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Math Lesson: Probability Grade Level: 3

Lesson Summary: The students begin by discussing their observations about the fairness of a spinner that is divided unequally. Students then use probability terms like less likely, equally likely, and more likely to describe the probability of spinning the different sections of the spinner. The teacher uses the spinner and combinations to teach students how to describe probability with numbers. For independent practice, students visit different probability stations and answer analysis questions about the experiments at the stations. Advanced learners solve problems about combinations, create models of probability experiments when given specific guidelines, and answer open-ended questions about probability. Struggling learners have guiding questions that will help them find the probability of different events.

Lesson Objectives:

The students will know…  How to determine the probability of an event.  How to find permutations.

The students will be able to…  Determine the probability of an event.  Find permutations.

Learning Styles Targeted:

Visual Auditory Kinesthetic/Tactile

Pre-Assessment: Project a copy of the Spinner* under a document camera, and give students a few moments to look at it. Ask students, “What do you notice about the spinner?” Elicit responses, leading a lengthy discussion about the spinner. If students haven’t brought up the fairness of the spinner, say, “Pretend you were using this spinner for a game. Is it a fair spinner?” Elicit responses, leading a lengthy discussion about the spinner’s fairness.

Whole-Class Instruction

Materials Needed: 1 copy of the Spinner* to project under a document camera, a document camera connected to a projector, 1 individual whiteboard per student, 1 dry-erase marker per student, 1 tissue per student, 3 colored tiles (1 red, 1 blue, and 1 yellow) per student, 1 copy of the recording sheet from the Independent Practice Activity* per student, 1 copy of each station page from the Independent Practice Activity*, writing utensils

Procedure:

1) Leave the projected copy of the Spinner from the Pre-Assessment up so that students have it to refer to. Explain to students that they are going to analyze the likelihood of different letters being spun. Tell students that the chance, or likelihood, of an event happening is called probability.

2) Write the terms equally likely, more likely, most likely, less likely, and least likely on the board. Explain to students that these terms can be used to measure probability. Tell students that you want them to talk with a partner or small group and come up with a sentence that describes the spinner using one of these terms. Give students an example by saying, “On this spinner, it is more likely to spin a B than a D.” Write this sentence on the board. When students understand what to do, give them 1-2 minutes to discuss. When students finish discussing, ask the pairs or groups to share their sentences. Record correct responses on the board, and discuss each one. Some possible answers that students might give include: “It is equally likely for you to spin an A and a C.” “It is more likely to spin a B than an A.” “It is most likely that you will spin a B.” “It is less likely that you

3) Explain to students that probability can also be measured with numbers. Write ____ out of ____ on the board, and tell students that this phrase can be used to measure probability. Have students write this phrase on their whiteboards as well. Again, have students look at the Spinner. Tell them that you want them to find the probability of spinning an A. Ask students, “How many sections say ‘A’ on the spinner?” Elicit responses, recording 2 in the first blank on the board. Students should do the same. Ask students, “How many total sections are there on the spinner?” Elicit responses, recording 8 in the second blank on the board. Students should do the same. Together as a group say, “The probability of spinning an A is 2 out of 8.” Have students erase the numbers from the blanks and ask them to find the probability of spinning a B. Students should answer on their whiteboards and then hold them up for you to check their work. Make sure students answer “3 out of 8.” If necessary, explain the correct answer. Repeat for the probability of C and D. Ask students, “Which number never changed in any of your answers?” Elicit responses, making sure students understand that 8 never changed. Ask students why the 8 was in every probability phrase that they answered. Elicit responses, making sure that students realize that there are 8 sections in the spinner, which never changed.

4) Give each student 4 colored tiles (1 red, 1 blue, and 1 yellow). Tell students that they are going to use the colored tiles to find all the possible ways that the three colored tiles can be put in order. Project the 3 colored tiles under a document camera. Make the following train with the colors: red, blue, yellow. Have students do the same. Say, “One way to put them in order is to place the red first, blue second, and yellow third.” Explain that you are going to keep track of all the ways they can be put in order, and write R, B, Y on the board. Have students record this on their whiteboards. Ask students, “Can you leave figure out another way to put the colored tiles in order with the red still in the first position?” Let students manipulate the colored tiles, and then walk around to make sure students left the red in the first position but switched the blue and yellow. When you see that all students are successful, record R, Y, B on the board. Students should do the same. Ask, “Are there any other ways to put the colored tiles in order with the red in the first position?” Students should say no. Discuss if necessary. Ask students, “Can you find two ways to place the colored tiles in order with the blue in the first position? Use your colored tiles help you and then record both ways on your whiteboards.” Walk around to make sure students have listed B, R, Y and B, Y, R on their whiteboards. Record these two combinations on the board. Repeat this process for having students find the combinations with yellow in the first position. When completed, the board should include the following combinations: R, B, Y; R, Y, B; B, R, Y; B, Y, R; Y, B, R; Y, R, B. Explain to students that you wanted them to find all the combinations with one color in the first position before moving on to another color in the first position was so that you could keep the list organized and not forget one combination.

5) Have students look at the list of six combinations. Give students the following scenario: “Let’s say you gave a friend a red, blue and yellow colored tile. You asked him or her to put them in any order they wanted. What is the probability that your friend will place them red, yellow, blue?” Remind students to use the _____ out of _____ phrase to answer this question on their whiteboards. Have students hold up their answers. Make sure students have answered 1 out of 6. If necessary, explain that there are 6 total combinations, and only one of them places the tiles in that order.

6) Give students the following scenario: Let’s say you gave a friend a red, blue, and yellow colored tile. You asked him or her to put them in any order they wanted. What is the probability that your friend placed the blue in the first position?” Have students answer on their whiteboards and then hold them up for you to see. Make sure students have answered 2 out of 6. If necessary, explain that there are 6 total combinations, and two of them begin with blue in the first position.

7) Give each student a copy of the recording sheet from the Independent Practice Activity, and tell students that they will be visiting 5 stations around the room that deal with probability. The questions are organized by station on the recording sheet. Put students in 5 groups, and place 1 copy of each of the station pages from the Independent Practice in 5 different locations around the classroom. Make sure students know the location of each station, and assign each of the groups to

Copyright © 2011 Study Island - All rights reserved. one station. Students should use the page at the station to answer the questions about that station on their recording sheets. When students understand what to do, allow them to go to their stations. Give students 2-3 minutes to answer that station’s questions before asking groups to rotate to the next station. Repeat the rotations until all groups have visited each station.

Advanced Learner

Materials Needed: 1 copy of the Advanced Learner Independent Practice* per student, writing utensils, 4 colored pencils per student (1 red, 1 yellow, 1 blue, and 1 green)

Procedure:

1) Give each student a copy of the Advanced Learner Independent Practice and 4 colored pencils (1 red, 1 yellow, 1 blue, and 1 green). Explain the directions to students, and allow students to work independently.

Struggling Learner

Materials Needed: 1 copy of the Struggling Learner Independent Practice* per student, writing utensils

Procedure:

1) Give each student a copy of the Struggling Learner Independent Practice. Explain the directions, and lead students through 1-2 examples, if needed. When students are ready, allow them to work independently. *see supplemental resources