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(From the book Accessible Mathematics by Steven Leinwand, Principle Research Analyst at the American Institutes for Research and former president of the National Council of Supervisors of Mathematics.) NWSC Cohort Workshops February 1-3, 2011

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Factors Impacting Student Achievement Coherent Curriculum Guides Aligned Assessments Access to Viable Print Materials Access to Technology Administrative Leadership and Support Supportive Parents/Guardians Quality of Instruction

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#1 Incorporate ongoing cumulative review into every day’s lesson Today’s Mini-Math 1. What is 1/10 of 450? 2. Draw a Quadrilateral and all of its diagonals. 3. The cost of a substance is directly proportional to its weight. If 30 grams of the substance costs $45, what is the cost of 6 grams of the substance? 4. A population P increases by 5% each year for 2 years. Write an expression for the population in terms of P after 2 years. 5. What number is 1000 less than 18,294

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# 1 Incorporate ongoing cumulative review into every day’s lesson Your Task: Make a record of concepts covered during first semester that need to be consistently reviewed. List by Strand

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# 1 Incorporate ongoing cumulative review into every day’s lesson What’s seen in an Effective Classroom: Ongoing, cumulative review of key skills and concepts Students given the opportunity to clarify their understandings Classes that waste no time and begin with substantive mathematics at the very start of every class. Classes that end with summarizing questions and/or exit slips The use of a brief review and discussion of mini-math questions

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#2 Adapt what we know works in our reading programs... Jane went to the store Can you read the sentence aloud? Can you tell me where Jane went? Can you tell me who went to the store? Can you tell me why Jane might have gone to the store? Do you think it made sense for Jane to go to the store? Differentiation Through Questioning

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#2 Adapt what we know works in our reading programs... Your Task: Write three open-ended questions that you will use within the next two weeks of instruction.

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#2 Adapt what we know works in our reading programs... What’s seen in an Effective Classroom: Consistent parallels between the types of questions that require inferential and evaluative comprehensions in reading instruction and the probing for ways in which the answers were found, alternative approaches, and reasonableness in mathematics instruction. Open-ended Questions and Parallel Tasks for purposes of differentiating the mathematics Answers greeted with a request for justification Reasonable homework assignments with the focus on explanation and understanding

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#3 Use multiple representations of mathematical entities. Draw at least 3 representations of “3 quarters” Draw at least 3 representations/models for adding integers Systems of equations X + Z = Y Y + Z = 9 Y – X = 2 X + 1 = 6

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#3 Use multiple representations of mathematical entities. Systems of equations Number Shapes 2 + = 9 - = 2 + = + 1 = 6

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#3 Use multiple representations of mathematical entities. Systems of equations using 3-Bean Salads Salad #1 contains 2 Lima beans Twice as many Red beans as Lima beans 10 beans in all Salad #2 contains 3 times as many Red beans as Black-eyed Peas One more Lima bean than Red beans 8 beans in all

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#3 Use multiple representations of mathematical entities. Systems of equations using Bars Julie packs her clothes into a backpack and it weighs 29 kg. Xavier packs his clothes into an identical backpack and it weights 11 kg. Julie’s clothes are three times as heavy as Xavier’s. What is the weight of the Xavier’s clothes? What is the weight of the backpack? Xavier: Julie:

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#3 Use multiple representations of mathematical entities. Your Task: Look at the skills and concepts you’ll be teaching over the next 3 weeks. Determine where you can provide multiple representations for at least 3 of these skills/concepts.

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#3 Use multiple representations of mathematical entities. What’s seen in an Effective Classroom: Frequent use of pictorial representations to help students visualize the mathematics Frequent use of the number line and bar models to represent numbers and word problems Frequent opportunities for students to draw or show and then describe what is drawn or show

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#4 Create language-rich routines Tell the person next to you three things you see and/or know about the numbers 73 and 63. Vocabulary strategies Wordles (handout in workshop packet) Wordles Math Reflections

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#4 Create language-rich routines Your Task: 1. List 30 key vocabulary words that need to be reviewed/used this second semester 2. Create at least one writing assignment where students are asked to explain their understanding of a concept.

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#4 Create language-rich routines What’s seen in an Effective Classroom: An ongoing emphasis on the use and meaning of mathematical terms, including their definitions and their connections to real-world entities and/or pictures Student and teacher explanations that make frequent and precise use of mathematics terms, vocabulary, and notation An extensive use of words walls that capture the key terms and vocabulary with pictures when appropriate

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#5 Take every available opportunity to support the development of number sense Number Sense is a comfort with numbers that includes estimation, mental math, numerical equivalents, a use of referents like ½ and 50%, a sense of order and magnitude, and a well-developed understanding of place value. Number Sense is one of the overarching goals of mathematics learning. How can we work to develop number sense?

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#5 Take every available opportunity to support the development of number sense By asking questions like Which is most or greatest? How do you know? Which is least or smallest? How do you know? What else can you tell me about those numbers? How else can we express that number? Is there still another way? About how much would that be? How did you get that? And by having students estimate the answer first!

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#5 Take every available opportunity to support the development of number sense Your Task: If you began class one day with the statement provided below, what are ten number sense questions you could use to help develop number sense? The statement: As of this morning, my age is 28,935,285.

