Math Tools Pp

8/2/2019 Math Tools Pp

1/34

2006 McREL

Hands-on LeUsing Math TAfterschool

Danette Parsley, Principal [email protected]

Heather Martindill, Sr. Cons

[email protected]

McREL


2/34

2006 McREL

What are Math Tools?

Mathematical tools can be definto include concrete materials (i

manipulatives), symbols, picturdrawings, and technology


3/34

2006 McREL

Personal Knowledge of Tools

Counters

Cuisenaire rods/Integer bars

Base 10 blocks

Unifix cubes

Tangrams

Pattern blocks

Paper M

Geoboar

Dice

Rulers &Measure

Judy Clo

CalculatoCompute


4/34

2006 McREL

Common Math To

CountersCuisenaireInteger Bar

UnifixCubes


5/34

2006 McREL

Common Math Tools

Tangrams

Dice


6/34

2006 McREL

Common Math Tools Geoboards

Rulers &Tape Measures


7/34

2006 McREL

Personal Knowledge of Tool

Counters

Cuisenaire rods/

Integer bars Base 10 blocks

Unifix cubes

Tangrams

Pattern blocks

Paper M

Geoboa

Dice Rulers &

Measur

Judy Cl

CalculaComput


8/34

2006 McREL

Counters & Color Tiles

Patterning

Estimating numbers

Keeping count during a

survey and formingsimple graphs

Solving number riddles/acting out word problems

Analyzing factors and

multiples Illustrating even and odd


9/34

2006 McREL

Cuisenaire Rods

Whole num Fractions Measurem

Ratio Area & pe Symmetry Three-dim

geometry

Patterns Functions


10/34

2006 McREL

Unifix Cubes

Counting

Patterns

Number c

Addition &

Fractions

Beginning

Probabilit


11/34

2006 McREL

Paper Money

Solving mrelated p(word pro

addition,

Showingdate usincombina

Exploring


12/34

2006 McREL

Tangrams

Forming shapes

Exploringpropertie

Combiniform ano

Identifyinand simi


13/34

2006 McREL

Pattern Blocks

Naming an

Investigatinbetween sh

Analyzing cshapes

Exploring p

Modeling afractions

Investigatinsymmetry, area, perimmeasure


14/34

2006 McREL

Dice

Probability

Random numbergenerator

Permutations &combinations

Games


15/34

2006 McREL

Judy Clocks

Telling ti

Solving tproblems


16/34

2006 McREL

Geoboards

Counting

Naming, forming,comparing and makinggeneralizations about

geometric shapes Illustrating and verifying

well-known formulas forfinding area and perimeter

Naming, forming,

comparing, andgeneralizing about angles

Exploring fractions


17/34

2006 McREL

Base 10 Blocks

Exploring and discoveringnumber relationships

Solving problems that

require addition,subtraction, division ormultiplication of multi-digitnumbers

Measuring in metric units

Modeling area of volume


18/34

2006 McREL

Rulers & Tape Measure

Measurement

Scale

Relationship betweenunits of measurement(metric & standard)


19/34

2006 McREL

Calculators & Computer

Computa

Complexsolving

Graphing

Program

Virtual M


20/34

2006 McREL

Phases of Mathematical Unde

Concrete Transitional


21/34

2006 McREL

Why does the practice of u

math tools work? Tools can help students see connectio

objects, symbols, language, and ideas

Tools help students think flexibly aboumathematics, use creativity to solve nemathematics problems, and explore mwith less anxiety.

Given the active and social aspects ofis an ideal environment for allowing stexplore, test, build, think, talk, connecwith mathematical tools.


22/34

2006 McREL

We remember 10% of hear, 30% of what we s

90% of what we d

-


23/34

2006 McREL

Activity 1

Using the tools on your table, sfollowing problem.

Be prepared to share how you tool to solve the problem with thgroup.


24/34

Draw a 7 X 7 squareon graph paper. Showhow to cut the square

into the least numberof smaller squares.Your cuts must be

along the lines of thegraph paper.

Problem from : TeProblem Deck AA

1980 Dale Seym


25/34

2006 McREL

2 x 2 2 X 2

3 X 34 X 4

3 X 3

2 X 2


26/34

2006 McREL

Activity 2

In groups of three, select a tool youuse to solve the problem presented

Each group at your table will work wtool.

After each group solves the problemyour table.

Why did you choose that tool? How did you solve the problem with th

chose?


