Real World Ratios

Student Sample One
Student Sample Two
Student Sample Three
Science:
Lesson Quiz
Lesson Spreadsheet
Student Sample Writeups
Student Sample One
Student Sample Two
Student Sample Three
Math:
Lesson Powerpoint
Lesson Worksheet
Lesson Quiz
Social Studies:
Lesson Rubric
Lesson Powerpoint
Recipe Checklist
Recipies Powerpoint

Name: Cara Coffin (Math); K. Chad Graham (Social Studies); Brian Trzaskos (Science)
Grade Range 5th
School: Jefferson Elementary School, Massena, NY
Subjects: Math, Science, Social Studies, Technology

Problem Statement
Students need to use ratios on a day to day basis to solve problems they may encounter requiring them to find relationships between numbers or items.

Our purpose in creating, implementing, and assessing our STEM project is to enhance student understanding of the concept of a ratio by providing several real world ratio scenarios across the disciplines. As a fifth grade team, we would like to challenge our students to work together to use ratio skills in science and social studies through gear design and recipe manipulation. We also aim to provide students with opportunity to work in teams while utilizing relevant technology as they reach higher levels of learning by publishing their own ratio problem using PowerPoint.

Essential Questions

1. How do we use ratios in daily life?
2. How do we change a recipe to ensure that there is the sufficient amount of servings?
3. How can we present your findings technologically to challenge classmates?
4. How do we model a ratio using Lego gears?

Assessment Plan
Learning Objectives:

1. Students will be able to create equivalent ratios.
2. SWBAT use ratios to analyze gear revolutions model given ratios using Lego gears.
3. SWBAT double, triple or halve US regional recipes using ratios.
4. SWBAT find, identify ingredients, and regionally/historically connect a favorite family recipe.
5. SWBAT work in teams to change their recipe to accommodate 60 servings and then select 2 ingredients to use in a ratio problem.
6. SWBAT develop a ratio word problem to challenge peers.
7. SWBAT present their project orally, visually and technologically with a PowerPoint slide.

New York State Learning Standards

• Standard 3 Mathematics
  • 5.N.6 Understand the concept of ratio
  • 5.N.7 Express ratios in different forms
  • 5.PS.7 Represent problem situations verbally, numerically, algebraically, and/or graphically.
  • 5.PS.5 Formulate problems and solutions from everyday situations.
  • 5.PS.13 Model problems with pictures/ diagrams or physical objects.
  • 5.PS. 23 Verify results of a problem.
  • 5.PS.13 Model problems with pictures/diagrams or physical objects
  • 5.CM.4 Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols in written and verbal form.
  • 5.RP.2 Understand that mathematical statements can be supported, using models, facts, and relationships to explain their thinking.
• Standard 3 Technology
  • 3 Computers as tool for design, modeling, information processing, communication and system control, have greatly increased human productivity and knowledge.
  • Use the computer as a tool for generating and drawing ideas
• Standard 3 Science
  • Standard 1 Analysis, Inquiry and Design Mathematical analysis: Key Idea 3
    • Critical Thinking skills are used in the solution of mathematical problems
    • Apply mathematical knowledge to solve real world problems and problems that arise from the investigation of mathematical ideas.
  • Standard 4 Physical Setting
    • PI 5.2c: Machines transfer mechanical energy from one object to another.
• Social Studies
• Standard 3: Geography
  • Use a variety of intellectual skills to demonstrate their understanding the characteristics, distribution, and complexity of cultures found in the United States.
  • Human characteristics of places in the United States.
• Standard 1: History of the United States
  • Different ethnic, national, and religious groups, including Native American Indians, have contributed to the cultural diversity of these nations and regions by sharing their customs, traditions, beliefs, ideas, and languages.

