Download in Grades 6-8

NJ ASK 6, 7, AND 8; TRANSITION TO THE
COMMON CORE STATE STANDARD
ASSESSMENTS 2012-2015
AN ASSESSMENT AND CURRICULUM
PERSPECTIVE
Michael Luke NJDOE
609-984-9637
[email protected]
1
SEQUENCE OF TOPICS
Introduction to Common Core
Structure/Terminology
 Resources
 Timelines for Implementation/Methods of
Implementation
 Curriculum Concerns Unique to NJ
 Progressions of Topics Across Grades
 New Topics/Deleted Topics by Grade
 Comments/Questions

2
TERMINOLOGY/ACRONYMS

Common Core State Standards (CCSS):


Arranged by Domain, Cluster, Standard
Example 8.EE.7b
Grade 8
 Domain- Expressions and Equations (4/5 per grade)
 Cluster (9-12 per grade, does not appear in code)- Analyze and
solve linear equations and pairs of simultaneous linear equations
(major, supporting, additional- see Content Frameworks)
 Standard 7b (one of two/five in this cluster)- Solve linear equations
in one variable
 b. Solve linear equations with rational number coefficients, including
equations whose solutions require expanding expressions using the
distributive property and collecting like terms.

3
TERMINOLOGY/ACRONYMS

NJ Core Curriculum Content Standards (CCCS)
Arranged by Cluster, Strand, and Cumulative Progress
Indicator (CPI)
 Example 4.3.8 D.2 Solve simple linear equations
informally, graphically, and using formal algebraic
methods (multi-step, integer coefficients only (although
answers may not be integers))(3- Patterns and Algebra,
D- Procedures)

Grade 6- CCSS- 42, CCCS- 63
 Grade 7- CCSS-37, CCCS-39
 Grade 8- CCSS- 33, CCCS-60

4
TERMINOLOGY/ACRONYMS
7.EE.3 Solve multi-step real-life mathematical
problems posed with positive and negative
rational numbers in any form, using tools
strategically.
 PARCC- Partnership for Assessment of
Readiness for College and Careers

5
CCSS DOMAINS ACROSS GRADES 6-8
DOMAIN/GRADE
6
7
Ratios and
Proportional
Relationships
X
X
The Number System
X
X
X
Expressions and
Equations
X
X
X
Geometry
X
X
X
Statistics and
Probability
X
X
X
Functions
8
X
6
RESOURCES

PARCC


CCSS



http://www.parcconline.org
Content Frameworkshttp://www.parcconline.org/sites/parcc/files/PARCC%20M
CF%20for%20Mathematics_Fall%202011%20Release.pdf
http://www.corestandards.org/
http://commoncoretools.wordpress.com/
NJ DOE

http://www.nj.gov/education/aps/cccs/math/cccsres.htm
7
CCSS CURRICULUM AND ASSESSMENT
IMPLEMENTATION IN NJ
Grades
Curriculum
Assessment
3-5, HS
September 2012
Spring 2013
6-8
September 2013
Spring 2014*
8
CCSS CURRICULUM AND ASSESSMENT
IMPLEMENTATION IN NJ (SLIDE 2*) GRADES
6-8
Year
Assessment/Alignment
Spring 2012
NJ ASK aligned to NJ CCCS
Spring 2013
NJ ASK aligned to NJ CCCS
Spring 2014
NJ ASK aligned to CCSS
School Year 2015 and beyond
PARCC aligned to CCSS
9
CCSS CURRICULUM AND ASSESSMENT
IMPLEMENTATION IN NJ GRADES 6-8
NJ ASK 6-8 Spring 2014
 Forms should look familiar to NJ students
 Spring 2012 and 2013- exclusively field testing
items that have alignments to both CCSS and
CCCS at a common grade
 Points (item numbers and selection) will be biased
towards Fluency Expectations, Culminating
Standards, and Major Clusters vs. Supporting and
Additional Clusters
 Score reporting still being discussed/developed

10
CURRICULUM CONCERNS UNIQUE TO NJ
8.EE.7a (MC, CS)- Solve linear equations with
rational coefficients, including equations
whose solutions require expanding expressions
using the distributive property and collecting
like terms. (major)
 3.8 D.2, 3.12 D.2- Solve simple linear
equations informally, graphically, and using
formal algebraic methods. (multi-step, integer
coefficients,…)

