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Teaching Addition and Subtraction for Meaning

Teaching Addition and Subtraction for Meaning. Carissa Connell, Stacey Daly, Jennifer Maxwell Mathematics Specialists Madison Public Schools ATOMIC Fall Conference, Cromwell, CT December 3, 2013. How would you solve these problems?. 326 + 497 = ?. 800 – 537 = ?.

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Teaching Addition and Subtraction for Meaning

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  1. Teaching Addition and Subtraction for Meaning Carissa Connell, Stacey Daly, Jennifer Maxwell Mathematics Specialists Madison Public Schools ATOMIC Fall Conference, Cromwell, CT December 3, 2013

  2. How would you solve these problems? 326 + 497 = ? 800 – 537 = ?

  3. Common Core State Standards Related to Addition and Subtraction • Kindergarten: CC.K.OA.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. CC.K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, etc. • First Grade: CC.1.NBT.4 Add within 100, including a two-digit number and a one-digit number, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. • Second Grade: CC.2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

  4. Common Core State Standards Related to Addition and Subtraction Third Grade: • CC.3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Fourth Grade: • CC.4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm (limited to wholenumbers less than or equal to 1,000,000.) A range of algorithms may be used.

  5. Addition & Subtraction Fluency • Explanations and Examples state: “Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.” Mathematics Arizona Academic Content Standards (2010)

  6. Involve Me and I Understand . . . Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand. (Native American Proverb)

  7. Visual Models to Develop Meaning • Subitizing • Visualizing addends • Seeing patterns

  8. Number Racks or Rekenreks Teacher Demonstration Size Free App! https://itunes.apple.com/us/app/number-rack-by-math-learning/id496057949?mt=8 Student Created Version – pipe cleaners & pony beads

  9. Using Ten Frames “Concept of 10”

  10. Number Bonds

  11. Missing Addend/ Subtraction • “Hide the Blocks” Balancing Equations

  12. Adding with Base Ten Blocks

  13. Adding with Base Ten Blocks Cont.

  14. Subtracting with Base Ten Blocks

  15. Using the Hundred Chart • Looking at patterns on the hundred chart • Skip counting by 10 from any number • Adding and subtracting using the hundred chart

  16. Adding with an Open Number Line

  17. Adding with An Open Number Line

  18. Subtracting with an Open Number Line 257 - 125

  19. Partial Sums 48 + 37 70 +15 85

  20. 48 + 37 Adding by Place Value Incremental Adding • 40 + 30 = 70 • And 8 + 7 = 15 • And 70 + 15 = 85 • (Breaking one number into tens and ones) • 48 + 10 = 58 • 58 + 10 = 68 • 68 + 10 = 78 • 78 + 7 = 85

  21. Compensation (Making a Friendly Number)48 + 37 48 + 2 = 50 37 – 2 = 35 50 + 35 = 85

  22. Subtracting In Steps 81 – 37 = ___ Incremental Subtracting Subtracting by Place Value • 81 – 10 = 71 • 71 – 10 = 61 • 61 – 10 = 51 • 51 – 1 = 50 • 50 – 6 = 44 • 81 – 30 = 51 • 51 – 7 = 44

  23. Partial differences 81 – 37 = ________ 80 – 30 = 50 1-7 = -6 50 -6 = 44 Answer: 44

  24. Adding Up to Subtract • 81 – 37 = ___ From Smaller to Larger Number 37 + 3 = 40 40 + 40 = 80 80 + 1 = 81 3 + 40 + 1 = 44

  25. Compensation (making a Friendly Number)1000 - 892 1000 = 999 + 1 999 – 892 = 107 107 + 1 = 108 Answer: 108

  26. Would you solve these problems differently? 326 + 497 = ? 800 – 537 = ?

  27. Discussion/Comments/Questions

  28. Resources • Arizona State Content Standards @ http://www.azed.gov/standards-practices/common-standards/ • Common Core State Standards (2010) @ http://www.corestandards.org/ • First Steps in Mathematics @ http://www.stepspd.com/au/courses/firststepsmath.htm • Math Learning Center @ http://www.mathlearningcenter.org/ • NCTM: Developing Essential Understanding of Addition and Subtraction (2011). • NCTM Illuminations @ http://illuminations.nctm.org/ • SMARTER Balanced Assessment Consortium @ http://www.k12.wa.us/smarter/

  29. Contact information Stacey Daly Carissa Connell Math Specialist Jeffrey School, Madison E-mail: dalys@madison.k12.ct.us Math Specialist Ryerson School, Madison E-mail: maxwellj@madison.k12.ct.us Math Specialist Island Avenue School, Madison E-mail: connellc@madison.k12.ct.us Jennifer Maxwell

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