27/34

2006 McREL

What do you do if you wan

math tools in afterschool? Determine what concepts and s

students are learning by talking

school teacher. Develop activities that students

Provide an assortment of tools

Allow students to discuss how stools contributed to their thinkin


28/34

2006 McREL

Implementation Tips

Plan for the use of mathematical to

Ensure students have access to a vtools

Explore the appropriate use of mathtools

Plan for frequent intervention and d

Communicate how the tools help ch


29/34

2006 McREL

Technology: Virtual Manip

Sample of Tangrams online using The National LibraManipulatives http://nlvm.usu.edu/en/nav/vlibrary


30/34

2006 McREL

Further Details on the useTools in Afterschoo

http://www.sedl.org/afterschoo

Afterschool Training Toolkit developed byPartnership for Quality Afterschool Learni


31/34

2006 McREL

I hear and I forget. I s

remember. I do an

understand.- Con


32/34

2006 McREL


33/34

National Partnership for Quality Afterschool Learning

McREL 2006

Hands-on Learning: Using Math Tools in Afterschool

Resources

(These are just a few of the online resources available)

Sites with printable templates for Manipulatives

http://mason.gmu.edu/~mmankus/Handson/manipulatives.htm

Provides templates for making your own manipulatives.

http://math.donnayoung.org/

Provides templates for fractions, money, clocks and much more.

http://mathcentral.uregina.ca/RR/database/RR.09.98/loewen2.html

Provides manipulative templates & activities for upper grades.

Sites with activities using manipulatives

http://teacher.sholastic.com/max/index.htm

Scholastics Maxs Math Adventures

Provides activities with supplemental student pages many of which contain manipulatives.

http://illuminations.nctm.org/

National Council of Teachers of Mathematics

Includes activities, lessons and web links for mathematics activities using various tools.

http://www.susancanthony.com/Resources/base10ideas.html

Includes some ideas for using Base 10 blocks with students.

Sites with Virtual Manipulatives

http://matti.usu.edu/nlvm/nav/vlibrary.html

National Library of Math Manipulatives

http://www.arcytech.org/java

Base 10 Blocks, Pattern Blocks, Integer Bars/ Cuisenaire Rods, Fraction Bars

http://standards.nctm.org/document/eexamples/chap4/4.2/

Geo Board

http://www.aaa.math.com/students/tools.html

Provides links to online calculators, especially good for upper grades

http://www.emints.org/ethemes/resources/S00000511.shtml

These sites explain how to create tessellations with polygons using rotation and reflection. Also

includes information about artist M.C. Escher and examples of his tessellation artwork. There areseveral interactive games for manipulating patterns online.


34/34

Hands-on Learning: Using Math Tools in Afterschool

References for Math Tools

Ball, D. (1992). Magical hopes: Manipulatives and the reform of math education. American

Educator, 16 (1), 14-18, 46-47.

Carpenter, T.P., Fennema, E., Frank, M.L., Levi, L., & Empson, S.B. (1999). Children's

Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann, Reston, VA:

NCTM.

Clements, D. H., & McMillen, S. (2002). Rethinking "concrete" manipulatives. In D. L.

Chambers (Ed.), Putting research into practice in the elementary grades (pp. 252-263). Reston,

VA: National Council of Teachers of Mathematics.

English, L., & Halford, G. (1995).Mathematics education: models and processes. Hillsdale, NJ:

Lawrence Erlbaum.

Fuson, K. C. (1992). Research on whole number addition and subtraction. In D.A. Grouws (Ed.),

Handbook of research on teaching and learning (pp. 243-275). Old Tappan, NJ: Macmillan.

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., &

Human, P. (1997).Making sense: teaching and learning mathematics with understanding.

Portsmouth, NH. Heinemann.

National Research Council. (2001).Adding it up: Helping children learn mathematics. J.

Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center

for Education, Division of Behavioral and Social Sciences and Education. Washington, DC:

National Academy Press.

Sowell, E. (1989). Effects of manipulative materials in mathematics instruction.Journal for

Research in Mathematics Education, 20, 498-505.

Stigler, J. W., & Barnes, R. (1988). Culture and mathematics learning. In E. Z. Rothkropf (Ed.)

Reveiw of research in education, 15 p. 253-306. Washington, D.C.: American Educational

Research Association.

Van de Walle, J. A. (2004).Elementary and middle school mathematics: Teaching

developmentally. Boston, MA: Pearson Education, Inc.

Documents

Math Tools Pp