### PARCC Mathematics CLG Training (PPT)

```PARCC General Criteria
for
Mathematics Core Leadership Reviewers
February 5-8, 2013
Note: all items included in this presentation are for illustrative training purposes only.
They are not representative of PARCC assessment items.
1
Question 1

2
Does the task measure the intended
evidence statement?
Alignment to Evidence Statements and
the CCSS
• assess the designated evidence statement
• align with one or more of the Common Core State Standards associated
with the evidence statement
• align with one or more of the Mathematical Practices associated with the
evidence statement
• conform to the content clarifications, limits, and emphasis associated with
the evidence statement
• elicit student performance that will provide evidence of the student’s level
of mastery of the mathematical standard(s) and practice(s) associated
with the evidence statement
• not be so broad in scope that it assesses multiple evidence statements
3
Sample #1a
Task Type: I Points: 1
Evidence Statement: 3.NF.2
3
4
Jonathan’s teacher wrote two fractions, and ,
10
5
on the board. Select four fractions that would lay,
on a number line, between the two fractions
Jonathan’s teacher wrote.
4
4
A)
13
3
C)
6
5
E)
3
2
B)
9
18
D)
30
29
F)
100
4
G)
5
Note: all items included in this presentation are for illustrative training purposes only. They are not representative of PARCC assessment items.
Evidence Statement Text, Clarifications, Limits,
Emphases and Other Information for 3.NF.2
5
Evidence Statement Text
Understand a fraction as a number on the number line;
represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by
defining the interval from 0 to 1 as the whole and partitioning
it into b equal parts. Recognize that each part has size 1/b and
that the endpoint of the part based at 0 locates the number
1/b on the number line.
b. Represent a fraction a/b on a number line diagram by
marking off a lengths 1/b from 0. Recognize that the resulting
interval has size a/b and that its endpoint locates the number
a/b on the number line.
Clarifications, Limits,
Emphases, and Other
Information
i) Fractions are not limited to values between 0 and 1.
ii) Fractions equal whole numbers in 20% of these tasks.
iii) Tasks have “thin context” or no context. .
iv) Tasks are limited to fractions with denominators 2, 3, 4, 6,
and 8. (See footnote CCSSM, p 24)
Sample #1b
Task Type: I Points: 1
Evidence Statement: 8.EE.2
Which values represent solutions to the equation 2x2 = 64?
Select all that apply.
6
A)
x = -16
D)
x= 4 2
B)
x = - 32
E)
x = 32
C)
x=-4 2
F)
x = 16
Note: all items included in this presentation are for illustrative training purposes only. They are not representative of PARCC assessment items.
Evidence Statement Text, Clarifications, Limits,
Emphases and Other Information for 8.EE.2
7
Evidence
Statement
Text
Use square root and cube root symbols to represent solutions to equations of the
form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots
of small perfect squares and cube roots of small perfect cubes. Know that 2 is
irrational.
Clarifications,
Limits,
Emphases,
and Other
Information
i) Pool should contain tasks with and without contexts.
ii) Tasks might for example take the form of algebraic word problems leading to
equations x2 = p or x3 = p, or geometric problems such as finding the edge length
of a cubical object with a given volume.
iii) In problems where p and – p are both relevant as solutions to x2 = p, both
of these solutions should be given. Note that p is nonnegative by definition.
iii) Solutions to equations x2 = p or x3 = p are represented as p or 3 p ,
respectively.
iv) Manipulations such as 8 = 2 2 are beyond the scope of grade 8. Students
need not simplify a solution such as 8 . But students should ultimately express
the following cases in the form of whole numbers: (a) the square roots of 1, 4, 9,
16, 25, 36, 49, 64, 81 and 100; (2) the cube roots of 1, 8, 27, and 64.
Question 2

8
Is the task mathematically correct and free
from errors?
Mathematical Accuracy
• contain content (text, stimuli, terminology, notation, art, etc.) that is
mathematically correct, precise, and generally accepted by math educators
• not contain unintended mathematical errors, misconceptions,
9
Sample #2
Task Type: I Points: 1
Evidence Statement: 6.G.1
This regular hexagon has been divided into congruent triangles.
12 in.
10 in.
What is the area of the hexagon?
square inches
10
Note: all items included in this presentation are for illustrative training purposes only. They are not representative of PARCC assessment items.
Evidence Statement Text, Clarifications, Limits,
Emphases and Other Information for 6.G.1
Evidence Statement
Text
Find the area of right triangles, other triangles, special quadrilaterals,
and polygons by composing into rectangles or decomposing into
triangles and other shapes; apply these techniques in the context of
solving real-world and mathematical problems.
Clarifications, Limits,
Emphases, and Other
Information
i)
11
The testing interface can provide students with a calculation aid
of the specified kind for these tasks
Question 3

12
Is the task (wording and art) clear, cohesive,
concise, accurate, grade-level appropriate,
and free from internal clueing?
