Download Claim 2 - Virgil Middle School

Cognitive Rigor, Depth of Knowledge
and SBAC Math Claims
CLT Meeting
December 3, 2014
Cognitive Rigor and Depth of Knowledge
•
The level of complexity of the cognitive demand.
– Level 1: Recall and Reproduction
• Requires eliciting information such as a fact, definition, term,
or a simple procedure, as well as performing a simple algorithm
or applying a formula.
– Level 2: Basic Skills and Concepts
• Requires the engagement of some mental processing beyond
a recall of information.
– Level 3: Strategic Thinking and Reasoning
• Requires reasoning, planning, using evidence, and explanations
of thinking.
– Level 4: Extended Thinking
• Requires complex reasoning, planning, developing, and
thinking most likely over an extended period of time.
Level 1 Example
Grade 8
Select all of the expressions that have a value between 0 and 1.
87  8–12
74
7–3
1
2
3
(–5)6
(–5)10

1
3
9
Level 2 Example
Grade 8
A cylindrical tank has a height of 10 feet and
a radius of 4 feet. Jane fills this tank with water
at a rate of 8 cubic feet per minute. How many
minutes will it take Jane to completely fill the
tank without overflowing at this rate?
Round your answer to the nearest minute.
Level 3 Example
Grade 8
The total cost for an order of shirts from a company consists of the cost for
each shirt plus a one-time design fee. The cost for each shirt is the same
no matter how many shirts are ordered.
The company provides the following examples to customers to help them
estimate the total cost for an order of shirts.
• 50 shirts cost $349.50
• 500 shirts cost $2370
Part A: Using the examples provided, what is the cost for each shirt, not
including the one-time design fee? Explain how you found your answer.
Part B: What is the cost of the one-time design fee? Explain how you found
your answer.
Level 4 Example
Grade 8
During the task, the student assumes the role of an architect
who is responsible for designing the best plan for a park with
area and financial restraints. The student completes tasks in
which he/she compares the costs of different bids, determines
what facilities should be given priority in the park, and then
develops a scale drawing of the best design for the park and an
explanation of the choices made. This investigation is done in
class using a calculator, an applet to construct the scale drawing,
and a spreadsheet.
Cognitive Rigor Matrix
This matrix from the Smarter Balanced Content Specifications for Mathematics draws from both Bloom’s
(revised) Taxonomy of Educational Objectives and Webb’s Depth-of-Knowledge Levels below.
Mathematics Assessment Claims
•
•
•
•
Claim 1: Concepts and Procedures
– Students can explain and apply mathematical concepts and interpret
and carry out mathematical procedures with precision and fluency
Claim 2: Problem Solving
– Students can solve a range of complex well-posed problems in pure
and applied mathematics, making productive use of knowledge and
problem solving strategies
Claim 3: Communicating Reasoning
– Students can clearly and precisely construct viable arguments to
support their own reasoning and to critique the reasoning of others
Claim 4: Modeling and Data Analysis
– Students can analyze complex, real-world scenarios and can construct
and use mathematical models to interpret and solve problems
Claim 1
Concepts and Procedures
Students can explain and apply mathematical concepts
and interpret and carry out mathematical procedures with
precision and fluency.
Grade Level
Number of
Assessment Targets
3
11
4
12
5
11
6
10
7
9
8
10
11
16
Claim 1 Assessment Targets
Grade 6
Ratios and Proportional Relationships
A. Understand ratio concepts and use ratio reasoning to solve
problems.
The Number System
Apply and extend previous understandings of multiplication and
division to divide fractions by fractions.
C. Compute fluently with multi-digit numbers and find common
factors and multiples.
D. Apply and extend previous understandings of numbers to the
system of rational numbers.
B.
Claim 1 Assessment Targets
Grade 6
Expressions and Equations
E. Apply and extend previous understandings of arithmetic to
algebraic expressions.
