Lesson Refinement Worksheet Mathematics Lesson: Grade 7 Standard(s) MACC.7.SP.3.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-­‐end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Common Core MACC.7.SP3.CCC.7a Content Compare actual results of simple experiment with theoretical probabilities. Connector : Lesson Gist Students will use a number cube to toss and collect data, then convert the data in terms of probability. Instructional Component: Instructional Goal(s) From This… To This… Students will be able to determine probability by predicting frequency and Students understand what probability models and probability events are and collecting data. can develop and compare models to observe frequencies, explaining possible discrepancies. a. Students can develop and use probability models to determine the probability of events. b. Instructional Component: Introduce the Lesson From This… To This… Guiding Questions: What are the guiding questions for this lesson? -­‐ What is probability and how can it be determined? -­‐ What is the difference between theoretical and experimental probability? -­‐ How does it relate to this activity? Prior Knowledge: What prior knowledge should students have for this lesson? -­‐ General understanding of fractions (part to whole) and percent -­‐ Equivalent Fractions -­‐ Converting fractions to percent -­‐ Organizing data on a table Instructional Component: Instructional Activities From This… To This… Teaching Phase: How will the teacher present the concept or skill to students? 1. Pose the question, “What is the probability that if I roll a number cube labeled 1 through 6, it will land on a 1?” 2. Ask students to think about the terms “theory” and “probability” and record their own definitions on a piece of paper. 3. Allow for random reporting for students to offer their definitions to the whole class. 4. Establish a class definition for each word. Ask the class how they can use these definitions to describe probability – what is meant by theoretical and experimental probability? 5. Tell students that today they will calculate theoretical probability for a variety of events involving dice. Then, they will carry out the experimental probability of the events. Guided Practice: What activities or exercises will the students complete with teacher guidance? 1. Calculate the theoretical probability as a class for: a. P(rolling an even number) b. P(rolling an odd number) c. P(rolling a multiple of 3) d. P(rolling a multiple of 5) 2. Calculate the theoretical probability out of 36 trials using the fractions in #1. 3. Pass out recording sheets. Attachment #1. Show them the example listed on the recording sheet. Tell them to ignore the last column until instructed later. 4. Pass out number cubes. They should record the outcomes of throwing a number die 36 times. 5. Once everyone is done, the teacher should use his/her data display to model to students how to calculate frequency as a fraction and percent. Students should independently attempt the same with his/her data. 6. Allow students to share out their findings. Invite students to explain how they arrived at their fractions and percent. Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson? 1. Pass out 3x5 index cards. Tell students to put his/her name on top. Tell them that you will pose a challenge question. Once they have it solved, they should bring the card to you. The teacher should keep them in order. Tell them that they have 2 minutes to solve the problem and return the card to you. Instructional Component: Lesson Closure From This… How will the teacher assist students in organizing the knowledge gained in the lesson? 1. Bring students’ attention back to the class definitions for theoretical probability and experimental probability. 2. Pass the 3x5 index cards back out. Instructional Component: Assessment From This… Formative Assessment: The teacher will review the 3x5 cards to determine if student learning occurred. Feedback to Students: Students will get the 3x5 card back at the end of the lesson with teacher feedback. Summative Assessment: This is an introductory lesson to calculating simple events. This should be part of a larger unit on probability. A concept practice worksheet is included and can be used as practice or assessment. Curriculum Media and Materials From This… Free Throw Recording Sheet Concept Practice Worksheet Index Cards Number Cubes To This… To This… To This… Roll 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Die Roll Recording Sheet Number Rolled Student Data Sheet Student 1 Strengths Preferences Needs Loves fiction; strong verbal/linguistic orientation Prefers to work independently Organizational issues 2 Enjoys helping other students, reads on grade level Loves to sing 3 Independent worker 4 Loves football Enjoys working on a computer; auditory learner Physical/kinesthetic learner; enjoys hands on activities 5 Reads on grade level Loves science fiction novels 6 Likes to work with others; visual/spatial learner Enjoys working on/with computers 9 Reads well above grade level, strong social skills Independent learner, reads above grade level Enjoys helping others, especially younger students Reads above grade level Poor math skills; very poor handwriting; below level reading skills Moderate behavior problems has ADHD; poor auditory processing and organizational skills Organizational problems, poor social skills, slightly weak written expression skills Easily bored 10 Good verbal communicator; creative Prefers working with peers, structured activities, using creativity during learning 11 Enjoys leading a group, and project management; likes to entertain 12 Great verbal communicator; strong visual reasoning/logic skills; good problem solving skills Loves dance and art 13 Enjoys baseball and art 14 Bilingual Reads on grade level; good reasoning skills; good social skills Enjoys helping other students; good social skills; creative Physical/kinesthetic learner; enjoys hands on activities Likes to work with others 7 8 15 16 Physical/kinesthetic learner Likes to work in a team Likes to work with others Prefers working with peers; physical/kinesthetic learner Enjoys working on a computer Easily bored; below level reading skills Easily bored Organizational problems, not a self-­‐
starter; easily bored Has ADHD and moderate behavior problems; easily bored Organizational issues, specifically with materials, difficulty with time management and monitoring progress Proofreading/checking work Below level reading skills; gives up easily; easily distracted Organizational issues; below level reading skills Below level reading skills; Easily bored Organizational issues; executive functioning issues 17 Enjoys working on/with computers; enjoys art and creative activities Loves animals Enjoys working on a computer; Prefers to work independently Reads on grade level; likes dirt bikes; good Prefers working with peers; prefers written and communication skills physical/kinesthetic activities; strong leadership skills Enjoys sports and making things with his Enjoys working on a computer; linear hands (carpentry) thinker Easily bored; prefers to work alone; poor social skills New to the country; from Puerto Rico; shy 21 Reads above grade level; loves to write Easily bored 22 Reads above grade level Physical/kinesthetic learner; enjoys hands on activities Likes to work with others 23 Loves dance Enjoys working in a group 24 Enjoys making things with his hands (carpentry) Has strong desire to do well; perseveres through struggles Prefers working alone 18 19 20 25 Reads on grade level Enjoys working in groups Easily bored; easily distracted Has moderate behavior problems Organizational issues; poor time management Poor math skills; very poor handwriting; significantly below level reading skills Significantly below level reading skills; easily bored; poor social skills Organizational issues; significantly below level reading skills; English Language Learner *Shaded rows indicate student has been identified as a student in need of intensive support within the content area