11
CURRICULUM CONCERNS UNIQUE TO NJ
8.EE.7A
Cohort
Last Aligned Instruction
Grade 8 Year
8; 13/14
3.7 D.2 Solve simple
linear equations informally
and graphically. (…integer
coefficients…)
13/14
7; 13/14
7.EE.4a Solve problems
leading to equations of
the form px+q=r and
p(x+q)=r, where p, q, and r
are specific rational
numbers.
14/15
6; 13/14
7.EE.4a, 6.EE.7 Solve realworld and mathematical
problems by writing and
solving equations of the
form x+p=q and px=q for
cases in which p, q, and x
and all nonegative rational
15/16
12
CURRICULUM CONCERNS UNIQUE TO NJ
7.SP.8 PROBABILITY

7.SP.8 a, b, and c (SC)- Find probabilities of
compound events using organized lists, tables,
tree diagrams, and simulation.

Grade 8 2013/14 cohort misses 4.8.B.2
Determine probabilities of compound events. SCP Use the rules of probability to compute
probabilities of compound events in a uniform
probability model.
13
CURRICULUM CONCERNS UNIQUE TO NJ
PROBABILITY 7.SP.5


7.SP.5 (SC) Understand that the probability of a
chance event is a number between 0 and 1 that
expresses the likelihood of the event
occurring…7.SP.7a …determine probabilities of events
4.5 B.1 and 4.6 B.1 Determine probabilities of
events… probability of certain event is 1 and of an
impossible event is 0.
Cohort
Last Aligned
Instruction
Grade 7 Year
7; 13/14
4.6 B.1
13/14
6; 13/14
4.5 B.1
14/15
14
CURRICULUM CONCERNS UNIQUE TO NJ
8.G.9



8.G.9 (AC)- Know the formulas for the volumes of
cones, cylinders, and spheres and use them to solve
real-world and mathematical problems.
Cones and spheres 2.8 E.4
Cylinders 2.6 E.3 Develop and apply…formulas for
finding …the volume of…cylinders.
Cohort
Last Aligned
Instruction
Grade 8 Year
8; 13/14
2.6 E.3
13/14
7; 13/14
2.6 E.3
14/15
6; 13/14
7.G.6 (segment
sides)
15/16
15
PROGRESSION 5-7
COMPUTATION NF, NBT, NS
5
•Completed + and - of
fractions
6
•Completed x and / of
fractions
7
•Completed computation with
rational numbers (1.8 B.1)
16
PROGRESSION 6-8
EXPRESSIONS AND EQUATIONS
6
• 6.EE.7 Solve real-world and mathematical problems by
writing and solving equations of the form x+p=q, px=q.
• p, q, and x nonnegative rational numbers
7
• 7.EE.4a Solve word problems leading to equations of the
form px+q=r and p(x+q)=r…
• p, q, and r specific rational numbers
8
• 8.EE.7b Solve linear equations with rational number
coefficients (distributive property and collecting like terms)
• 8.EE.8b Solve systems of two linear equations in two
variables algebraically …
17
PROGRESSION 7-HS
SIMILARITY AND CONGRUENCE
7
•7.G.1 Scale Drawings
8
•8.G.2, 8.G.3 and 8.G.4 Similarity and
congruence of 2-dimensional figures
from a transformational perspective.
HS
•HS.G More formal treatment of
congruent and similar triangles.
18
PROGRESSION 6-8
STATISTICS AND PROBABILITY
6
•Descriptive Statistics
•6.SP.5c Giving quantitative measures of center (median, mean) and
variability (interquartile range, mean absolute deviation) as well as
describing any overall pattern
7
•Inferential Statistics 7.SP.4 Use measures of center and variability for
numerical data from random samples to …comparative inferences
about two populations.
•Beginning probability through 7.SP.8 Find probabilities of compound
events using organized lists, tables, tree diagrams, and simulation.
8
•8.SP Bivariate data- scatter plots, “informally fits a straight line”, “Use
the equation of a linear model to solve problems in the context of
bivariate measurement data…” , and “Construct and interpret a twoway table…”
19
PROGRESSION 7-8
FUNCTIONS
6
•Functions not in CCSS at this grade, use of word
“function” still not introduced
•6.EE.9 Use variables to represent two quantities in
a real-world problem that change in relationship to
one another; write an equation …
8
•8.F.4 Construct a function to model a linear
relationship between two quantities.
•8.F.5 Describe qualitatively the functional
relationship between two quantities by analyzing a
graph (…increasing/decreasing,
linear/nonlinear…)
20
TOPICS NEW TO GRADE 6
6.EE.1 “…evaluate numerical expressions involving
whole number exponents.” (squares and cubes of
whole numbers)
 6.EE.3 Distribution and GCF factoring on algebraic
expressions (CCCS-7)
 6.NS.7 Absolute value (CCCS-8)
 6.G.3 Use of all four quadrants (quadrant 1 only)
 6.G.4 Surface area of 3-D figures using nets
composed of rectangles and triangles

