<p>Title: Tree Diagrams and Counting Principle Teachers: Julieth Hoayeck and Karen Soto</p><p>CAST’s UDL LESSON BUILDER Goals Unit Goals: Students will use both geometric and real-life models to learn about outcomes by using tree diagram, organized charts, counting principle and predicting probabilities. Lesson Objective: -Use a tree diagram to predict the total amount of outcomes from different combinations of items. -Find a rule for counting the number of combinations possible in selecting an item from each set. State Standards: NJCCCS 4.4.C.1, 4.4.C.2, 4.4.C.3 </p><p>Methods (e.g., Anticipatory Set, Introduce and Model New Knowledge, Provide Guided Practice, Provide Independent Practice) Anticipatory Set Start with a simple example: If you go to the ice cream store and they have two different flavors of ice cream and you can get either a cup or a cone. How many different combinations of ice cream can you make? Ask the students how they came up with the answer. Using http://illuminations.nctm.org/activitydetail.aspx?id=3 the students will work on double tree diagrams on the Smartboard</p><p>Watch a video (3 choices): http://www.teachertube.com/view_video.php? viewkey=eac35191fd615fff3efe </p><p> http://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem- 431141.html </p><p>Spanish Version: http://www.phschool.com/atschool/academy123/spanish/academy123_content/wl- book-demo/ph-342ss.html </p><p>Class Activities After the students provide their answers to the introductory example we will use a tree diagram to organize this data on the Smartboard. Give a simple example of a double tree diagram that they can draw in their notebooks. You work on a restaurant that serves three types of tacos (bean, beef and chicken). Each can be ordered with a hard shell or soft shell. Create an organized tree diagram to find how many types of tacos you can have. Introduce the Triple Tree Diagram Project: The students will work in groups of three to create their own tree diagram. In a poster board the students will show the total amount of possible combinations that can be created from three colors of shirts, two colors of pants, and two colors of hats. The teacher will provide the clothing models and materials needed to complete this project. The students will present the project to the class and explain the mathematical reasoning of finding the outcomes without creating the tree (Counting Principle). </p><p>CAST 2006 Adapted from http://lessonbuilder.cast.org Independent Practice -Each member of the team will be responsible for creating one third of the triple tree diagram and add it to the poster board. The students will then work collaboratively to explain how to find the possible amount of outcomes without using a tree. -The students will then create their own tree diagram. -Homework: Page 604 (1-15)</p><p>Materials Smart Board Projector Speakers Math Textbook Practice Worksheet Paper Pencil Scissors Construction Paper Poster Board Glue Clothing Models Ruler Markers Calculators</p><p>Evaluation Assessment (i.e., Formative/Ongoing Assessment or Summative/End of Lesson Assessment) Teacher’s Observation Interactive Practice http://regentsprep.org/regents/Math/tree/PracTre.htm Student’s Poster Boards (Projects) Class presentation using the poster board Homework Textbook and Worksheet Written Test</p><p>UDL Principles Multiplication means Multiplication means of Multiplication means of of representation action and expression engagement Diagramming Written Test Interacting with Manipulatives Presentation Smartboard Visuals Becoming the teacher Manipulatives Personal Connect Graph Group Activities Build Model Relating to own lives Graphic Organizers Give them choices</p><p>CAST 2006 Adapted from http://lessonbuilder.cast.org</p>