Mathematical Practices
Connecting Content Standards and 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.
36
Mathematical Practices (cont.)
Connecting Content Standards and Mathematical Practices
 Practices combine easily, and a single student behavior could be thought of as
exhibiting multiple practices at once.
- Not a checklist.
 There is an expectation that the mathematical practices develop through the
grades as students grow in mathematical maturity and in the sophistication with
which they apply mathematics.
- Need to ensure grade-level appropriate expectations.
 Assessment is moving toward measuring mathematical practices and will be
assessed by PARCC in spring 2015.
37
NJ ASK Mathematics Grades 6-8:
2014 Updates
• Assessment and Score Reporting for SPRING 2014 will be
aligned exclusively to the Common Core State Standards
for Mathematics (CCSSM) (corestandards.org).
• Raw scores will be reported in the five CCSSM Domains at
each grade.
• The available points in each Domain reflects the Content
Emphases by Cluster in the PARCC Model Content
Frameworks (http://www.parcconline.org/parcc-modelcontent-frameworks).
• No score will be reported for the Mathematical Practices.
55
Mathematics: Points by Domain
Point Breakdown
Grade 6
Grade 7
Grade 8
8
8
0
The Number
System
14
12
6
Expressions and
Equations
14
15
14
Functions
0
0
10
Geometry
7
7
13
Statistics and
Probability
6
7
6
Total Points
49
49
49
Ratios and
Proportional
Relationships
56
NJ ASK Mathematics Grades 6-8:
2014 Reference Sheets
• New reference sheets have been developed for grades 6,
7 and 8 to be consistent with the content of the CCSSM.
• The punch-out ruler and protractor remain at all three
grades.
• The equivalents/conversion factors have been altered to
be consistent with the PARCC reference sheets at the
appropriate grade
(http://www.parcconline.org/assessment-administrationguidance).
57
NJ ASK Mathematics Grades 6-8:
2014 Reference Sheets (cont.)
• Geometric formulas no longer necessary due to the
alignment change have been deleted (e.g.: Grade 6Volume and Surface Area of a Cylinder).
• Additional information no longer necessary due to the
alignment change have been deleted (e.g.: Grade 8Permutations Formula).
• The new Reference Sheets have been posted at
http://www.state.nj.us/education/assessment/ms/58/ref/math/
58
NJ ASK Mathematics Grades 6-8:
Additional Updates
 ALL students are allowed to use blank grid/graph paper
during ALL parts of the Mathematics section of the NJ
ASK 6-8.
59
NJ ASK 6-8 Mathematics:
Calculator Use Policy
• Part 1 of the test (10 short constructed-response items) is
non-calculator for all students, including students with
disabilities.
• Three of the remaining 5 parts (parts 4 through 6) are
calculator active for all students. These parts will include
multiple-choice (MC) and extended constructed-response
(ECR) items.
60
NJ ASK 6-8 Mathematics:
Calculator Use Policy (cont.)
 Parts 2 and 3 are non-calculator, except for students with
disabilities. These parts will include multiple-choice (MC)
and extended constructed-response (ECR) items.
 Students classified with a specific disability that limits
them from calculating mathematically may use a
calculator and/or manipulatives (i.e., abacus, number
line, counting chips) on parts 2 and 3.
61
NJ ASK 6-8 Mathematics:
Calculator Use Policy (cont.)
• Students accommodated through the use of calculators
must have the assessment administered to them in an
alternative setting.
• The use of a calculator or other specific manipulatives as
an instructional and assessment accommodation must be
documented in the student’s IEP or 504 plan. The SCR
part will remain non-calculator.
• Please see the Test Examiners Manual for more
information about the Calculator Use Policy.
62
Mathematics (Grades 6-8 Unchanged for
Spring 2014)
MC- multiple choice, 1 raw score point
SCR- short constructed-response, 1 raw score point
ECR- extended constructed-response, 3 raw score points
Grade 6
Grade 7
Grade 8
MC
32
32
32
SCR
8
8
8
ECR
3
3
3
Total raw score
points possible
49
49
49
Approximate total
testing time
(including field test
content)
133 minutes
133 minutes
133 minutes
Item
Count by
Type (does
not include
embedded
field test
content)
63
Mathematics Sample MC Item
Grade 7
CCSSM Standard to be Assessed:
7.G.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the
relationship between the circumference and area of a circle.