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#5 Take every available opportunity to support the development of number sense What’s seen in an Effective Classroom: An unrelenting focus on estimation and justifying estimates to computations and to the solution of problems An unrelenting focus on a mature sense of place value Frequent discussion and modeling about how to use number sense to “outsmart” the problem Frequent opportunities to put the calculator aside and estimate or compute mentally when appropriate

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#6 Build from graphs, charts, and tables Ticket Sales for Country Music Concerts ConcertTickets Sold Kenny Chesney Brad Paisley Martina McBride Lady Antebellum 385, , , ,982 About how many tickets sold? Which concert was probably least popular? About how many more tickets were sold for Chesney than for Paisley? Which concert sold closest to 300,000 tickets? About what percent of the total tickets did the McBride concert sell?

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#6 Build from graphs, charts, and tables Your Task: Develop 5 questions around the following data from the Federal Highway Administration: Increasingly Crowded Roads in the United States 1996Growth since 1970 Miles driven Number of vehicles Number of drivers Population Miles of roads 2.5 billion million million million 3.9 million 123% 90% 61% 30% 7%

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#6 Build from graphs, charts, and tables Use the 4 Representations Identify where in the next month you will have the opportunities to “work the data”

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#6 Build from graphs, charts, and tables What’s seen in an Effective Classroom An abundance of problems drawn from the data presented in tables, charts, and graphs Opportunities for students to make conjectures and draw conclusions from data presented in tables, charts, and graphs Frequent conversion, with and without technology, of data in tables and charts into various types of graphs, with discussions of their advantages, disadvantages, and appropriateness

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#7 Tie the math to such questions as “How big?” “How much?” and “How far?” to increase use of measurement Rocky Rococo Pizza, with its rectangular pizzas, once had billboards displaying the following: 20% More! We Don’t Cut Corners!

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#7 Tie the math to such questions as “How big?” “How much?” and “How far?” to increase use of measurement Using your scope and sequence for the next couple of months, determine where there is opportunity to work with measurement before the MCA’s

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#7 Tie the math to such questions as “How big?” “How much?” and “How far?” to increase use of measurement What’s seen in an Effective Classroom Lots of questions are included that ask” how big? How far? How much? How many? Measurement is an ongoing part of daily instruction Students are frequently asked to find and estimate measures, to use measuring, and to describe the relative size of measures that arise during instruction. Frequent reminders that measurement is referential

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#8 Minimize what is no longer important, and teach what is important... If we can answer WHY? (or can’t answer WHY?) we teach a concept then we can determine WHAT to teach and WHAT not to teach. Why do we teach multi-digit multiplication such as 2953 multiplied by 12.5? Why do we teach division of fractions?

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#8 Minimize what is no longer important, and teach what is important... Your Task: Read #15 Less Can Be More in Faster Isn’t Smarter Note 2 to 3 key points to discuss at your table

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#8 Minimize what is no longer important, and teach what is important... What’s seen in an Effective Classroom A curriculum of skills, concepts, and applications that are reasonable to expect all students to master Implementation of a district & state curriculum that includes essential skills and understandings for a world of calculators & computers A deliberate questioning of the appropriateness of the mathematical content, regardless of what may or may not be on the high-stakes state test, in every grade and course

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#9 Embed the mathematics in realistic problems and real-world contexts Dan Meyer’s Math Class Needs a Makeover Dan Meyer’s Math Class Needs a Makeover "I teach high school math. I sell a product to a market that doesn't want it but is forced by law to buy it.“ Dan Meyer

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#9 Embed the mathematics in realistic problems and real-world contexts Your Task: Read #1 Math for a Flattening World in the Faster Isn’t Smarter book Discuss at your table the 4 th and 5 th Questions in the Reflection and Discussion for Teachers section on p. 6.

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#9 Embed the mathematics in realistic problems and real-world contexts What’s seen in an Effective Classroom Frequent embedding of the mathematical skills and concepts in real-world situations and contexts Frequent use of “So. What questions arise from these data or this situation?” Problems that emerge from teachers asking, “When and where do normal human beings encounter the mathematics I need to teach?”

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#10 Make “Why?” “How do you know?” “Can you explain?” mantras Questioning Templates

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#10 Make “Why?” “How do you know?” “Can you explain?” mantras Your Task: Choose one of the Questioning Templates and make a commitment to use it throughout the rest of this school year. Make a poster or a laminated bookmark of it but use it and make it part of what you do in every class every day.

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#10 Make “Why?” “How do you know?” “Can you explain?” mantras What’s seen in an Effective Classroom Every student answer is responded to with a request for justification Both teachers and students consistently and frequently use “Why?” “Can you explain that?” “How do you know?” or equivalent questions Dismissive responses such as “Not,” “ Wrong,” “Not quite,” and their equivalents are absent from the classroom

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The 10 Instructional Shifts: 1. Incorporate ongoing cumulative review into every day’s lesson 2. Adapt what we know works in our reading programs and apply it to mathematics instruction. 3. Use multiple representations of mathematical entities. 4. Create language-rich routines. 5. Take every available opportunity to support the development of number sense. 6. Build from graphs, charts, and tables. 7. Tie the math to such questions as: “How big?” “How much?” “How far?” to increase the natural use of measurement throughout the curriculum. 8. Minimize what is no longer important. 9. Embed the mathematics in realistic problems and real-world contexts. 10. Make “Why?” “How do you know?” “Can you explain?” classroom mantras

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Punting Is Simply No Longer Acceptable Implementing these shifts takes time and it takes planning. We are expected to find ways to make math work for far more kids. We live in a world of calculators and computes and in a world that expects, even requires, deeper understanding and far greater problem-solving skills Planning Templates

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Wrap Up Faster Isn’t Smarter #40 Seven Steps to Becoming a Better Teacher Evaluations

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