Backward Design Lesson Plan for a Pre-Algebra Class The Trail Mix Recipe

1. Backward Design Lesson Plan for a Pre-Algebra ClassThe Trail Mix Recipe Hattie Fourcade, Diana Obstfeld, Randy Weiss, and Bill Lester June 15, 2006 Number and Operation in Secondary Mathematics NS 696V

2. Safety Concerns • Peanuts!

3. Warm-Up Joke! • What is green and homeomorphic to the open unit interval?

4. Answer • The real lime! • Rentein and Dundes, 2005 – Bad Mathematical Joke

5. NCTM Standard/Colorado Standard 1 • Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

6. Benchmarks for Grades 5-9 • Use the relationships among fractions, decimals, and percents, include the concepts of ratio and proportion, in problem-solving situations.

7. Indicators • Scale Factor • Similarity or Proportionality • Unit Rate

8. Goal/Target What will students know and be able to do? • Students will apply proportional reasoning to modify cooking recipes to serve quality food. • Trail Mix • Play Dough • Mrs. Field’s Cookies • Navy Bean Soup • Smoothies • Pizza • Salsa Dip

9. Assessment Objectives • Students modify a Trail Mix recipe to accommodate a specific number of people and produce the Trail Mix. • Students modify a Play Dough recipe to accommodate a specific number of people and produce the Play Dough. • Students communicate the process to modify the original recipe and share the results. • Students describe a situation, other than in cooking, where proportional reasoning can be used.

10. Understanding • Students will understand • that they can take any measurement or combination of measurements to increase or decrease the measurement of an item or the combination of the items for a desired outcome. • that there are multiple paths to use for achieving the desired outcome when increasing or decreasing given measurements. • For example: If we have pie recipe for six people, how do we change the recipe for eight people. We can use at least three skills: scale factor; proportionality, and unit rate.

11. Essential Question(s) • How does math help you plan a better party? • How do you find and use a scale factor? • How do you set-up and use a proportion? • How do you find and use a unit rate? • Rigor • Relationship • Relevance

12. Assessment Evidence • The Evidence of Learning includes • the modified Trail Mix recipe; • the modified Play Dough recipe; • the communication of the recipe solutions and the presentation of the students’ products. • everyone receives a serving of Trail Mix and Play Dough to mold.

13. Learning Plan • Prior Learning Activities/Experience include • Direct Instruction • Warm-Ups • Activity - Buying Pizza – Navigations Series • Activity - Exchanging Currency – Navigations Series • Activity - Changing Rates – Navigation Series • Guided Practice and Problem Solving - Using Unit Rates –– 5-5 – Scott Foresman & Addison Wesley • Independent Practice or Cooperative Learning - Problem Solving Using Rates and Proportions – 5.6 – Scott Foresman & Addison Wesley • Independent Practice or Cooperative Learning - Solving Proportions Using the Unit Rate – 6.7 – Alternative Lesson – Scott Foresman & Addison Wesley • Independent Practice - Solving Proportions Using Unit Rates – 6.7 – Scott Foresman & Addison Wesley • Activity - Using a Unit Rate to Solve Problems – Navigation Series • Activity - Decision Making – 6.5 – Extend your thinking – Scott Foresman & Addison Wesley • Formative Assessments – Quizzes • Scale factor • Similarity or Proportionality • Unit Rates

14. Gorp Trail Mix Original Recipe • Materials • 2 lbs M & M’s® • 15 oz dry roasted peanuts • 15 oz raisins • 8 oz sunflower seeds • 6 oz peanut butter morsels • Combine all ingredients together in large bowl and store tightly sealed in Ziploc bags • Recipe serves 5 people.

15. Chocolately Trail Mix Original Recipe • Materials • 1 c. semi-sweet chocolate mini chips • ½ c. salted sunflower seeds • ½ c. dry roasted peanuts • ½ c. raisins • ½ c. chopped dried fruit • Toss ingredients together in a bowl. Store in Ziploc bags. • Serves 6 people.

16. Modification Activities • A group of students will modify the Gorp Trail Mix Original Recipe to serve a total of 7 people using unit rates. (The group needs to convert ounces into grams) • A group of students will modify the Gorp Trail Mix Original Recipe to serve a total of 8 people using a scale factor. (The group needs to convert ounces into grams)

17. Modification Activities • A group of students will modify the Chocolately Trail Mix Original Recipe to serve a total of 4people using similarity or proportionality. • A group of students will modify the Chocolately Trail Mix Original Recipe to serve a total of 8people using a skill of its choice – scale factor, similarity/proportionality or unit rate.

18. Play Dough • Materials: • Flour • Salt • Powdered Alum • Water • Food coloring • Measuring cups • Measuring spoons • Plastic bag • Bowl • Paper towels • Gloves

19. Play Dough Recipe • Combine and mix the dry ingredients: • 2 ½ cups flour; 1 ¼ cups salt; 9 Tbsp powdered alum in a mixing bowl • Add 1 ¼ cups water and 3 drops of food coloring to the mixed dry ingredients • Using the gloves, mix the ingredients with your hands. • Store in a plastic bag in the refrigerator.

20. The Six Facets of Understanding • Explanation: