Sharp Math
Expressions and Equations
Standard
6th
7th
8th
M-EE-1
Standard
Standard
Standard
Write and evaluate numerical
Apply properties of operations
Know and apply the properties
expressions involving whole-
as strategies to add, subtract,
of integer exponents to
number exponents.
factor, and expand linear
generate equivalent numerical
expressions with rational
expressions. For example,
coefficients.
32 × 3–5 = 3–3 = 1/33 = 1/27.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
I can write numerical
I can combine like terms with
I can explain the properties of
expressions involving
rational coefficients.(K)
integer exponents to generate
1.
whole number
2.
exponents. Ex. 53 =
I can factor and expand linear
5x5x5 (K)
expressions with rational
I can evaluate
coefficients using the
numerical expressions
distributive property. (K)
involving whole
3.
number exponents. (K)
I can apply properties of
I can solve order of
operations as strategies to add,
operation problems that
subtract, factor, and expand
contain exponents. (K)
linear expressions with
equivalent numerical
expression. (K)
I can apply properties of
integer exponents to produce
equivalent numerical
expressions. (K)
rational coefficients.(R)
M-EE-2
o
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Write, read, and evaluate
Understand that rewriting an
Use square root and cube root
expressions in which letters
expression in different forms
symbols to represent solutions
stand for numbers.
in a problem context can shed
Write
expressions that record
operations with numbers and
with letters standing for
numbers. For example, express
light on the problem and how
the quantities in it are related.
For example, a + 0.05a = 1.05a
means that “increase by 5%” is
the same as “multiply by 1.05.”
to equations of the form x2 = p
and x3 = p, where p is a positive
rational number. Evaluate
square roots of small perfect
squares and cube roots of small
perfect cubes. Know that √2 is
irrational.
the calculation “Subtract y from
5” as 5 – y.
Identify parts of
o
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.
Evaluate
o
expressions at specific values of
their variables. Include
expressions that arise from
formulas used in real-world
problems. Perform arithmetic
operations, including those
involving whole-number
exponents, in the conventional
order when there are no
parentheses to specify a
particular order (Order of
Operations). For example, use the
formulas V = s3 and A = 6 s2 to
find the volume and surface area
of a cube with sides of length s =
1/2.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
A.
I can write equivalent
I can use square root and cube
1. I can use numbers and
expressions with fractions,
root symbols to represent
decimals, percents, and
solutions. (K)
variables to represent desired
operations. (K)
2. I can translate written phrases
into algebraic expressions.(K)
3. I can translate algebraic
integers. (K)
I can rewrite an expression in
I can evaluate square roots of
small perfect squares. (K)
expressions into written
an equivalent form in order to
I can evaluate cube roots of
phrases.(K)
provide insight about how
small perfect cubes. (K)
B.
4. I can identify parts of an
expression using mathematical
quantities are related in a
problem context. (R)
terms. (sum, term, product,
I can explain that the square
root of 2 is irrational. (K)
factor, quotient, coefficient) (K)
5. I can identify parts of an
expression as a single entity, even
if not a monomial. (K)
C.
6. I can substitute specific values
for variables. (K)
7. I can evaluate algebraic
expressions including those that
arise from real-world problems.
(K)
8. I can apply order of
operations when there are no
parentheses for expressions that
include whole number
exponents. (K)
M-EE-3
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Apply the properties of
Solve multi-step real-life and
Use numbers expressed in the
operations to generate equivalent
mathematical problems posed
form of a single digit times a
with positive and negative
whole-number power of 10 to
rational numbers in any form
estimate very large or very
(whole numbers, fractions, and
small quantities, and to express
decimals), using tools
how many times as much one
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.
strategically. Apply properties
of operations to calculate with
numbers in any form; convert
between forms as appropriate;
and assess the reasonableness
of answers using mental
computation and estimation
is than the other. For example,
estimate the population of the
United States as 3 times 108
and the population of the
world as 7 times 109, and
determine that the world
population is more than 20
strategies. For example: If a
times larger.
Teacher Target
Teacher Target
Teacher Target
Student Target:
woman making $25 an hour
gets a 10% raise, she will make
an additional 1/10 of her
salary an hour, or $2.50, for a
new salary of $27.50. If you
want to place a towel bar 9 3/4
inches long in the center of a
door that is 27 1/2 inches
wide, you will need to place
the bar about 9 inches from
each edge; this estimate can be
used as a check on the exact
computation.
1.
Student Target
Student Target
I can generate
I can convert between
I can express numbers as a
equivalent expressions
numerical forms as
single digit times an integer
appropriate. (K)
power of 10. (K)
I can solve multi-step real-life
I can use scientific notation to
and mathematical problems
estimate very large and/or very
posed with positive and
small quantities. (K)
using the properties of
operations. (e.g.
distributive property,
associative property,
adding like terms with
the addition property of
equality) (K)
2.
