Subject and Level - 6th Grade Math, Fractions

Learner Description -

There are 27 students from a pre-algebra class who were selected to complete this project. These learners are all gifted or bright in the area of mathematics.

Overview -

The question that serves as a framework to this unit is how do you serve exactly 29 people?

To answer this question, the students master multiplying fractions with whole and mixed numbers through direct instruction and practice. Then they apply this concept by finding recipes on the Internet that have 2 fractions and 1 mixed number. They use these recipes to change serving sizes. These changes are recorded in a packet.

Upon completion of the packet, the students work in teams to find a meal they could cook for the class. In order to do this, each student is responsible for his/her own entree to contribute to his/her team's meal. The catch is that they have to calculate for exactly 29 eaters (27 students and 2 teachers). Since recipes don't typically serve 29, students have to modify the original recipe. Specifically, they are required to calculate the exact amount and then round the result to a benchmark fraction. When the students finish their calculations, they create a website with their recipes and need to link the recipe with their team's website. When the teams finish their websites, some students volunteer to create a class home page to link all the websites together.

In the end, the class is able to make their own online recipe book. And because the students actually try making their meal for the class, they are able see if their calculations were accurate.

Rationale -

Why would you teach this unit?

The purpose of this unit is to give students a real life application for fractions. Fractions are typically the most difficult number representation to understand, yet its usefulness is significant especially in areas related to measurement such as cooking.

Why would this qualify as an engaged learning unit?

"Just Enough for Us" is an engaged learning unit because the students are responsible for their learning. The students initiated the requirements, due dates, and assessed themselves and their teammates. The project was also engaging because it was collaborative. The students worked together to determine a theme for their meal and helped each other problem solve.

Why is technology an important component of this unit?

Technology is an important aspect of this unit because it is a means for organizing and representing the data students collect. The cookbook is web-based because it allows the recipes to be easily linked together, and it is an easy and cost effective way to share information.

Why is this project authentic/meaningful , and challenging for students?

  "Just Enough for Us" is a real world problem. People have to change serving sizes when they cook fairly frequently. As a result, students are able to see how math relates to other aspects of life and consequently have an invested interest in the project.

Goals - Content, Cognitive and Social -  

What new attributes (knowledge, skills, attitudes) do you expect students to gain?

Students will gain knowledge about how fractions fit into the world they live in. For example, a very specific piece of knowledge students learn is that when someone says they're going to divide something in half, they don't mean it to be taken literally. This is because if you follow the procedure for dividing fractions, dividing something in half would actually double it. As a result, the students learn that a fraction "of" a quantity means to multiply and that people should say "divide it in two" or "multiply it by a half" instead.

What school, district, state and national standards/benchmarks are addressed?

Mathematics Standards:

1. State Goal 6 A: Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.

- Students become familiar with different ways to express fractions.

2. State Goal 6 B: Investigate, represent and solve problems using number facts, operations, and their properties, algorithms, and relationships.

- Students multiply and divide fractions.

3. State Goal 6 C: Compute and estimate using mental mathematics, paper-and-pencil methods, calculators, and computers.

- Students compute new ingredient amounts if the serving sizes change.

4. State Goal 7 A: Measure and compare quantities using appropriate units, instruments, and methods.

- Students measure ingredients in their recipes.

5. State Goal 7 B: Estimate measurements and determine acceptable levels of accuracy.

- Students estimated results to the nearest benchmark fractions.

6. State Goal 7 C: Select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings.

- Students use the computer to create their own web-based cookbook.

7. State Goal 8 D: Use algebraic concepts and procedures to represent and solve problems.

 - Students use a formula for changing serving sizes by taking the ingredient amount and multiplying it by the ratio of the serving size that is desired over the serving size given.

Learning Activities - The activities required to achieve the goals.

1. Develop procedures for multiplying and dividing fractions and master them through practice.

2. Apply mastery of multiplying and dividing fractions by changing serving sizes of recipes on the Internet.

3. Apply skill in a new way by creating a web-based cookbook for the class. Manipulate ingredient amounts to serve exactly 29 eaters.

4. Create meal for the class to test calculations.

Student Assessment- Enables student and teacher to measure student's attainment of goals.

What are my scoring characteristics?

The scoring was based on several components: 1. The students' ability to manipulate fractions, 2. Completion of each task, 3. Overall contribution to the project.

What will indicate that students are novices, practitioners, or experts?

The novices attempt procedures to solve problems but do not notice when they're heading in the wrong direction. (I.e., They would divide a recipe in half and not notice they were doubling something they should have halved.)

The practitioners attempt procedures to solve problems and aren't afraid to ask for directions. If they find they're heading in the wrong direction, they turn around, go back, and try a new direction. (I.e. They would divide a recipe in half and realize that something in their solution doesn't make sense.)