Procedure
Cara’s Part
(Note: unit is labeled as consecutive days; this was not how it was taught. Due to scheduling and the way I run my classroom (certain days are small group review days or testing days); these 5 lessons were spread out over two weeks)

• Day 1: On the first day of the unit I introduced to concept of a ratio with a simple situation that intended to grab the students’ attention; I made them punch. I modeled the recipe and presented the idea that I didn’t have enough- easy solution! The students said, double it! From there we explored the concept of a ratio, as a comparison of two values, and the idea of equivalent ratios while they sipped their punch. The second half of class introduced the students to the three different forms of expressing a ratio, which we then practiced.
• Day 2: After reviewing the previous day’s material, we moved on to using ratios to solve simple problems, such as: ‘There are 12 boys and 10 girls in a class. How many students are there?’ The second chunk of class was spent on furthering knowledge of equivalent ratios. We completed a worksheet using ratio boxes to help visualize why ratios can be called equivalent. The third lesson ‘chunk’ challenged students to use ratio boxes to solve situations in which they had to (in partners) double, triple, quadruple, halve, etc., different ratios.
• Day 3: After a solid review of the previous two lessons, students were exposed to the website, http://www.thinkingblocks.com/ThinkingBlocks_Ratios/TB_Ratio_Main.html. After examining and solving two word problems, we headed to the computer lab where students, individually, worked on level one of this computer program.
• Day 4: On the fourth day we put it all together with review, especially of the website: wemodeled with a picture what they had done to help them solve the word problems. We also covered a second way (without a picture model) to approach the word problems. Together we solved 4 word problems on my PowerPoint.
• Day 5: Students solved a challenge problem with partners, then attempted to create their own
  problem. Several student made problems were then shared with the class. I read the book Counting On Frank to expose students to ratios in the form of proportions (students have used proportions previously to assist them in changing customary and metric units of length) and to allow their imaginations to be filled with the idea that math is always around them. After reading and discussing the book, we solved the peas problem for ourselves, to see if it was true. After the peas students worked in pairs to see how many steps they would walk in a mile by counting the number of steps taken in a line of 10ft.
• Over the next two weeks, I continued to review ratios skills through bellringers, centers,
  homework, and NYS Math Test Preparation. It was after these two weeks that students were tested on their ratio knowledge. In comparison to last year, students’ comfort level was huge and it showed, they out performed the previous year when tested on the knowledge.

Chad’s Part

• Lesson 1: Cultural Diffusion
  On the first day of class students explored the concept of cultural diffusion. As a bell ringer question, students were asked the meaning of the word culture. After discussing the bell ringer, students completed a Cooperative Learning activity (Round Table/Team Stand and Share) where they explored the following question: What are some cultural characteristics that have been brought into the US from other countries?
  After the class finished sharing their thoughts, a discussion followed focusing on the movement of ideas and traditions from Latin American cultures. Students identified many Latin American influences on our country, especially through the culinary arts. As a closure to the lesson students were presented with a recipe for Salsa and Guacamole. The class examined where in the US, the ingredients can be grown and what has enabled the movement of these cultural traditions throughout the US. The class was then informed that they would be creating a class cookbook and each student would be responsible for bringing a recipe from home that is reflective of their cultural heritage.
• Lesson 2: The Food We Eat
  After reviewing the ideas of cultural diversity and the movement of traditions throughout the United States, the class returned to the recipes for Salsa and Guacamole. Noting the serving size for each recipe, we discussed what would have to happen in order to make enough salsa and guacamole for the entire class to enjoy. The class reviewed mathematic rules for doubling and tripling recipes, and the teacher modeled tripling all the ingredient quantities for the salsa recipe. Students were then asked to identify the ratio of tomatoes to peppers in the salsa recipe and then were presented with a model of an essential ratio question concerning salsa ingredients.
  If I have a total of 14 peppers and tomatoes, what is the ratio of tomatoes to peppers?
  Working with their shoulder partners, students solved the essential question. They were then asked to develop another essential question with their table group, using the same recipe. Groups shuffled, and students took turns challenging the others at their desk pod to solve the different essential questions created. For homework, students were given a copy of the guacamole recipe and were instructed to make the necessary ingredient conversions for the recipe to serve the entire class.
• Lesson 3: Agricultural Resources
  At the onset of class, students reviewed the similarities and differences between corporate and family farms in the United States. The class looked at what ingredients in Guacamole could be grown/produced in the US and where. The class went over their homework assignment, converting the guacamole recipe, and students were asked to identify the ratio of avocadoes to tomatoes in the recipe. After the ratio was established groups attempted to design an essential question using avocadoes and tomatoes. The essential questions were shared and solved then the class discussed how the geographic location of an area can also affect many of their beliefs and traditions. Students were then shown a recipe for Ambrosia Salad. Using the Effective Teaching Interactive Sequence, students were asked to think and discuss what region of the country the recipe originated, and what led them to this conclusion. As a homework assignment, students were told to bring in a recipe that reflected the cultural/geographic diversity of our country. Students were given 3 days to obtain a recipe from home. The teacher had a number of appropriate cookbooks on hand that students could use if they were unable to obtain a recipe from home.
• Lesson 4 (3 days later): Diversity Within our Town.
  At the start of class students used an Inside/Outside Circle to share the recipe they brought from home (or obtained from teacher cookbooks). Returning to their desk pods, each group selected one of their homework recipes to analyze in the following activity. Students were instructed to create a short written piece explaining what cultures influenced the chosen recipe and where in the United States many of their ingredients could be grown. The teacher modeled the writing process using the think aloud strategy (Interwrite Tabled Utilized).Groups had various resource books at their disposal to help them gather the information for the writing piece, as well as access to Grolier’s online database, using the classroom computers. As homework, students had to copy their recipe onto a sheet of paper, and convert the ingredients into a proportion that would serve the entire class. A brief review of that procedure was shown. Students were presented with a checklist outlining all required components of this assignment.
• Lesson 5: Sharing Recipe Analyses
  Using the writing activity from the previous day, each group created a short Aural/visual presentation to share with the other groups. The class then took part in the Cooperative Learning Activity 3 Stay 1 Stray and taught other groups about the cultural/agricultural elements behind their recipe. After the culminating class sharing time, the class teacher explained that they would be using their recipe, with its ingredient conversions, to develop an essential question of their own concerning a ratio. Returning to the Ambrosia Salad recipe, students were presented with one final model of the essential question, which they solved.
• Lesson 6: Computer Lab
  Students went into the computer lab to type their recipes, using Microsoft Word. Teacher modeled certain typing skills that were needed for this assignment; using tab to create 2 columns of ingredients, how to bullet/numer directions, changing fonts. Students were reminded of the checklist that they were presented concerning the recipe requirements and were told to use that as a guide while they were typing the final copy of the recipe. Teacher saved all completed recipes and compiled a class cookbook.

