Lesson Topic: Tree Diagrams Grade: 7 Subject: Math 7 Student Teacher: Jordan Hunt Virginia Standards of Learning Objective  Standard 7.10  Strand: Probability and Statistics  Grade Level 7 o “The student will determine the probability of compound events, using the fundamental (basic) counting principle.” Lesson Objective  By the end of this lesson, students will be able to draw tree diagrams in order to illustrate possible outcomes of events. This lesson will prepare students for the next lesson on the fundamental counting principle.  The students will demonstrate their understanding of this lesson in several ways: o Illustrating their own family tree with a group o Presenting their family tree o Homework assignment Task Analysis  Essential understandings, knowledge, and skills: o Compute the number of possible outcomes by using the Fundamental (Basic) Counting Principle.  Do students know what outcomes are? o Students have heard the word in Math 6, but a review will be necessary.  Do students know what the Fundamental (basic) Counting Principle is? o No, students do not know what the FCP is. Key Terms (Teacher Input)  Outcome- One possible result of a probability event. For example, 4 is an outcome when a number cube is rolled.  Sample Space- The set of all possible outcomes of a probability experiment.  Tree Diagram- A diagram used to show the total number of possible outcomes in a probability experiment.  Fundamental (Basic) Counting Principle- Uses multiplication of the number of ways each event in an experiment can occur to find the number of possible outcomes in a sample space.

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Anticipatory Set: o Today’s lesson will start with the warm-up. The warm-up will just be one question today and will serve as a pre-assessment for the lesson today.  The students will have four minutes and thirty seconds to work on the prompt independently. After four minutes and thirty seconds the slide will change. The next slide asks students to discuss their findings with the person sitting next to them. Allow students to discuss for about two minutes, then ring the bell.  With the whole class, ask for volunteers to answer the questions given on the second slide. This discussion will lead to the teacher input portion of the lesson.

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Teacher Input o After the pre-assessment warm-up, the teacher should begin the PowerPoint on tree diagrams.  Introduce the lesson as a method and way to solve the problem they saw in the warm-up today.  The first slide says the objective of the lesson. Remind students of some of the vocabulary written on this slide. For example, outcomes and combinations. Also give an example of when we would want to count outcomes and combinations.  The second slide gives the actual definition of a tree diagram. Tell students that this definition is given to them on their notes outline.  The third slide reintroduces the problem we did in the warm-up activity.  The fourth slide shows how to make a tree diagram for this specific situation.  When this slide first comes up it will only say “First we make columns based on the number events or decisions.”  Press the space bar three times and make, color, and class will come up individually. These are the events or decisions.  Then, press the space bar again and the three will makes will fly in under the make column.  Press the space bar again and then colors will come up, connecting make and color.  Press the space bar one more time and the classes will come up, connecting all three columns.

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After our tree diagrams are built, the teacher should teach the students how to read the tree diagrams to find the combinations.  After the combinations are made, be sure to count how many combinations there are. The fifth slide gives us another similar situation with sandwich decisions. The sixth slide builds the tree diagram.  In a similar manner as the car situation, go over this slide and the combinations that will be made. The seventh slide gives one last situation with outfits. The eight slide builds the specific tree diagram.  On this slide, the students should become more involved. Ask students key questions: o What should my columns be? o What should I write under each column? o What are my combinations? o How many combinations are there? The ninth slide asks students to form groups to do an activity.  The teacher should prepare groups ahead of time based on skill level. There should be students who are above average, average, and below average in each group.  The students will be given specific situations (shown on the next slide) to draw tree diagrams. Encourage students to be creative!  Next class, the students will present their diagrams to the class and we will hang them up around the classroom. Next class, the students will reconvene with their groups and answer specific questions about their diagrams. These questions should be answered within student presentations. Again, these questions will be given next class. The tenth slide gives the format in which the students should draw their tree diagrams. The eleventh slide gives each group’s situation. Students are allowed the rest of class time to work on their diagrams and they will present next class.

Modeling o The teacher will be modeling throughout the PowerPoint presentation. The teacher will be modeling how to draw the diagrams, how to read them and its usefulness.

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Check for Understanding o As students work on their diagrams, the teacher should be monitoring the classwork and fielding any and all questions. Students will be graded on accuracy, so it is important that students understand the task at hand.

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Guided Practice o Students should be grasping the concept of drawing tree diagrams by the third example in the PowerPoint. At that time, the teacher will be asking the key questions outlined above. o Also, while students are working on their tree diagrams, the teacher should be guiding them and helping them draw the diagrams.

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Independent practice o For homework, students will be given three situations in which they will need to draw tree diagrams. o Students are encouraged to draw pictures and/or write words.

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Differentiation o Bodily/Kinesthetic learners will like moving into their different groups to work together. o Auditory learners will most likely learn best from the teacher talking about and modeling problems. o Interpersonal learners will like working with a group to create a tree diagram and talking to their neighbors about the warm-up whereas intrapersonal learners will more likely enjoy thinking about the warm-up on their own and writing their own notes outline. o Visual learners will really like this lesson because it is one time in math where kids can really get creative and drawing works really, really well to solve problems. o Logical/mathematical learners will enjoy thinking about the warm-up and deciding what the most logical way to find all of the combinations is.

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Closure o After the PowerPoint, students have the entire class to work on their diagrams. o Before students leave, they will be given a homework assignment due next class. o Next class, we will culminate the tree diagrams lesson by presenting their posters to the class.

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Assessment o The pre-assessment will be the warm-up. The warm-up is a way to see how the students are thinking about making combinations. It will be interesting to see if anyone has seen tree diagrams before. o The formative assessment will be in the form of working on their tree diagrams. The teacher should be monitoring this classwork. The homework will also be a form of formative assessment/independent practice. The homework will be checked for completion next class. o Presentations next class will serve as the summative assessment for this lesson.

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Materials o SmartBoard o Warm-up o PowerPoint o Notes outline o Paper, crayons/colored pencils/ markers o Homework

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Technology Integration o A PowerPoint will be used to give this lesson today. The PowerPoint is important to this lesson because it will allow the teacher to introduce words one at a time. This will give students a better understanding and visual of the steps to drawing a tree diagram.

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Reflection