7WB6 -
2014 University of Utah Middle School Math Project in partnership with the
Utah State Office of Education. Licensed under Creative Commons, cc-by.
Chapter 6: Real World Equations and Inequalities
(2-3 Weeks)
UTAH CORE Standard(s)
1. 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.” 7.EE.A.2
2. 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. 7.EE.B.3
3. Use variables to represent quantities in a real-world or mathematical problem, and construct simple
equations and inequalities to solve problems by reasoning about the quantities. 7.EE.B.4
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? 7.EE.B.4a
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. 7.EE.B.4b
4. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to
write and solve simple equations for an unknown angle in a figure. 7.G.5
CHAPTER OVERVIEW:
This chapter brings together several ideas. The theme throughout however is writing equations or inequalities to
represent contexts. In the first section students work with ideas in geometry and represent their thinking with
equations. Also in that section students solidify their understanding of the relationship between measuring in
one-, two-, and three-dimensions. In the second section, students will be writing equations for a variety of real
life contexts and then finding solutions. The last section explores inequalities. This is the first time students
think about solutions to situations as having a range of answers.
VOCABULARY:
algebraic, inequality, equation, inverse operations, solution, at most, at least, less than, greater than, ,
supplementary, complementary, vertical angles, adjacent angles, intersecting lines
CONNECTIONS TO CONTENT:
Prior Knowledge
In Chapter 3 students learned how to solve one-step and simple multi-step equations using models. In this
chapter students extend that work to more complex contexts. In particular they build on understandings
developed in Chapter 5 about geometric figures and their relationships. Work on inequalities in this chapter