Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Unit Title: Genetics & Bioengineering 10 Days Algebra Lesson Plan 2013-2014 School Year 7th Grade Mathematics Teacher Grade: 7th Grade Mathematics Lesson Title: Genotypes vs. Phenotypes STRANDS Probability Permutations Combinations LESSON OVERVIEW Summary of the task, challenge, investigation, career-related scenario, problem, or community link. In this unit, students will be learning about Genetics. The unit will start with a brief discussion of Bioengineering. Students will have the opportunity to do a taste test of traditionally grown foods. They will make observations to determine the difference in taste, texture, and color and record this data on bar graphs. Students will analyze this data in math class later in the unit. Students will also be discussing probability with a professional statistician and discussing how probability is used in real-life. Students will be using what they know about probability to make predictions. Students will also make a connection to Science by completing a task on experimental v. theoretical probability and how it relates to genetics. MOTIVATOR Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature) The taste test activity during the Bioengineered Foods Project will serve as the motivator for the unit. Students will taste foods of four different lettuces and recording their physical traits. DAY Objectives (I can….) 1 I can create a bar graph to show frequencies of certain physical traits. Materials & Resources Data from class involving hair color Data from Taste Test using different breeds of lettuce iPads Instructional Procedures Differentiated Instruction Assessment EQ: - How can graphs be used to communicate data from an experiment? - How can I create a bar graph showing frequency in a real world situation? ½ Project Day – Bioengineered Foods Set Graphing calculators Graphs PPT Students will respond to the following questions: 1. What are bar graphs? 2. How are bar graphs related to measures of frequency? 3. How are they different from other graphs, give examples? 4. Provide two different scenarios that could be communicated utilizing bar graphs. Teaching Strategy Direct Instruction Graphs Whole Group Discussion How can I best represent data in math class and beyond? Students will review their bar graphs created during today’s project. Students created bar graphs by recording quantitative data from the taste test of different lettuce types. The bar graphs were based on the traits of the lettuce. Students will analyze the data from their frequency graphs. Summarizing Strategy Project Reflection Think-Pair-Share - Students will work in pairs to discuss their individual project reflections. - Students reflected the frequency of physical traits and what it has to do with genotype as opposed to phenotype. Students reflected on what they felt, tasted, Enrichment: 1) Same Data, Different Graphs: Using scale and interval to represent data differently. Students will represent the class data using bar graphs with different scale of frequency and intervals. 2) Heterogeneous grouping 3) Peer tutoring via student grouping Remediation: 1) Teacher will provide students with several different graph scales and intervals to choose from. 2) IXL Practice: Interpret bar graphs, line graphs, and histograms. 3) IXL Practice: Create bar graphs, line graphs, and histograms. Formative: 1) Informal observation 2) Whole Group Discussion 3) Student-created bar graphs. 4) Project Reflection Think-Pair-Share Summative: 1) Bioengineered Foods Project etc. from today’s experiment? 2 I can determine interquartile range from a box plot Calculators EQ: Quick Write / Quick Draw Template Box and Whisker Plots PPT What are Box and Whisker Plots? - How can I make a five-point summary of a data set (use box and whisper plot) and find the interquartile range? Set Ice cream data sheet iPad Exit Ticket - Students will complete a Quick Draw / Quick Write on the following topic: What is your favorite ice cream flavor? How did you determine this is your favorite flavor? Teaching Strategy Direct Instruction Box and Whisker Plots Ice Cream Data Challenge Give students a data set of different brands and flavors of ice cream with information describing the ice cream that has artificial additives and those with just natural flavoring. Use this data to create box and whisker plots to model this data with a five-point summary. Students will also find the interquartile range. Show students that the ends of the “box” is the endpoints of 50% of the data and therefore the subtraction of the endpoints of this “box” will always give the interquartile range. Summarizing Strategy Students will complete an exit ticket including the following questions: 1. Summarize their procedures and why the “box” will always have 50% of the data set. Enrichment: 1) CK-12 March Madness: Real-World Application of Box and Whisker Plots (Alternatively, similar data may be tailored to meet student interest while demonstrating realworld application) Remediation: 1) Individualized instruction for developing learners during the Ice Cream Data Challenge. 