M.J.Hobbs Senior Public School Mathematics. D.I. Team Project. Grade 7-8 DI Project Example, 2009

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1 D.I. Team Project 1

2 Differentiated Instruction Product Outline Teachers Involved: Lori Brooks: Grade 7 Homeroom and French Teacher Jessica Powell: Grade 8 Homeroom and Physical Education Teacher Angie McCormack: Grade 6 Homeroom Teacher Jaime Edwards: Grade 8 Math and Science Teacher Project Description Problem solving in mathematics with the use of the Smartboard/manipulatives. Student groupings of readiness or interest (Multi-grade). Use of choice Use of several D. I. strategies Product Description The product produced by the D.I. team at M.J. Hobbs consists of a SMART Notebook file that outlines the process of integrating differentiated instruction strategies into the mathematics curriculum. The project also explains in detail several of the strategies that were used throughout the year at M.J Hobbs and teacher reflections on how these strategies affected student engagement and understanding. 2

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4 Grade 8 Math Introductory Unit 4

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7 Multiple Intelligences Survey 1999 Walter McKenzie, Surfaquarium Consulting Part I Complete each section by placing a 1 next to each statement you feel accurately describes you. If you do not identify with a statement, leave the space provided blank. Then total the column in each section. Section 1 I enjoy categorizing things by common traits Ecological issues are important to me Hiking and camping are enjoyable activities I enjoy working on a garden I believe preserving our National Parks is important Putting things in hierarchies makes sense to me Animals are important in my life My home has a recycling system in place I enjoy studying biology, botany and/or zoology I spend a great deal of time outdoors TOTAL for Section 1 Section 2 I easily pick up on patterns I focus in on noise and sounds Moving to a beat is easy for me I ve always been interested in playing an instrument The cadence of poetry intrigues me I remember things by putting them in a rhyme Concentration is difficult while listening to a radio or television I enjoy many kinds of music Musicals are more interesting than dramatic plays Remembering song lyrics is easy for me TOTAL for Section 2 7

8 Section 3 I keep my things neat and orderly Step-by-step directions are a big help Solving problems comes easily to me I get easily frustrated with disorganized people I can complete calculations quickly in my head Puzzles requiring reasoning are fun I can t begin an assignment until all my questions are answered Structure helps me be successful I find working on a computer spreadsheet or database rewarding Things have to make sense to me or I am dissatisfied TOTAL for Section 3 Section 4 It is important to see my role in the "big picture" of things I enjoy discussing questions about life Religion is important to me I enjoy viewing art masterpieces Relaxation and meditation exercises are rewarding I like visiting breathtaking sites in nature I enjoy reading ancient and modern philosophers Learning new things is easier when I understand their value I wonder if there are other forms of intelligent life in the universe Studying history and ancient culture helps give me perspective TOTAL for Section 4 Section 5 I learn best interacting with others The more the merrier Study groups are very productive for me I enjoy chat rooms Participating in politics is important Television and radio talk shows are enjoyable I am a team player I dislike working alone Clubs and extracurricular activities are fun I pay attention to social issues and causes TOTAL for Section 5 8

9 Section 6 I enjoy making things with my hands Sitting still for long periods of time is difficult for me I enjoy outdoor games and sports I value non-verbal communication such as sign language A fit body is important for a fit mind Arts and crafts are enjoyable pastimes Expression through dance is beautiful I like working with tools I live an active lifestyle I learn by doing TOTAL for Section 6 Section 7 I enjoy reading all kinds of materials Taking notes helps me remember and understand I faithfully contact friends through letters and/or It is easy for me to explain my ideas to others I keep a journal Word puzzles like crosswords and jumbles are fun I write for pleasure I enjoy playing with words like puns, anagrams and spoonerisms Foreign languages interest me Debates and public speaking are activities I like to participate in TOTAL for Section 7 Section 8 I am keenly aware of my moral beliefs I learn best when I have an emotional attachment to the subject Fairness is important to me My attitude effects how I learn Social justice issues concern me Working alone can be just as productive as working in a group I need to know why I should do something before I agree to do it When I believe in something I will give 100% effort to it I like to be involved in causes that help others I am willing to protest or sign a petition to right a wrong TOTAL for Section 8 9

10 Section 9 I can imagine ideas in my mind Rearranging a room is fun for me I enjoy creating art using varied media I remember well using graphic organizers Performance art can be very gratifying Spreadsheets are great for making charts, graphs and tables Three dimensional puzzles bring me much enjoyment Music videos are very stimulating I can recall things in mental pictures I am good at reading maps and blueprints TOTAL for Section 9 Part II Now carry forward your total from each section and multiply by 10 below: Example: Section Total Forward Multiply Score Section x Section Total Forward Multiply by 10 Score Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9 10

11 Part III Now plot your scores on the bar graph provided: Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 Sec 6 Sec 7 Sec 8 Sec 9 Part IV Key: Section 1 This reflects your Naturalist strength Section 2 This suggests your Musical strength Section 3 This indicates your Logical strength Section 4 This illustrates your Existential strength Section 5 This shows your Interpersonal strength Section 6 This tells your Kinesthetic strength Section 7 This indicates your Verbal strength Section 8 This reflects your Intrapersonal strength Section 9 This suggests your Visual strength 1999 Walter McKenzie, Surfaquarium Consulting This survey may be printed, used and/or modified by educators as long as the copyright tag remains in tact. 11

12 Social Skills Anchor Charts Anchor Charts are developed together with the class to make thinking permanent and visible. They allow the class to clarify thinking, make connections, and/or remember a specific skill, strategy, or concept. These skills will be used throughout the year while doing group work/ cooperative activities. The charts can be kept and reviewed periodically, as needed. Encouraging Others Why is it important to encourage others? All ideas and students are respected. People feel good when others encourage them. Students feel like a team and enjoy working together. It is safe to take risks. So students want to participate in group activities. Looks like Watching the speaker Nodding the head Smiling Sounds like That is interesting. Tell me more. That is a great movie. 12

