Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 48227
"Analyzing Wordless Stories" An Introduction to Solving
Unit Rates
In this lesson, students will apply their understanding of ratios and prior knowledge of division to determine the unit rate for a given ratio. After some
initial instruction on unit rates, students will determine unit rates from diagrams with teacher guidance, and they will determine unit rates from
narrative descriptions independently.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Suggested Technology: Computers for Students,
Basic Calculators, Microsoft Office
Instructional Time: 45 Minute(s)
Freely Available: Yes
Keywords: unit rates, ratios, solve, rate, define, recognize, convert, and describe.
Instructional Design Framework(s): Direct Instruction
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 define the term "unit rate" and demonstrate understanding by giving various examples.
Students will recognize a ratio written as a unit rate, explain a unit rate, and give an example of a unit rate.
Students will convert a given ratio to a unit rate.
Students will describe the ratio relationship represented by a unit rate.
Students will state the ratio relationship using unit rate wording which means students are proficient at stating unit rates using words such as: "for each 1", "for
each", "for every", and "per."
Students will determine mathematically the unit rate for any given ratio. Instead of writing a basic ratio, students will be challenged to invert the ratio and express
the unit rate in terms of the other unit in the ratio. This will be illustrated by the structure of the task and questioning in the Illustrative Mathematics task price per
pound and pounds per dollar.
Prior Knowledge: What prior knowledge should students have for this lesson?
Multiplication and Division concepts
Fluent use of multiplication and division
The concept of a ratio as a comparison between two quantities
Guiding Questions: What are the guiding questions for this lesson?
What is a rate?
What is a unit rate?
What operation would help you determine the unit rate in a ratio?
What does the word "per" mean in a unit rate? How else can the unit rate be stated?
page 1 of 4 Why are labels necessary for all unit rates?
What would be the unit rate if you inverted the ratio?
Since ratios and rates can be inverted, how do you determine which version of a unit rate is most practical?
Teaching Phase: How will the teacher present the concept or skill to students?
Show students 2 bags of M&M's: a 1.69 ounce bag that cost $0.99, and a 3.14 ounce bag that cost $1.79.
Share with the students that you purchased the bags yesterday,but you weren't sure which of the two was the better buy. Have students think-pair-share their
thoughts.
Introduce vocabulary term "unit rate". Discuss how we have previously defined a "rate" as a ratio comparing two different values or measurements. A "unit rate" is a
comparison of two measurements, where one of the terms has a value of 1. Write the definition of unit rate on the board. Teacher will inform students that these are
all rates and have a denominator of 1. They are also unit rates.
Identify a few different examples of unit rates that the students have likely heard of (e.g $0.69 a pound, 55 miles per hour) for the students, and the return to the
M&M problem
Use the following sequence of questions to teach students to solve unit rate problems:
1. What ratio represents the rate of dollars to ounces for each bag of M&M's? (Answer: $0.99 : 1.69 oz. and $1.79 : 3.14 oz.)
2. What question are we trying to answer when you are asked to find the unit rate for the two bags? (Answer: What is the cost per ounce for each bag of M&M's?)
3. What will these unit rates have in common with all other unit rates? (Answer: One value in each ratio will be a 1)
4. What operation is necessary to determine a unit rate from a regular rate? (Answer: Division. Divide one value by the other. Bag A - 0.99 divided by 1.69 and Bag B
1.79 divided by 3.14)
5. What is the unit rate for each bag of M&M's? (Answer: Bag A approx. $0.59 per oz., Bag B. approx. $0.57 per oz. - Stress the importance of including appropriate
labels and using appropriate unit rate language.)
6. Which bag is the better value according to the unit rates? (Answer: Bag B is a slightly better value because it approximately $0.02 cheaper per ounce.)
7. You might also have students consider the following question: How are rates and unit rates similar?
Display the general sequence of questions about unit rates on the board for students to reference during the lesson. The teacher should also create a list of
appropriate phrases that can be used to express unit rates: per, for each, each, for every, every.
Students may also benefit from additional examples. Have them think about when you go into a grocery store and you see 3lbs. of bananas for $0.69. How can you
find out what you will pay for 1 pound?
Here are two additional rates that can be compared for apple juice. This example also provides a nice transition into the Guided Practice portion of the lesson:
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will complete the activity "Analyzing a Wordless Story" with a partner, which can be used as a Formative Assessment to assess student understanding of unit
rates.
1. Distribute the "Analyzing a Wordless Story" worksheet to each student. (Answer key link can be found here.)
2. Divide students into pairs and show them how to solve the problems by completing item one with them.
3. Working with a shoulder partner, students should write a story about information given in a diagram. Encourage students to be creative in writing the story
problem. Students should have fun and think about each context and what the diagram is telling them. Teacher will provide sufficient time for students to write their
story problems. Teacher will walk around to each group encouraging correct use of grammar, spelling, and sentence structure.
For item 1 provide this example story: "A family left the Tampa area at 10:15 AM and drove 60 miles to Disney World. Because of bad traffic, they arrived 2
hours later at 12:15 PM."
4. Instruct students to write the rate given in the scenario as a ratio using appropriate labels.
For item 1 this ratio would be 60 miles : 2 hours. NOTE: Some students may choose to write the ratio as 2 hours : 60 miles, which will result in a different unit
rate in the next step. This is not an error, just an alternate way of viewing the ratio
5. Instruction students to use division to determine the unit rate for the problem, and refer the definition of unit rate on the board from the Teaching Phase. Be sure
students use appropriate unit rate language and labels.
