Ratio and Proportion Standards Posters
At the beginning of each unit, I post the standards on individual posters. These standards are written in simplified language to make them more studentfriendly. They are also broken down (multiple posters per standard) if there are many parts to the standard. I like having the standards posted so that I can refer back to standards we have addressed previously. I write our focus standards for that day's lesson on the board under the "I can" portion of our board.
Task 1: Introduction to Ratios and Ratio Language (6.RP.1)


To begin, students must have a basic understanding of ratios. The lesson allows students to interact with the SMARTboard to create visuals which match ratios, see the three formats for writing a ratio, and an introduction to equivalent ratios and unit rate.
Unit rate can be compared to making sports teams. Each team needs only one captain or coach, and each team must have the same amount of players. Students can find the unit rate by determining which group is the coaches and which is the players being divided among them evenly.
To followup, ratio pictures are printed and posted around the room. Students do a gallery walk, and write a ratio (practicing a variety of the three formats) for each picture. This can be done individually or in partners. Students must label their ratios (i.e. 6 pairs of boots to 5 pairs of sandals, 6/5, 6:5).
As an extension, students can try to find the unit rate for the ratios which they wrote.
Unit rate can be compared to making sports teams. Each team needs only one captain or coach, and each team must have the same amount of players. Students can find the unit rate by determining which group is the coaches and which is the players being divided among them evenly.
To followup, ratio pictures are printed and posted around the room. Students do a gallery walk, and write a ratio (practicing a variety of the three formats) for each picture. This can be done individually or in partners. Students must label their ratios (i.e. 6 pairs of boots to 5 pairs of sandals, 6/5, 6:5).
As an extension, students can try to find the unit rate for the ratios which they wrote.
Task 2: Legs Task (Mathematical Practices and 6.RP.1)
This task allows students to begin using a variety of strategies to solve a problem which has multiple answers. It encourages students to follow the Mathematical Practices (nearly all 8 of them!). This is the most difficult shift for students from teachercentered to studentcentered math instruction. Student are able to draw visual models, use addition, subtraction, multiplication, and division strategies to solve this task.

Task 3: Sticker Ratios  Understanding Unit Rate (6.RP.2, 6.RP.3a)
Using packages of foam stickers (or other variety of small items) bought at the Dollar Store, students create their own ratios from the groups of items. They complete a chart which asks them to write a sentence context for their ratio, draw a simple diagram of their ratio, write their ratio in the three formats, create a ratio table, and list the unit rate in three formats.
As you circulate, students may need assistance understanding how to find unit rate when it does not group evenly. See the example file for a variety of strategies. 

Task 4: Foodbank Task  Using Unit Rate (6.RP.3, 6.RP.3b)

Task 5: Grocery Store  Finding Unit Rate (6.RP.2, 6.RP.3b)
Our local grocery store changes its advertisements every Wednesday. On Tuesday, I went and gathered enough of the old ads for each of my students. I then created a worksheet where students have to find the unit rate (cost per ounce, per package, per pound, etc.) This can be altered based on the ad, and the difficulty desired. Some prices will not work out to be an even unit rate, and are therefore more complicated to find.

Task 6: Practice Showing Your Thinking (Mathematical Practice #3 and #4)


I found that my students had a difficult time understanding the different ways to show their thinking. I introduced the ratio table far too soon, and all of my students began to use it as an algorithm (simply plugging in numbers without understanding how to use it.) I decided to take a step back and spend time allowing students to demonstrate their understanding of the context before they were asked to do any problem solving.
I did this in three different ways depending on the needs of my group. For all students, I reminded them of Practice Standard # 4  I can show my work in many ways, as well as Practice Standard #3  I can explain my thinking and try to understand others.
For the independent group, I had them do a gallery walk around the room. I printed the scenarios and questions, taped them up around the room, and had them travel around answering the questions on their notebook paper.
For my intermediate group, I had them do several scenarios whole class on their whiteboards first. I used the "basic" Powerpoint so they were introduced using easier number sets. After drawing their diagram, creating their number line, using a ratio table, or other method, they took a gallery walk around the classroom with their whiteboard markers. They paused at their neighbors' desks, tried to see if they understand the person's approach, and then put a check mark if they understood and a question mark if they had questions. When they returned to their seats, they tried to clarify if there were lots of question marks by adding to their work or trying another method. Those whose work was clear, were encouraged to try an approach which they saw at someone else's desk. After a few of these, I had them do the independent gallery walk around the room to complete the same scenarios with more difficult number sets.
For the basic group, I spent more time doing the whole group discussion piece from the intermediate group. I then encouraged them to do #1  #6 on the independent gallery walk. If they finished, I had them go on to the other questions.
I did this in three different ways depending on the needs of my group. For all students, I reminded them of Practice Standard # 4  I can show my work in many ways, as well as Practice Standard #3  I can explain my thinking and try to understand others.
For the independent group, I had them do a gallery walk around the room. I printed the scenarios and questions, taped them up around the room, and had them travel around answering the questions on their notebook paper.
For my intermediate group, I had them do several scenarios whole class on their whiteboards first. I used the "basic" Powerpoint so they were introduced using easier number sets. After drawing their diagram, creating their number line, using a ratio table, or other method, they took a gallery walk around the classroom with their whiteboard markers. They paused at their neighbors' desks, tried to see if they understand the person's approach, and then put a check mark if they understood and a question mark if they had questions. When they returned to their seats, they tried to clarify if there were lots of question marks by adding to their work or trying another method. Those whose work was clear, were encouraged to try an approach which they saw at someone else's desk. After a few of these, I had them do the independent gallery walk around the room to complete the same scenarios with more difficult number sets.
For the basic group, I spent more time doing the whole group discussion piece from the intermediate group. I then encouraged them to do #1  #6 on the independent gallery walk. If they finished, I had them go on to the other questions.
Task 7: Cookie Task  Double Ratio Table (6.RP.3a, 6.RP.3b)
The application of unit rate, and combining numbers from the ratio table correctly are the focus areas of this task. Packaging contexts often lead to ratio and proportional reasoning. In this lesson, students must think what it means when the number of bags of cookies change. A common misconception is that as one bag is added, students will only add one cookie. They must have a clear understanding that the unit rate means that for every bag, a GROUP of cookies is added.

Task 8: Dog Food Task  Comparing Rates (6.RP.3b)

This task also requires students to use a common unit rate to find the final answer. The context does not explicitly tell them that they must find the unit rate as it is compared to 1 pound of dog food. Rather, they are able to decide if they want to bring the price down to price per pound. Or, they may choose to bring the number of pounds up until the number of pounds in each bag is equal. This requires the least common multiple of pounds. Whichever method they choose, they will find that one price is better than the other. This task also allows them to use previous knowledge from the first questions to answer the next questions and extensions.
Task 9: Lawn Mowing Task

Task 10: Baking Cookies (Review Activity)
I used PhotoStory 3 (a free online software) to create this video of my baking adventures. I created a set of questions which accompany the video. Students will be reviewing a variety of Ratio and Proportion Standards, as well as some basic fraction ideas.
My hope is that my students will be able to produce their own PhotoStory 3 videos of a mathematical problem which they design for their peers. This will be part of their final project for this unit. I expect students to take 2 days of classroom time to complete the worksheet, and another 2 days to write their own ratio and proportion problems.

