

Honors6

Honors7 PeAlg

Hon.Alg8

Use distance formula

Applydist. formula

Use distance formula

Apply dist. formula

Reviewon own

LOW ALG.9

LOW GEOM10

LOW ALG211

SEN.MATH12

Textbook

Use & Apply Dist. formula

Apply Dist. formula

+ STEM statistics

HIGH SCHOOL ALGEBRA

ALGEBRA GEOMETRY ALGEBRA-II Pre-Calculus Textbook

Use Dist.Formula

Apply Dist.Formula

Review on own

All + STEM statistics

MIDDLE-SCHOOL ALGEBRA

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-7NJASK-8 content, format, vocabulary

FORMAT ALGEBRA STANDARDS:

DOMAIN: A-SSE Seeing Structure in Expressions

CLUSTER: Interpret the structure of expressions

STANDARD:

1. Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expression (terms, factors, coefficients)

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. Interpret P(1+r)n as the product of P and a factor not depending on P.

ALGEBRA (NEW CONTENT)

QUADRATIC EQUATIONS in one variable

-completing the square

x2 + 6x -9 = x2 + 6x + (3x)2 -9 –(3x)2

DISCUSS ALGEBRA

REASONING & SENSE MAKING

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?

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.

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

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.

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)

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