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Singapore Math Computation Strategies

Singapore Math Computation Strategies. June 2012 “ Understanding is a measure of the quality and quantity of connections that an idea has with existing ideas.” ( VandeWalle , Pg. 23). Mathematical proficiency has 5 strands:. Conceptual understanding Procedural fluency Strategic competence

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Singapore Math Computation Strategies

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  1. Singapore Math Computation Strategies June 2012 “Understanding is a measure of the quality and quantity of connections that an idea has with existing ideas.” (VandeWalle, Pg. 23)

  2. Mathematical proficiency has 5 strands: • Conceptual understanding • Procedural fluency • Strategic competence • Adaptive reasoning • Productive disposition Source: Common Core (Pg. 6)

  3. Number Sense Definition: Number sense is a “good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” (Van de Walle, Pg. 119)

  4. Why Singapore Math? • According to a 2007 Trends in International Mathematics and Science Study, Singapore students are among the best in the world in math achievement. • The Singapore model drawing approach bridges the gap between the concrete and abstract models we tend to jump to in the US. • Model drawing reinforces students’ visualization and understanding of math processes. • Model drawing can be used effectively to solve 80 percent of problems in all texts.

  5. Why Singapore Math? Cont. • Computation is about students comprehending what they are doing, not following a set of rules. • Students need to understand both what to do and why. • Students will have a variety of strategies to solve problems. • Changes students attitudes toward math and problem solving. • Language based learning- think alouds and math talks • Can be used as a supplement to an adopted curriculum • Singapore Math Video

  6. C-P-A Concrete, Pictorial, Abstract • Instruction begins at the concrete level with manipulatives to build understanding of basic concepts and skills. (begin with proportional manipulatives) • Then students are introduced to the pictorial stage: model drawing. • Students are not introduced to formulaic or algorithmic procedures, the abstract, until they have mastered model-drawing.

  7. Manipulatives

  8. How do you know when manipulatives are and are not needed? Discuss. Catch thinking on chart paper. Write a summary paragraph.

  9. I Do, We Do, We Do, We Do, You Do • Teacher modeling and thinking aloud about the strategy • Students practice with the teacher • Students practice in small groups • Students practice in partners • Independent practice

  10. Math Talk-Teacher Think Alouds • Purpose: Modeling, communicating, promoting a more efficient strategy, promoting reasoning, moving to a more sophisticated level of thinking. • “I’m thinking…” “I’m wondering…” “What are you thinking?” “How did you figure that out?” “Is there another way?” “Why did you choose this way?” “How do you know this answer is correct?” “What would happen if?” • Model clear, explicit language about concepts • Mathematical thinking and language promote more understanding than memorization or rules

  11. Teacher Think Aloud Example • 346+475= • First, I’m going to add the hundreds. That means 300+400=700. Now I will add the tens, four tens (40) plus seven tens (70) equals eleven tens. I can make 110. So now I have 700+100+10. Now I will add the ones and 6+5 makes 11. This is one ten and one 1 so I have 700+100+10+10+1. My answer is 821. • Place Value Talk is critical!

  12. Math Talk – Ask a Math Question Purpose: “Unstick” someone, get help, clarify, promote deeper thinking, make connections

  13. Math Talk – Partner Prompts Purpose: Promote productive math conversations Example: Practicing questions in multiple-choice format • Step 1: Solve individually. Write down your answer. • Step 2: Compare. Same or different? • Step 3: Explain why you chose that answer.

  14. Math Talk – Expand the Use of Vocabulary Purpose: Use words that proficient mathematicians would use, make connections Example: End of Year Jeopardy Review Game. • 500 point question: What is addition?

  15. Trying to Help Someone? • Lookat their work. • Do the model, the picture, and the equation match the question and each other? • Read or listen to their explanation. • Ask a math question. • Seek professional help – Ask a student expert, the teacher, or other adult.

  16. Instructional Materials • Place Value Strips • Place Value Disks • Place Value Chart • Number-bond cards • Part-whole cards • Decimal Tiles • Decimal Strips • Gratiot Isabella ISD Maniplatives Link

  17. Addition • Begin with no regrouping • Sequence • Number bonds • Decomposing numbers • Left-to-right addition • Place value disks and charts • Vertical addition • Traditional addition

  18. Number Bonds

  19. A Collection of Number Relationships- Relationships Among Numbers 1 Through 10 • Spatial Relationships • pattered arrangements • One and Two More, One and Two Less • counting on and counting back • 7 is 1 more than 6 and it is 2 less than 9 • Anchoring Numbers to 5 and 10 • using 5 and 10 to build on and break from is foundational for working with facts • Part-Part-Whole Relationships • understand that a number is can be made of 2 or more parts

