SWBAT successfully solve several problems involving different types of ratios presented in context uncovering the standards that they have yet to master

Station Discoveries: Reviewing all standards presented in Unit 2 using station activities

5 minutes

In today's lesson, I will have my students engage in several activities to help them review for the upcoming unit assessment. To start off today's lesson, I will first providemys tudents with the rules as they pertain to working in stations. The rules are as follows:

- Stay focused on the task
- Stay involved in the activity
- Stay in your group
- Stay diligent (don't give up... Work until time is called).
- Do your very best
- Use your inside voices
- ALL group members MUST participate

Next, I will separate my students into groups based upon ability. The reason I want to troup them based upon ability is to force more participation from all students. Grouping the students this way will keep students who are struggling from relying too heavily on those students who have been progressing well throughout the unit.

Normally, when my students work together, I create groups of mixed ability to provide opportunities for struggling students to learn from those student who show promise of mastery. But, this particular lesson is taking place right before a unit quiz that will provide information as to what each student needs in order to succeed. After that quiz, they will then be put into flexible groups to address only those areas in which they are in need of help. Because of this, I need to see what students have learned and how far they can take what they have learned. Thus the reason for the homogeneous groups. This forces struggling students to persevere in the solving of problems without have the "crutch" of an expert in their group. But, they still have each other to rely on and bounce ideas off of.

5 minutes

In this lesson, the "Try It Out" portion is, mostly, built into the groups. As the teacher, I will be traveling the room to facilitate learning at all groups. However, I will spend most of my time with the group of students that are struggling so that I can make sure that they are off to a good start and don't get stuck. To get them going and keep them going, I ask the group members probative and strategic questions that will help guide them in the successful completion of the task.

Also, as part of the "Try It Out", I will spend time explaining each of the stations that the students will visit during today's class time.

In all, there will be 4 stations and the students are to spend no more than 15 minutes at each station and no less than 10 minutes at each station. The stations that the students will visit are as follows:

**Station 1: THE RATIO STATION** - At this station, the students will prove that they thoroughly understand the concept of ratios. This station will require that students identify ratios, rates, and unit rates when given a real-world mathematical situation.

**Station 2: PROPORTIONAL PROBLEMS** - When the students arrive at this station, they will be presented with 3 problems that require proportional reasoning. They will have to identify the type of problem they are dealing with (ratio & proportion, percentage, rate, conversion, or geometric). They have to identify the type of problem to help them see that there are many types of problems that can be solved using the concept of proportional reasoning.

**Station 3: PERCENTAGES** - This station will require students to solve a problem given a complex situation involving sales and tax. This station will mimic what happens when you go shopping for clothing. The students will be given an opportunity to "shop" (you can use cutouts to represent clothing or you can use catelogs). Then the students will have to calculate the cost of their clothes by calculating the sale price, the price after a coupon, and tax.

**Station4: MEASURE IT** - Here, the students will practice converting different measurements of real objects that are located in the classroom. The students will calculate their length in one unit when given the length in a different unit. Then, the students will then, check their answers by actually measuring the objects in the resulting units.

*** The objects my students will measure are: width of a door, desk, pencil (unsharpened), math textbook, whiteboard, and paperclip.

40 minutes

During the independent exploration, the students will complete the stations that I described in the "Try It Out" section. The descriptions of the stations are written below. With those descriptions, I have included details about the stations as well as links to the documents that accompany each station.

**Station 1: THE RATIO STATION** - At this station, the students will prove that they thoroughly understand the concept of ratios. This station will require that students identify ratios, rates, and unit rates when given a real-world mathematical situation.

- The students will read a mathematical situation. After reading the situation, they will need to identify the ratio represented in the problem. they will have to identify the ration as a ratio, rate, or unit rate. Furthermore, the students will have to explain how they know that the ratio represented is the identified ratio. Then, they will have to change any rates that they have found into the two possible unit rates that can be created from those rates.

**Station 2: PROPORTIONAL PROBLEMS** - When the students arrive at this station, they will be presented with 3 problems that require proportional reasoning. They will have to identify the type of problem they are dealing with (ratio & proportion, percentage, rate, conversion, or geometric). They have to identify the type of problem to help them see that there are many types of problems that can be solved using the concept of proportional reasoning.

- This station will have students complete three problems that require proportional reasoning in an unconventional way. For instance, one of the problems will require that they students measure a shape using paper clips and then pinto beans. The students will then have to compare the paper clips to the pinto beans as a ratio and explain the meaning of that comparison (Example: It takes more pinto beans to measure the length of this shape because the pinto beans are smaller than the paperclips. In fact, there are 3 pinto beans for every 1 paper clip). Another problem will ask the children about shrinking the Eiffel Tower to fit on a given square. The last problem will be a simple word problem involving proportional reasoning.

**Station 3: PERCENTAGES** - This station will require students to solve a problem given a complex situation involving sales and tax. This station will mimic what happens when you go shopping for clothing. The students will be given an opportunity to "shop" (you can use cutouts to represent clothing or you can use catelogs). Then the students will have to calculate the cost of their clothes by calculating the sale price, the price after a coupon, and tax.

- When the students arrive at this station, they will encounter a stack of cards that are face down, the students will need to choose one of these cards without looking (these cards will represent their coupon). Then, the students will choose a card of another color. Once again, they must choose the card without looking (this card will represent the sale going on in the store at this time). Then, the students will get an opportunity to "shop." For my class, I will provide my students with cutouts of different apparel. For instance, there will be jeans, shirts, book bags, shoes, and jackets. These cutouts will have price tags attached to them. The students will have to choose one of each item then calculate the cost of their items according to the sale going on in the store, their coupon, and a 7% tax.

**Station4: MEASURE IT** - Here, the students will practice converting different measurements of real objects that are located in the classroom. The students will calculate their length in one unit when given the length in a different unit. Then, the students will then, check their answers by actually measuring the objects in the resulting units.

*** The objects my students will measure are: width of a door, desk, pencil (unsharpened), math textbook, whiteboard, and paperclip.

- At this station, the students will be asked to measure convert the width of a door from yards to inches, the desk from centimeters to inches, a pencil from inches to centimeters, a textbook from centimeters to inches, a whiteboard from inches to yards, and a paperclip from centimeters to millimeters. Then they will have to use the proper measuring tool (i.e. ruler, tape measure, or yardstick).

All stations require students to make use of the following mathematical practice standards: **MP1, MP2, MP4, MP5, and MP7**

20 minutes

To close out this lesson, my student groups will present their solutions to each of the stations side by side. I will say, "Station 1." And two representatives from each group will need to come up and present their solutions. I will do the same with, station 2, 3, and 4. Every group member must take at least one turn as a presenter however, the group members that are seated may participate in answering questions after their groupmates have presented, if their groupmates are in need of assistance. **(MP3 and MP6)**

Be aware that often times, the presentations can roll over into another day and therefore, you may be tempted to skip this portion of the lesson or cut it short. My suggestion to you is to allow it to roll over into the next day and finish the closing. The closing is the most important part of your lesson because it allows your students the opportunity to articulate their understanding of mathematical concepts. Students get to practice speaking mathematics which is integral to their success in this content area.

At the conclusion of this, the students should have a clear understanding of proportional relationships and using proportional relationships to solve problems. To demonstrate their understanding, I will have my students write an essay to describe what they have learned about proportional relationships and how they can be used to solve problems. **(MP3 and MP6)**