1. Michael Luke NJDOE 609-984-9637 michael.luke@doe.state.nj.us
NJ ASK 6, 7, and 8; Transition to the Common Core State Standard Assessments An Assessment and Curriculum Perspective
Michael Luke NJDOE

2. 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

3. 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.

4. Terminology/Acronyms
NJ Core Curriculum Content Standards (CCCS)
Arranged by Cluster, Strand, and Cumulative Progress Indicator (CPI)
Example 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

5. 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

6. CCSS Domains Across Grades 6-8
DOMAIN/GRADE 6 7 8
Ratios and Proportional Relationships X
The Number System
Expressions and Equations
Geometry
Statistics and Probability
Functions

7. Resources PARCC- CCSS NJ DOE http://www.parcconline.org
Content Frameworks-
CCSS
NJ DOE

8. CCSS Curriculum and Assessment Implementation in NJ
Grades
Curriculum
Assessment
3-5, HS
September 2012
Spring 2013
6-8
September 2013
Spring 2014*

9. Assessment/Alignment
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
Spring 2014
NJ ASK aligned to CCSS
School Year 2015 and beyond
PARCC aligned to CCSS

10. 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 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

11. 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,…)

12. 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 real-world 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 numbers.
15/16

13. 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 /14 cohort misses 4.8.B.2 Determine probabilities of compound events. S-CP Use the rules of probability to compute probabilities of compound events in a uniform probability model.

14. 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

15. 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
14/15
6; 13/14
7.G.6 (segment sides)
15/16

16. Progression 5-7 Computation NF, NBT, NS
Completed + and - of fractions 6
Completed x and / of fractions 7
Completed computation with rational numbers (1.8 B.1)

17. Progression 6-8 Expressions and Equations
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 …

18. Progression 7-HS Similarity and Congruence
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.

19. Progression 6-8 Statistics and Probability
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 two-way table…”

20. Progression 7-8 Functions6
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…)

21. 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

22. 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)

23. 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).

24. Topics No Longer in Grade 6
Any probability.
Factorials/permutations/combinations/ multiplication principle of counting to HS (S-CP-9).
Mode/range
Vertex-edge graphs (possibly to HS, N.VM.6 with matrix).

25. 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)

26. 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- & 2-dimensional figures).

27. Topics No Longer in Grade 7
Systematic listing and counting (see grade 6 comments) (only for representing a sample space).

28. 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 B.2 “…using graphing techniques…”).

29. 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) ( C.1).
8.SP.4 “Construct and interpret a two way table…” (bivariate data).

30. 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.

31. 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

32. Comments/Questions Deemphasized Quadratic equations in HS N.CN.7
Prime numbers (factoring)- 4OA.4 Find all factor pairs for numbers from and determine if a number from 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…”

33. 1-609-984-9637 michael.luke@doe.state.nj.us
Michael Luke NJDOE