Aligning Performance Tasks
with the CCSS for Mathematics
and the Illinois Design / PreConstruction Expectations
August 3, 2011
Springfield, Illinois
Introduction
In this presentation we will:
Provide an overview of an approach that Achieve has developed with a
large urban school district to integrate the CCSS with classroom instruction.
Introduce a process for determining alignment of a performance task with
the Common Core State Standards (CCSS) and the Illinois Design/PreConstruction expectations.
Walk through a performance task to learn how to use this approach.
Break into small groups to review/modify tasks supplied by workshop
participants.
Review and offer feedback on the tasks being modified/developed by other
small groups.
Discuss the implications of this approach and brainstorm ideas about how
you might use and adapt these tools in your district and schools.
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Components of a High-Quality
Instructional Task
A High Quality Instructional Task Should:
Be based on, and aligned to, standards (in our case, the CCSS for Mathematics
and the Knowledge and Skill statements that apply to the Design/PreConstruction pathway)
Reflect strong instructional practices
Prepare students for college and careers
Assess student knowledge and skill across the full performance continuum
Support a culture of continuous improvement that can guide good instruction
Elicit complex student demonstrations or applications
Assess all students, including high and low achieving students and ELL
students and students with disabilities
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Steps for Aligning Mathematics Tasks to the
CCSS and the Illinois Design/Pre-Construction
Expectations
Step 1. Work the task thoroughly.
Step 2. Compare your work with the answer key/rubric and other
instructional support materials and/or with the work of colleagues.
Step 3. Identify the content and performances required to complete the
task.
Step 4. Compare task performances to the CCSS Standards for
Mathematical Practice
a)
identify and list on the purple recording sheet those Mathematical Practices
reflected in the task
b)
rate the degree of alignment using the 0-3 rating scale provided
c)
make note of important points concerning alignment between the task and each
standard, as appropriate.
d)
make note of strengths and weaknesses of the task with respect to each
standard and ways the alignment of the task to the standards might be
improved, as appropriate.
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Steps for Aligning Mathematics Tasks to the
CCSS and the Illinois Design/Pre-Construction
Expectations
Step 5. Compare task content and performances to the grade-level
(grades 6-8) and high school CCSS
a)
identify and list on the blue recording sheet those CCSS standards
reflected in the task
b)
rate the degree of alignment using the 0-3 rating scale provided
c)
make note of important points concerning alignment between the task
and each standard, as appropriate
d)
make note of strengths and weaknesses of the task with respect to
each standard and ways the alignment of the task to the standards
might be improved, as appropriate.
5
Steps for Aligning Mathematics Tasks to the
CCSS and the Illinois Design/Pre-Construction
Expectations
Step 6. Compare task content and performances to the Knowledge and
Skills statements that apply to the Design/Pre-Construction pathway
a)
identify and list on the orange recording sheet those Knowledge and
Skill statements reflected in the task. Pay particular attention to the
Cluster and Pathway Knowledge and Skill statements, since they
provide the greatest level of specificity and detail.
b)
rate the degree of alignment using the 0-3 rating scale provided
c)
make note of important points concerning alignment between the task
and each Knowledge and Skill statement, as appropriate
d)
make note of strengths and weaknesses of the task with respect to
each Knowledge and Skill statement and ways the alignment of the
task to the statements might be improved, as appropriate.
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What Does This Alignment Process Tell Us?
What Are the Next Steps?
Is the task, as written, of high quality and well-aligned with the CCSS Standards
for Mathematical Practice, CCSS grade-level/high school standards, and the
Design/Pre-Construction cluster/pathway Knowledge and Skill statements?

If so, it is “ready to go.”
Are there ways that the task can be improved to enhance alignment with the
relevant standards and better meet the needs of teachers and the range of
students they encounter in their classrooms?

If so, the task “needs improvement.”
Is the task so poorly aligned with the CCSS and the cluster/pathway Knowledge
and Skill statements that it is not really usable?

If so, discard the task.
