# Manipulatives —Concrete and Virtual—Across the Grades

Manipulatives Concrete and Virtual Across the Grades Why? multiple representations analogies Hofstadter social nature of knowledge Lave, Wenger, Brown, Zygotsky,

conversations/justifications experiences plausible reasoning Polya More Why conceptual knowledge

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

Concrete Manipulatives race games www.soesd.k12.or.us/files/race_games.pdf www.soesd.k12.or.us/files/place_value_mat.pdf diffies www.soesd.k12.or.us/files/diffy_blank.pdf length vs. area skip counting arrays

multiplication facts partial products Virtual Manipulatives base 10 blocks at NLVM http://nlvm.usu.edu/en/nav/vlibrary.html diffies http://nlvm.usu.edu/en/nav/frames_asid_326_g_2_t_1.html length vs. area

skip counting arrays multiplication facts partial products Assembling a base 10 kit Subtractioncreate your own http://nlvm.usu.edu/en/nav/frames_asid_155_g_3_t_1.html Diffiesonline

http://nlvm.usu.edu/en/nav/frames_asid_326_g_2_t_1.html Diffies on paper http://www.soesd.k12.or.us/files/diffy_blank.pdf get random numbers with virtual 10-sided dice Multiplication: number line arrays counting skip counting (length)

skip counting grid grid pieces stack up to area 7 + 7 + 7 becomes Grid patterns www.amblesideprimary.com/ambleweb/mentalmaths/scribblesquare.html Grid patterns online www.amblesideprimary.com/ambleweb/mentalmaths/scribblesquare.html www.amblesideprimary.com/ambleweb/mentalmaths/scribbletable.html

Draw your own! Arrays counting by fives facts with 5 x 5 = 25 (just a blank) 6x7

with base 10 blocks 40 12 200 23 6

30 12 x 23 6 30 40 200 276 Arrays and partial products

specify the dimensions fill it in! http://nlvm.usu.edu/en/nav/frames_asid_189_g_3_t_2.html?open=activities partial products x+2 x

2 2x + 3 6 3x 4x 2x + 3 4x 6

2x2 3x 2x2 2x2 + 7x + 6 What if x = 10 ? 12 23

40 200 6 30 12 x 23 6 30

40 200 276 Here s 1 x 2 1 x

2 3 5 3 5 = 3

10 Animations mimic procedural knowledge Do-it-yourself PowerPoints www.soesd.k12.or.us/support/training Flash, Java, and PowerPoints on the Web www.soesd.k12.or.us/files/manipulinks.pdf 3-5 = -2 -5

-2 3 0 + Area of a triangle =

(base x height) 2 1 2 36 11

5 3 4 5 7 8

4 5 2 3 4 5

Sliding side c along the base to the center of the square c also makes a parallelogram 1 = 3 Graph:

Y 7 +3 3 +7 X m = 3

7 or 3 7 More Why + Goodbye pedagogical efficiencies We can do things with math in earlier grades that make math easier for students in the long run.

analogy and automaticity Algebra is like arithmetic. Mathematicians know this. Our students need to know it too. Larry Francis Computer Information Services, Southern Oregon ESD [email protected] and 541.858.6748 www.soesd.k12.or.us/support/training and www.soesd.k12.or.us/math

## Recently Viewed Presentations

• investigate how tourism developed in the 1920s and 1930s. Charabancs. Paid Holiday. Butlins. ... Use the information provided to make your own revision flashcards. Try working in groups to create a set of flashcards. On one side have a question....
• Missouri Health Strategic Architectures And Information Cooperative (MOHSAIC) Fully Integrated Database Births (1995) Immunizations (1995) Family Planning (1997) Lead Licensing (2000) Child Care Licensing (2001) SHCN - Service Coordination (2001) Metabolic Screening (2002) Newborn Hearing (2002) Lead Poisoning (2002) Tel...
• The cost of manufacture The wheels were made from argonite that was quarried on Palau and Guam. Guam is 550 miles from Yap; Palau is 300 miles. ... cola, gas, timber, minerals, and water Highest level of specialization with large...
• History of Herbaria. Due to nature of plant biochemistry (e.g., cell wall, lignin), dried, pressed plants can last for centuries (even millennia)
• Hi! This pathfinder is a tool for you to use with the Famous Americans unit assignment. Here you will find a list of resources (books, websites) that will give you all the information you need. You will be able to...
• CHARLATAN (NOUN) ~imposter/fake The fortune-teller was a charlatan. ERUDITE (ADJECTIVE) educated/learned having/showing great knowledge ETYMOLOGY (NOUN) the study of the origin of words. EXTOL (VERB) praise enthusiastically Ms. Smith made sure to extol Tim's excellent decorum.
• Creating Value: Producing Quality Goods and Services ... of Facility Layout Process Product Cellular Fixed-position Process Layout Made-to-order products Process arrangement Specialized employees Specialized materials Product Layout Mass production of few items Process arrangement Continuous ...
• It is a great program for Priest-age boys in the church. 1999 LDS Church Video on Scouting [Continued] "While the Venturing program is an optional program in the church…as we look down the training path of a young man, we...