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Lesson Content

Lesson Plan Template:
Confirmatory or Structured Inquiry

Learning Objectives: What will students know and be able to do as a result of this lesson?
Students will gain a stronger understanding of ratios and finding unit rates in various situations. They will show this understanding by doing the following.
Students will be able to recognize and describe ratios.
Students will be able to recognize that a unit rate emphasizes the "for every 1" or "per" relationship and equivalent ratios can be made from this unit rate.
Students will use different ways to find the unit rate in word problems.
Students will be able to recognize a ratio as a multiplicative comparison of two quantities.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know that ratios can represent the comparison of a part to a whole. (boys to the whole class)
Students should know that ratios can represent the comparison of a quantity with another quantity of different units or same units.
Students should be fluent with multiplication and division.
Students should be able to use ratio language to describe a ratio relationship.
Students should have some ability to make sense of problems and persevere in solving them as they do math.

Guiding Questions: What are the guiding questions for this lesson?
What does each part of the ratio represent in the word problem?
What would happen if I changed this part?
What does this tell us about ratios?
What operation are we using to find equivalent ratios? (multiplication) Why? (The two parts of a ratio can be thought of as a composed unit. You must iterate or partition this composed unit to find an equivalent ratio. The multiplicative comparison (Value) between the two parts of a ratio must always stay the same.)
Where can examples of ratios and rates be found in the realworld?
How can I model and represent ratios?

Introduction: How will the teacher introduce the lesson to the students?
The Activation of Prior Knowledge
Open the lesson with the Formative Assessment:
White Boards  each pair of students gets a white board and a different color dryerase marker. Allowing only 1 per two students should promote a quick discussion of the answers on the board. However, be sure each partner has a turn with the marker. If you do not want partner discussion, then give each student a white board.
For this lesson, the quick assessment will focus on writing a correct representation of a ratio in notation form.
 3 cups of juice for every 2 bagels (3:2)
 50 feet in 20 seconds (50:20)
 $2 for every 3 notebooks (2:3)
Be sure to have the students discuss a sentence that would explain the ratio.

Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be used to answer the question(s)?
Show the Power Point Presentation and tell a story similar to the following to the students as you move through the slides.
Teacher: Imagine we go on a field trip to the beach. I promise everyone an ice cream cone of any flavor with one topping. There are 2 famous ice cream shops at the beach: Sally's and Freezy's. Which place should we go?
Student: responses
Teacher: Well, let's walk along the beach and check out the shops. Show the Power Point Presentation. A sign in Sally's read, "6 cones for $12.00". Do you think that is a good deal? I also see a sign in Freezy that reads, "8 cones for $14.00". If I have to buy 24 ice cream cones, which shop will cost me the least amount of money? Who would like to make a prediction? (Allow students to respond and have a discussion about why they are making those predictions.)
How do I figure this out?
Student: responses
Teacher: Work with your partner on the white boards to create a representation or a table that will help you solve this problem and prove that your answer is correct.
Note to teacher: If the students go directly to a division algorithm of $12 divided by 6 and $14 divided by 8 they will miss out on the proportional thinking and reasoning. If students do go directly to this division algorithm, tell them they have to prove their answer is correct on the whiteboard. This means they must either write sentences justifying their strategy or create drawings or tables. This should help them think about $12:6 and $14:8 as a ratio.

Analyze: How will students organize and interpret the data collected during the investigation?
Circulate around the rooms to observe and help students. As you circulate, make notes of the specific examples you wish to show during the closure.
Questions might include:
 "What do the numbers represent at the ice cream shop?" (how many cones they can buy for a certain price)
 "Can you explain your thinking to me?"
 "How are you organizing your work so that you can clearly see your answers?" "Why are you using this method?"
 "How does this ratio match the word problem?"
 "What does this number represent in the word problem?" Why?
 "What roadblock is stopping you from finding the cost of 24 ice cream cones?" Why?
 "Which shop should we go to get the cheapest ice cream cones? How do you know?"
 "What if we subtracted 2 instead of divided by 2? Would we find the unit rate? Why or why not?
 "What pieces of knowledge about ratios does this activity point out? How?"
Possible Solutions
Possible Solutions 2

Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Check to see if the students are recording their work in an organized efficient manner.
Ask for a volunteer to display his/her work using the document camera and explain his/her thinking of how they solved it.
Depending on what the students created, you can show the tables or lines in the Possible Solutions. Explain that this is also called a ratio table. Focus on the meaning of the terms "for every", "for each 1", and "per" because these are equivalent ways of stating unit ratios.
If your students did not create these solutions then you could present them and ask the students if they are correct and how they represent what is happening in the mathematics.
Be sure students have pieces of knowledge written in their notebooks and applaud their hard work and brilliant thinking. Suggest they go home and tell everyone they are math superstars.
Administer the Summative Assessment attached in the Summative Assessment section.

Summative Assessment
Listening to students conversations during the Guided Practice and the Closure will provide a teacher with information on the students' understanding. A more formal assessment is attached. The questions require reasoning and explanations. Answering 3 out 4 questions would indicate a strong understanding of the topic. Please see the answer key for model responses to the explanations.
Attachments:
Summative Assessment
Summative Assessment Answers

Formative Assessment
Please see the Introduction of the lesson for the steps for the Formative Assessment. The teachers should continuously analyze student responses and ask the Guiding Questions to probe and guide student thinking.

Feedback to Students
During the activity, circulate among the students to monitor their work, probe their thinking and scaffold the task for students needing assistance.
If the student does not know how to write the ratio, ask him/her to think about a parttopart relationship or a parttowhole relationship.
Please use the Guiding Questions to clarify and probe student thinking.
Assessment
 Feedback to Students:
During the activity, circulate among the students to monitor their work, probe their thinking and scaffold the task for students needing assistance.
If the student does not know how to write the ratio, ask him/her to think about a parttopart relationship or a parttowhole relationship.
Please use the Guiding Questions to clarify and probe student thinking.
 Summative Assessment:
Listening to students conversations during the Guided Practice and the Closure will provide a teacher with information on the students' understanding. A more formal assessment is attached. The questions require reasoning and explanations. Answering 3 out 4 questions would indicate a strong understanding of the topic. Please see the answer key for model responses to the explanations.
Attachments:
Summative Assessment 47460.docx
Summative Assessment Answers 47460.docx
Accommodations & Recommendations
Accommodations:
A model/paper could be created showing how to draw a table and write a ratio
Check for understanding.
English Language Learners may benefit from having unfamiliar vocabulary words defined with examples kept on their desk.
Extensions:
Ask the students to think of another way to represent the mathematics in the problem. Ask the students to figure out how much money could be saved by purchasing the least expensive cone.

Suggested Technology: Document Camera, Computer for Presenter, LCD Projector
Special Materials Needed:
Straight edge or ruler for tables and double number line or tape diagrams may be useful.
Further Recommendations:
You may wish to keep a clipboard nearby to record which students struggled with the concept, so you can work with them in a small group. You may also want to make note of specific students to spotlight. Classroom Management Tips: While you do not want anyone student teaching others all the time, this is a good activity for letting those who complete an activity practice their communication skills by helping another student. If you have many students who are stuck, ask another student who was successful to explain his/her strategy to a struggling student. Using the camera to take and post pictures of student work helps motivate students to record clearly.
Additional Information/Instructions
By Author/Submitter
By Author/Submitter: This lesson also addresses Mathematical Practice Standards: MAFS.K12.MP.3 : Construct viable arguments and critique the reasoning of others, because they will provide evidence of their thinking while working through the problems to find the unit rates and MAFS.K12.MP.4: Model with mathematics, because they will analyze the relationship between ratios to find the unit rate of an item.
Source and Access Information
Contributed by:
Cassie Meyers
Name of Author/Source: Cassie Meyers
District/Organization of Contributor(s): Flagler
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.