I can apply the
properties of operations
to generate equivalent
expressions. (R)
negative rational numbers in
any form using tools
strategically. (R)
I can compare quantities to
express how much larger one
is compared to the other. (R)
I can assess the reasonableness
of answers using mental
computation and estimation
stratagies.(R)
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
M-EE-4
Standard
Standard
Standard
Identify when two expressions
Use variables to represent
Perform operations with
are equivalent (i.e., when the two
quantities in a real-world or
numbers expressed in scientific
expressions name the same
mathematical problem, and
notation, including problems
number regardless of which
construct simple equations and
where both decimal and
value is substituted into them).
inequalities to solve problems
scientific notation are used. Use
by reasoning about the
scientific notation and choose
quantities.
units of appropriate size for
For example, the expressions y +
y + y and 3y are equivalent
because they name the same
number regardless of which o
number y stands for. Reason
about and solve one-variable
equations and inequalities.
Solve word
problems leading to equations
of the form px + q = r and p(x +
q) = r, where p, q, and r are
specific rational numbers.
Solve equations of these forms
measurements of very large or
very small quantities (e.g., use
millimeters per year for
seafloor spreading). Interpret
scientific notation that has
been generated by technology.
fluently. Compare an algebraic
solution to an arithmetic
solution, identifying the
sequence of the operations
used in each approach. For
example, the perimeter of a
rectangle is 54 cm. Its length is
6 cm. What is its width?
Solve word
o
problems leading to
inequalities of the form px + q
> r or px + q < r, where p, q,
and r are specific rational
numbers. Graph the solution
set of the inequality and
interpret it in the context of the
problem. For example: As a
salesperson, you are paid $50
per week plus $3 per sale. This
week you want your pay to be
at least $100. Write an
inequality for the number of
sales you need to make, and
describe the solutions.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
1. I can identify when two
I can fluently solve euations of
I can perform operations using
expressions are equivalent.
the form px=r and p(x+q)=r
numbers expressed in scientific
2. I can prove that two equations
are equivalent no matter what
number is substituted. (R)
with speed and accuracy.(K)
notations. (K)
I can identify the sequence of
I can use scientific notations to
operations used to solve an
algebraic equation of the form
px+q>=r and p(x+q)=r (K)
I can graph the solution set of
the inequality of the form
px+q>r or px+q<r, where p, q,
and r are specific rational
numbers. (K)
express very large and very
small quantities. (K)
I can interpret scientific
notation that has been
generated by technology. (R)
I can choose appropriate units
of measure when using
scientific notation. (R)
I can use variables and
construct equations to
represent quantities of the
form px+q=r and p(x+q)=r (R)
I can solve word problems
leading to equations of the
form px+q=r and p(x+q)=r,
where p,q, and r are specific
rational numbers. (R)
I can solve word problems
leading to inequalities of the
form px+q>r or px+q<r where
p,q, and r are specific rational
numbers.(R)
I can interpret the solution set
of an inequality in the context
of the problem. (R)
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
M-EE-5
Standard
Standard
Standard
Understand solving an equation
Graph proportional
or inequality as a process of
relationships, interpreting the
answering a question: which
unit rate as the slope of the
values from a specified set, if any,
graph. Compare two different
make the equation or inequality
proportional relationships
true? Use substitution to
represented in different ways.
determine whether a given
For example, compare a
number in a specified set makes
distance-time graph to a
an equation or inequality true.
distance-time equation to
determine which of two
moving objects has greater
speed.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
1. I can recognize solving an
I can graph proportional
equation or inequality as a
relationships. (K)
process of answering “which
values from a specified set, if any,
I can compare two different
make the equation or inequality
proportional relationships
true?” (K)
represented in different ways.
2. I can know that the solutions
(see example in standard)(R)
of an equation or inequality are
the values that make the equation
I can interpret the unit rate of
or inequality true. (K)
proportional relationships as
3. I can use substitution to
the slope of the graph. (R)
determine whether a given
number in a specified set makes
an equation or inequality true.
(K)
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
M-EE-6
Standard
Standard
Standard
Use variables to represent
Use similar triangles to explain
numbers and write expressions
why the slope m is the same
when solving a real-world or
between any two distinct points
mathematical problem;
on a non-vertical line in the
understand that a variable can
coordinate plane; derive the
represent an unknown number,
equation y = mx for a line
or, depending on the purpose at
through the origin and the
equation y = mx + b for a line
hand, any number in a specified
set.
intercepting the vertical axis at
b.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
1.
