Major Cluster Standards

Apply and extend previous
understandings of arithmetic to algebraic expressions.^{2}

6.EE.A.1

Write and evaluate numeric expressions involving
wholenumber exponents.

6.EE.A.2

Write, read, and evaluate
expressions in which letters stand for numbers.
a.
Write
expressions that record operations with numbers and with letters standing
for numbers. For example, express the
calculation “Subtract 𝑦
from 5” as 5 − 𝑦.
b.
Identify
parts of an expression using mathematical terms (sum, term, product,
factor, quotient, coefficient); view one or more parts of an expression as
a single entity. For example,
describe the expression 2(8 + 7) as a product of two factors; view (8 + 7)
as both a single entity and a sum of two terms.
c. Evaluate expressions at specific
values of their variables. Include expressions that arise from formulas
used in realworld problems. Perform arithmetic operations, including those
involving wholenumber exponents, in the conventional order when there are
no parentheses to specify a particular order (Order of Operations). For example, use the formulas 𝑉=𝑠^{3}
and 𝐴𝐴=6𝑠^{2}
to find the volume and surface area of a cube with sides of length .

6.EE.A.3

Apply the properties of
operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+𝑥)
to produce the equivalent expression 6+3𝑥; apply the distributive
property to the expression 24𝑥+18𝑦
to produce the equivalent expression 6(4𝑥+3𝑦);
apply properties of operations to 𝑦+𝑦+𝑦 to produce the equivalent
expression 3𝑦.

6.EE.A.4

Identify when two
expressions are equivalent (when the two expressions name the same number
regardless of which value is substituted into them). For example, the
expressions 𝑦+𝑦+𝑦 and 3𝑦 are equivalent
because they name the same number regardless of which number 𝑦 stands for.

Reason about and solve onevariable equations and
inequalities.^{3}

6.EE.B.5

Understand solving
an equation or inequality as a process of answering a question; which values
from a specified set, if any, make the equation or inequality true? Use
substitution to determine whether a given number in a specified set makes
an equation or inequality true.

6.EE.B.6

Use variables to
represent numbers and write expressions when solving a realworld or
mathematical problem; understand that a variable can represent an unknown
number, or, depending on the purpose at hand, any number in a specified
set.

6.EE.B.7

Solve realworld
and mathematical problems by writing and solving equations in the form 𝑥+𝑝=𝑞 and px=𝑞 for cases in which
𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers.

6.EE.B.8

Write an
inequality of the form 𝑥>𝑐 or 𝑥<𝑐 to represent a constraint or condition in a realworld
mathematical problem. Recognize that inequalities of the form 𝑥>𝑐 or 𝑥<𝑐 have infinitely
many solutions; represent solutions of such inequalities on number line
diagrams.

Represent
and analyze quantitative relationships between dependent and independent
variables.

6.EE.C.9

Use variables to
represent two quantities in a realworld problem that change in
relationship to one another; write an equation to express one quantity,
thought of as the dependent variable, in terms of the other quantity,
thought of as the independent variable. Analyze the relationship between
the dependent and independent variables using graphs and tables, and relate
these to the equation. For example, in a problem involving motion at
constant speed, list and graph ordered pairs of distances and times, and
write the equation 𝑑=65𝑡 to represent the relationship between distance and time.

Foundational Standards

Understand
and apply properties of operations and the relationship between addition
and subtraction.

1.OA.B.3

Apply properties
of operations as strategies to add and subtract.^{4} Examples:
If 8+3=11 is known, then 3+8=11 is also known. (Commutative property of addition.) To add 2+6+4, the second two numbers can be added to make a ten, so 2+6+4=2+10=12. (Associative property of addition.)

Understand properties of multiplication
and the relationship between multiplication and division.

3.OA.B.5

Apply properties of operations as strategies to multiply and
divide. Examples: If 6×4=24 is known, then 4×6=24 is also known. (Commutative property of multiplication.) 3×5×2 can be found by 3×5=15, then 15×2=30, or by 5×2=10, then 3×10=30.(Associative property of multiplication.) Knowing that 8×5=40 and 8×2=16, one can find 8×7 as 8×(5+2)=(8×5)+(8×2)=40+16=56
(Distributive
property.)

Gain familiarity
with factors and multiples.

4.OA.B.4

Find
all factors for a whole number in the range 1–100. Recognize that a whole
number is a multiple of each of its factors. Determine whether a given
whole number in the range 1–100 is a multiple of a given onedigit number.
Determine whether a given whole number in the range 1–100 is prime or
composite.

Geometric measurement:
understand concepts of angle and measure angles.

4.MD.C.5

Recognize
angles as geometric shapes that are formed wherever two rays share a common
endpoint, and understand concepts of angle measurement:
a. An angle is measured with
reference to a circle with its center at the common endpoint of the rays,
by considering the fraction of the circular arc between the points where
the two rays intersect the circle. An angle that turns through of a circle is called a “onedegree
angle,” and can be used to measure angles.
b. An angle that turns through 𝑛 onedegree angles is said to
have an angle measure of 𝑛
degrees.

4.MD.C.6

Measure angles in wholenumber degrees using a protractor.
Sketch angles of specified measure.

4.MD.C.7

Recognize angle measure as additive. When an angle is
decomposed into nonoverlapping parts, the angle measure of the whole is
the sum of the angle measures of the parts. Solve addition and subtraction
problems to find unknown angles on a diagram in real world and mathematical
problems, e.g., by using an equation with a symbol for the unknown angle
measure.