Brian’s Part

• Day 1: Form teams of two. Give each team a bag of materials and instructions on how to construct the gear train base model. Have them build a simple gear train. Introduce students to vocabulary terms that will be used in this lesson: gear, gear train, driver, driven, idler, and mesh. Discuss the question “How does the size and/or position of gears affect the way that they move?” with the class. Let students reflect on the day’s activities. Use http://auto.howstuffworks.com/gears.htm as a way to review the day.
• Day 2: Hand out bags of materials and student record sheets. Teams must record the gear trains they produce and any observations they make. They should identify: that gears that mesh move in opposite directions; that large drive gears and small driven gears will speed up the rotation; that (conversely) small drive gears and larger driven gears will result in a slower rotation; that idler gears can affect the direction, but not speed, of the rotation of the driven gear.
• Day 3: Hand out bags of materials and student record sheets. Students will be asked to construct gear trains and use them to lift a 100g. weight from the floor. Students will record observations. Students should infer that a large driver and small driven will get the job done quicker, but is more difficult to operate. Whereas, a small driver coupled with a large driven is much easier to operate, but takes longer to complete its task. They will be asked to identify how different combination of given gears work.
• Day 3 and 4: Students will design and construct a mystery LEGO® “machine” that contains a gear train. They must describe why they choose the gear ratio that they used (what they hoped to accomplish.). Students will exchange “machines” and try to determine the ratio of the hidden gear train. They will also try to determine the other characteristics of the “machine”.

Cara’s Part: The Sequel

• After the students had finished their recipes with Chad, I was responsible for turning their raw material into a word problem. I had intended to model the problem, have them write theirs, and edit all in one day. We were able to finish their problems, but the editing took several days, because each student’s situation was different. I edited while students were working on different projects, pairs activities, and centers.

All Three Teachers

• After the editing process was complete, we each, separately, taught our students how to use PowerPoint and helped them create a slide to publish their problem. We spent a total of 1 and ½ hours in the computer lab to complete this.
  Using the LCD project the teacher demonstrated how to access basic tools of PowerPoint; for example, how to add and delete text boxes, change fonts and colors, insert word art, insert and delete clip art, set background color (optional), and most of all, how to create a custom animation sequence. After each demonstration the students were given time to practice, explore, and adjust their own slide.