I can recognize that a
I can identify characteristics of
variable can represent
similar triangles. (K)
an unknown number or
any number in a
specified set.(K)
2.
I can relate variables to
a context. (R)
3.
I can write expressions
when solving a real-
I can find slope of a line. (K)
I can determine the y-intercept
of a line. (K)
I can analyze patterns for
world or mathematical
points on a line through the
problem. (R)
origin. (R)
I can derive an equation of the
form y=mx for a line through
the origin. (R)
I can analyze patterns for
points on a line that do not pass
through or include the origin.
(R)
I can derive an equation of the
form y=mx+b for a line
intercepting the vertical axis at
b (the y intercept). (R)
I can use similar triangles to
explain why the slope m is the
same between any two distinct
points on a non-vertical line in
the coordinate plane. (R)
M-EE-7
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Solve real-world and
Solve linear equations in one
mathematical problems by
variable.
writing and solving equations of
the form x + p = q and px = q for
Give
o
examples of linear equations in
cases in which p, q and x are all
one variable with one solution,
nonnegative rational numbers.
infinitely many solutions, or no
solutions. Show which of these
possibilities is the case by
successively transforming the
given equation into simpler
forms, until an equivalent
equation of the form x = a, a =
a, or a = b results (where a and
b are different numbers).
Solve linear
o
equations with rational
number coefficients, including
equations whose solutions
require expanding expressions
using the distributive property
and collecting like terms.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
1.
I can define inverse
operation. (K)
I can solve one step equations
2.
I can explain how
that has one solution. (K)
inverse operations can
I can solve one step equations
be used in solving one-
that has multiple solutions. (K)
variable equations. (K)
3.
I can apply rules of the
I can solve one step equations
form x+p=q and px=q
that have no solutions. (K)
for cases in which p, q,
and x are all
I can solve linear equations
nonnegative rational
numbers, to solve real
with rational number
world and mathematical
coefficients. (K)
problems. (R)
4.
I can solve equations whose
I can develop a rule for
solving one-step
solutions require expanding
equations using inverse
expressions using the
operations with
distributive property and/or
nonnegative rational
collecting like terms. (K)
coefficients. (R)
5.
I can solve and write
equations for real-world
mathematical problems
containing one
unknown. (R)
M-EE-8
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Write an inequality of the form x
Analyze and solve pairs of
> c or x < c to represent a
simultaneous linear equations.
constraint or condition in a realworld or mathematical problem.
Understand
o
Recognize that inequalities of the
that solutions to a system of
infinitely many solutions;
variables correspond to points
form x > c or x < c have
two linear equations in two
represent solutions of such
of intersection of their graphs,
because points of intersection
inequalities on number line
satisfy both equations
diagrams.
simultaneously.
o
Solve systems
of two linear equations in two
variables algebraically, and
estimate solutions by graphing
the equations. Solve simple
cases by inspection. For
example, 3x + 2y = 5 and 3x +
2y = 6 have no solution
because 3x + 2y cannot
simultaneously be 5 and 6.
Solve real-
o
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.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
1.
I can identify the
I can identify the solution to a
constraint or condition
system of two linear equations
in a real-world or
mathematical problem
in order to set up an
inequality. (K)
2.
I can recognize that
inequalities of form x>c
or x<c have infinitely
many solutions. (K)
3.
I can write an inequality
of the form x>c or x<c
to represent a constraint
or condition in a realworld or mathematical
problem. (R)
4.
Represent solutions to
inequalities or the form
in two variables as the point of
intersection of their graphs. (K)
I can describe the point of
intersection between two lines
as points that satisfy both
equations simultaneously. (K)
I can define inspection. (K)
I can identify cases in which a
system of two equations in two
unknowns has no solution. (K)
I can identify cases in which a
x>c or x<c, with
system of two equations in two
infinitely many
unknowns has an infinite
solutions, on a number
number of solutions. (K)
line. (R)
I can solve a system of two
equations (linear) in two
unknowns of algebraically. (K)
I can solve simple cases of
systems of two linear equations
in two variables by inspection.
(K)
I can estimate the point of
intersection for a system of two
equations in two unknowns by
graphing the equations. (R)
M-EE-9
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Use variables to represent two
quantities in a real-world
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.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
Standard Demonstrator
Standard Demonstrator
1.
I can define independent
and dependent
variables. (K)
2.
I can use variables to
represent two quantities
in a real-world problem
that change in
relationship to one
another. (K)
3.
I can write an equation
to express one quantity
(dependent) in terms of
the other quantity
(independent). (R)
4.
I can analyze the
relationship between the
dependent variable and
independent variable
using tables and graphs.
(R)
5.
I can relate the data in a
graph and table to the
corresponding equation.
(R)
Standard Demonstrator