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?
• 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 3-12
3-5, HS
New
NJASK,
HSPASAT
(transition)
NJASK,
HSPA,
2012-13
NJASK,
HSPA,
2013-14 HS
6-8 CCSI
New
NJASK,
HSPASAT
3-5 CCSI
2014K?-Alg.
NEW*
2013-14 6-8 CCSI
NJASK, HSPA
• from
• Algebra-EOC test to quarterly
benchmarks for all students
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
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.)
CONNECTICUT: F = 10 (S-55) + 40
What is the fine for driving 72 mph?
(Maximum speeding fine in Ct. is $350)
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.
TRANSITION PHASE:
“Mathematics Grade-8” (pre-algebra)
FOCUS: 3 CRITICAL AREAS p.521- 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: 5 DOMAINS
Mathematics Grade-8 Overview
(p.53)(pre-algebra)
1.
2.
3.
4.
5.
The Number System
Expressions and Equations
Functions
Geometry
Statistics and Probability
EXPRESSIONS
Price plus 6% sales tax
p + .06p
or p(1.06)
Perimeter:
L
L+w+L+w
L+L+w+w
2(L) + 2(w)
2(L + w)
W
W
L
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
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
MIDDLE-SCHOOL ALGEBRA
Algebra
8
Geom
9
Use distance Apply
formula
dist. formula
Honors
6
Honors
7 PeAlg
Use distance Apply
formula
dist. formula
Hon.Alg
8
Review
on own
HIGH SCHOOL ALGEBRA
LOW ALG.
9
ALGEBRA
Use
Dist.Formula
LOW GEOM
10
LOW ALG2
11
Use & Apply
Dist. formula
Apply
Dist. formula
SEN.MATH
12
Textbook
+ STEM
statistics
GEOMETRY ALGEBRA-II
Pre-Calculus
Apply
Review
Dist.Formula on own
All + STEM
statistics
Textbook
WHERE: ALGEBRA?
HIGH SCHOOL
√ content for each level of Algebra
topics to appropriate course
CCSS not completed gr.8 and HSPA
MIDDLE SCHOOL
√ content to be included from CCSS Alg.
topics to learn on own
CCSS skills not completed grade-7
NJASK-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/OTHERS
BEYOND 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