Language Clarity and Appropriateness
• convey a clearly defined task or problem in concise and direct
language
• use the language of the evidence statements and standards
when appropriate
• exclude information that is construct irrelevant (e.g., sports
knowledge that is needed to answer the question but is not
provided)
• use a variety of approaches rather than a canned approach
13
Sample #3
Task Type: I Points: 1
Evidence Statement: 7.NS.2b-2
3 1
3
¸
Which situation can be represented by the expression
?
4 3
1
A) The width of a nightstand is the width of a dresser. If the width of
3
3
the dresser is 3 feet, what is the width of the nightstand?
3 4
B) There are 3 cups of flour in a container. How much flour is left in the
4
1
container after a baker takes cup of flour from it?
3
3
C) A relay race is 3 miles long. This distance is divided into equal parts
4
1
that are mile each. How many parts are there in the race?
3
1
D) A puppy’s weight increased by pound. What is the puppy’s new
3 3
weight if its original weight was 3 pounds?
4
14
Note: all items included in this presentation are for illustrative training purposes only. They are not representative of PARCC assessment items.
Evidence Statement Text, Clarifications, Limits,
Emphases and Other Information for 7.NS.2b-2
Evidence Statement
Text
Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
c. Interpret quotients of rational numbers by describing real-world
contexts.
Clarifications, Limits,
Emphases, and Other
Information
15
–
Question 4

16
If technology is involved in the task, is it
used effectively?
Appropriateness of Technology
• include the number of options and correct answers that are
appropriate for the grade level
• use a format that is sufficiently simple yet interesting and
engaging for students
• include directions that are clear and detailed
17
Sample #4
Task Type: I Points: 1
Evidence Statement: N-CN.2
As part of a mathematics homework assignment for practicing FOILing
with complex numbers, a student needs to simplify the expression
(3 + 4i)(5 + 2i). The homework assignment is due tomorrow at the
beginning of math class. What should the student write for the
simplified form of (3 + 4i)(5 + 2i) to receive full credit for the answer
to the mathematics homework assignment for practicing FOILing with
complex numbers?
Select the simplified expression.
7 + 26i
18
15 + 34i
15 + 8i
23 + 26i
Note: all items included in this presentation are for illustrative training purposes only. They are not representative of PARCC assessment items.
Evidence Statement Text, Clarifications,
Limits, Emphases and Other Information for
N-CN.2
Evidence Statement
Text
Clarifications, Limits,
Emphases, and Other
Information
19
Use the relation i2 = –1 and the commutative, associative, and
distributive properties to add, subtract, and multiply complex
numbers.
–
Question 5

20
For Type II and Type III tasks, is the scoring
guide/rubric clear, correct, and aligned with
the expectations for performance that are
expressed in the task?
Scoring Rubrics
Scoring Rubrics should:
• be clear enough so that the person scoring the response will
know how to assign points based on different parts of the
response
• assign more of the points to the explanation
(reasoning/modeling) provided in the response and less of the
points to a correct response
21
Sample #5 Task Type: II
Points: 4
Evidence Statement: 5.C.6/5.MD.5c
Rosa needs to calculate the volume of a right prism. This diagram shows the
dimensions of the prism. All angles in the base of the prism are right angles.
5 in.
4 in.
7 in.
7 in.
6 in.
12 in.
11 in.
Show how Rosa can calculate the volume of the right prism. Be sure to explain why
you chose the operations you use in your calculation, and include the volume of the
prism.
22
Note: all items included in this presentation are for illustrative training purposes only. They are not representative of PARCC assessment items.
Evidence Statement Text, Clarifications, Limits,
Emphases and Other Information for 5.C.6 and
5.MD.5c
Evidence Statement
Text
Content Scope: Knowledge and skills articulated in 5.MD.C
5.C.6
Clarifications, Limits,
Emphases, and
Other Information
Evidence Statement
Text
–
Relate the operations of multiplication and addition and solve real
world and mathematical problems involving volume.
c. Recognize volume as additive. Find volumes of solid figures
composed of two non-overlapping right rectangular prisms by
adding the volumes of the non-overlapping parts, applying this
technique to solve real world problems.
5.MD.5c
Clarifications, Limits,
Emphases, and
Other Information
23
Base explanations/reasoning on concrete referents such as diagrams
(whether provided in the prompt or constructed by the student in
her response).
i) Tasks require students to solve a contextual problem by applying
the indicated concepts and skills.
Scoring Rubric for Sample #5
Scoring Rubric
The task is worth 4 points; 1 point for computation and 3 points for reasoning.
Computation component: 582 cubic inches
Reasoning component:
1 point is awarded for a correct process in which the student shows or explains how to divide
the prism into two (or more) right rectangular prisms
1 point is awarded for showing or explaining the correct calculations for determining the
volume of each rectangular prism
1 point is awarded for showing or explaining that the volumes need to be added together to
determine the volume of the entire prism.
24
Questions?
```