The students encounter the problems of adding two fractions with like denominators to produce an improper fraction, and interpreting the meaning of the result. They learn to convert improper fractions to mixed numbers. Then the instructions are reversed, requiring them to convert mixed numbers to improper fractions. This activity is motivated by a Cyberchase episode at "Frogsnots" with Professor Dumbleshore adjusting recipe sizes in order to confer power on sorcerers.
Part I: Learning Activity
1. Read the following to the students: "Shari Spotter attends a school for sorcerers, 'Frogsnots,' where Professor Dumbleshore has asked her to bake (and not burn) eight crumpets. Each year 8 sorcerers share the power by each eating 1 cosmic crumpet. Shari burns them, by accident. She goes to the library to get the recipe to make more crumpets, and bumps into Matt. The recipe is for 4 crumpets, and she needs to make 8. She has to double the recipe shown in Handout 1.
2. Distribute Handout 1: Crumpet Recipe and Adjustments .
3. Ask the students to work "Crumpet Recipe and Adjustments," by trying to fill in the blanks with the amount of each ingredient required to double the recipe.
4. Tell the students that they will watch a video that shows how the CyberSquad and Shari Spotter doubled the recipe. Ask them to compare the CyberSquad's solution to their own.
5. Show the Crumpets Recipe QuickTime Video .
6. Discuss with the students how the CyberSquad, Shari, and Digit decided what the "top-heavy fraction" means.
7. Ask the students to complete Handout 2: Improper (Top-heavy) Fractions .
8. Tell the students that they will watch another video clip. Read the following set-up to the students: "The sorcerers meet to eat the crumpets, which are their source of the power, but Hacker sneaked in as a sorcerer and stole nearly all the power for himself, destroying most of the crumpets. Professor Dumbleshore says that the only way to stop Hacker is to share the remaining 1 3/4 crumpets equally among the 7 remaining sorcerers. Watch this video clip and see how they figure out how to make equal shares from a mixed number."
9. Show the Reclaiming the Power QuickTime Video .
10. Distribute Handout 3: Mixed Numbers and Improper Fractions and ask the students to complete it.
Part II: Assessment
Assessment: Level A (proficiency): Students are asked to triple a recipe, and to express the new ingredient quantities in terms of both improper fractions and mixed numbers, if possible.
Assessment: Level B (above proficiency): Students are asked to change mixed numbers to improper fractions, and vice versa.