SID Day 2 Mathematics Workshop
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  • 1. Mathematics SummitSouthern Indiana Deanery: Focus on Mathematics Instruction
  • 2. Standards for the Day• Deepen understanding of new Common Core State Standards for mathematics• Create understanding of using multiple representations and approaches to problem solving• Apply a variety of strategies to support and promote the learning of mathematics Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 3. AgendaDAY II• Analysis of New Common Core State Standards• Using Multiple Representations to Develop Deeper Understanding• Using Number lines and manipulatives to support conceptual understanding Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 4. Quick WriteFrom our time together yesterday,What ideas, strategies, concepts, routines do you want to revisit as you plan your classroom for the upcoming year? Which do you want to focus on initially? & How do you plan on accomplishing this? Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 5. Reasoning Abstractly and Quantitatively• 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 6. • Working in non-grade level groups (2-3) Divide 365÷4 (by hand) using three different methods. (Keep in mind, we are developing reasoning and sense-making, and multiple approaches/methods to use with our students ) Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 7. Method 1 of ∞Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 8. Method 2 of ∞Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 9. Method 3 of ∞Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 10. Method 4 of ∞Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 11. Method 5 of ∞ 112/4 = 28 112/4 = 28 112/4 = 28 24/4 = 6 5/4 = 1 R1365 = 112+112+112+24+5 = 28+28+28+6+1+¼ = 91¼ 4 4 Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 12. Common Core State Standards for Mathematics K-8 Mathematics Content Operations & Number & Number & Ratios & Counting & Measurement The Number Expressions Statistics &DOMAINS Algebraic Operations Geometry Operations: Proportional Functions Cardinality & Data System & Equations Probability Thinking in Base Ten Fractions Relationships K X X X X X 1 X X X X 2 X X X X 3 X X X X X 4 X X X X X 5 X X X X X 6 X X X X X 7 X X X X X 8 X X X X X Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 13. 6 7 8Proportional Understand ratio concepts and use ratio Analyze proportional relationships and use reasoning to solve problems them to solve real‐world and mathematicalRelationships problems.The Number Apply and extend previous understandings Apply and extend previous understandings Know that there are numbers that are not of multiplication and division to divide of operations with fractions to add, rational, and approximate them by rationalSystem fractions by fractions. subtract, multiply, and divide rational numbers. Compute fluently with multi‐digit numbers numbers. and find common factors and multiples. Apply and extend previous understandings of numbers to the system of rational numbers.Expressions Apply and extend previous understandings Use properties of operations to generate Work with radicals and integer exponents. of arithmetic to algebraic expressions. equivalent expressions. Understand the connections betweenand Equations Reason about and solve one‐variable Solve real‐life and mathematical problems proportional relationships, lines, and linear equations and inequalities. using numerical and algebraic expressions equations. Represent and analyze quantitative and equations. relationships between dependent and independent variables.Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities.Geometry Solve real‐world and mathematical Draw, construct and describe geometrical Understand congruence and similarity using problems involving area, surface area, and figures and describe the relationships physical models, transparencies, or volume. between them. geometry software. Solve real‐life and mathematical problems Understand and apply the Pythagorean involving angle measure, area, surface area, Theorem. and volume. Solve real‐world and mathematical problems involving volume of cylinders, cones, and spheres.Statistics and Develop understanding of statistical Use random sampling to draw inferences Investigate patterns of association in variability. about a population. bivariate data.Probability Summarize and describe distributions. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use and evaluate probability models. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 14. Content AnalysisIn grade level groups:• Identify new content for your grade level• Identify different opportunities for using multiple representations, approaches, number forms• Develop a priority list of content & approaches to be developed during the transition period. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 15. Content AnalysisIn school groups:• Outline content priorities at each grade level• Identify both major and minor shifts• Shift emphases – decide that teachers will pay more attention to x and y in 2011-2012 and less attention to z Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 16. Quick WriteBased on this morning’s conversations, what do you want to remember? How have you added any more thinking to the routines/processes that you are planning on implementing this year? Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 17. Working with Manipulatives• Don’t assume that students make the connections between the different forms/representations of the problems You must be intentional in doing this!• As with any process, students need to develop understanding of the process prior to attempting to learn new material. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 18. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 19. Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 20. How do we represent in mathematics? Number Algebra Graphical SentenceCollaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 21. Grade Level ContentWorking in multi-grade groups work through several of the problems on the page.What does it look like?How do the ideas progress across thegrades?How do I support, develop student skills inthis area? Collaborative for Teaching andCTL, Mathematical Learning 21 SID: Focus on Mathematics Instruction Literacy August 3, 2011
  • 22. Literacy in Mathematics Reading Vocabulary DevelopmentSpeaking/Listening Writing2Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 23. Community Wiki sidmath.pbworks.comCollaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011
  • 24. Community Wiki sidmath.pbworks.com By the way, what is a Wiki? rodaniel@ctlonline.orgCollaborative for Teaching and Learning SID: Focus on Mathematics Instruction August 3, 2011