Number & Base Ten Building a Founda,on for Later Grades Delise - - PowerPoint PPT Presentation

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Number & Base Ten Building a Founda,on for Later Grades Delise - - PowerPoint PPT Presentation

Feb 12, 2023 275 likes •618 views

Number & Base Ten Building a Founda,on for Later Grades Delise Andrews Math Coordinator, Grades 3-5 Lincoln Public Schools dandrews@lps.org Why is place value so tricky? We o%en fail to take advantage of opportuni3es to support

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Building a Founda,on for Later Grades

Delise Andrews

Math Coordinator, Grades 3-5 Lincoln Public Schools dandrews@lps.org

Number & Base Ten

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Why is place value so tricky?

  • We o%en fail to take advantage of
  • pportuni3es to support children with the

language of place value.

  • Standard algorithms frequently obscure place

value.

  • We move too quickly to abstract

representa3ons.

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Base Ten

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100 1 101 10 102 100

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Base Five

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50 15 51 105 52 1005

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Name this Number (in base five!)

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4 ones 45

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Name this Number (in base five!)

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2 fives 205

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Name this Number (in base five!)

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1 five + 1 one 115

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Name this Number (in base five!)

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1 five + 1 one 115

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Name this Number (in base five!)

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2twenty-fives + 2 fives 2205

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Basic Facts in Base Five

  • Work together with your table group to

construct an addi3on table in base five.

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Base 5 Addition Table + 0 1 2 3 4 0 0 1 2 3 4 1 1 2 3 4 10 2 2 3 4 10 11 3 3 4 10 11 12 4 4 10 11 12 13

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Addi,on in Base Five

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235 + 345

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Addi,on in Base Five

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1045 + 4015

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Subtrac,on in Base Five

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44 5 − 325

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Subtrac,on in Base Five

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325 − 245

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Let’s revisit Base Ten

  • Solve this problem using

manipula3ves.

  • What knowledge about place

value does a student need to use to find the sum?

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78 + 89

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91 − 19

Let’s revisit Base Ten

  • Solve this problem using

manipula3ves.

  • What knowledge about place

value does a student need to use to find the difference?

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Representa,ons

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  • Concrete (well chosen manipula3ves)
  • Representa3onal (math drawings)
  • Abstract (symbolic nota3on)
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Building Capacity with Representa,ons

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  • Verbal

Symbolic Visual Contextual Physical

  • Principles to Actions
Ensuring Mathematical Success for All
  • NCTM. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
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SLIDE 19

Building Capacity with Representa,ons

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Webb, D. C. (2008). Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding. Mathematics Teaching in the Middle School, 14(2), 110-113.

formal notations

pre-formal representations

floating capacity

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SLIDE 20

Building Capacity with Representa,ons

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Webb, D. C. (2008). Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding. Mathematics Teaching in the Middle School, 14(2), 110-113.

formal notations floating capacity

3× 29

29 3

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Building Capacity with Representa,ons

  • “Understanding a mathema3cal idea

thoroughly requires that several possible representa3ons be available to allow a choice

  • f those most useful for solving a par3cular
  • problem. And if children are able to use a

mul3plicity of representa3ons, it is important that they be able to translate among them.”

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

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3× 29 y = 3x + 3

Building Capacity with Representa,ons

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formal notations floating capacity

29 3

y = 3x + 3

3 × 28

( ) + 3

3× 2+ 4 x + 5 = 8

Building Capacity with Representa,ons

Webb, D. C. (2008). Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding. Mathematics Teaching in the Middle School, 14(2), 110-113.

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Lessons from Research

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  • Non-tradi3onal strategies are o%en more

meaningful and frequently more efficient than the tradi3onal algorithms

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Lessons from Research

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  • Math Talk and non-tradi3onal algorithms

improve number sense

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Lessons from Research

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  • Over 90% of the computa3on done outside

the classroom is done without pencil and paper, using mental computa3on, es3ma3on,

  • r a calculator
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Lessons from Research

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  • Manipula3ves must be used regularly and in

meaningful ways

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Lessons from Research

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  • Focus on thinking, not remembering
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Lessons from Research

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  • Manipula3ves should not be limited to

demonstra3ons – students have to interact with them

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Lessons from Research

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  • Explicit connec3ons must be made between

manipula3ves, representa3onal drawings, and symbolic nota3on

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Lessons from Research

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  • Ability to replicate procedures does not

equate to understanding

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Summarize & Reflect

Think about your instruc,on around place value concepts.

  • I want to stop (or change)…
  • I need to keep...
  • I plan to start...

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Disclaimer

The National Council of Teachers of Mathematics is a public voice

  • f mathematics education, providing vision, leadership, and

professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all

  • students. NCTM’s Institutes, an official professional development
  • ffering of the National Council of Teachers of Mathematics,

supports the improvement of pre-K-6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics ideas, activities, and pedagogical strategies, and for sharing and interpreting research. The Institutes presented by the Council present a variety of

  • viewpoints. The views expressed or implied in the Institutes,

unless otherwise noted, should not be interpreted as official positions of the Council.

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