5 A Focus on the Practice Standards Elementary PD CommentsWhat is clear?“Change is coming, modeling math w/real world situations is important, discussion is essential.”“We need to push them further & use more discussion during lessons (critique & reason).”What are your next steps?“Infusing the practices learned today to help students become better mathematicians.”MS – 9 hoursHS – 6 hoursElementary – 1 – 12 hoursMS PD CommitmentsUtilize:Strand 25 & Connected Math Project ActivitiesWord WallsWriting in Math JournalsNext Steps:Rubric DevelopmentTechnology TrainingStrategiesInstructional supportHS PD CommitmentsFocus on:Problem solvingModelingDeveloping argumentsNext Steps:StrategiesInstructional support
6 What does it look like?The biggest challenge is to show what the standards mean and how that will change classroom practice.
8 From this Identify each number as prime or composite to …
9 Mathematical Practices 1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.Which one is different? Explain your reasoning.Find more than onepossible answer.
11 Mathematical Practices 1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.An international fast food chain reports that 8% of the people in the United States eat at its restaurants each day. The fast food chain currently has 12,800 stores in the United States. The most recent Census Bureau report states that approximately 310 million people live in the United States. Make a conjecture as to whether or not you believe the report from the fast food chain to be accurate. Create a mathematical argument that validates your conclusion.
12 From this Today we will use Area = ½ (b1+b2) to solve area of trapezoid problems…to …
13 Mathematical Practices 1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.The area of a trapezoid can be determined from the what you know about the area of rectangles and parallelograms. Determine how the areas of these figures are related using your manipulatives. Explain your reasoning.
14 From thisA rectangle has side lengths of 7 m and 9 m. A square with side length 5 m is cut out of the rectangle. Find the area of that rectangle after the square is cut out.to…
15 Below is a satellite photo of Geoff’s yard. He is interested in re-soddinghis entire yard. Help him out byproviding a cost estimate.Develop a list of questionsyou would need answeredbefore you can solve theproblem.Contributed by Bristol Central Geometry Teachers
21 Elementary Schools Curriculum Development and Implementation K, 2, 4 Introduction of enVision MathCommon CoreProfessional DevelopmentJob embedded coachingPD DaysWednesday afternoonsPrincipals Guide and PD
22 A Principal’s Guide to Elementary Mathematics Instruction K-5 Lesson ComponentsWhat the teacheris doing…What the studentsare doing…Assessment of learningInstructional Delivery(15-20 min.)Observing individual and group workListening and probing furtherUsing quick-checks to gauge student understandingEngaging students in self-assessLaunching investigation of a concept or real-world problemModeling new conceptsPosing a variety of levels of questionsProviding opportunities to move between diff. representationsIntroducing new vocabulary and utilizing the word wallFacilitating discussions, noting key ideas and uncovering misconceptionsWorking independently or cooperatively in small groupsAsking questions to clarify and deepen understandingParticipating and actively listening to discussionsSharing strategies and solutionsMaking connections to the real world, among math concepts and other disciplinesRecording work/important concepts
23 A Principal’s Guide to Elementary Mathematics Instruction K-5 Lesson ComponentsWhat the teacheris doing…What the studentsare doing…Assessment of learningActive Learning(20–30 min.)Facilitating small group learning and independent practiceUsing a workshop model to differentiate instructionProviding students with a variety of problems, centers, games or rich tasks for practice and extensionWorking independently or cooperatively in small groupsAsking questions to clarify and deepen understandingMaking connections to the real world, among math concepts and other disciplinesDeveloping proficiencyObserving individual and group workListening and probing furtherCollecting and analyzing written work
24 A Principal’s Guide to Elementary Mathematics Instruction K-5 Throughout the lesson students should be: (CT Common Core Mathematical Practice Standards)Problem Solving – Rich problems are part of the lessons. Students make sense of problems, know how they relate to similar problems, plan and persevere in solving problems using a variety of methods and recognize when an answer makes sense or doesn’t.Reasoning Mathematically – Situations are presented that require students to make sense of the numbers involved, the relationship between them and be able to use numbers and symbols to match the situations. Students interpret and write story problems.Justifying and Explaining – Opportunities are created for students to communicate about their strategies and solutions orally and in writing. They listen to other strategies, point out when a solution is mathematically valid or not, explain why and adopt more efficient ones.Modeling with Mathematics – Real-world scenarios are discussed and presented. Students use appropriate mathematical representations (number sentences, geometric shapes) to represent problems and solve them. Students interpret a solution in context.Using Appropriate Tools – Tools, manipulatives and technology are used. Students know what tools to use to solve a problem (e.g. base- ten blocks, calculator, ruler, pen and paper) and explain why. They estimate solutions prior to computing.Using Precise Vocabulary, Symbols and Labels – Everyone is accountable for mathematical language. Students use mathematical terms and know their definitions. They understand what symbols mean and correctly label and assign units when appropriate.Looking For and Make Use of Structure and Regularity – Patterns and the structure of math is highlighted. Students recognize and describe patterns in their problem solving. They apply mathematical properties and find shortcuts to solve similar problems.
25 Principal’s Guide“ I Love it. (It) focuses on just the lesson design and delivery and is great for teachers that have management and rapport, climate down. ”Rochelle SchwartzPrincipalEllen P. Hubbell School
32 Strategies to Promote the MPS Pose meaningful problemsPlan and use higher order questionsDevelop perseveranceExamples include:Ask 3 then meGroup diplomatsFermi problemsPoster methodExplorations
33 Strategies to Promote the MPS Encourage communication & listeningCreate an environment for questionsDevelop thinkersExamples include:Ask Why? Do you agree? Why? Why not?Four CornersPhilosophical ChairsTurn and talkThink(Jot)-Pair-ShareQuick DrawSummarizationMultiple Methods
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