  20. A Collection of Number Relationships - Relationships for Numbers 10 to 20 • A Pre-Place Value Relationship with 10 • 11 through 20, think 10 and some more • Extending More and Less Relationships • i.e. 17 is one less than 18 like 7 is one less than 8 • Double and Near-Double Relationships • special cases of the part-part-whole construct • use pictures

  21. 2 Strategies to Emphasize Build Up and Down through 10 Break Apart to Find an Unknown Fact

  22. Number Sense and the Real World • Estimation and Measurement • More or less than _______? • Closer to _____ or _____? • About _______. • More Connections • Add a Unit to Your Number • Is It Reasonable? • Graphs • Make bar graphs and pictographs

  23. Basic Facts Big Ideas: • Number relationships provide the foundation for strategies that help children remember the basic facts. (i.e. relate to 5, 10, and doubles…) • “Think addition” is the most powerful way to think of subtraction facts. • All of the facts are conceptually related. You can figure out new or unknown facts from those you already know. • What is mastery? 3 seconds or less

  24. Decomposing Numbers47 10 10 10 10 1 1 1 1 1 1 1 7 40

  25. Left-to-Right Addition • 33+56= • Decompose each number by place value. • Put the tens together and one ones together. • (30+50) + (3+6) • (30+50) + (3+6) • 80 + 9 = 89 30 50 3 6

  26. Place Value Disks and Charts • 35 +26 10 10 10 10 1 1 1 1 1 1 1 1 1 1 10 10 1

  27. Place Value Disks and Charts • 35 +26 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 10 10 1

  28. Place Value Disks and Charts • 35 +26 6 1 10 10 10 10 10 10 10 1

  29. Vertical Addition • 36 +28 50 +14 64 Add from left to right.

  30. Traditional Addition • 38 +85 123

  31. Subtraction • Begin with no regrouping • Sequence • Number Bonds • Place Value Disks and Charts • Traditional Subtraction

  32. Number Bonds

  33. Place Value Disks and Charts • 86-8 10 10 10 10 10 1 1 1 1 1 10 10 10 1

  34. Place Value Disks and Charts • 86-8 10 10 10 10 10 1 1 1 1 1 10 10 10 1 1 1 1 1 1 1 1 1 1 1

  35. Place Value Disks and Charts • 86-8 • 70 + 8 = 78 • 86-8=78 10 10 10 10 10 1 1 1 1 1 10 10 1 1 1 1 1 1 1 1 1 1 1

  36. Traditional Subtraction • 54 - 28 26

  37. Multiplication • Before “memorizing” multiplication facts, students must first understand the concept of multiplication----they must know it is repeated addition with special attention to place value • Stages • Number bonds • Place value disks and charts • The distributive property • Area model • Traditional multiplication

  38. Number Bonds • 16 4 16 16 or 4 4 4 16 16 2 8 1 16 Vocab: Factor x Factor=Product

  39. Place Value Disks and Charts • 141x3 1 100 10 10 10 10 10 10 1 100 10 10 10 10 1 100 10 10

  40. Place Value Disks and Charts • 141x3 100 1 100 10 10 10 10 10 10 1 100 10 10 10 10 1 100 10 10

  41. Place Value Disks and Charts • 141x3 4 2 3 141x 3=423 100 1 100 1 100 10 10 1 100

  42. The Distributive Property • 45x3 (40x3) + (5x3) 120 + 15 = 135

  43. Area Model • 6x33 30 3 6 180 18 6x33=180+18 180+18=198

  44. Area Model • 15x26 20 6 10 200 60 5 100 30 15x26=(200+100)+(60+30) 300 + 90 =390 15x26=390

  45. Traditional Multiplication

  46. Division • Begin by introducing division as repeated subtraction • Use number bonds to demonstrate the inverse relationship of multiplication and division • Sequence for teaching • Number bonds • Place value disks and charts • The distributive property • Partial quotient division • Traditional long division • Short division

  47. Number Bonds 9 • 27 ? What should the second factor be? Vocab: Dividend ÷ Divisor=Quotient

  48. Place Value Disks and Charts • 64÷5 • Step 1 Build with disks 10 10 10 10 10 1 1 1 1 10

  49. Place Value Disks and Charts • 64÷5 • Step 2: The divisor tells us how many groups we need: Draw 5 rows • 1 • 2 • 3 • 4 • 5 1 1 1 1 10 10 10 10 10 10

  50. Place Value Disks and Charts • 64÷5 • Step 3: Begin with the tens. Do we have enough tens to put one in every row? Yes • 1 • 2 • 3 • 4 • 5 10 1 1 1 1 10 10 10 10 10

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