1 / 24

Early Number Sense The “Phonics” of Mathematics

Early Number Sense The “Phonics” of Mathematics. Presenters: Lisa Zapalac, Head of Lower School Kevin Moore, 4 th Grade Math Brooke Carmichael, Kindergarten. November 19, 2010 10:15 – 11:30 a.m. www.austintrinity.org. 3,996 + 4,246. Simplify the following expression:.

ossie
Download Presentation

Early Number Sense The “Phonics” of Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Early Number SenseThe “Phonics” of Mathematics Presenters: Lisa Zapalac, Head of Lower School Kevin Moore, 4th Grade Math Brooke Carmichael, Kindergarten November 19, 2010 10:15 – 11:30 a.m. www.austintrinity.org

  2. 3,996 + 4,246 Simplify the following expression:

  3. Is this how you simplified it? 1 1 1 1 3,996 +4,246 8,242

  4. 2nd Grader Simplifying 3,996 + 4,246 Example of 2nd Grader Using Compensation

  5. How did the 2nd grader simplify the expression? He used an addition strategy called compensation, but there are many underlying concepts that are embedded in compensation He noticed that 3,996 is 4 less than 4,000 He recognized 4,246 as being equivalent to 4,242+ 4 He then associated (3,996 + 4) + 2,242

  6. Possesses a repertoire of mental computation strategies Number Sense Recognizes unreasonable conclusions Recognizes values in their various forms Demonstrates proficiency with estimation and evaluation of quantities Evidence of Number Sense

  7. Let’s try another expression 50 x 48 4th Grade Video

  8. Is this how you simplified it? 4 48 x 50 00 +2400 2400 4 48 x50 2400

  9. 4th Graders Simplifying48 (50) Example 1 Example 2 Example 3

  10. One more… 4th Grader Solve 76 x 89

  11. Number Sense…. How do we build it? There are many effective strategies for building number sense. At Trinity, “strings” are one power practice used.

  12. Using “Strings” to Develop Number Sense Strings are a set of arithmetic problems in which the children are developing very specific strategies. Strings are generally done mentally. Each string begins with a known expression and moves towards the unknown, scaffolding the development of key strategies. The following slides contain examples of strings at various grade levels.

  13. 1st Grade String 5 + 5 5 + 6 6 + 6 6 + 7 7 + 7 7 + 8 8 + 8 9 + 7 6 + 8

  14. Building Number Sense through Facts Possesses a repertoire of mental computation strategies 5 + 5 5 + 6 6 + 6 6 + 7 7 + 7 7 + 8 8 + 8 9 + 7 6 + 8 • Doubles plus or minus 1 • Ex. 6 + 7 = 6 + 6 + 1 (or 7 + 7 – 1) = 13 • Doubles plus or minus 2 • Ex. 5 + 7 = 5 + 5 + 2 (or 7 + 7 - 2) • Working with the structure of five • Ex. 6 + 7 = 5 + 1 + 5 + 2 = 10 + 3 = 13 • Making tens • Ex. 8 + 4 = 8 + 2 + 2 • Using tens to solve nines • Ex. 9 + 7 = 10 + 7 - 1 • Using compensation • Ex. 6 + 8 = 7 + 7 (adding one to one addend, while subtracting one from the other addend)

  15. Recognizes values in their various forms Using Tools and Models to Develop Number Sense The rekenrek, or arithmetic rack, is a tool consisting of two rows of ten beads with two sets of five in each. The rekenrek was developed by AdriTreffers, a researcher at the Freudenthal Institute in the Netherlands, and it provides a powerful model for exploring the composing and decomposing of number (Treffers1991)

  16. Kindergarten String Example Possesses a repertoire of mental computation strategies Recognizes values in their various forms Kindergarten String 5 on the top, 5 on the bottom 7 on the top, 3 on the bottom 4 on the top, 6 on the bottom 6 on the top, 4 on the bottom 8 on the top, 2 on the bottom

  17. Moving Beyond Facts Modeling 38 + 42 2 40 The open number line is a tool used to model students’ thinking. In this problem, 38 + 42, a student might solve it by moving to a landmark number first. Or, they might first make jumps of ten. 80 38 40 40 2 78 80 38

  18. Example of 2nd Grade StringBig Idea: Keeping One Number Whole and Taking Leaps of 10 75 + 20 75 + 25 75 + 24 55 + 30 55 + 39 69 + 21 69 + 29 2nd Grade String

  19. Building Number Sense with Multiplication Constructing facts through relationships and models 4(4) = 16 2[(4)2] or 2(8)

  20. Multiplication(3rd & 4th Grade Strategies) Possesses a repertoire of mental computation strategies • Doubling • 6 x 6 = 2 x 3 x 6 • Halving and doubling • 4 x 3 = 2 x 6 • Using the distributive property • 7 x 8 = (5 x 8) + (2 x 8), or • 7 x 8 = (8 x 8) – (1 x 8) • Using the commutative property • 5 x 8 = 8 x 5

  21. Example of 4th Grade String 4th Grade Multiplication String 4 x 8 14 x 8 6 x 9 26 x 9 12 x 13 15 x 24

  22. 4th Grade String Revisited – Connecting to Algebra a (8) (a + b) 8 (3a)2 (2a + c) (5) (a + 3) (a + 2)

  23. Number sense is the bridge between arithmetic and algebra Number Sense Arithmetic Algebra

  24. Resources Books Ma, L. (1999). Knowing and Teaching Elementary Mathematics. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. Devlin, K. (2000). The Math Gene. Great Britain:Weidenfeld & Nicolson Stigler & Hiebert (1999). The Teaching Gap. New York, NY: The Free Press Fosnot, C., & Dolk, M. (2001). Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann Fosnot, C., & Dolk, M. (2001). Young Mathematicians at Work: Constructing Multiplication and Division. Portsmouth, NH: Heinemann Carpenter, T., Franke, M., & Levi, L. (2003). Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann Fosnot, C. & Uittenbogaard, W. (2007). Minilessons for Early Addition and Subtraction. Portsmouth, NH: Heinemann Fosnot, C. & Uittenbogaard, W. (2007). Minilessons for Extending Addition and Subtraction. Portsmouth, NH: Heinemann Fosnot, C. & Uittenbogaard, W. (2007). Minilessons for Early Multiplication and Division. Portsmouth, NH: Heinemann Fosnot, C. & Uittenbogaard, W. (2007). Minilessons for Extending Multiplication and Division. Portsmouth, NH: Heinemann Articles Faulkner, V. (2009). The Components of Number Sense – An Instructional Model for Teachers. –Teaching Exceptional Children, Vol. 41, No. 5, 24-30 Gersten, R. & Chard, D. (2010). Validating a Number Sense Screening Tool for Use in Kindergarten and First Grade: Prediction of Mathematics Proficiency in Third Grade – School Psychology Review, Vol. 39, No. 2, 181-195 Harel, G. & Rabin, J. (2010). Teaching Practices Associated With the Authoritative Proof Scheme – Journal for Research in Mathematics Education, Vol. 41, No. 1, 14-19 Web Sites DreamBox Learning - www.dreambox.com To order a rekenrek: www.eNasco.com

More Related