7.EE.1
2012
Domain: Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions.
Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational
coefficients.
Essential Questions
Enduring Understandings

 Using the order of operations
will simplify and generate
equivalent expressions.
How does seeing
something from a
different perspective
help you think about a
situation in a new way?
Content Statements
 Identify that rational
linear expressions are
linear expressions where
the coefficients and
constants are all rational
numbers--integers,
fractions, or decimals.
 Simplify and write
equivalent algebraic
expressions.
 Use the Distributive
Property to expand a
linear expression with
rational coefficients.
 Apply the Distributive
 Factoring an expression is
changing a combination of
terms to be a multiplication
of terms.
 A common factor helps you
rewrite an algebraic
expression into a product of
two or more terms.
 Adding and subtracting
algebraic expressions allows
you to create equivalent
expressions in simplified
form.
Activities, Investigation, and Student Experiences
Solution:
The Greatest Common Factor (GCF) is 2, which will be the
width because the width is in common to both rectangles. To get
the area 2a multiply by a, which is the length of the first
rectangles. To get the area of 4b, multiply by 2b, which will be
the length of the second rectangle. The final answer will be 2(a
+ 2b).
Activities:
 Hand out index cards with various terms to all students.
Ask students to find one that looks similar to what is on
their card. Students should then combine their like terms.


Identify the GCF of two given composite numbers.
Write an addition expression using the two given
numbers. Demonstrate how to rewrite the expression a
product of common factors.
Example:
7.EE.1
Property to factor a
linear expression with
rational coefficients.
 Add and subtract linear
expressions with rational
coefficients.
 Compare the similarities
and differences when
using the Distributive
Property and Order of
Operations.
Assessments

2012
Find the GCF of 16 and 24. Students respond 8. Write the
expression 16 + 24 on board. Show 16 + 24 is equivalent to (8 ∙
2) + (8 ∙ 3). Model rewriting expression as 8(2+3) and relate
directly to the distributive property of equality a(b+c) = ab + ac.
Continue the example using 5y and 3y…
5y + 3y…(5 ∙ y) + (3 ∙ y)…y(5 + 3)…8y

Create 3 sets of cards… one set has several expanded
expressions, another has the factored form, and last set is
simplified. Students have to match up their equivalent
forms.
Example: 2a + 3b + 3a
a(2 + 3) + 3b
5a + 3b

What is the perimeter of a triangle with sides the
following lengths: 2a + 4c, 3c + 7, and 6a – 4.
Simplify the expression.
A rectangle is twice as long as its width. One way to
write an expression to find the perimeter is w + w + 2w
+ 2w. Write the expression in two other ways.
Video: How to combine like terms of rational linear equations


Suzanne says the two expressions 2(3a – 2) + 4a and 10a
– 2 are equivalent? Is she correct? Explain why or why
not?

Write an equivalent expression for 3(x + 5) – 2.

Write equivalent expressions for: 3a + 12.

An equilateral triangle has a perimeter of 6x + 15. What
is the length of each side of the triangle?
When
5
1
1
1
x + 1 is subtracted from 1 x - 5 , what is the
8
3
4
6
result?
Write an expression that is equivalent to
4
2
x4 .
3
3
***Be mindful that all activities should include examples with
fraction, decimal, and integer coefficients.***
7.EE.1


2012
Simplify the following linear expression:
1
2
x  ( x  7)
2
5
Equipment Needed:
Teacher Resources:
Interactive whiteboard

http://www.illustrativemathematics.org/standards/k8
Index cards with expressions

http://insidemathematics.org/index.php/7th-grade

http://www.algebralab.org/activities/activity.aspx

http://www.ncpublicschools.org/acre/standards/com
mon-core-tools/

http://www.schools.utah.gov/CURR/mathsec/Core/7t
h-Grade-Core/7EE1.aspx

http://illuminations.nctm.org/