21
TOPICS NEW TO GRADE 6
6.SP.2 Focus on center, spread, and overall
shape of data sets
 Measures of spread- interquartile range and
mean absolute deviation (MAD) (previously just
range, range not in CCCS)

22
TOPICS NO LONGER IN GRADE 6








LCM- of two numbers less than or equal to 12.
GCF- of two numbers less than or equal to 100.
Pascal’s triangle and Fibonacci sequence to high school (F-IF
and A-APR-5).
Pattern strand deemphasized – 4.OA.5 a single pattern of
numbers or shapes, 5.OA.3 two patterns, and arithmetic and
geometric sequences to high school (F-BF-2).
No mention of Venn Diagrams in CCSS.
Volume of cylinders (8.G.9).
Geometric transformations to grade 8.
Interior angle sum of a triangle (8.G.5).
23
TOPICS NO LONGER IN GRADE 6
Any probability.
 Factorials/permutations/combinations/
multiplication principle of counting to HS (S-CP9).
 Mode/range
 Vertex-edge graphs (possibly to HS, N.VM.6
with matrix).

24
TOPICS NEW TO GRADE 7
7.G.3 Describe plane sections of three
dimensional figures.
 7.SP.5, 7.SP.7a Simple probability (uniform
probability model). Grade 7 is first occurrence
of probability in CCSS.
 7.SP.8 Probabilities of compound events (4.4.8
B.2) (using a sample space, formal rules in HS,
S-CP)

25
TOPICS NO LONGER IN GRADE 7
Compound interest (4.3.7 C.2)(recursive
functions) to HS (A.SSE.3c, F-BF, F-IF).
 Volume of a cone (8.G.9).
 Volume of a pyramid to HS (G.GMD.3).
 Relationship of pyramid (cone) volume to prism
(cylinder) volume.
 All geometric transformations to grade 8 (also
true for grade 6, and only on 1- & 2dimensional figures).

26
TOPICS NO LONGER IN GRADE 7

Systematic listing and counting (see grade 6
comments) (only for representing a sample
space).
27
TOPICS NEW TO GRADE 8
8.EE.1 Negative integer exponents (4.1.8 B.2
was limited to whole number exponents)
 8.EE.7 Variables on both sides of a linear
equation with no limitation on coefficients
 8.EE.8b “Solve systems of two linear equations
in two variables algebraically,…”. (more rigorous
than 4.3.12 B.2 “…using graphing
techniques…”).

28
TOPICS NEW TO GRADE 8
First use of the word “function”.
 8.F.4 Create linear functions (more rigorous than
CCCS- from two points).
 8.G.6 “Explain a proof of the Pythagorean
Theorem and its converse.”
 8.G.8 Distance formula (applications of
Pythagorean Theorem to coordinate plane) (4.2.12
C.1).
 8.SP.4 “Construct and interpret a two way table…”
(bivariate data).

29
TOPICS NO LONGER IN GRADE 8
Operations with integers (4.1.8 B.1).
 Exponential growth (4.3.8 b.2) to HS (F.IF.8b).
 Graphing linear inequalities of the form
y>mx+b (4.3.8 D.2) to HS (A.REI.12).
 Any probability.

30
COMMENTS/QUESTIONS
No mention of complementary events, interior
angle sum of a quadrilateral (polygon), flow
charts, weighted means
 Deemphasized

 Classification
of triangles by sides/angles- first
mention of isosceles is HS G.CO.10 ; 4.G.2
(scalene?); 5.G.3 & 5.G.4
 Trapezoids
 Simple perimeter 3.MD.8
31
COMMENTS/QUESTIONS

Deemphasized
 Prime
numbers (factoring)- 4OA.4 Find all factor
pairs for numbers from 1-100 and determine if a
number from 1-100 is prime or composite .
Quadratic equations in HS N.CN.7
 4.OA.4 Compare two decimals to thousandths.
 7.G.4 “Know the formulas for the area and
circumference of a circle…”

32
1-609-984-9637
[email protected]
MICHAEL LUKE NJDOE
33