Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55124
Equivalent Expressions?
This lesson helps build the student's ability to see relationships and meanings of algebraic expressions. Students utilize prior knowledge of properties
to identify equivalent expressions. Percent problems are not utilized in this lesson.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Suggested Technology: Document Camera, LCD
Projector
Instructional Time: 1 Hour(s) 40 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: equivalent, expressions, quantity, sum, difference, quotient, product, grouping, order of operations
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will:
translate verbal expressions into algebraic expressions.
use prior knowledge of properties to rewrite expressions into equivalent expressions.
think about the relationships between math ideas as they find equivalent expressions.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should:
recognize and be able to apply the commutative, associative, and distributive properties.
be able to combine like terms.
be able to translate English phrases and scenarios to algebraic expressions and equations. (See the 6th grade lesson "Let's Translate!!")
Guiding Questions: What are the guiding questions for this lesson?
1. What are some words that indicate grouping symbols are required?
Possible answer: quantity, sum, difference, product, quotient, total
2. What operations are not commutative?
Possible answer: Subtraction and division
3. Can you find an equivalent expression without actually doing any computation? How do you know it is equivalent?
4. Can you use relational thinking to explain why this works?
5. What does this number (expression, variable, symbol) represent in the situation?
6. What is the action in the problem and what operation does this action?
7. How does this equation match the word problem?
8. Compare your answer to this expression. What is the same? Different? Why?
9. Does this work for all numbers?
10. Which one is correct? How do you know?
page 1 of 4 Teaching Phase: How will the teacher present the concept or skill to students?
Give the Formative Assessment on a day prior to the lesson. Provide review and remediation as needed. Please see the Further Recommendations for worksheets to
practice writing math expressions that represent verbal phrases.
Bellwork (Warmup activity):
Post the following situation on the board or document camera and ask the students to represent it mathematically.
You are going to purchase a gift for each of four friends. Each gift will cost the same amount of money. You have $200 you could spend but you would like to have
exactly $20 to purchase dinner while you are shopping. Represent this situation as an inequality, an equation or as an expression.
Hopefully, you will get multiple correct solutions from your students. Observe their answers and ask several with different solutions to post them on the board. Do not
comment on whether the students are correct or not.
You will start the lesson by establishing that there are different ways to represent a math situation. Encouraging the students to be flexible in their thinking will
promote reasoning.
Possible solutions (although there are others):
200 = 20 + 4x
200 = 4x + 20
4x + 20 = 200
20 + 4x = 100
(200 ­ 20) ÷ 4 = x
Once 4 or 5 students have written their representations on the board, ask the students which one is correct. Pause to allow thinking. Let the students debate the
answer but come to the conclusion that they are all different representations of the same situation. Point out to the students that being able to represent a math
situation in different ways can be very useful. There will be many times when it can make the math easier or simpler to compute.
In order for students to meet this standard, they need to reason about the quantities in equations and how they are related. Some experts call this Relational Thinking.
With a bit of drama, tell the students there is magic in the air in math today.
Post this equation on the board and tell the students you can figure out the missing number without having to find the sum of 4.6 and 3.8, just magic.
4.6 + 3.8 = ? + 3.4
Ask the students if anyone else can find the missing number without adding 4.6 + 3.8. Let any student explain his/her thinking. You are looking for students who think
about the whole equation and the relationship between the parts. If a student does this, be sure to point it out to all students. If no student can do this, you can give
the following explanation:
You are adding, so both totals must be the same. This is a part to whole relationship. You can take from one part and give it to the other part and the total will not
change (property of equality). This allows you to find the missing number. So, 3.4 is 0.4 less than 3.8. Add the 0.4 to 4.6 and you will get 5. So, 5 is the missing
number.
4.6 + 3.8 = 5 + 3.4
Say something like, "Magic, right? No, it's being strategic. It's thinking about the relationships within the complete equation before doing anything. Let's try another."
Post this equation on the board:
12.4 ÷ 8 = ? ÷ 4
Use the Guiding Questions to help students think about the complete equation. Allow students to fill in what number is the question mark. Ask the students to find the
answer without finding the answer to 12.4 ÷ 8.
Students should notice that 4 is 1/2 of 8 so the missing number should be 1/2 of 12.4, which is 6.2.
12.4 ÷ 8 = 6.2 ÷ 4
Is it magic? No, just reasoning mathematically by looking for relationships in the equation.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Use the Illustrative Mathematics task Ticket to Ride as the Guided Practice.
You will want to click on the PDF link, then copy each part onto separate PowerPoint slides and project each part separately on your computer and projector. You could
also print out the PDF and show each part under the document camera. Or, you could print the task for the students. I prefer working then discussing each part at a
time.
Ask the students to answer one part then discuss this as a class. After about 2 minutes of independent thinking, you could have partners discuss and solve each part
together.
Please read the commentary section on the PDF for possible solutions and discussion.
Use the Guiding Questions to facilitate a discussion about each part of this task.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will receive a worksheet. This worksheet could be completed in class or just started in class to ensure that students are confident enough to complete it.