2) IXL Practice: Interpret Box and Whisker Plots Formative: 1) Informal observation 2) Quick Draw/Quick Write 3) Box and whisker in-class activity 4) Discussion 5) Exit Ticket 3 I can determine theoretical and experimental probability. I can explain reasoning and persevere in solving problems. Eight pair of dice Explain why the difference of the two endpoints of the “box” will always give the interquartile range. - How can I determine theoretical and experimental probability? How can I explain reasoning and persevere in solving problems? EQ: iPad Theoretical and Experimental Probability PPT Doceri app 2. Set Students will complete a Venn Diagram on the following topic: What is the difference between theoretical and experimental probability? How is reasoning and persevere related to problem solving? Teaching Strategy Direct Instruction Theoretical and Experimental Probability Probability Challenge Ask students what number (sum of two dice) would they choose to be rolled the most often on a pair of dice. After allowing different opinions and why, tell them that as groups we will all roll a pair of 50 times and record the sums. Students will learn about experimental probability and theoretical probability through this challenge. Have students make bar graphs above the numbers 2,3,4,5,6,7,8,9,10,11, and 12 to show frequency of the number (sum) rolled. Airplay or project to display different graphs and discuss the reasons they are different. Have students make a 6x6 area model grid to find the theoretical probability. The theoretical grid has 36 possible outcomes, while the experimental chart we created was based on 50. Enrichment: 1) Article: Is a pregnant woman’s chance of giving birth to a boy 50 percent? 2) Heterogeneous grouping 3) Peer tutoring Remediation: 1) Heterogeneous grouping 2) Peet tutoring 3) Use of calculator 4) IXL Practice: Theoretical Probability 5) IXL Practice: Experimental Probability Formative: 1) Venn Diagram 2) Informal observation 3) Probability Challenge 4) Mini Poster - Have students list probabilities for both (e.g., P(1)= ,P(2)= ,P(3)= ,etc.) the bar graph and the grid. Summarizing Strategy (5 to 10 minutes in length) 4 I can determine expected value and therefore conclude if a game is fair or not. Presentation with practice problems EQ: Enrichment: - iPads Expected Value PPT How can I determine expected value? How can I determine if a game is fair (e.g., expected value is equivalent for all players)? Set Video Challenge Independent Practice Students will work in table groups to create a mini poster on Doceri to respond to the following questions: Why does experimental probability approach theoretical probability? Discuss and list the differences between theoretical and experimental probability. What is the Law of Large Numbers (the larger the number of events, the closer the experimental probability approaches the theoretical)? Reflection Template Show students an area model that has at least two colors and in patterns of squares or rectangles. Students will create a think, write, draw writing task on the following topic: Ask them which color would be more likely to be landed on if all areas of the rug have equal chances of being landed on (make sure the colors are not half and half). Teaching Strategy Direct Instruction Expected Value Video Challenge Students will watch a video of a board game (video clip of participants playing the game or commercial clip for a board game). 1) Peer tutoring 2) Heterogeneous grouping 3) Expect Madness: What is the relationship between expected value and the NCAA Basketball Tournament? Remediation: 1) Peer tutoring 2) Heterogeneous grouping 3) Use of calculator Formative: 1) Think-Write-Draw 2) Video Challenge and Independent practice assignments 3) Individual Reflection - The students will be directed to pay special attention to the spinner used in the game. Students will create a visual representation (of their choice – utilizing their iPad technology) that explains which color or space on the spinner is most likely to be landed on during this game. Students will share with their visual representations with their assigned table groups. Student table groups will share their best visual representation and explain how their illustration is related to expected value. Students will post their visual representations to the class website. Independent Practice This lesson involves various area model worksheets to be used to divide the up the areas of different colors to determine probability and also expected value. The expected value will come into play when points or values are given to the colors. The expected value is figured by multiplying the probability (of a color being landed on randomly) times the points or value (given that color). Before working on each area model ask students which color they would choose to win. After figuring the expected value, they will see the theoretical answer to their question. Summarizing Strategy Individual Reflections - 5 Students will write a reflection explaining why probability of an area model is different from the expected value of that same area model if points or values are added as conditions for the area models’ colors. Project Day – Genetics Guest Speakers 6 I can use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes. Entrance Ticket EQ: - Fundamental Theorem of Counting PPT Fundamental Theorem of Counting Guided Practice How can I use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes? Set Sandwich topping manipulatives Mathematics exit ticket iPads Entrance Ticket – Students will respond to the following question: Your family is ordering a family-sized submarine sandwich. There are four toppings from which to choose (ham, cheese, lettuce, tomato). You have a coupon for a three-ingredient sandwich. Determine all the different three-ingredient sandwiches you could order. Create a list, diagram or table on chart paper to show possible outcomes and counting techniques. Teaching Strategy Graphing calculators Three, Two, One Writing Activity Template Direct Instruction - Fundamental Theorem of Counting Guided Practice - Fundamental Theorem of Counting Challenge Students will work in teams of three to complete the provided challenge. Students will explore combinations in a variety of applications. Assign each situation to two groups so the groups may compare results after completing the task. There will be a minimum of 3 sets of challenge situations (total of 6 teams of 3). Challenge scenarios include: 1. How many different ways can you choose two ice cream toppings from three? Enrichment: 1) Peer tutoring 2) Heterogeneous grouping 3) Allow students to choose a real life commodity of their choice and apply the fundamental counting theorem. Remediation: 1) Peer tutoring 2) Heterogeneous grouping 3) Vary the number of combinations by beginning small and progressing to more complex problems/tree diagrams. Formative: 1) Entrance Ticket 2) Guided Practice 3) Individual Reflection 4) Challenge Scenarios 5) 3-2-1 Writing Activity 2. - - - - How many different ways can four students be seated at two desks? 