Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 32282
Percent of Change
Students will investigate percent of change in real-world situations and will differentiate between an increase or a decrease. The students will use a
formula to find the percent of change.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Suggested Technology: Document Camera, Basic
Calculators
Instructional Time: 50 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: percent of change, percent of increase, percent of decrease
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Percent Change Worksheet.doc
32282 Percent of Change Worksheet.docx
FloridaMinimumWageHistory20002013.pdf
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 solve:
problems involving percent of change.
multi-step, real-world problems posed with rational numbers in any form using tools strategically.
Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to starting this lesson, students should have a foundation applying properties of operations as strategies to multiply and divide (MAFS.3.OA.2.5) as well as
MAFS.3.OA.4.8 - Solve two-step word problems involving the four operations.
This lesson on percent of change also requires that students have an understanding of MAFS.6.RP.1.3 - Use ratio and rate reasoning to solve real-world and
mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c - Find a percent of a
quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Students should have already been introduced to MAFS.6.NS.3.5 - Understand that positive and negative numbers are used together to describe quantities having
opposite directions or values, in order to understand the process of adding zero pairs in this lesson.
Guiding Questions: What are the guiding questions for this lesson?
What is the distinction between finding the difference between two numbers and the percent of change between two numbers?
When would someone need to know the percent of change?
Teaching Phase: How will the teacher present the concept or skill to students?
page 1 of 4 The teacher will start the lesson by showing the differences between finding the difference between two values and finding the percent of change between two values.
1. The teacher says, "Last year Miranda worked as a babysitter and earned $9.50 per hour for her services. This year, she earns $10.25 per hour for each hour
shebabysits. How did her hourly rate change?"
Students may respond with, "She earns more. She makes $0.75 more per hour."
It would be unexpected if a student responds with, "Her rate increased 8%."
2. The teacher says, "IfLebron James averaged 37.9 minutes of play time in the 2012-2013 season, and is averaging 36.8 minutes of play time in the 2013-2014
season, how has his play time changed?"
Students may respond with, "He plays less than last year. His playing time decreased. He plays an average of 1.1 less minutes this season."
It would be unexpected if a student responds with, "He plays 3% less than last year."
3. The teacher says, "If my baby brother was 19 inches long when he was born, and at his first year check up he was 28 inches tall. How has his height changed
during his first year?"
Students may respond with: "He is longer. He grew 9 inches."
It would be unexpected if a student responds with: "He grew by 47%."
The teacher explains that the difference between two values shows how far apart the two numbers are, while another way to describe the difference is to use a
percent of change, or the rate at which change happens. We can use the percent of change when we are looking for how values change over time for prediction.
The first step is to determine whether you are looking for an increase or a decrease. By determining this beforehand, the students can use the same process for both
increase and decrease. For example:
If a restaurant expects to have 200 customers come in for dinner, and 225 customers come in, that is a difference of 25 customers, but it is a 13% increase. The
restaurant can use the percent of increase to find out how more food to order if the number of customers remains that high.
We find the percent of change by finding the difference between the values and then dividing by the original value. Using the restaurant example:
This is a 13% increase because there were more customers than were anticipated. (Showing the students how to work through an exact value and then
approximate is a golden opportunity to emphasize Mathematical Practice 6, attend to precision.)
This helps. If they have to order 15 different ingredients, all in different amounts, instead of figuring out exactly how many steaks, how many heads of lettuce,
potatoes, carrots, spices, butter, condiments, etc., the manager can just increase his quantity of ingredients each by 13%.
Here is an example for the teacher to pose to the class, and he or she can work the problem as the students try to work the problem at their seats.
A cargo plane was carrying 37,500 pounds of cargo. Cargo was removed, and now the plane is carrying 34,750 pounds. What is the percent of change of cargo
weight?
The explanation is as follows:
Instead of describing the exact number of pounds removed, we found the ratio between the number of pounds removed and the number of pounds allowed.
Another way to introduce and embed the concept for deeper understanding is to describe it in real-world situations that are meaningful. Using the Florida Minimum
Wage History table provided by the Florida Department of Economic Opportunity, the teacher can compare the minimum wage from different years. This would offer
the teacher an opportunity for students to make sense of a problem and persevere through solving it by seeing the relevance of the application in a real-world setting
(Mathematical Practice 2).
The teacher will provide the student with the Percent of Change Practice Worksheet, provide instructions, and demonstrate the first problem.