Assesment Plan
Informal: Students were continually assessed informally through bell ringer activities, a daily ticket out the door problem, Cooperative Learning information sharing techniques, Effective Teaching interactive sequence, partner sharing, and teacher observation.

Formal: Students were assessed formally through homework assignments, a math quiz taken after 4 weeks, a typed copy of a recipe with ingredient conversions, and through their Recipe Ratio Problem Project (using a rubric).

Assessment Tools

1. Equivalent Ratio Worksheet
2. Quiz
3. Gear Ratio Data Sheet
4. Gear Ratio Quiz
5. Written Recipe Checklist
6. Rough Draft Planning Page
7. Culminating Project Rubric (Ratio Recipe Rubric)

Integration of Math, Science, Technology
The rationale behind our Learning Experience (Unit) comes from the previous teaching year and the struggle of students to understand and solve ratio problems. The partnership of our 3 teacher team has come together to create a multi-discipline (math, science, social studies, and technology) approach to increase the degree of student success. Spreading out the unit over 7 weeks allowed students more time to become familiar and comfortable with their skills. This approach was intentional; with the hope that repetition, in different disciplines, over time, will improve retention and application in the future.

Reflection
Cara:
I think that the students this year have a much better understanding of ratios and a higher aptitude for solving word problems with equivalent ratios. I enjoyed the way that I taught the ratio unit this year, starting out with punch got their attention- food is always the number one motivator. My PowerPoint presentation was very successful, as were the ratio boxes. The STEM grant afforded me with the time to create both of these. I think that the time for the students to use the online manipulatives available in the website we used was amazing to get them to see how to solve ratio problems. It was the fastest, most effective way to give them time and opportunity to practice at their own pace. I didn’t have anyone waiting for the next problem while I helped those struggling.
The recipe word problem component really made me see how much the students need to create their own word problems. It is such a challenge for most of the students, and eye opening to what they perceive to be a complete word problem. We practice so much how to solve them- that they can sleep their way through it. But when creating one, they really have to understand the pieces of the problem, as well as the answer, to craft a challenging problem. We needed to practice this more, before expecting them to be able to create their own. We ran out time editing so I did verbal conferencing- the students and I talked about what they wanted to write. More practice creating word problems is one of my goals for next year. The students may have had a hard time with writing the word problem, but it is amazing how quickly they acclimated to PowerPoint. The custom animation was by far their favorite and it really got their attention. I’d like to use PowerPoint to publish a problem again next year.

Chad:
This project was a great way to reinforce basic geographic skills. It is important for students to leave 5th grade with a solid understanding of the 5 different themes within geography; location, place, movement, interaction, and region. Food is a great example to use with students, when dealing with the themes of interaction, movement, and place. They are able to see real world application that influences their everyday lives. In the past students have been able to effectively grasp the meaning of each theme of geography, and have been able to identify examples of each themes, but their understanding seemed to go to an entire new level, when they were able to make personal connections with recipes that have become part of their family’s traditions. I was impressed how excited the students were with this activity, every day they were very eager to tackle the next step in the challenge.
At first I was a little worried about what types of recipes students would bring in for this activity. Would there be a decent variety? Would they show different cultural influences? Students, however, rose to the occasion and brought in very interesting and diverse recipes. Due to the fact that not all students were able to obtain a recipe at home, I was able to guide the hand of diversity. Through the reference cookbooks provided for student perusal, I was able to consciously enable greater cultural and agricultural variance from students not bringing a recipe from home. Using technology, both as a reference guide, and as a publishing tool were very exciting for the students. They always enjoy an activity that allows them to work with computers. Technology is also quite helpful as a direct instructional aid, as the use of PowerPoint presentations and the Interwrite tablet makes whole group instruction much more effective. I did find that it took a little longer than I had planed to create the PowerPoint Slides. While some students were able to finish in the allotted time, it took others a little longer. Rather than take them to the computer lab, I simple had students finish slides on my 4 classroom computers during study halls and morning time.

