Download Common Core Learning Standards GRADE 7 Mathematics

Common Core Learning Standards
GRADE 7 Mathematics
EXPRESSIONS & EQUATIONS
Common Core Learning
Standards
Use properties of operations to
generate equivalent expressions.
Concepts
operations
with linear
expressions
7.EE.1.
Apply properties of operations as strategies to
add, subtract, factor, and expand linear
expressions with rational coefficients.
Embedded Skills
Add linear expressions with rational coefficients.
Subtract linear expressions with rational
coefficients.
Factor (GCF) linear expressions with rational
coefficients.
Expand(Distributive property) 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.
Rigorous Sample Tasks
Vocabulary
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Rational
Coefficients
Add
Subtract
Factor
GCF
properties of
operations
expand
(distribute)
Constant
Like Terms
Monomial
Binomial
Variable
Scaffolded Sample Tasks
Sue earns $15.95 per hour (h) plus a $100 bonus. Steve earns $8.50
per hour (h) plus a $300 bonus. If they combine their incomes, how
much does the household make?
Simplify the following: 15a + 3a
(5x – 4y) – (3x + 7y)
Simplify the expression: 3m + 4w + 6m + 5w
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
John has 6 boxes of b baseball cards and 17 additional cards. Mark
has 4 boxes of b baseball cards and 200 additional cards. What’s the
difference between them?
Frank earned $10.80 per hour (h) plus $200.00 sales bonus for each
of eight consecutive weeks. Write two different expressions to
represent his income during this timeframe.
The area of a rectangular cornfield is represented by 24x + 54. The
length of the field is represented by (4x + 9). What is the width of the
field?
An architect is designing a rectangular fountain for the city park. Its
area is represented by 16x – 40. Factor this binomial to determine
the greatest whole number the length of the fountain could be.
3
8
Evaluate:  12 x 
1
1
  4  7x
2
8
Evaluate: 9x – 6.2(7.4x – 12)
Will was told to fully factor the expression 8x – 4y + 12. His answer
was 2(4x – 2y + 6). Explain why Will’s answer is not fully factored.
Find the difference between 18.5 and 9.03
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
Simplify -7(3b – 12) + 15b
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Use properties of operations to
generate equivalent expressions.
Concepts
rewriting
algebraic
expressions
7.EE.2.
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.”
Embedded Skills
Translate situation problems to algebraic
expressions.
Simplify expressions.
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Expressions
Rewrite expressions to help analyze problems.
Explain how an equivalent expression relates to the
original situation problem.
Rigorous Sample Tasks
In finding the circumference of a circle, Mary said that she used the
formula
Cindy said that she used the formula C=2πr. Their
teacher said that they both were correct. Explain how can this be?
The cost of a Sabres jersey is represented as j. The jersey is on sale
for 20% off the retail price. Write two equivalent expressions that
represent the sale price.
At a restaurant, Theresa 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%
Vocabulary
Scaffolded Sample Tasks
20% x – 11 – 15%x + 16
Change each percent to a decimal and then simplify the expression
Combine like terms:
7
x – 2 + 0.5x
4
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Solve real-life and mathematical
problems using numerical and
algebraic expressions and equations.
Concepts
Embedded Skills
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.
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.
Rigorous Sample Tasks
John says 2/3 is 2.3. Ida says John is incorrect. Who do you agree
with and why?
Erin bought 2 pairs of jeans for $29.99 each and 3 shirts for $17.99
each.
Vocabulary
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Rational
numbers
Estimation
mental
Computation
Integers
Fractions
Decimals
Equivalent
Explain the significance between different forms of
equivalent rational numbers.
Scaffolded Sample Tasks
Write 25% as fraction and a decimal
Write 1/5 as a percent and decimal
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
a.) If she has a $25 off coupon, how much will she pay before
tax?
b.) What percent of the original price did she save (round to the
nearest whole number)?
Mrs. Aumer will be hanging a 3 foot poster in her classroom. From
corner to corner the length of the wall is 62
Explain how to convert 0.6 to a percent
1
inches long. After the
4
poster is hung, what is the distance, in inches, from the edge of the
poster to the corner?
Emerson had a 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 Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Solve real-life and mathematical
problems using numerical and
algebraic expressions and equations.
fluency with
two step
equations
Embedded Skills
Construct and solve two step linear equations from
real-world problems.
Translate verbal situations to two step linear
equations.
Vocabulary
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Solve two step linear equations.
Explain the steps used in solving the equation.
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?
Solve two step linear equations fluently.
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Identify the sequence of operations used to solve a
problem.
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Compare algebraic solutions to arithmetic solutions.
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Rigorous Sample Tasks
Wendy is buying hand knitted hats for d dollars for 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.
The length of a rectangle is three times its width. The perimeter is 40
cm. Write and solve an equation to determine the dimensions of the
rectangle? You may use a picture to help you.
Mike saves ¾ of his paycheck and his parents contribute $15 to his
savings. If the total amount saved was $75, how much is his
paycheck?

Algebraic
solution
Arithmetic
solution
Two-step
linear
equations
Property of
Equality
Inverse
Operations
Linear
equations
Distributive
Property
Scaffolded Sample Tasks
Solve the equation 7.5(3x – 2) = 120. Explain each step you used to
solve for x.
Henry 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.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
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.
Rigorous Sample Tasks
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.
Explain when and why it is necessary to change an
inequality symbol.
Explain when/why an open or closed dot is used on
a number line.
Write a linear inequality from a given graph.
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
Explain how the solution set relates to the problem.
Scaffolded Sample Tasks
Thomas received a $5.00 i-tunes gift card from his friend for his
birthday. He already has $15.52 saved in an account. He wants to
purchase songs for his iPod. How many $ 0.95 songs (s) can Thomas
purchase? Find your solution by writing an inequality.
Solve and graph the solution on a number line. 2x – 3 < 12
If the perimeter of a rectangle is at most 72 feet, find the largest
dimension for the width if the length is 19 feet.
Solve and graph the solution on a number line. 5 – 7x ≥ 54
The new sign regarding height requirements at the entrance of the
Viper Roller Coaster ride at Darien Lake is shown below. Your friend
meets the sign’s requirements. Write an algebraic inequality to show
his height (h) and write a replacement sign in word form that could
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
be used at the Viper’s Entrance.
47
48 49 50 51 52 inches
Explain the steps involved in solving this inequality: -8a + 1.7 < 0.1
When solving which of the following inequalities would result in a
solution of x > 9:
a) -5 x +8 < -37
b) 6x – 3 < 51
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.