13 Taking Turns Why do we take turns? Each person has a chance to speak. Everyone knows their thinking is important. The group benefits from everyone s ideas. Looks like Only one person speaks at a time. Group members watch the speaker. Group members are smiling. Sounds like It is your turn next. Who is next? Tell us your thinking. I like your idea. Active Listening and Summarizing Why do we summarize? It encourages active listening when hearing each other s ideas. It clarifies and helps check for understanding. It encourages students to pick out key information, give examples, organize their thinking, and draw conclusions. Students learn to summarize their thinking and consider other strategies for solving problems. It encourages participation. Looks like Making eye contact, nodding head Taking turns Encouraging others Listening carefully to everyone's ideas Sounds like Is there anything I missed? I think this is the main idea of what you were saying You seem to be saying The strategy you used was and your conclusion is Be sensitive to the fact that in some cultures it is considered disrespectful to maintain direct eye contact with another person. 13

14 Including All Participants Why do we include all participants? Everyone feels valued and important. People want to participate if they are included. Everyone is willing to take risks when solving problems. People enjoy working together as a team. Looks like All group members are focused. Eyes are on the speaker. Smiles on everyone s faces. Each person takes a turn speaking. Sounds like It is your turn now. Do you have an idea to share? What do you think about this idea? Does this make sense to you? Do you mean? Be sensitive to the fact that in some cultures it is considered disrespectful to maintain direct eye contact with another person. Disagreeing in an Agreeable Way Why do we disagree in an agreeable way? Everyone feels their ideas are being considered even if there are differences of opinion. It is important to hear everyone s ideas because a combination of ideas often produces the best idea. People want to participate if they are treated with respect. Everyone is willing to take risks when solving problems. People enjoy working together as a team. Calm, quiet, controlled voices contribute to a positive classroom climate. Looks like Making eye contact with a slight shake of the head Listening to someone's entire idea before speaking Smiling at the speaker Giving a puzzled or questioning look Sounds like It is your turn next. I understand what you are thinking but have you ever considered.? Your idea is important but have you thought about? I think I understand what you are saying but have you thought about? Be sensitive to the fact that in some cultures it is considered disrespectful to maintain direct eye contact with another person. 14

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16 Why is it important to encourage others? Encouraging others Encouraging others... Looks like Sounds like 16

17 Taking Turns Why do we take turns? Taking turns... Looks like Sounds like 17

18 Active Listening and Summarizing Why do we summarize? Active Listening and Summarizing... Looks like Sounds like 18

19 Why do we include all participants? Including all Participants Including all Participants... Looks like Sounds like 19

20 Why do we disagree in an agreeable way? Disagreeing in an Agreeable Way Disagreeing in an Agreeable Way... Looks like Sounds like 20

21 Students working collaboratively to solve a problem Good Group Work... Looks like Sounds like 21

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24 Math Fermi Problem How much milk do the students at M.J. Hobbs consume in a year? 24

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34 In your group of 4 solve the following Fermi Problem. What is a Fermi Problem? A Fermi problem is a multi-step problem that can be solved in a variety of ways, and whose solution requires the estimation of key pieces of information. Linking Assessment, p. 116 Why Start Grade 8 with Fermi Problems? The purpose of the first week of school is to set the tone for a positive academic environment and community of learners, which foster both mathematical processes and affective processes. The Fermi problems and social skills introduced in the first week of classes combine to generate the kind of involvement and thinking processes that are at the root of quantitative literacy. Because important information is missing, students must ask themselves more questions about what they need to know and what they already know. Then they must construct a path of estimates that leads from the knowledge they have to the knowledge they need to acquire. The focus of this activity is on the process rather than the answer a process that mirrors the number sense we apply in everyday life when we make ballpark estimates of our fuel consumption, our bank balances, or the time we ll need to mark a class test. Impact Math, Number Sense, p. 17 Who was Enrico Fermi? Fermi ( ), a famous physicist, was known to mathematicians for his legendary estimation problems. He was able to answer impossible questions by mentally estimating large quantities for which there seemed to be insufficient information. How many piano tuners are there in Chicago? was one of his well-known problems. This seemingly unanswerable question often puzzled people. Fermi developed a series of subordinate questions leading to an estimate that was the right order of magnitude. The information in the table below is a summary of the sequence of questions, answers, and estimates listed in Impact Math, Number Sense. 34

35 uestion Answer What is the population of Chicago? To estimate pianos should we estimate people or households? Approximately how many households are there in Chicago? What proportion of households in Chicago has pianos? How many piano tuners are needed to tune those pianos? How many piano tuners are there in Chicago? Households rather than individuals tend to own pianos. There may be an average of 4 people per household in Chicago, so the number of households is about Maybe about 1 in 10 households has a piano. That would suggest that there are about or pianos in Chicago. Assuming a piano is tuned once a year, then piano tunings are needed. If a piano tuner tunes approximately 3 pianos a day, and works 200 days a year, the number of tuners needed is about or 125. There are about 125 tuners in Chicago. Setting a Context for Solving Fermi Problems: Fermi problems at first might appear not to have an answer. Your initial response may be I need more information or there is not enough information. There are many different ways to solve a Fermi problem. Be creative. Use any necessary tools. You may use a variety of estimation strategies and need to take a few risks. Don t be afraid to piggyback on someone else s ideas. You will be working as a team and sharing strategies and ideas, encouraging and supporting each other using social skills that we will reinforce each day. 35

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