1. Backward Design Lesson Plan for a Pre-Algebra Class The 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 ►T►T►T►The real lime! ►R►R►R►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 4 people using similarity or proportionality. ► A group of students will modify the Chocolately Trail Mix Original Recipe to serve a total of 8 people 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: