Download 7.EE.4_11_29_12_final

7.EE.4
2012
Domain: Expressions and Equations
Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Standards: 7.EE.4 Use variables to represent quantities in a real-world or mathematical problems, and construct simple
equations and inequalities to solve problems by reasoning about the quantities.
a. 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?
b. 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.
Essential Questions
Enduring Understandings
Activities, Investigation, and Student Experiences
 When is it useful to
model a relationship
with an equation?
 Writing two equivalent
expressions will help you
solve problems.
 How does rewriting an
equation help one think
about the relationship in
a new way?
 Real world applications or
mathematical problems can be
modeled using equations or
inequalities.
Activities:
 Using a geo-board, have students create different sizes of
rectangles. Students are to count the perimeter and
should create an equation to determine the width of the
rectangle given the length. The students can count the
units representing the width to check whether or not the
equation is valid.
 How does modeling a
problem help to show
the connection between
real-world problem
solving and equations?
 How is solving a twostep equation similar to
solving a one-step
 Some equations require
multiple operations to
determine the solution.
 Solutions to an inequality will
consist of more than one
solution and the solution to an
equation has exactly one
solution.

Using point system from Fantasy Football, students are
asked to calculate total points given various scenarios:
http://www.yummymath.com/2010/are-you-ready-forfootball/

Partner problems: One student solves an expression
while the other writes reasons why steps work.

Provide students with various real-life situations with
specific constraints. Ask students to determine solution
7.EE.4
equation?
 Two different inequalities can
describe the same situation.
 Are the steps used in
solving different types of
equations similar?
 Graphing inequalities can make
sense of the inequality in
context.
 How do you translate in
algebra?
Content Statements
 Write and solve singleand multi-step equations
and inequalities.
 Solve equations and
inequalities using the
appropriate Properties of
Equality. (Addition,
Subtraction,
Multiplication,
Division).
 Write two-step equations
and inequalities for real
world situations.
 Use algebra tiles to
model and solve twostep equations.
 Write and solve
equations and
inequalities using the
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and describe the strategies they used to arrive at their
solution. Group students in pairs, groups or use various
Kagan Structure such as think-pair –share, etc.
7.EE.4
Distributive Property for
real world situations.
 Use variables to
represent quantities in
real-world problems.
 Write and solve
inequalities involving
multiple operations to
represent a real-world
situation.
 Compare and contrast
solving multi-step
equations and
inequalities.
Assessments

Last year a phone company had a loss of $25 million.
This year the loss is $14 million more than last year.
Write an equation and solve an equation to determine
this year’s loss.

Kelly swam 4 times as many laps as Kathy. Adding 5
to the number of laps Kelly swam gives you the
number of laps Julie swam. If Julie swam 9 laps, how
many laps did Kathy swim?

Three friends each pay $4.15 to buy a pizza. A basic
pizza costs $9.45. Additional toppings cost $1 each.
How many toppings were on the pizza?

Marina bought 4 books. Jose bought half as many
books as Ben Bought. Together, the 3 friends bought
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7.EE.4
13 books. How many books did Ben buy?

Three times the perimeter of a triangle is the same as
75 decreased by twice the perimeter. What is the
perimeter of the triangle?

John and his friend have $20 to go to the movies.
Tickets are $6.50 each. How much will they have left
for candy? Connect the arithmetic and algebraic
methods.
Write and solve an inequality for the problem:

There are at least a dozen eggs left.

There are at least 17 more bus riders than walkers in a
class. If there are 7 walkers, how many bus riders are
there?

It costs a candle company $51 to make a dozen
candles. How many candles must it sell at $7 apiece
to make a profit?

A cyclist has $7.00. At the first stop on the tour,
energy bars are $1.15 each, and a sports drink is
$1.75. What is the greatest number of energy bars the
cyclist can buy if he buys one sports drink?

Florencia has at most $60 to spend on clothes. She wants
to buy a pair of jeans for $22 dollars and spend the rest
on t-shirts. Each t-shirt costs $8. Write an inequality for
the number of t-shirts she can purchase?

Solve:
1/2 x + > 2 and graph your solution on a number line.
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7.EE.4
2012
Example Unit Assessment from Georgia
Equipment Needed:
Geo-boards/rubber bands
Teacher Resources:

Online Practice from IXL (7.EE.4.a)
Single-variable equations: Solve one-step linear
equations

Algebra Lab (7.EE.4.a)
Translating Word Problems into Equations

Comprehensive problem demonstrating do to write an
inequality statement based on given situation:
http://illustrativemathematics.org/standards/k8

Online Practice from IXL (7.EE.4.b)
Inequalities: Inequalities on number lines (Seventh
grade - W.1)

XPMath Game: Fly a space ship thru asteroid fields by
matching correct inequality Inequality Wars

http://www.schools.utah.gov/CURR/mathsec/Core/7t
h-Grade-Core/7EE2.aspx

http://illuminations.nctm.org/
Virtual geo-board
Index cards with situations and constraints.
Computers with Internet access