GMU COMPLETE Center Candy Dilemma A VDOE SPONSORED MSP PROFESSIONAL DEVELOPMENT OPPORTUNITY THROUGH GEORGE MASON UNIVERSITY Cyndi Madden Mona SamahaPatricia Drummond Geeta Myers Catherine Monheim Herndon Elementary SchoolSangster Elementary School Fairfax County Public Schools GMU Complete Center

GMU COMPLETE Center Introduce your Cognitive Demand Task I bought a box of candy for myself last week. However, by the time I got it home I had eaten ¼ of the candies. As I was putting the groceries away, I ate ½ of what was left. There are now 6 chocolates left in the box. How many chocolates were in the box to begin with?

GMU COMPLETE Center The Essential Mathematics Highlight the learning goals and the big mathematics ideas. What are some common misconceptions? Vertical connections among grade levels? Learning Goals : The student will learn to represent and model problem solving in a real life situation. In particular, multiplication of fractions. Misconceptions : Adding fractions instead of multiplying. Multiplying ¼ X 1/8 Computation error. Misinterpretation of the phrase “What was left?” Using ¼ as the amount left versus what was eaten. Vertical connections among grade levels: Applying the concept of ¼ and ½ in complex situations.

GMU COMPLETE Center The Candy Dilemma We connected our ‘Candy Dilemma’ to similar problems. Our problem solving strategy- Putting it into ‘real life’.

GMU COMPLETE Center EXPLORE Describe in detail the exploration experience in this lesson. Explorations will vary depending on the type of lesson How did your task elicit students to “Do mathematics” Students were given the Candy Dilemma problem, a work mat to show their work on, and they had access to resource materials like fraction strips. Math strategies were reviewed briefly and students were reminded of the anchor chart to use if they needed more ideas. The students worked together to solve the problem. Many of the kids started by writing down the numbers from the problem and from there they discussed how to work with the numbers to find the original total number of candies in the box. After coming up with an answer students were encouraged to test their answer for accuracy. Many of the groups used the fraction strips to model the problem, it is at this point that many of them also found their errors and the correct answer.

GMU COMPLETE Center EXPLAIN the Different Models Describe how students communicate the results of their explorations. How can this task be modeled using concrete manipulatives, virtual manipulatives, pictures, diagrams, tables, graphs, and/or symbols? Anticipate how STUDENTS will explain their thinking and their strategies. Include as many different possibilities as possible (Pix of Students working) The students used numerical sentences to solve the problem. They also used fraction strips and visuals to show their work.

GMU COMPLETE Center ELABORATE Discuss connections between representations and strategies. Discuss relevance in the real world or to other curriculum areas. The idea here is that students use their new knowledge to build their growing knowledge base

GMU COMPLETE Center ELABORATE Discuss connections between representations and strategies. At the end of the lesson, several students were able to come up to the board and share their representations and strategies. Each person was asked “How is what you did connected to what the previous person(s) did?” Some used graph paper to draw their representations, some used numbers and operations, and some used fraction strips to model the problem Discuss relevance in the real world or to other curriculum areas. Problem solving is relevant to actual situations the students face in the real world, as they frequently need to think through similar situations.

GMU COMPLETE Center EVALUATE Explain how your students demonstrate their new understanding and skills. What is the learning goal and learning product for this lesson? INCLUDE a sample rubric with novice, apprentice, proficient and expert students’ work

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Sharing the outcomes: Ideas: How did your task engage students in doing mathematics? Short videoclip/photos NOTE: Slide for sharing teachers lessons Slides for Host teacher Maybe a slide for the other teachers who tried it after tweaking after the lesson study

GMU COMPLETE Center Lesson study in Geeta’s class

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GMU COMPLETE Center REFLECTION What modifications? After reflecting on the lesson together we noticed that the students needed some prompting to use alternative methods of exploring and solving the problem. Observers also prompted the students to prove their answers. This is where the students discovered errors and started the exploration process over again. Related problems? We discussed the value of extending this lesson with other problems like the “mango problem.” Students would benefit from additional real life problems using the variety of strategies discussed. What did you learn about teaching and assessing this concept? We learned the value of using fraction strips and other methods to model problems and outcomes. Student misconceptions were cleared up through the use of multiple methods of problem solving. This is a skill that they are still building on and refining.