Common Core Learning Standards
GRADE 7 Mathematics
EXPRESSIONS & EQUATIONS
Common Core Learning
Standards
Use properties of operations to
generate equivalent expressions.
7.EE.1.
Apply properties of operations as strategies to
add, subtract, factor, and expand linear
expressions with rational coefficients.
Concepts
operations
with linear
expressions
Embedded Skills
Add linear expressions with rational coefficients.
Subtract linear expressions with rational
coefficients.
Factor linear expressions with rational coefficients.
Expand linear expressions with rational coefficients.
Apply properties of operations to all operations
with rational coefficients.
Translate word situations to algebraic expressions.
Identify the GCF of rational coefficients in linear
expressions.
Identify like terms.
Vocabulary
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Rational
Coefficients
Add
Subtract
Factor
GCF
properties of
operations
(list them?)
expand
(distribute)
Constant
Like Terms
Monomial
Binomial
Variable
SAMPLE TASKS
I.
II.
III.
IV.
V.
VI.
Simplify the following: 15a + 3a
Simplify the expression: 3m + 4w + 6m + 5w
Sue earns $15.95 per hour plus $100 bonus. Steve earns $ 8.50 per hour plus a $300. If they combine their incomes, how much
does the household make?
Find the difference between 18.5m and 9.03m.
(5x – 4y) – (3x +7y)
John has 6 boxes of b baseball cards, plus 17 addition cards. Mark has 4 boxes of b baseball cards, plus 200 addition cards.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
VII.
VIII.
IX.
X.
XI.
XII.
What’s the difference between them?
What is the GCF of (16m + 40)?
What is the GCF of (12w – 9wx)?
Factor the expression (8a + 6b – 10)?
Simplify the expression 7(4y +11)?
Simplify 6(9a – 4) – 123a?
Frank earned $10.80 per hour (h) plus $200.00 sales bonus for eight consecutive weeks. Write and two different expressions to
represent his income during this timeframe.
Common Core Learning
Standards
Use properties of operations to
generate equivalent expressions.
7.EE.2.
Concepts
rewriting
algebraic
expressions
Embedded Skills
Translate words to expressions. (?)
Translate situation problems to algebraic
expressions.
Simplify expressions.
Vocabulary
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Expressions
Rewrite expressions to help analyze problems.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Understand that rewriting an expression in
different forms in a problem context can shed
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.”
Explain how an equivalent expression relates to the
original situation problem.
SAMPLE TASKS
I.
II.
III.
IV.
In finding the circumference of a circle, Mary said that she used the formula 𝐶 = 𝜋𝑑 . Cindy said that she used the formula
C=2πr. Their teacher said that they both were correct. Explain how can this be?
Sabres jerseys represented as j are on sale for 20% off the retail price. Write two equivalent expressions that represent the sale
price.
At a restaurant, Fred estimated the 15 % tip by multiplying the total bill by 1.15. Explain why this method can be used.
Simplify 4.5c + ¾ c + 20%c
Common Core Learning
Standards
Concepts
Embedded Skills
Vocabulary
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Solve real-life and mathematical
problems using numerical and
algebraic expressions and equations.
7.EE.3.
Solve multi-step real-life and mathematical
problems posed with positive and negative
rational numbers in any form (whole numbers,
fractions, and decimals), using tools
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 strategies. For
example: If a 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.
multi-step
equations
Solve multi-step real-world problems involving all
types of rational numbers.
Justify the reasonableness of solutions using mental
computation and estimation.
Apply properties of operations to solve multi-step
real-world problems with all rational numbers.
Convert fluently between forms for common
decimals, fractions, and percents.
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rational
numbers
estimation
mental
computation
integers
fractions
decimals
equivalent
Explain the connection between different forms of
equivalent rational numbers.
SAMPLE TASKS
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II.
III.
IV.
V.
VI.
VII.
Write 25% as a fraction and a decimal.
Write 1/5 as a percent and decimal.
Write 0.6 as a percent and fraction.
John says 2/3 is 2.3. Is he correct? Why or why not?
Patience says that 1/3 is 0.3. IdaLena says that Patience is incorrect. Who do you agree with and why?
Erin bought 2 pairs of jeans for $29.99 each, 3 shirts for 17.99 each, and had a $25 off coupon. How much was her total
order (without tax)? What percent of the original price did she save?
Emerson had vegetable garden last year with dimensions of 15 feet by 20 feet. This year, he wants to increase each
dimension by 5-1/2 feet, what is the new area of the garden?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
VIII.
Common Core Learning
Standards
Concepts
Embedded Skills
Solve real-life and mathematical
problems using numerical and
algebraic expressions and equations.
fluency with
two step
equations
Construct and solve two step linear equations from
real-world problems.
Translate verbal situations to two step linear
equations.
Solve two step linear equations.
Explain the steps used in solving the equation.
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Solve two step linear equations fluently.
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Identify the sequence of operations used to solve a
problem.
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7.EE.4a.
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 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?
Vocabulary
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Compare algebraic solutions to arithmetic solutions.
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algebraic
solution
arithmetic
solution
two-step
linear
equations
Property of
Equality
Inverse
Operations
Linear
equations
Distributive
Property
SAMPLE TASKS
I.
II.
Henri earns $8.50 per hour (h) that he works. He received a $100 sales bonus and his gross pay was $308.25. Write and solve an
equation to determine how many hours he worked.
The length of a rectangle is three times its width. The perimeter is 40 cm. What are the dimensions of the rectangle? First, solve
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
III.
IV.
using an organized list/ table. Then, solve it algebraically by writing an equation to find the dimensions. Which method do you
prefer and why?
Wendy is buying hand knitted hats for d dollars each of her four daughters and herself. She also wants to purchase a cute$3.00
flower for each hat. Her total order (without tax) is $75.00. What is the cost of each hat? Explain how the distributive property
can be used to help solve this problem.
Solve the equation 7.5(3x -2) = 120. Explain each step you used to solve for x.
Common Core Learning
Standards
Concepts
Solve real-life and mathematical
problems using numerical and
algebraic expressions and equations.
fluency with
two step
inequalities
7.EE.4b.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.
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.
Embedded Skills
Construct and solve two step linear inequalities
from real-world problems.
Graph the solution set of two step linear
inequalities from real-world problems.
Interpret and describe the solution in the context of
the problem.
Insert the solution in the context of the problem.
Vocabulary
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two-step
linear
inequalities
At least
At most
≤, <,>,≥
Inequalities
Number line
Closed dot
Open dot
Solution set
Graph the
solution set
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.