Aligning Performance Tasks with the Common Core, Part 2 – Expert Alignment
Carol’s Numbers – Grade 2
CCLS Aligned Content/Practices Standards
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MP.1 Make sense of problems and persevere in solving them.
2.NBT.1 Understand that the three digits of a three-digit number represent
amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens,
and 6 ones. Understand the following as special cases:
a)100 can be thought of as a bundle of ten tens — called a “hundred.”
b)The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two,
three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number
names, and expanded form.
2.NBT.4 Compare two three-digit numbers based on meanings of the
hundreds, tens, and ones digits, using >, =, and < symbols to record the
results of comparisons.
2.MD.6 Represent whole numbers as lengths from 0 on a number line
diagram with equally spaced points corresponding to the numbers 0, 1, 2, ...,
and represent whole-number sums and differences within 100 on a number
line diagram.
For this task 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 estimate and
judge reasonableness o solutions, especially for part 3.*
NA
3
NA
2
NA
3
Students are required to explain their thinking and justify their
solution. There is no requirement to critique the reasoning of
others.
This task requires that students communicate precisely as they
explain/justify their solution.
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3
For parts 1 and 2 the student must understand the value of a 3digit number and compare the three possible numbers. The special
cases are not specifically addressed but would not be required to
be for every task aligning to this standard stem.
3
2
3
2
MP.3 Construct viable arguments and critique the reasoning of others.
MP.6 Attend to precision.
Alignment Comments
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2
1
Students must read and write the 3-digit answers for parts 1 and 2
and the 2-digit numbers for part 3. They do not need to use
expanded form for this task.
Comparison of the three possible 3-digit numbers is necessary for
parts 1 and 2. However the use of comparative symbols is not
required.
Part 3 requires that students place 2-digit numbers on a number
line, estimating the distances from zero. Sums and differences are
not required for this task.
Cell Phone Plans – Grade 8
CCLS Aligned Content/Practices Standards
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Alignment Comments
3
For this task 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 check the reasonableness of their
solution, continually asking themselves, “Does this make sense?”
MP.1 Make sense of problems and persevere in solving them.
NA
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of
others.
NA
3
NA
2
NA
3
NA
3
3
2
This task involves quantitative relationships. It requires that students make
sense of quantities and their relationships in the problem situation. They
must attend to the meaning of the quantities and pay attention to units as
they represent the quantities and measures in a table and then translate to a
statistical report.
This task requires that students explain their thinking and justify their
response. A critique of the thinking of others MIGHT have been required but
is not clearly stated in the prompt.
This task is an application from everyday life requiring that the student
create a mathematical representation (model) that can replace the situation
described in the prompt. They must identify important quantities in the
practical situation and analyze their relationships using equations that
represent the situations.
This task requires that students communicate precisely, organizing their
information, as they show their mathematical thinking.
MP.4 Model with mathematics.
MP.6 Attend to precision.
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
8.EE.8a Understand that solutions to a system of two linear
equations in two variables correspond to points of intersection
of their graphs, because points of intersection satisfy both
equations simultaneously.
8.EE.8c Solve real-world and mathematical problems leading to
two linear equations in two variables. For example, given
coordinates for two pairs of points, determine whether the line
through the first pair of points intersects the line through the
second pair.
2
3
3
3
In this task students must analyze a pair of linear equations but are not asked
to solve the system directly. They must, however, explain how they know the
solution exits.
Part c of this task asks students to explain how they know the intersection
exists. This explanation will be based on the conceptual knowledge of the
connection between the inputs/outputs of a pair of equations and possibly
their graphs. Students may not, however, use a graphic explanation for part
c.
This task is in context and asks questions related to the two equations, each
representing the individual plan.
2
CCLS Aligned Content/Practices Standards
8.EE.7 Solve linear equations in one variable.
8.EE.7b Solve linear equations with rational number
coefficients, including equations whose solutions require
expanding expressions using the distributive property and
collecting like terms.
8.F.1 Understand that a function is a rule that assigns to each
input exactly one output. The graph of a function is the set of
ordered pairs consisting of an input and the corresponding
output.
8.F.4 Construct a function to model a linear relationship
between two quantities. Determine the rate of change and
initial value of the function from a description of a relationship
or from two (x, y) values, including reading these from a table or
from a graph. Interpret the rate of change and initial value of a
linear function in terms of the situation it models, and in terms
of its graph or a table of values.
Alignment Comments
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3
3
Equations become single-variable linear equations when a value is
substituted in parts a and b.
3
In part b of the task students must first solve for the number of texts in
Jumel's plan then solve for the cost in Ashley's plan. Both are 2-variable
equations until the known values are substituted. Then they become singlevariable linear equations that must be solved.
2
2
3
2
3
An understanding of the input-output rule is required for the evaluation of a
function at a given number of texts or a given cost (parts a and b). Graphing
is a conceptual base of this task even though students are not asked to
create a graph. This statment is one of fact that requires only an
understanding of the creation of a function.
In part a the student must translate Ashley's plan from a verbal description to
an equation in order to compare with Jumel's plan.
3
Aussie Fir Tree - HS
CCSS Aligned Content/Practices Standards
MP.1 Make sense of problems and persevere in solving them.
MP. 3 Construct viable arguments and critique the reasoning of others.
MP. 4 Model* with mathematics.
MP. 6 Attend to precision.
MP. 7 Look for and make use of structure.
F.BF.1 Write a function that describes a relationship between two
quantities.★
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NA
3
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3
NA
3
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3
NA
3
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3
Alignment Comments.
Finding the equation requires some perseverance on the student’s part.
Descriptions, explanations, and demonstrations are required in parts 1 to 3
and 5.
The equation (function) found in part 4 is a mathematical model that
generates the pattern.
Precise terms and notation are required when presenting a mathematical
explanation.
Finding and using patterns is a key component of this task.
The equation required in part 4 is the function that models the design.
F.BF.1a Determine an explicit expression, a recursive process, or steps for
calculation from a context. ★
3
3
Determination of the recursive and explicit processes are required in parts 1
to 3, and 4.
F.IF.3 Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
3
3
This CCSS connects the sequence to the equation that must be created from
the patterning used in the task.
A.CED.1 Create equations in one variable and use them to solve problem.
Include equations arising from linear and quadratic functions.
A.REI.4 Solve quadratic equations in one variable.
A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49),
taking square roots, completing the square, the quadratic formula and
factoring, as appropriate to the initial form of the equation. Recognize
when the quadratic formula gives complex solutions and write them as a
± bi for real numbers a and b.
The equation is created in part 4.
3
3
3
3
In part 5 the explanation requires finding a solution (or not finding one) for
the equation found in part 4.
2
In part 5 the quadratic equation found in part 4 must be solved. Students
may use any method and may even stop short of solving if, by inspection,
they are able to determine that the solutions are irrational.
3
4