For item 1 the unit rate would be 30 miles per hour (30 miles : 1 hour). NOTE: If students chose to write the inverted ratio earlier, their unit rate would be
approximately 0.067 hours per mile (0.067 hours : 1 mile). While correct, this would be a great time to point out that some unit rates are more practical and
easier to understand than others. For example, very few people would fine the inverted unit rate of hours per mile very helpful even though a different ratio of
hours to miles might be really helpful for estimating travel times.
6. After solving this initial problem with students have pairs of students solve the rest of the problems together.
7. As students are working in pairs, the teacher walks around and listens to the discussions within the groups to see how the students are thinking in this activity. The
teacher should also facilitate with Guiding Questions found above. This will determine the level of foundational knowledge and understanding students possess in
regards to unit rates. Teacher will use this time to help inform the type and level of scaffolding and guidance needed to incorporate during lesson
8. After most pairs have completed their problems, have groups share out their stories and unit rates. Be sure to emphasize the definition of unit rate each time, the
page 2 of 4 operation used (division), correct unit rate language, and appropriate labels.
9. Teacher will ask students to recall when they have heard of or used expressions with the word "per", such as dollars per gallon. Students will make a list of the
different types of expressions that be used for unit rates (See Learning Objectives above)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Distribute the Independent Practice/Summative Assessment worksheet to each student. NOTE: The answer key for the assessment is on the second page, so be sure
not to distribute this to students.
Students will solve problems involving unit rates.
Students will work alone, but will compare answers with a partner when both have completed solving problems involving unit rates and they have reviewed their work.
Students should not only provide a labeled answer for each question, but they should show their understanding of solving unit rates well.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
After each team has completed their story problems, students will share out (in groups). Additionally, students will discuss their rates/ unit rates they came up with.
Students will discuss as an entire class the mathematics incorporated.
The teacher will be sure to emphasize the main points about unit rates that are described in the Learning Objectives and the Teaching Phase above.
Summative Assessment
By the end of this lesson, students will be asked to calculate unit rates given different scenarios. The worksheet completed during the Independent Practice section may
serve as the Summative Assessment. Answering 3 out of 4 questions would indicate understanding of the topic.
Formative Assessment
The teacher will check for student understanding about unit rates during the "Analyzing Wordless Stories" activity, which is administered during the Guided Practice
phase of the lesson. See Feedback to Students below for ideas for adjusting instruction based on the students' performance.
Feedback to Students
During the "Analyzing Wordless Stories" activity, circulate among the students to monitor their work, probe their thinking and scaffold the task for students needing
assistance. Make sure that the students are describing the story, writing the original ratio indicated by each diagram, rewriting the rate with a denominator of 1, and
that they use appropriate unit rate language and labels.
If the teacher determines that students are gaining proficiency with unit rates, they may proceed to the Independent Practice section of the lesson. If students are
having difficulty, the teacher may choose to provide additional accommodations are more explicit assistance before allowing them to proceed to the Independent
Practice portion of the lesson.
The teacher may also use the Guiding Questions below to probe for student understanding and to prompt them to think about the definition of unit rate and the skills
involved in determining them.
Note: A strategy in deciding which is better (when comparing cost) would be to find the unit cost.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
For the struggling students, use rates with smaller values(whole numbers)
Provide struggling students with a printed copy of the problem solving question sequence that is presented during the Teaching Phase for reference throughout the
lesson. This should also include a list of expressions to use when writing unit rates.
When pairing students make sure that there is a "strong" student and a "weak" student so that the stronger student can help the weaker one. Some students don't
always "get it" from the teacher.
Students are allowed to use a calculator to complete calculations. Students will be working in a small group. The teacher will monitor and check frequently with
each group on their progress and understanding of the tasks. Because students will finish required tasks at varied times the teacher should circulate continuously
and encourage students to help their peers who have not finished(if time permits)
Extensions: This lesson can stand alone or be the first in a series of lessons using the same theme. In further lessons, students can build on a question about
Columbia, the first space shuttle, which was launched April 12, 1981 at Kennedy Space Center.
"If the shuttle flies 15,500 miles in one hour, would it make it from Los Angeles to Orlando in more or less than 1 hour?"
Suggested Technology: Computers for Students, Basic Calculators, Microsoft Office
Special Materials Needed:
No special materials were needed for this.
Further Recommendations: There are no further recommendations
Additional Information/Instructions
By Author/Submitter
This lesson is likely to support student engagement in the following the Mathematical Practices:
MAFS.K12.MP.1- Makes sense of problems and preserve in solving them.
Students have to understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0.
MAFS.K12.MP.2- Reason abstractly and quantitativly.
Students will use rate language in the context of a ratio relationship.
MAFS.K12.MP.4- Model with mathematics.
page 3 of 4 Students will use different ratios to solve problems.
MAFS.K12.MP.7- Look for and make use of structure.
Students will use tables of equivalent ratios, double number line diagrams, or tape diagrams.
SOURCE AND ACCESS INFORMATION
Contributed by: Sondrea Hudson
Name of Author/Source: Sondrea Hudson
District/Organization of Contributor(s): Volusia
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.6.RP.1.2:
Description
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context
of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of
flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
page 4 of 4