Write and interpret numerical expressions.

5.OA.A.2

Write simple expressions that record calculations with
numbers, and interpret numerical expressions without evaluating them. For
example, express the calculation “add 8
and
7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as
large as 18932 + 921, without having
to calculate the indicated sum or product.

Analyze patterns and
relationships.

5.OA.B.3

Generate two numerical patterns using two given rules.
Identify apparent relationships between corresponding terms. Form ordered
pairs consisting of corresponding terms from the two patterns, and graph
the ordered pairs on a coordinate plane. For example, given the rule
“Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe
that the terms in one sequence are twice the corresponding terms in the
other sequence. Explain informally why this is so.

Understand the place value
system.

5.NBT.A.2

Explain
patterns in the number of zeros of the product when multiplying a number by
powers of 10, and explain patterns in the placement of the decimal point
when a decimal is multiplied or divided by a power of 10. Use wholenumber
exponents to denote powers of 10.

Graph points on the coordinate
plane to solve realworld and mathematical problems.

5.G.A.1

Use a pair of perpendicular number lines, called axes, to
define a coordinate system, with the intersection of the lines (the origin)
arranged to coincide with the 0 on each line and a
given point in the plane located by using an ordered pair of numbers,
called its coordinates. Understand that the first number indicates how far
to travel from the origin in the direction of one axis, and the second
number indicates how far to travel in the direction of the second axis,
with the convention that the names of the two axes and the coordinates
correspond (e.g., 𝑥axis and 𝑥coordinate, 𝑦axis and 𝑦coordinate).

5.G.A.2

Represent
real world and mathematical problems by graphing points in the first
quadrant of the coordinate plane, and interpret coordinate values of points
in the context of the situation.

Understand ratio concepts and
use ratio reasoning to solve problems.

6.RP.A.3

Use
ratio and rate reasoning to solve realworld and mathematical problems,
e.g., by reasoning about tables of equivalent ratios, tape diagrams, double
number line diagrams, or equations.
a. Make tables of equivalent ratios
relating quantities with wholenumber measurements, find missing values in
the tables, and plot the pairs of values on the coordinate plane. Use
tables to compare ratios.
b. Solve unit rate problems
including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4
lawns, then at that rate, how many lawns could be mowed in 35 hours? At
what rate were lawns being mowed?

Compute fluently with
multidigit numbers and find common factors and multiples.

6.NS.B.4

Find the greatest common factor of two whole numbers less
than or equal to 100 and the least
common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole
numbers 1–100 with a common
factor as a multiple of a sum of two whole numbers with no common factor. For
example, express 36 + 8 as 4 (9+2).

Standards for
Mathematical Practices

1.
Make sense of problems and persevere
in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and
critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8. Look
for and express regularity in repeated reasoning.

Instructional Outcomes
·
6.EE.A.1:
o I can write numerical expressions involving whole number exponents.
o I can evaluate numerical expressions involving whole number exponents.
o I can evaluate expressions using the order of operations.
·
6.EE.A.2:
·
6.EE.A.2a
o I can evaluate expressions with variables.
o I can evaluate expressions using specific values for variables.
o I can translate written phrases into algebraic expressions.
o I can translate algebraic expressions into written phrases.
·
6.EE.A.2b
o I can identify parts of an expression using mathematical terms (sum,
term, product, factor, quotient, coefficient).
o I can understand that parts of an expression can have more than one
name.
·
6.EE.A.2c
o I can substitute specific values for variables.
o I can write real world and mathematical problems.
·
6.EE.A.3
o I can create equivalent expressions using the properties of operations
(e.g. distributive property, associative property, adding like terms with
the addition property or equality, etc.).
o I can apply the properties of operations to create equivalent
expressions.
·
6.EE.A.4
o I can recognize when two expressions are equivalent.
o I can prove (using various strategies) that two expressions are
equivalent no matter what number is substituted.
·
6.EE.B.5
o I can determine which values make an equation or inequality true.
o I can use the solution to an equation or inequality to prove that the
answer is correct.
o I can use substitution to decide if a number makes an equation or
inequality true.
·
6.EE.B.6
o
I can recognize that a variable
can represent one number, or, a set of numbers.
o
I can use variables to
represent numbers.
o
I can write expressions when solving
a realworld or mathematical problem.
·
6.EE.B.7
o
I can define an inverse
operation.
o
I can use inverse operations to
solve equations.
o
I can apply rules of the form x
+ p = q and px = q, for cases in which p, q and x are all positive rational
numbers, to solve real world and mathematical problems. (There is only one
unknown quantity).
o
I can solve real world and
mathematical problems by writing and solving equations.
·
6.EE.B.8
o
I can identify the constraint
or condition in a realworld or mathematical problem in order to set up an
inequality.
o
I can recognize that
inequalities of the form x>c or x<c have an infinite number of
solutions.
o
I can write an inequality of
the form x>c or x<c to represent a set of solutions for a realworld
or mathematical problem.
o
I can graph solutions to
inequalities on a number line.
·
6.EE.C.9
o
I can define independent and
dependent variables .
o
I can use variables to
represent two quantities in a realworld problem that change in
relationship to one another.
o
I can write an equation to
express one quantity (dependent) in terms of the other quantity
(independent).
o
I can analyze how dependent and
independent variables change in tables and graphs.
o I can understand that a graph, table and an equation can
all represent the same real world problem.