F. Reason about and solve one-variable equations and
inequalities.
G. Represent and analyze quantitative relationships between
dependent and independent variables.
Geometry
H. Solve real-world and mathematical problems involving area,
surface area, and volume.
Statistics and Probability
I.
J.
Develop understanding of statistical variability.
Summarize and describe distributions.
Claim 1 Assessment Targets
Grade 7
Ratios and Proportional Relationships
A. Analyze proportional relationships and use them to solve real-
world and mathematical problems.
The Number System
B.
Apply and extend previous understandings of operations with
fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations
C. Use properties of operations to generate equivalent expressions.
D. Solve real-life and mathematical problems using numerical and
algebraic expressions and equations.
Claim 1 Assessment Targets
Grade 7
Geometry
Draw, construct and describe geometrical figures and describe the
relationships between them.
F. Solve real-life and mathematical problems involving angle
measure, area, surface area, and volume.
E.
Statistics and Probability
G. Use random sampling to draw inferences about a population.
H. Draw informal comparative inferences about two populations.
I. Investigate chance processes and develop, use, and evaluate
probability models.
Claim 1 Assessment Targets
Grade 8
The Number System
A. Know that there are numbers that are not rational, and
approximate them by rational numbers.
Expressions and Equations
Work with radicals and integer exponents.
Understand the connections between proportional relationships,
lines, and linear equations.
D. Analyze and solve linear equations and pairs of simultaneous linear
equations.
B.
C.
Functions
E.
F.
Define, evaluate, and compare functions.
Use functions to model relationships between quantities.
Claim 1 Assessment Targets
Grade 8
Geometry
G. Understand congruence and similarity using physical models,
transparencies, or geometry software.
H. Understand and apply the Pythagorean theorem.
I. Solve real-world and mathematical problems involving volume of
cylinders, cones and spheres.
Statistics and Probability
J.
Investigate patterns of association in bivariate data.
Claims 2, 3, and 4
•
•
Assessment Targets for Claims
2, 3, and 4 are not divided into a
grade-by-grade description.
A general set of assessment targets
applicable across grade levels.
Assessment Targets
Claim 2 – Problem Solving
Claim 2: Students can solve a range of complex well-posed problems in
pure and applied mathematics, making productive use of knowledge
and problem solving strategies.
A. Apply mathematics to solve well-posed problems arising in
everyday life, society, and the workplace
B. Select and use tools strategically
C. Interpret results in the context of the situation
D. Identify important quantities in a practical situation and
map their relationships.
Assessment Targets
Claim 3 – Communicating Reason
Claim 3: Students can clearly and precisely construct viable
arguments to support their own reasoning and to critique the
reasoning of others.
A.
B.
C.
D.
E.
F.
G.
Test propositions or conjectures with specific examples.
Construct, autonomously, chains of reasoning that justify or refute
propositions or conjectures.
State logical assumptions being used.
Use the technique of breaking an argument into cases.
Distinguish correct logic or reasoning from that which is flawed,
and—if there is a flaw in the argument—explain what it is.
Base arguments on concrete referents such as objects, drawings,
diagrams, and actions.
Determine conditions under which an argument does and
does not apply.
Assessment Targets
Claim 4 – Modeling and Data Analysis
Claim 4: Students can analyze complex, real-world scenarios and
can construct and use mathematical models to interpret and
solve problems.
A.
B.
C.
D.
E.
F.
G.
Apply mathematics to solve problems arising in everyday life, society,
and the workplace.
Construct, autonomously, chains of reasoning to justify mathematical
models used, interpretations made, and solutions proposed for a
complex problem.
State logical assumptions being used.
Interpret results in the context of a situation.
Analyze the adequacy of and make improvement to an existing model
or develop a mathematical model of a real phenomenon.
Identify important quantities in a practical situation and map their
relationships.
Identify, analyze, and synthesize relevant external resources to pose
or solve problems.