The experts know the procedures and point others in the right direction. (I.e., They would recognize that in order to take half of a quantity, they could either divide by 2 or multiply by a half and see the connection between the two procedures. They would also be able to share this information with others.)

How will I measure and communicate student progress on the goals?

The students will be checked to see that they did correct calculations and that all websites and links are functioning correctly. Work will not be accepted until it meets the minimum requirements established by others. In other words, when the students were given the ambiguous task of creating a web-based cookbook, requirements were created daily as students found particularly effective ways to organize and represent their data. Basically, they took the idea of a web-based cookbook and determined for themselves how to implement it.

How can students be involved in establishing goals and criteria for the assessment?

The students decide how many points the project would be worth and how they would grade it. The result will be to have students evaluate the activity, themselves, and their teammates.

How will the assessments be implemented to ensure that they are generative? Seamless and ongoing? Equitable for all students? An authentic task?

The assessments are generative because the end product is that students create the recipe they manipulated to serve the class.

They are seamless and ongoing because prior to the culminating activity of creating the meal, students have to stop at several checkpoints to see if they know where they are going (i.e., completion of fraction multiplication exercises, quizzes, and an individual check of calculations and websites).

They are also equitable for all students because even though it was a team project, the students are assessed for their individual efforts and contribution to the team. Additionally, modifications were made to ensure that students put in a fairly equal amount of work. For example, a student may attempt to do a recipe that doesn't demand any fraction calculations. Instead of requiring the student to start over, he/she would create the easy recipe and supplement his/her work by doing calculations for a more difficult recipe.

The authentic aspect of the assessment is that all the students and teachers in the class ate the meals each team created. If there were any major mistakes in the calculations, the class would be able to taste it.

How will students demonstrate their knowledge and skills?

The students will demonstrate their knowledge and skills through the practice problems, quizzes, Internet recipe packet, calculation check, website, creation of their entrees, and self/peer evaluation.

Resources -

What resources will you need to do this unit?

Human

- Teacher, teacher's aides, technology assistant, parents

Technological

- Computers, Internet, Netscape Navigator

Other

-Kitchen, ingredients, cooking utensils

Management

How will you manage student work individually and in groups?

Students are held responsible for their individual contribution to the unit. Each student found their own recipe, manipulated it, created a website of it, and made the entree. The team aspect was that the entree had to fit the team's theme for a meal and that the students had to decide who brought what. Students that did not fulfill their individual responsibilities would not meet the requirements of the unit and would be evaluated poorly by their team.

How will the room(s) be arranged?

Since the majority of the project occurs in the computer lab, this was not a consideration that had any effect on the result. The only thing necessary is to have a computer for every student and be able to sit teams in the same general location so they can communicate. For the days in the classroom, the students are eating the meals. As a result, they were allowed to move the seats wherever they felt comfortable within reason.

Where will equipment and materials be located to promote maximum use?

During the time when students are investigating recipe websites and creating their own website, all the equipment should be in the computer lab. When the students are eating their meal, all the food should be placed in an easy to serve area. The teachers put food on the plates and the students that are catering pass them out. All the students work together to clean up at the end.

Where will students need to work and how can they be accommodated?

Students will need to work in the computer lab. If they run into technological glitches and run behind, the accommodation can be to have them use the computers in the classroom outside of class time.

How will students with special needs be helped?

The students with special needs should be grouped with students who work well with him/her and have an expertise of the subject area. He/she may have a teacher's aide. Additionally, extensions of due dates or shortening of the assignments may be provided based on the individual needs of each child.

Unit Evaluation

What will I need to do, be aware of, and/or gather while teaching the unit in order to answer these questions:

What was effective?

- Allowing students to determine their own due date s

- Keeping the tasks open-ended

- Having an individual and team components in the project

- Being flexible to make modifications as needed

What wasn't effective?

The one component of "Just Enough for Us" that was the most difficult was serving the meals students created. The teacher is completely dependent on the students to bring everything they need to cater their meal to the class. While it is a necessary risk if the teacher wants the student to take responsibility, it promotes extra stress and anxiety on him/her.

Lunch periods are 30 minutes. There are 29 people to serve. If there will be any time to eat, each eater must be served in less than a minute. This is a difficult task, if a group is unprepared. Additionally, some students brought in complex meals that needed to be heated. Unless the teacher is lucky enough to have a plan period right before lunch, students who don't have their meals dropped off may have to serve luke warm or cold food. s

What will I do differently next time?

  In order to prevent some of the stress of serving the food, students should be required to have the food precut and if possible, already on plates. Food that needs to be kept warm should only be made if a parent/guardian is available to drop it off right before lunch.

Additionally, there might be a better way to assess the students. For example, now that one class has completed the project and there is an end-product, it might be a good idea to go back and decide if there are specific requirements students should be aware of prior to the activity.