Lesson Title: ______________________________________________ Course: ___________________________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical
problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any
number in a specified set.
Which Mathematical Practices do you expect students to engage in during the lesson?
MP2: Reason abstractly and quantitatively.
MP4: Model with mathematics.
MP5: Use appropriate tools strategically.
MP7: Look for and make use of structure.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Testing prior knowledge/refresh on translating
algebraic expressions:
Students (in groups of 3 or pairs) are given a list of
expressions. They are asked to take 3 minutes to
categorize (sort) the phrases into no more than 4
groups. Sort Activity
Student groups will share their categories. Discuss
similarities/differences in categories as a class.
Eventually develop the 4 operations as categories:
addition, subtraction, multiplication, and division and
determine the correct placement of each phrase.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
Describe a strategy you use for translating a word problem
into an algebraic expression. How do you know a given
situation is an expression and not an equation?
And/or:
Translate the following word problem to an algebraic
expression. Determine the variable and describe exactly
what it represents. What number(s) would make sense to
substitute the variable with.
The cost for a membership to a gym is $35.00 per month,
and a one-time $50.00 sign-up fee. Represent the cost of
membership for the year.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Lesson Launch—Discuss the general category of Algebraic Expressions as a group. Ask students to describe
an algebraic expression (combination of number(s), variable(s), and one or more operation).
Discuss that we will continue to look at expressions and equations this unit, and today we will relate these ideas to
owning a Business/Entrepreneurship—Ask students: where/when do you think companies use expressions, and/or
equations?
2. Task 1—Opening a Business. Congratulations! Your request for a small bank loan has been approved. You are
the new proud owner of one of the three following business: A cupcakery, a bookstore, or a sporting goods
store. In groups of 3, students will be able to choose one of the three company situations to explore. Business
Task [UDL III. 7, 8] Before students start, explain that our goal is to explore the situations and eventually
represent them as a mathematical expression. Display the follow-up questions on the board so that students can
think about these as they work. If they finish early, they can start to answer the follow-up questions in their
group. [UDL II. 6, III. 9]
Students may work off of a computer for text to speech or visual support
(MP7: Students are analyzing the structure of the statements and the words used to help them
determine the correct expression to match each scenario)
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: ______________________________________________ Course: ___________________________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Follow Up Questions:
1. What is the variable in each situation, and how did you determine it?
2. Describe what a variable is…does it represent one number or more than one? What type of situations might
include a variable that represents just one number?
3. In each situation, what is the relationship between the variable (number of hours, or number of months) and
the money?
4. How can we use this information to write a mathematical expression for each situation?
(Look for evidence of MP2.)
When finished, come together as a class, and allow student groups to share their company situation, questions, and
conclusions. Be sure to address the follow up questions from above.
As a group, choose one of the situations from the Business Task to write an algebraic expression. Then allow
students the opportunity to individually write an algebraic expression for the other expressions.
Explain to the students that in the next task, one of the options is to create a graph to represent the situation. Ask
students to think about the cost of rent of the building in Company 1 ($1,350m + 500). Can you predict the trend of
the graph or plot? Moving up, down, remain the same? Allow students time to answer the question (may want to use
Think, Pair, Share)
3. Task 2—Students will individually (or in pairs) choose a situation to extend. Explain that the first option is to
look at Company 1 or 2 with a picture, graph, or scatter plot. Students may use plain paper, chart paper, or
glogster if they choose this option. [UDL II. 4, 5] The second option is to graph the mathematical relationship in
Company 3 with a graphing calculator. Business Task Extension [UDL II. 4, III. 7]
(Look for evidence of MP4 & MP5.)
When finished, come together as a class, and allow student groups to share their extensions and conclusions.
4. Application—Students will practice translating different situations into algebraic expressions and vice versa.
Before students start, display the follow-up questions below on the board, and tell students to think about these
as they are working. If they finish early, they may start to answer these questions. Word Problem Practice
Follow Up Questions to Discuss:
1. What are some different strategies you used to solve? (Underline key words, rewrite question in your own
words)
2. How would a word problem change if it represented an algebraic equation instead of an algebraic
expression? Give an example with your explanation.
3. What might be a way to check if your solution is correct?
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 be able to identify a variable in a real-world or mathematical problem.
Students will be able to articulate what a variable represents.
Students will be able to translate a real-world or mathematical problem into an algebraic expression.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Expression, equation, variable
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: ______________________________________________ Course: ___________________________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Students may translate “Mike scored 6 less points than Devin,” into 6 – d where d represents the amount of points
Devin scored, instead of d – 6. Be sure to have the articulate that these two expressions are not equivalent—
however, with addition and multiplication, commutative property would allow this.
Although an input, output table is a good way to represent situations, be sure students are aware that the output
would represent the y value in an equation.
Students may translate “per” to division when writing algebraic expressions. “Per” something is usually the unit
rate, so to find any other amount requires multiplication.
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?
Sort Activity, scissors
Graphing calculator
Chart Paper, markers
Business Task
Business Extension
Application Problems
6.EE.6 Homework
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson objectives
and evidence of success, will you use to reflect on the effectiveness of this lesson?
Do all of my students have a strong understanding of what a variable is? Can they translate word problems into
algebraic expressions? Do they know the difference between an expression and an equation?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.