Note: Previously, calculating the area and circumference of a circle were taught in grade 6- see 4.2.6 E.2 of the NJ Core Curriculum Content
Standards (CCCS).
Item: Find the area, in square centimeters, of the circle to the nearest integer.
15
cm
A. 47 (student finds circumference)
B. 154 (student rounds radius to 7)
C. 177 (correct for 3.14, 22/7, or π button on calculator
D. 707 (student uses 15 for radius)
Note: Correct answer is C. Distractors contain common student errors. Area and circumference formulas are on reference sheet (see
previous slides for more information). Item stems frequently specify units, so units would not be required in these answer choices.
64
Mathematics Sample Non-Calculator
Multiple-Choice Item
Grade 6
CCSSM Standard to be Assessed:
6.NS.2: Fluently divide multi-digit numbers using the standard algorithm.
Note: The expectation is, using the standard algorithm, students will fluently divide multi-digit
numbers with and without remainders. 6.NS.2 is a PARCC fluency expectation. See PARCC
End of Year (EOY) Evidence Statement key 6.NS.2.
Item:
Divide 3647 by 14.
A. 26 7/26 (quotient place error, incorrect remainder)
B. 26 ½ (quotient place error)
C. 260 7/26 (incorrect remainder)
D. 260 ½ (correct answer)
65
Grade 8
Mathematics Sample ShortConstructed Response Item
CCSSM Standard to be assessed:
8.EE.8b: Solve systems of two linear equations in two variables algebraically, and estimate
solutions by graphing the equations.
Note: This content was previously in NJ CCCS 4.3.12 B.2.
Item: Find the coordinates of the point of intersection of the graphs of y=6x-6 and 5y=-30x.
Note: For an SCR item students place their answer on a space provided in the answer folder.
Answers such as (½,-3); x=.5 and y=-3; .5,-3; etc. would all be graded as correct. No partial
credit is awarded on SCR items- the score is a 0 or a 1.
66
Mathematics Sample ShortConstructed Response Item
Grade 7
CCSSM Standard to be Assessed:
7.SP.7a: Develop a uniform probability model by assigning equal probability to all
outcomes, and use the model to determine probabilities of events.
Note: The CCSSM clusters the topic of probability into grade 7 during the middle
school grade band (6-8). This is different than the NJ CCCS which spread
probability across all three grades.
Item: A middle school choir consists of 10 sixth grade students, 8 seventh grade
students, and 6 eighth grade students. The choir director selects a member of
the choir at random. What is the probability the director selects a member who
is in the eighth grade?
Note: Hand scoring of SCR items allows 6/24, ¼, .25, or any equivalent to be scored
correct.
67
Mathematics Sample ExtendedConstructed Response Item
Grade 8
CCSSM Standard to be Assessed:
8.F.2: Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions).
Item:
Shown below are two functions
Function #1
Function #2
x
y
2x-y=-5
1
-2
3
4
4
7
7
16
68
Mathematics Sample ExtendedConstructed Response Item (cont.)
 What is the rate of change of function #2? Show your work or
explain your answer. (Correct answer 3)
 Which function has the greater rate of change? Show your
work or explain your answer. (Correct answer function #2)
 Express function #2 as an equation. Explain your answer.
(Correct answer y=3x-5)
Note: Extended-constructed response items are scored on a 3point maximum item specific rubric. See the Spring 2014
Parent, Student and Teacher Information Guide for more
details.
69
Mathematics Sample MultipleChoice Item
Grade 6
CCSSM Standard to be Assessed:
6.EE.4: Identify when two expressions are equivalent.
Item: Which of the following expressions is NOT equivalent to 15x+9?
A. 15x+8+1
B. 10x+5x+9
C. 3(5x+9)
D. 3(5x+3)
Note: Correct answer C. The second term in the binomial 5x+9 should
be 3. Important or key words can be bold and capitalized.
70
http://www.state.nj.us/education/sca/
http://www.corestandards.org
http://www.parcconline.org/
71