3. How many different ways can two food items be chosen from six food items? 4. How many ways can you choose three chores from five to do before dinner (clean your room, feed the fish, take the trash out, cook dinner, wash dishes)? Direct groups to create lists or tree diagrams to organize the data and then use counting techniques to determine a numerical result for each situation. Model how to create a tree diagram or list if necessary. Have groups share with another group and teach that group about their problem situation, or compare solutions with the other group completing the same scenario. Assess students understanding by observing their methods for organizing (i.e., tree diagrams, lists or other) and listening to their discussions. Each team will complete three challenge scenarios for practice. Summarizing Strategy 7 I can use counting techniques, such as permutations Sandwich topping manipulatives Combinations PPT Three, Two, One Writing Activity - Students will rate their level of comprehension through this simple self-assessment writing tool. Students will create a pyramid graphic organizer the includes: The base: 3 concepts that they have learned during today’s lesson. The middle: 2 questions that they have about this lesson. The top: 1 math problem related to today’s topic EQ: - How can I use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes? Enrichment: 1) Peer tutoring 2) Heterogeneous Formative: 1) Think-Pair-Share 2) Class Discussion 3) Individual Reflection and combinations, to determine the total number of options and possible outcomes. Mathematics exit ticket Set grouping iPads Graphing calculators Short homework assignment Digital presentation Think Pair Share – Students will work with a partner to respond to the following question: Think about the sandwich ingredient combinations you found in the previous lesson. You chose three ingredients from four. Determine how many ways you can assemble a sandwich with ONLY three ingredients. This will depend on the order that ingredients are placed on the sandwich. For example, putting on ham, then tomato, then cheese is different than putting on tomato, then cheese, then ham. Working with your Think, Pair, Share partner create a list, diagram or table on chart paper to show possible outcomes and counting techniques. Teaching Strategy Direct Instruction Combinations Whole Class Discussion Review the term “combination”. Explain that they have been finding combinations over the past two days, and ask them to describe/explain the processes they used and what they believe a combination is. Be sure students understand the concept and term before proceeding. Give students an opportunity to write a definition for combination in their own words in journals or notebooks. Challenge Present the following scenario and discuss reasonableness of using tree diagrams and/or lists to count possible outcomes. The Innovation Academy Eighth Grade Mathematics Team won the county Math-a-Thon Competition. The reward was a six topping pizza. At the local pizza parlor, 10 toppings were offered. How many combinations of six-topping pizzas could be chosen? Discuss if a tree diagram or a list is appropriate to determine Remediation: 1) Peer tutoring 2) Heterogeneous grouping 3) IXL Practice: Compound events 4) Challenge Scenario 5) Exit Ticket - - the total number of ways to choose six pizza toppings from 10. Why or why not? Students begin to realize that if the numbers are too large, these methods may be too tedious to be efficient. Have pairs of students create two problem situations that can be solved using combination methods for solution. Each situation should use lists or tree diagrams and counting techniques. On separate pieces of paper, students find the numerical solutions for each situation. Remind them to consider if their solutions are reasonable. Have pairs exchange problem situations with another pair and solve for numerical solutions for each other’s problem situations. Have pairs verify numeric solutions and methods used to find the solution. Summarizing Strategy Exit Ticket - Ask students to describe a combination in their own words with a partner or by writing a Mathematics Exit Ticket. They should include a definition and an example of a combination in their description. Collect the tickets as students leave at the end of the class. Use tickets as a formative assessment by quickly reading to determine what students understand after the lesson. Use the analysis to inform future instruction. 8 Project Day – Pedigrees-Family Health History 9 I can use probability to iPad horse race EQ: - How can I use probability to make logical decisions? Formative: make logical decisions. I can explain reasoning and persevere in solving problems. calculation stats Probability and Mathematics PPT How can I explain reasoning and persevere in solving problems? Set Students will watch a short video of a horse race. Students will choose a horse and based on its record (go to calculation stats) will calculate it’s expected value of winnings. Based on this calculation, they can predict the horse’s earnings on all future starts. Teaching Strategy Direct Instruction - Probability and Mathematics Research Students will learn work in teams to research statistics associated with horse racing – particularly statistics of wins and prizes won by horses, jockeys, and owners. Partners Practice Students will work in pairs to calculate the expected value of their choice (horse, jockey, or owner) and predict the horse’s (or jockey’s or owner’s) earnings on any future start. Student groups will present their results to each other and the whole class, discussing expected value as a tool that helps to level out data to make informed predictions. Enrichment: 1) Opening set problem. 