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Common Practice Task 1: Building Construction
Step 1: Work task
Step 2: Compare solutions
Step 3: Identify content and
performances
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Common Practice Task 1: Building
Construction
Task
The Smiths are working with an architect and
contractor to finalize their building plans with
the dimensions in Figure 4.
1. The building plan calls for a slate roof. The Smith’s request
an estimate for shingles. To give an estimate the
contractor must calculate the area of the roof. What is the
roof’s area?
2. The architect suggests painting the siding to get the color
preferred by the Smith’s. She asks the contractor for an
estimate of the cost to paint the house. The area to be
painted includes the two triangular gable ends. (One of
the gables is visible in Figure 4.) The paint covers about
350 square feet per gallon. How many gallons of paint
should be included in the estimate if the building will get
two coats?
3. If 10% of the building’s four rectangular walls are windows
that do not need painting, does the amount of paint
needed by the painter decrease?
Source: Adapted from ResourceMap, used with permission
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Common Practice Task 1: Building
Construction Solution
Source: Adapted from ResourceMap, used with permission
10
Common Practice Task 1: Building Construction
Step 4: Compare task performances to
the CCSS Standards for Mathematical
Practice
Which of the Standards for Mathematical
Practice align with the requirements of
the task?
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Common Practice Task 1: Building Construction
Mathematical Practices aligned
with the task:
MP.1 Make sense of problems and persevere in solving them
MP.2 Reason abstractly and quantitatively
MP.4 Model with mathematics
MP.6 Attend to precision
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Rating Scale for Performance
3 = Excellent: The performances of the task are clearly consistent with the
performances of the identified standard.
2 = Good: This rating is used for a partial match. Performances addressed in the
task are consistent with the most critical performances of the identified standard.
However, supporting performances of the standard may not be addressed (possibly
by design).
1 = Weak: This rating is used for a partial match when the most critical
performances addressed in the identified standard are NOT addressed in the task.
However, supporting performances of the standard are addressed.
0 = No Alignment: None of the performances addressed in the task match the
performances of the identified standard. (Delete this standard from the list of
standards identified as aligned with the task.)
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Ratings and Alignment Comments for
Performance: Building Construction
Math Practice
MP.1 Make sense of
problems and persevere
in solving them
MP.2 Reason abstractly
and quantitatively
MP.4 Model with
mathematics
Performance
Rating
Alignment Comments
3
Students analyze givens, constraints, relationships, and goals.
They must make conjectures about the form and meaning of the
solution and plan a solution pathway. They must make sure their
answers make sense in the context of the problem.
3
Students make sense of quantities and their relationships in
problems situations. They must create a coherent representation
of the problem at hand, considering units and attending to the
meaning of quantities.
3
Students apply the mathematics they know to solve a workplace
problem. They use measurement and geometric knowledge and
skills to solve a pre-construction problem. They interpret results
in the context of the problem.
3
Students need to calculate accurately and express answers with a
degree of precision appropriate for the problem.
MP.6 Attend to precision
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Common Practice Task 1: Building Construction
How might this task be rewritten to align even more strongly with
the Standards for Mathematical Practice?
Students might be presented with dimensions of the house, rather than an
image, and asked to sketch a model of the house.
Students might be asked to justify or explain their answer to the third part of
the question.
Students might be asked to prepare a presentation for the client, presenting
various cost options based on such things as variations in roofing materials,
quality of paint, and different design features desired by the client.
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Common Practice Task 1: Building Construction
Step 5: Compare task content and
performances to the grade-level (grades
6-8) and high school CCSS
Which of the grade-level and/or high
school CCSS align with the requirements
of the task?
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Common Practice Task 1: Building Construction
Grade Level / High School Standards aligned with the task:
G.MG.1 Use geometric shapes, their measures, and their properties to describe
objects
7.G.6 Solve real-world and mathematical problems involving area, volume and
surface area of two- and three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes, and right prisms.
N.Q.1 Use units as a way to understand problems and to guide the solution of
multi-step problems; choose and interpret unites consistently in formulas;
choose and interpret the scale and the origin in graphs and data displays.
