Cluster Summary for: Apply and extend previous
understandings of arithmetic to algebraic expressions
Grade Level: 6
Domain: Expressions and Equations
Cluster Priority: (check) _x_ Major Cluster
__ Supporting Cluster __ Additional Cluster
SCALE
TRIMESTER 1
TRIMESTER 2
TRIMESTER 3
4: Advanced
In addition to score 3, in-depth inferences and applications go beyond Mathematics, are applied to other disciplines, and are utilized in real-world contexts.
3: Proficient
Write and evaluate numerical
Write and evaluate numerical expressions involving
Write and evaluate numerical expressions involving whole
The student exhibits
expressions involving whole number
whole number exponents.
number exponents.
no major errors or
exponents.
Write, read, and evaluate expressions in which letters
Write, read, and evaluate expressions in which letters
omissions.
Write, read, and evaluate expressions stand for numbers.
stand for numbers.
in which letters stand for numbers.
Identify parts of an expression using mathematical
Identify parts of an expression using mathematical terms
Identify parts of an expression using
terms (sum, term, product, etc.)
(sum, term, product, etc.)
mathematical terms (sum, term,
Evaluate expressions at specific values of their variables Evaluate expressions at specific values of their variables in
product, etc.)
in real-world problems using order of operations.
real-world problems using order of operations.
Evaluate expressions at specific values Apply the properties of operations to generate
Apply the properties of operations to generate equivalent
of their variables in real-world
equivalent expressions and identify when two
expressions and identify when two expressions are
problems using order of operations.
expressions are equivalent.
equivalent.
Proficiency Example
Solve 72 – 24 ÷ 3 + 26
3(2 + x) = 6 + 3x
Evaluate 7xy when x = 2.5 and y = 9
A=LxW
24x + 18y = 6(4x + 3y)
W = 5 ft L = 7 ft
A = 7 ft x 5 ft = 35 ft2
Prove that y + y + y = 3y
4x = 64 Solve for x
Evaluate 5(n + 3) – 7n, when n = 4
What is the area of a square with a side length of 3x?
It costs $100 to rent the skating rink plus $5 per person.
Write an expression to find the cost for any number (n) of
people. What is the cost for 25 people?
Are the expression equivalent? Explain your answer.
4m + 8
4(m+2)
3m + 8 + m
2 + 2m + m + 6 + m
2: Partially Proficient
There are no major errors or omissions regarding the simpler details and processes as the student recognizes or recalls terminology and performs basic processes.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
1: Novice
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0: No Evidence
Even with help, no understanding or skill demonstrated.
Mathematical Practices Best Taught in this Cluster: (check those that apply)
__ Make sense of problems & preserve in solving them __ Reason abstractly & quantitatively __ Construct viable arguments & critique the reasoning of others
__Model with mathematics __Use appropriate tools strategically __Attend to precision __Look for and make use of structure __Look for & express regularity in repeated reasoning
Key Vocabulary for the Cluster:
Evaluate (solve), sum, term, product, factor, quotient, coefficient, distributive property, equivalent, numerical expressions, algebraic expressions, base, exponents, order of operations,
quantity, constant, like terms, equivalent expressions, variables