2) Class Discussion 3) Exit Ticket 1) Peer tutoring 2) Heterogeneous grouping Remediation: 1) Peer tutoring 2) Heterogeneous grouping 3) Use of calculator 4) IXL Practice: Probability Summarizing Strategy 10 I can determine compound probability, Permutations PPT Exit Ticket Students will write a reflection of their idea of probability of an event in comparison to the expected value of an event. EQ: - Skittles probability How can I determine compound probability, combinations, and permutations? Enrichment: 1) Peer tutoring Formative: 1) Opening set problem. combinations, and permutations. activity sheet Set iPad Skittles fun packs (one per student) Students will watch a short video of a horse race. Students will choose a horse and based on its record (go to calculation stats) will calculate it’s expected value of winnings. Based on this calculation, they can predict the horse’s earnings on all future starts. Teaching Strategy Direct Instruction Permutations Explain that they have been finding permutations, ask them to describe or explain the process they used and what they believe a permutation is. Be sure that students understand the concept and term before proceeding. Give students an opportunity to write a definition for permutation in their own words in journals or notebooks. Challenge Provide problem situations that allow students to explore permutations in a variety of applications. Divide students into groups of three or four. Assign each situation to two groups. Scenarios include: 1. How many different ways could four students exit a room? 2. How many different ways could the letters K, A and B be ordered? 3. How many different ways could the following colors be arranged in horizontal stripes to create a flag? (red, black, yellow, orange and green) 4. How many different ways could four students be placed at two desks? (Desk A, Desk B) Direct the groups to organize the data and then use counting to determine a numerical result for each situation. Regroup students by taking one person from each of the scenario groups and combining them. 2) Heterogeneous grouping 3) Students can be given more challenging permutations and combinations with the skittles to determine all possible combinations. Remediation: 1) Peer tutoring 2) Heterogeneous grouping 3) Use of calculator 4) IXL Practice: Permuations 5) Students can be given fewer choices to calculate easier combinations and permutations. 2) Challenge 3) In-class practice 4) iMovie closure - Each student shares the solutions for the problem situation and explains the strategies used. Each student in the group presents. This instructional strategy makes every student accountable for understanding the problem situation and teaching it to others. Tree Diagram Practice Present the following scenario to discuss reasonableness of using tree diagrams and lists to count possible outcomes: The softball coach was putting together a batting order for the first game of the season. There are nine players whom the coach has to order. How many possible ways could the coach order the batters? Discuss whether a tree diagram or a list is appropriate to determine the total number of ways that you could arrange nine players in a batting order. Why or why not? Students will begin to realize that if the numbers are too large, these methods may be too tedious to be efficient. Have students create two problem situations that use permutation methods to find possible outcomes. Students solve situation using lists or tree diagrams and counting techniques. On separate pieces of paper, students find the numerical solutions for each situation. Remind them to consider if their solutions are reasonable. Instruct pairs to exchange problem situations with another pair. The pairs continue to exchange papers and solve problems until about 10 minutes remain in the period. Observe student discussions and solutions. Pairs join those with whom they exchanged papers to verify numeric solutions and methods used. Probability Practice Students will be completing a probability activity with fun packs of skittles. They will start by finding basic probabilities of selecting a specific color of skittle. Students will then move on to finding compound probabilities such as a red or green OR a red and green. - Students should find the compound probabilities when skittles are replaces and when they are not. Finally, students should find the possible combinations or permutations of skittles based on their favorite flavor combinations. Summarizing Strategy STANDARDS iMovie Students will create a short movie discussing their favorite skittle combinations and how likely they are to pick this combination (or permutation) out of a bag of skittles. Identify what you want to teach. Reference State, Common Core, ACT College Readiness Standards and/or State Competencies. 7.SP.C.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. CP.A.1 - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). CP.A.2 - Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. CP.A.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. CP.A.4 - Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. CP.A.5 - Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. CP.B.9 - Use permutations and combinations to compute probabilities of compound events and solve problems. MD.B.5 - Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. MD.B.5a - Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. MD.B.5b - Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.