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Rating Scale for Content
3 = Excellent: The content of the task is clearly consistent with the content of the
identified standard.
2 = Good: This rating is used for a partial match. Content addressed in the task is
consistent with the most critical content of the identified standard. However,
supporting content of the standard may not be addressed (possibly by design).
1 = Weak: This rating is used for a partial match when the most critical content
addressed in the identified standard is NOT addressed in the task. However,
supporting content of the standard is addressed.
0 = No Alignment: None of the content addressed in the task matches the content
of the identified standard. (Delete this standard from the list of standards identified as
aligned with the task.)
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Ratings and Alignment Comments for Content
and Performance: Building Construction
CCSS
C
G.MG.1: Use geometric shapes, their
measures, and their properties to
3
describe objects.
7.G.6 Solve real-world and mathematical
problems involving area, volume and
surface area of two- and three2
dimensional objects composed of
triangles, quadrilaterals, polygons, cubes,
and right prisms.
N.Q.1: Use units as a way to understand
problems and to guide the solution of
multi-step problems; choose and
2
interpret units consistently in formulas;
choose and interpret the scale and the
origin in graphs and data displays.
P
Alignment Comments
While area is one way to describe an object, the
2 simple calculation of area is likely not as robust a
description as intended by this standard.
This task does not call for the determination of
3 volume and deals with simple geometric shapes
including triangles and rectangles.
While this problem involves the use of units (feet,
square feet, gallons), it does not require students to
make any choices about units. Choosing and
2 interpreting the scale and origin in graphs and data
displays is not addressed.
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Common Practice Task 1: Building Construction
How might this task be rewritten to align even more strongly with
the CCSS?
The exterior design of the building might be made more complex, perhaps
involving the use of multiple types of building materials configured in ways
that capitalize on more types of geometric shapes—making area and
surface area calculations more robust.
Students might be asked to assume the role of an architect and use
geometric shapes and their measures to describe options for the design of
a building to a client.
This task could be made more robust and realistic if students were
presented with measurements that required some unit conversion (e.g., if
some of the measurements were in feet and inches, students would need
to choose which unit to use and how to interpret subsequent solutions).
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Common Practice Task 1: Building Construction
Step 6: Compare task content and
performances to the cluster/pathway
Knowledge and Skill statements
Which of the cluster/pathway Knowledge
and Skill statements align with the
requirements of the task?
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Common Practice Task 1: Building Construction
CTE cluster/pathway Knowledge and Skill statements aligned with
the task:
ACC01.01.02 Use geometric figures to determine areas and volumes of various
structures.
ACC01.01.05 Use appropriate formulas to determine measurements of
dimensions, spaces and situations.
ACC01.01.06 Conceptualize a three-dimensional form from a two-dimensional
drawing to visualize proposed work.
ACC03.01.03 Estimate resources/materials required for a specific project or
problem.
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Ratings and Alignment Comments for Content
and Performance: Building Construction
Cluster/Pathway Knowledge and Skill
Statement
ACC01.01.02: Use geometric figures to
determine areas and volumes of various
structures.
ACC01.01.05 Use appropriate formulas
to determine measurements of
dimensions, spaces and situations.
ACC01.01.06: Conceptualize a threedimensional form from a twodimensional drawing to visualize
proposed work.
ACC03.01.03: Estimate
resources/materials required for a
specific problem.
C
P
Alignment Comments
2
3
This task requires area calculations but not
volume calculations.
3
3
3
3
3
3
It is assumed that students are using the
formulas for area of a rectangle and area
of a triangle to perform the calculations.
While conceptualization and visualization
may be hard to assess, they are required
skills in this task since students need to
make sense of the two-dimensional model
in order to perform the appropriate
calculations.
Estimation of the amount of paint needed
is addressed in Questions 2 and 3 of this
task.
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Aligning Performance Tasks
with the CCSS for Mathematics
and the Illinois Design / PreConstruction Expectations
August 3, 2011
Springfield, Illinois