Manipulatives Concrete and Virtual Across the Grades

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Manipulatives Concrete and Virtual Across
the Grades
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Why?

• multiple representations
• analogiesHofstadter
• social nature of knowledgeLave, Wenger, Brown,
  Zygotsky,
• conversations/justifications
• experiences
• plausible reasoningPolya

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More Why
conceptualknowledge
proceduralknowledge
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What?

• base 10 blocks
• 10-sided dice
• grid paper
• animations and slide shows
• paper-and-pencil sketches
• index cards, egg cartons, etc.

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Concrete Manipulatives

• race gameswww.soesd.k12.or.us/files/race_games.pd
  fwww.soesd.k12.or.us/files/place_value_mat.pdf
• diffieswww.soesd.k12.or.us/files/diffy_blank.pdf
  
• length vs. area
• skip counting ? arrays
• multiplication facts
• partial products

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Virtual Manipulatives

• base 10 blocks at NLVMhttp//nlvm.usu.edu/en/nav/
  vlibrary.html
• diffieshttp//nlvm.usu.edu/en/nav/frames_asid_326
  _g_2_t_1.html
• length vs. areaskip counting ? arrays
• multiplication facts
• partial products

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Assembling a base 10 kit
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Subtractioncreate your own
http//nlvm.usu.edu/en/nav/frames_asid_155_g_3_t_1
.html
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Diffiesonline
http//nlvm.usu.edu/en/nav/frames_asid_326_g_2_t_1
.html
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Diffies on paper
http//www.soesd.k12.or.us/files/diffy_blank.pdf
get random numbers with virtual 10-sided dice
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Multiplication number line ? arrays

• counting ? skip counting (length)
• skip counting ? grid
• grid pieces stack up to ? area

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Grid patterns
www.amblesideprimary.com/ambleweb/mentalmaths/scri
bblesquare.html
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Grid patterns online
www.amblesideprimary.com/ambleweb/mentalmaths/scri
bblesquare.html
www.amblesideprimary.com/ambleweb/mentalmaths/scri
bbletable.html
Draw your own!
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Arrays
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counting by fivesfacts with 5 x 5 25
(just a blank)
6 x 7
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with base 10 blocks
12 x 23 6 30 40 200 276
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23
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Arrays and partial products
specify the dimensions
fill it in!
http//nlvm.usu.edu/en/nav/frames_asid_189_g_3_t_2
.html?openactivities
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partial products
x 2 2x 3 6 3x 4x 2x2
2x2 7x 6
x 2
2x 3
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What if x 10 ?
12 x 23 6 30 40 200 276
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Animations mimic procedural knowledge

• Do-it-yourself PowerPointswww.soesd.k12.or.us/sup
  port/training
• Flash, Java, and PowerPoints on the
  Webwww.soesd.k12.or.us/files/manipulinks.pdf

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3 - 5

- 2
- 5
3
-2
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Area of a triangle
(base x height)

2
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Sliding side c along the baseto the center of
the square
c
also makes a parallelogram
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1¾ ½ 3 ½
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Graph
?7
3
?3
m ?3? 7?
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or 3? ?7?
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More Why Goodbye

• pedagogical efficienciesWe can do things with
  math in earlier grades that make math easier for
  students in the long run.
• analogy and automaticityAlgebra is like
  arithmetic. Mathematicians know this. Our
  students need to know it too.

Larry Francis Computer Information Services,
Southern Oregon ESD larry_francis_at_soesd.k12.or.us
and 541.858.6748 www.soesd.k12.or.us/support/trai
ning and www.soesd.k12.or.us/math