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Overview of the 2011 Massachusetts Curriculum Framework for Mathematics

Overview of the 2011 Massachusetts Curriculum Framework for Mathematics Incorporating the Common Core State Standards for Mathematics.

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Overview of the 2011 Massachusetts Curriculum Framework for Mathematics

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  1. Overview of the 2011 Massachusetts Curriculum Framework for Mathematics Incorporating the Common Core State Standards for Mathematics • If you are interested in seeing the entire set of Massachusetts Mathematics Standards please click on the link http://www.doe.mass.edu/frameworks/math/0311.pdf

  2. This presentation is intended to illustrate some of the changes in elementary math as a result of the new standards. • Teaching Strategies • Addition & Subtraction • Multiplication & Division

  3. A major strength of the Common Core is its unity of teaching strategies and teaching tools in all grades. The presentation deliberately highlights this unity.

  4. It all begins with … The 8 Standards for Mathematical Practice These standards are common across all grade levels- Kindergarten through Grade 12.

  5. The 8 Standards for Mathematical Practice are listed below. The goal of the new standards is to ensure students are using these skills daily to connect one skill/concept learned to the next. 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. If you are interested in learning more about these standards please click on the link http://thinkmath.edc.org/index.php/CCSS_Mathematical_Practices. This website describes how the Standards of Mathematical Practice relate specially to the elementary classroom. • If you are interested in learning more about these standards please click on the link http://thinkmath.edc.org/index.php/CCSS_Mathematical_Practices. This website describes how the Standards of Mathematical Practice relate specifically to the elementary classroom.

  6. These standards are best understood by grouping them. Numbers 1 and 6 are the nuts and bolts of mathematics teaching: 1. Make sense of problems and persevere in solving them.6. Attend to precision. Students need to solve problems precisely.

  7. Standards 4 and 5 deal with types of problems used and and how they are solved: 4. Model with mathematics. 5. Use appropriate tools strategically. Modeling is essentially using real world situations . Tools has a wide meaning, many new “tools” in elementary are explained in this presentation.

  8. Standards 2 and 3 deal with reasoning: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. Students need to reason about problems, explain their reasoning to others, and understand the reasoning of other people.

  9. Standards 7 and 8 deal with understanding and using the basic structure of our number system: 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. These two standards are used extensively in teaching calculation skills . They are used throughout this presentation.

  10. Standards for Mathematical Teaching Practice 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 use of ten frames, hundreds charts, number lines, arrays and non traditional algorithms all fall within these standards. When using these tools strategically and appropriately, we are teaching students to make use of structure and repeated reasoning.

  11. These mathematical practices are linked together by how we teach numbers.…...for example…..make use of structure…… Compose & Decompose Numbers. 5 = 2 + 3 5 = 4 + 1 5 = 10 - 5

  12. This skill is used repeatedly in teaching computation. Over time, students become very agile at composing and decomposing numbers. All of the following are used later in this presentation. 50 = ½ x 100 14 = 2 x 7 7 = 5 + 2 13 = 10 + 3 12 = 10 + 2 12 = 2 x 6 27 = 20 + 7 35 = 30 + 5 6 = ½ x 12 25 = 20 + 5

  13. The skill of subitizing is essential. It is now explicitly taught and another fundamental building block. • su·bi·tize [soo-bi-tahyz] verb (used without object), -tized, -tiz·ing. -to perceive at a glance the number of items presented, the limit for humans being about seven.

  14. As adults, we all recognize these dot patterns as 5 and 6 without having to count them. This is subitizing and it is the foundational skill to numeracy.

  15. Students should practice subitizing skills with the dot patterns on both number cubes and ten frames. Students should also be able to recognize how many fingers are held up without having to count. • For more subitizing activities you can go to: Below are links to activities that will develop subitizing skills. • http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf • http://illuminations.nctm.org/ActivityDetail.aspx?ID=74 • http://illuminations.nctm.org/ActivityDetail.aspx?ID=218 • http://illuminations.nctm.org/ActivityDetail.aspx?ID=219 • http://illuminations.nctm.org/ActivityDetail.aspx?ID=73 .

  16. Subitizing with 5 is extremely important….

  17. Connecting subitizing to addition & subtraction

  18. Students should avoid using an un-organized pile of objects to add and subtract….

  19. 8 + 7 =

  20. We want to encourage students to use the structure of the ten frame tool to solve problems. It is the frequent use of the structure and tools that will allow students to ultimately become flexible in their thinking.

  21. 8 + 7 = 15

  22. 8 + 7 = 15

  23. Solving for an unknown using the structure of the ten frame tool. The same ten frame can represent different problems.

  24. 8 + =10 10 - 2 = OA standards based on solving for unknown

  25. In presenting all problems, it is important to phrase and discuss the same problem in different ways, enhancing problem solving and modeling.

  26. Doing calculations……. with understanding.

  27. Addition & subtraction learned based on place value using tools to find structure & generalize. (Back to standards of teaching practice)

  28. Four BIG tools: • Ten Frames • Hundreds Charts • Number Lines • Alternate Algorithms

  29. Ten Frames • Build on subitizing 5 • Composing & decomposing • Flexible thinking

  30. 18 + 17 NBT standards based on place value

  31. 18 + 17 = 20 + 15 = 35 NBT standards based on place value

  32. Hundreds Chart • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

  33. 26 +13

  34. 26 +13

  35. 26 +13

  36. Number Line……a great tool for relative structural position of numbers.

  37. +10 +2 61 49 59 49 + 12 = 61

  38. Non-Traditional Algorithms • Lead to traditional algorithms. • Based on use of tools. • Use structure of the number system.

  39. An example of the Partial Sums Algorithm: 1 8 + 1 7 2 0 Step 1: Add the tens (10 + 10 = 20) and write the sum. NBT standards based on place value

  40. An example of the Partial Sums Algorithm: 1 8 + 1 7 2 0 Step 1: Add the tens (10 + 10 = 20) and write the sum. 1 5 Step 2: Add the ones (8 + 7 = 15) and write the sum. NBT standards based on place value

  41. An example of the Partial Sums Algorithm: 1 8 + 1 7 2 0 Step 1: Add the tens (10 + 10 = 20) and write the sum. + 1 5 Step 2: Add the ones (8 + 7 = 15) and write the sum. 3 5 Step 3: Add the partial sums to get 35 NBT standards based on place value

  42. An example of the Partial Sums Algorithm: 1 8 + 1 7 2 0 Step 1: Add the tens (10 + 10 = 20) and write the sum. + 1 5 Step 2: Add the ones (8 + 7 = 15) and write the sum. 3 5 Step 3: Add the partial sums to get 35 Note connection with ten frames NBT standards based on place value

  43. Examples Student Problem Solving 13 – 9 = ____

  44. Student Problem Solving Student A 13 - 9 I know that 9 plus 4 equals 13. So 13 minus 9 is 4.

  45. Student Problem Solving Student B 13 - 9 Instead of 13 minus 9, I added 1 to each of the numbers to make the problem 14 minus 10. I know the answer is 4. So 13 minus 9 is also 4.

  46. Student Problem Solving Student C 13 - 9 9 is 3 and 6. 13 minus 3 is 10. 10 minus 6 is 4. So 13 minus 9 is also 4.

  47. Multiplication & Division… With Understanding…... Using Tools, Structure & Repeated Reasoning.

  48. Three BIG Tools: • Arrays • Area • Non-Traditional Algorithms

  49. Arrays • Display the structure of multiplication. • Display the repeated patterns in multiplication.

  50. 2 x 7 is 14…

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