This should require 15-20 minutes.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The Percent of Change Practice Worksheet will be used to guide and model the students through two problems, and then they will proceed through the rest of the
sheet as independent practice.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
The teacher will continue to circulate throughout the classroom and be available to students to provide guidance with questions, answer questions, and observe
students' methods for solving problems as they work on the Percent of Change Practice Worksheet.
This should take 15 - 20 minutes.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
To close the lesson, the teacher will facilitate a whole group discussion by asking students to describe percent of change and how it can be calculated. Students will
verbally summarize what has been learned during this lesson and contribute to class discussion.
This should take 3 - 5 minutes.
Summative Assessment
The Percent of Change worksheet can be used as a summative assessment. The students will spend 10 minutes answering the questions on the worksheet.
Formative Assessment
The teacher will ask students scaffolding questions that will activate prior knowledge of comparing rational numbers and recognizing when numbers increase and
page 2 of 4 decrease. The teacher will pose the following questions, one at a time, on a document camera, and students will respond at their seat with either increase or
decrease on a dry erase desk board:
If you buy a brand new car for $15,999, drive it off the lot, and get into an accident, the car will be worth $11,499. Does the car's value increase or decrease?
You buy a baseball card in a package for $0.60. In 25 years, it will be worth $2,600.00. Will the value have an increase or decrease?
The temperature at sunrise is 71 degrees Fahrenheit. At noon, the temperature is 84 degrees Fahrenheit. At sunset, it is 69 degrees Fahrenheit. Has the
temperature had an increase or decrease from sunrise to sunset?
The class starts with 22 students. By the midterm, there are 18 students enrolled. Is that an increase or decrease?
The football team averages 21.1 points per game at the start of the season. By the end of the season, the team is averaging 23.7 points per game. Is that average
an increase or decrease?
A scuba diver jumps off a dive boat into the water and descends 30 feet below sea level. He rises 10 feet to swim above a coral head, then swims back down 8 feet
to the top of a submerged wreck. Has his depth shown an increase or decrease from his initial descent?
A plant grows an average of 4 inches per month during the summer months. The same plant grows at an average of 3.8 inches per month during the winter
months. Is that an increase or decrease?
The teacher will determine students' understanding of an increase or decrease through these questions and will determine if further instruction on this should be
implemented before the lesson proceeds. This should take approximately 5-7 minutes.
Another gauge of students' ability to work proficiently during the coming lesson is to determine students' knowledge of multiplying with different forms of numbers. Put
the following problems on the board for the students to work on independently. The teacher will observe student responses and adjust the lesson accordingly. Again,
teacher will pose the following questions on a document camera, and students will respond by writing their answers on a dry erase desk board and hold their
responses up for the teacher to observe.
What is 50% of 250? (125)
What percent of 10 is 4.7? (47%)
80% of what number is 12? (15)
0.225 is 30% of what number? (0.75)
What number is 3.125% of 1,280? (40)
What number is 0.20% of 85? (0.17)
These questions will allow the teacher to determine students' ability to find percents of numbers and work with different forms of numbers. This should take
approximately 10 minutes.
Feedback to Students
Students will receive immediate verbal feedback to their responses during the formative assessment from the teacher and be able to correct their thinking of what
constitutes an increase or a decrease, or their calculations and how they arrived at their answers. The teacher will ask questions to guide students and correct
misconceptions.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Copies of questions that the teacher uses in the formative assessment can be provided for students with auditory processing issues, so they are able to read the
situations and answer without having to process what they are hearing and then form an answer.
Provide support for English Language Learners with translations, dictionaries, and/or examples of unfamiliar vocabulary words.
Extensions:
The teacher will ask students to write a paragraph describing how percent of change can tie into finding tax, tip, and interest.
Suggested Technology: Document Camera, Basic Calculators
Special Materials Needed:
Florida Department of Labor Minimum Wage Scale 2000-2013 handout
Class set of worksheets used in the Guided and Independent Practice
Dry erase boards/markers/erasers
SOURCE AND ACCESS INFORMATION
Name of Author/Source: Anonymously Submitted
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form
page 3 of 4 (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.
MAFS.7.EE.2.3:
Remarks/Examples:
Fluency Expectations or Examples of Culminating Standards
Students solve multistep problems posed with positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. This work is the culmination of many progressions of learning in
arithmetic, problem solving and mathematical practices.
Examples of Opportunities for In-Depth Focus
This is a major capstone standard for arithmetic and its applications.
MAFS.7.RP.1.3:
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups
and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
page 4 of 4