Students might then complete this at home. Beginning the worksheet in class will allow those students that require assistance to receive individual attention.
page 2 of 4 Equivalence Classwork
Equivalence Classwork Answer Key
As students are working, build their ability to discuss and reason by asking the Guiding Questions. Be sure to ask those relational questions, such as how expressions
are the same and different. I, often, walk the classroom with a clipboard that has questions to be asked on it so I remember what questions to ask. I also use the
clipboard to make notes on student performances.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Discuss the answers to the worksheet. Since you are trying to build the ability to reason, constantly use the Guiding Questions to deepen this conversation.
Summarize by asking students what key ideas they should have learned from this lesson. The following should be mentioned:
When you think of equivalent expressions, you want to look at an expression and/or the situation and think of other ways to write it.
Each part of an expression should represent a part in the story problem.
Thinking about the properties of operations helps to create other equivalent expressions.
Thinking about the order of operations helps to create other equivalent expressions.
Administer the Summative Assessment when you believe the students are ready. Please see the Summative Assessment section.
Summative Assessment
Administer the Summative Assessment when you believe students are ready for it.
Equivalence Summative
Equivalence Summative Answer Key
Formative Assessment
This lesson has two directions. First, you will find review worksheets for students who need more help with the ability to translate verbal phrases into algebraic
expressions. Many of our students need this practice even though it is a 6th grade standard. These worksheets are found in the Further Recommendations section.
Second, the heart of this lesson will focus on the intent of this standard to help students develop relational thinking using equivalent expressions. Please consider the
ability of your students and use the materials best suited for them.
On a day prior to the lesson, give the students the attached Formative Assessment. If any student does not show mastery of this prior knowledge, you will want to
work with them in small groups before this lesson.
Formative Assessment Equivalent Expressions
Formative Assessment Equivalent Answers
Throughout the lesson, the teacher should interact with students by asking questions. The Guiding Questions are good examples for these questions.
Students should be able to identify and utilize the commutative, associative and distributive properties as well as identify equivalent expressions.
Feedback to Students
This lesson is very interactive. Feedback should be ongoing as you respond to the students' questions and answers. Encourage students to answer all questions that
are presented and redirect questions when applicable to ensure students understand equivalencies.
If students begin to solve equations without looking at the complete equation and searching for a way to make equivalence, strongly encourage them to stop (sit on
their hands, if needed) and reason first. Tell them this is being strategic. Find another (maybe simpler or easier) way to solve the challenge without doing all of the
calculations. Help them understand we are trying to build their ability to reason, not just do calculations.
Circulate as students are doing individual work, ensuring all work is scanned for accuracy. This is a great time for individual attention if needed.
Use the Guiding Questions to probe and clarify student thinking.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
The following activity may be completed with students who need additional practice with representing verbal statements with algebraic equations or expressions.
Students will review utilizing an activity with five different colors of cardstock. They should be labeled as follows:
Green: variables (two that have x written)
Blue: symbols for operations (four that have plus, four times, four subtraction)
Yellow: numbers (two each of the numbers 4, 5, 2, -3, -6)
Orange: grouping symbols (two sets of open/close parenthesis)
Red: equal symbol (2 sets)
A group discussion should be held on expressions. Remind students that this lesson will continue to build on what was learned during their 6th grade year.
Have a set of volunteers come to the front of the classroom. Using the signs, have them model the following expressions:
1. Twice the sum of a number and negative six
Answer: 2(x + -6)
Have another volunteer model it another way.
2. Five times the difference of some number and negative three
Answer: 5(x – ­3)
Have another volunteer model it another way.
3. Four increased by the quantity of negative six times some number and five
4 + (-6x + 5)
Have another volunteer model it another way.
Ask students if this can be expressed in a different way. Students should recognize that this problem can be expressed as -6x + 9.
page 3 of 4 Additional accommodations:
Assign peer tutors to slow readers.
Use highlighters to identify important words in the verbal phrase.
Highlight the verbal phrase and the math symbol (expression, variable) that represent it in the same color.
Extensions:
Allow partners to create their own representative word situations and algebraic equations, then exchange and check each other's work.
Suggested Technology: Document Camera, LCD Projector
Special Materials Needed:
Students:
Class set of worksheets:
Formative Assessments
Practice Equivalent Expressions
Summative Assessments
(Optional) Further Recommendations 1 and 2
Red, green, blue, yellow and orange cardstock
Highlighters may be used, but not required
Teachers:
Answer keys to worksheets
Further Recommendations:
Teachers may want to use CPALMS Lesson 55214, "Let's Translate!!" as a precursor lesson.
Here are worksheets to practice the skill of representing verbal phrases with algebraic expressions.
Equivalence Practice 1 with answer key
Equivalence Practice 2 with answer key
Additional Information/Instructions
By Author/Submitter
This lesson is likely to support student engagement with the following Standards for Mathematical Practice:
MAFS.K12.MP.4.1 Model with mathematics, as they write expressions that represent situations.
MAFS.K12.MP.2.1 Reason abstractly and quantitatively, as they represent real world situations with math symbols, expressions and variables.
SOURCE AND ACCESS INFORMATION
Contributed by: Dena Davis
Name of Author/Source: Dena Ward
District/Organization of Contributor(s): Jackson
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.EE.1.2:
Description
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.”
page 4 of 4