Lesson Title: __Evaluating Solutions of One step equations and Inequalities___Course:____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a
specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a
specified set makes an equation or inequality true.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Which of the following are equations?
a)6  n  13
b)5  w  3
c)12  x
d)12  x  3
What is the difference between an equation and an
expression?
Answers: a) and d) are equations, b) is an inequality
and c) is an expression.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
Tom wants to buy a pair of shoes and a t-shirt. The shoes
cost $65. He has $82 to spend.
1. Write an inequality to represent this situation.
2. What could the cost of the t-shirt be?
Answers:
65  t  82 , where t represents the cost of a t-shirt.
The t-shirt must be $17 or less for Tom to be able to
make the purchase.
An expression is a mathematical sentence that has
numbers and/variables and at least one operation
, , ,   . An equation is a mathematical sentence
that contains the equal sign.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Explain that solving an equation or inequality is the same as finding one or more values that make the statement
true.
2. Present students with the statement 5  __ 14 . Ask students to determine a number that would make this
statement false. Have students share ideas and explain why it is false. Then have students determine which
number(s) would make the statement true. Students should be able to identify that 9 is the only number that
would make the statement true.

3. Relate equations to the idea of a balance scale. Ask students to write the following equation: 3 n 11. Explain
that 3  n is the left side of the scale and 11 is the right side of the scale.
4. Place 11 cubes on the right side of the scale and 3 cubes on the left side of the scale. Have students determine
how many cubes to add to the left side of the scale in order to balance the scale. Ask a student to place 5 or fewer
 we need to add more or
cubes on the left side of the scale. The scale should not balance. Ask, “Do you think

fewer cubes in order to make the scale balance?” If their answer is more, take the 5 cubes away and ask another
student to place 10 or fewer (but more than 5) cubes on the left. If the students choose 10 cubes, the scale
should not balance. Ask students, “Five cubes were not enough to balance the scale, and 10 cubes were too
many. How many cubes do you think we need to add to the left side in order to balance the scale?” Take the 10
cubes away and ask another student to predict what number greater than 5 but less than 10 will make the
equation true. Have students experiment with numbers to find out that 8 cubes will balance the scale. Say, “ To
solve an equation means to find the value of the variable that will make the equation balance. For the above
example the value of n = 8, because 8 cubes balanced the scale.” As another strategy, have the students work
backwards to see that 11 3  8.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise
student achievement. Portsmouth, NH: Heinemann.

Lesson Title: __Evaluating Solutions of One step equations and Inequalities___Course:____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________
5. Have students work in pairs to solve the following, substituting the variable with the given numbers:
1. n – 3 = 9
Which of these numbers will make the equation true? 6, 9, 0,12
2. 15 + n = 19 Which of these numbers will make the equation true? 1, 4,10, 7
Circulate to check students’ work. Ask students if more than one number can make the equations true? Have
students explain their reasoning.
7. Display the problem, “A mother has $21 to give to her three daughters. If each daughter receives an equal
amount of money, what amount could each girl receive?” Have students write an equation to represent this
solution and determine a possible solution. (Solution: 3n = 21, Each girl could receive $21.)
Have students substitute their solution(s) into the equation in order to determine the number that makes the
equation true. After students determine an answer, ask what strategies they could use to narrow down the
possible correct answers and find a correct solution.
m
8. Display
 3 . Have students work in pairs to determine a solution and at least three non-solutions. Have pairs
5
share their solutions and the strategies they used to determine the solutions. (As an extension, have students
write a scenario that would represent this equation.)
9. Introduce the statement n  3  9 . Ask students to compare this statement to n – 3 = 9. How would the
solutions compare? Have students generate a list of possible solutions (values that make the statement true.)
10. Assign students to small groups. Give each group the problem, “Antonio has $20.00 to spend at the County Fair.
He would like to ride the go-carts and play some of the other games. The go-carts ride costs $5.50. How much
money could Antonio spend on other games?” Have groups write an inequality to represent the scenario and
generate a list of potential solutions.
11. If time permits, have the groups complete this problem, “Antonio has decided that he just wants to ride the gocart ride with his $20. How many times could Antonio ride the go-carts if each ride costs $5.50? Could Antonio
ride 5 times? Why or why not? Could he ride 3 times? Why or why not?” Have groups write an inequality to
represent the scenario and generate a list of potential solutions.
Extension: Explain that students are going to work in teams to generate a “Quiz the Class” game.
a. Group students into threes or fours.
b. Have each team generate a problem with four values to substitute, one of which is the solution.
c. Have teams take turns displaying their questions under the document camera and have the class use
whiteboards to find the solution to the team’s problem.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will determine whether or not specific values are solutions to equations through substitution.
Student mastery will be measured by class discussion, monitoring student work, and through the “Quiz the Class”
game.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Vocabulary: Equation, Expression, Variable
Typical misconception: Students may not know that a coefficient and a variable together is a multiplication
(example: 4m is the same as 4 multiply by the variable m)
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise
student achievement. Portsmouth, NH: Heinemann.
Lesson Title: __Evaluating Solutions of One step equations and Inequalities___Course:____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Scale
Cubes
Lesson scenarios
Dry-erase boards (optional)
Which of the following is a solution to n – 5 = 19?
a. n=10
b. n=11
c. n=24
d. n=16
Now, can you write a problem with possible solutions like
this one?
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
Are the students able to substitute the variable with a number in order to make the equation true?
Are the students able to understand that only one number can make a one-step equation true?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise
student achievement. Portsmouth, NH: Heinemann.
Lesson Title: __Evaluating Solutions of One step equations and Inequalities___Course:____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________
Lesson Scenarios
A mother has $21 to give to her three daughters. If each daughter
receives an equal amount of money, what amount could each girl
receive?
Antonio has $20.00 to spend at the County Fair. He would like to ride
the go-carts and play some of the other games. The go-carts ride costs
$5.50. How much money could Antonio spend on other games?
Antonio has decided that he just wants to ride the go-cart ride with his
$20. How many times could Antonio ride the go-carts if each ride costs
$5.50?
 Could Antonio ride 5 times? Why or why not?
 Could he ride 3 times? Why or why not?”
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise
student achievement. Portsmouth, NH: Heinemann.