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Strategies for Whole Number Computation

Strategies for Whole Number Computation. Progression. Starts with Addition and goes through Subtraction, Multiplication, and Division Level of the problem (single digit to double digit). Invented Strategies. Direct Modeling. Traditional Algorithms ( if desired ). Ways to develop.

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Strategies for Whole Number Computation

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  1. Strategiesfor Whole Number Computation

  2. Progression • Starts with Addition and goes through Subtraction, Multiplication, and Division • Level of the problem (single digit to double digit) InventedStrategies DirectModeling TraditionalAlgorithms (ifdesired)

  3. Ways to develop • Use Story Problems • Use the three-part lesson format • Select numbers with care • Integrate computation with place-value development • For grades 3-4 chapter 2 in the 3-5 book (page 51-56)has good activities to emphasize the place-value development. For 2-3 grade its page 145 in the K-3 book. • Progression from direct modeling

  4. How do you feel about the traditional algorithms? What place to you think they have in the classroom if any?

  5. Addition/ SubtractionBeginning • Start with adding and subtracting single digits and then progress onto hundreds and 10s. • To move on relate single digits to the multiple digit problems • Page 164 (K-3), or 108 (3-5)

  6. Addition/ SubtractionExtending • Students will often count by 10s and 1s • 46+30 as 46, 56, 66, 76 • Some Strategies • Add Tens, Add Ones, Then Combine • Move Some to Make Tens • Counting up (Subtraction) • Take Away (Subtraction) • Extensions • Bridging • Larger Numbers

  7. Moving towards the traditional • Begin with Models Only • Use models to extend to the traditional • Grouping Models • Develop Written Record • Do and then Record approach to see the connection • Pay attention to difficulties- exchanging across 0

  8. Multiplication • Representations • Don’t be concerned with the order • Connect to Addition • Strategies • Complete-Number • Partitioning • Compensation • Extending to double digit multiplication

  9. Division • Connect to multiplication • Invented Strategies • Sharing and measurement problems • Missing Factor Strategies • Traditional Algorithm • Not always faster, but it has a place in the classroom • Follow the same model for introducing as with addition and subtraction, but make sure to record explicit trades • Two-Digit Divisors

  10. Math Textbooks • Math Connects • Everyday Math • Investigations

  11. Activity What is inside the cup? As you solve these problems think about what strategies you used. Talk about solving them as a table.

  12. Articles • Children's Mathematical Understanding and invented Strategies for Multidigit Multiplication • Direct Modeling and Invented Procedures: Building on Students' Informal Strategies. • Invented Strategies Can Develop Meaningful Mathematical Procedures.

  13. How do you feel about the traditional algorithms? What place to you think they have in the classroom if any?

  14. References • http://elementarymathvideos.edublogs.org/2010/02/23/4th-grade-division/ • http://www.proteacher.net/discussions/showthread.php?p=1414813 • Baek, Jae Meen. "Children's Mathematical Understanding and invented Strategies for Multidigit Multiplication." Teaching Children Mathematics 12.5 (2005): 242-247. Academic Search Premier. EBSCO. Web. 17 Oct. 2010. • Chambers, Donald L. "Direct Modeling and Invented Procedures: Building on Students' Informal Strategies." Teaching Children Mathematics 3.2 (1996): 92-95. ERIC. EBSCO. Web. 17 Oct. 2010. • Carroll, William M., and Denise Porter. "Invented Strategies Can Develop Meaningful Mathematical Procedures." Teaching Children Mathematics 3.7 (1997): 370-74. ERIC. EBSCO. Web. 17 Oct. 2010. • Math Textbooks: • Investigations • Everyday Math • Math Connections

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