Brian:
When Cara suggested Ratios as the object of our triad’s work, I immediately thought about using Legos and gears as a way to get some hands on work in the area of Science. Even though 5th Grade Science in Massena is basically Life Science, I also thought the change would be good. It would give them a real world application that they could appreciate, and maybe apply to what they already know. Besides, it would be FUN!
I wanted to use a discovery approach, to see what the students would/could find out for themselves. Unfortunately, I didn’t fully anticipate how much just plain fun they would have when they were given their bags of materials. “Discovery” was random and arbitrary. I quickly had to add a little order to their data collection. I gave them sets of gears to investigate and report on, and grouped them as to make switching easier. I also had to standardize on a structure for attaching gears that was durable and useful. I believe these changes will make it easier in the future.
Student teams were totally involved, counting, figuring, and calculating (then recounting and recalculating!) Many students were able to correctly calculate the ratio between the teeth on the input and output gears. But when reporting it as a gear ratio, as it is actually an inverse relationship. It is counter-intuitive. For example, a 10 tooth driver (input) gear, paired with a 30 tooth driven (output) gear, results in a 3:1gear ratio (requiring 3 turns of driver for each complete turn of driven) instead of a 1:3 ratio. Some students just couldn’t make the switch!
I was impressed by how they were able to discover the mechanical force and speed relationships that gear ratios represent. They that saw that pairing a large driver and small driven gear got the work done more quickly, but it was harder to operate. Conversely, a smaller driver and larger driven gear was slower but easier to use.
The final activity, their mystery “machine” left me a little disappointed. While they were eager to “play”, I didn’t see much creativity, most opting for a typical solution. All were very similar. While most showed a rudimentary understanding, a couple showed promise and a few showed extra work was needed.
All in all, I think it was a good activity that, with a little work can be very worthwhile to continue in the future.

Resources
Teachers:

• cups
• bowl
• ladle
• ginger ale
• fruit punch
• LCD project
• computer
• Interwrite tablet
• PowerPoint presentations (attached)
• Counting On Frank
• tape
• overhead projector and transparencies
• http://www.thinkingblocks.com/ThinkingBlocks_Ratios/TB_Ratio_Main.html
• equivalent ratio worksheet
• Glencoe Math textbook
• Book series Portrait of America
• Book Series Discovering America
• http://www.go.grolier.com
• American Grub: Eats For Kids From All 50 States
• American Regional Cooking Library Series
• Lego® blocks and gears
• ratio data sheets
• gear ratio quizzes

Students:

• pencils
• notebooks
• computers
• PowerPoint
• recipes
• Glencoe math textbooks
• http://www.thinkingblocks.com/ThinkingBlocks_Ratios/TB_Ratio_Main.html

Instructional Modifications
To accommodate all levels in the classroom:

1. Note taking assistance: Students, who are unable to take notes at a grade level expectation, take notes with the assistance of the teacher or teacher’s assistant.
2. Organizational assistance: teacher or teacher’s assistant helps student keep track of all items needed.
3. Activities in the classroom are altered for individual students, for example, students at a higher level were encouraged to shoot for a higher level of the website, while students at a lower level were never left unattended while working on the website.

Time Required

• Planning- 2 hours of work at STEM Grant Conferences, 1 ½ hours on PowerPoint, 3-5, 40 min planning periods.
• Implementation
  Unit Timeline:
  • Weeks 1 & 2 (5 – 45 min lessons)
    Students are taught ratio concepts in regular math class setting and in computer
    lab.
  • Weeks 3 & 4 (5-10 min each day)
    Students continue to practice and develop ratio skills in small group (center)
    activities, bell ringers, homework, and classroom challenges.
  • Weeks 5 & 6 (5- 45 min lessons, then ~10 min each day, also 1 ½ hours in Computer Lab)
    Students work with ratios in Social Studies with relation to ratios. In math they take what they have learned, found, and practiced to create their own word problems with the intent of challenging their classmates to solve how they changed their recipe (using 2 equivalent ratios). Students are also, simultaneously, introduced to PowerPoint and use their new skills to create a slide; publishing their own problem.
  • Week 7 (3- 45 min lessons)
    Students are introduced to gears, revolutions, and how ratios pertain to science.
• Assessment- 2 grading hours
• Triad: 4 conference days, 3 planning periods, and the better part of a weekend typing this up.