Free Exploration of Math Materials: Application and Extension (Pre K-2)

"Only when children have had time to play and explore new materials in their own way, will they be able to see the materials as learning materials and be able to focus on mathematical concepts rather than on the materials themselves. Without free exploration, children's play interests are unsatisfied and until this need is fulfilled, the children will pursue this priority relentlessly." 

-Mary Baratta-Lorton, Math Their Way

The Jars

For this activity, you will need assorted jars, all different, varying in height, circumference, volume and shape. You will also need a set of measuring cups and spoons. You will also need either water or rice.

Students are left on their own to explore the jars, filling them up with the water or rice. Put a few drops of food coloring and/or extract such as peppermint or lemon as a pleasant change.

Weighing Common Objects

For this activity, you will need a balance scale. If you want, you can make one with two milk or orange juice cartons, washed and cut down to about 1-2 inches. For each one, punch a hole with a hole-punch in each side and thread a piece of string through the holes. Tie the strings at the top and attach to a rubberband. You can attach the rubberband to a  ruler taped to a table. Make two so that comparisons of the weight of objects can be made. Have the students weight two objects such as school supplies or fruit and determine which weighs more or less.

Mirrors 

Many explorations can be made with mirrors. Once explorations with one mirror have been exhausted, two mirrors can be taped together and more discoveries can be made.

Food Coloring

Students fill a cup or jar with water and look at the pattern and colors formed when they drop food coloring in the water.

At another time, put out salt and sugar so that they can compare salt and sugar water patterns.

Reproducing Designs

This beautiful handmade geoboard is from Craftmatter.

On the Geoboard
Have one child make a design on a geoboard and then have him copy the designs on dot paper. Once two have made their designs on dot paper, they can trade their dot papers and reproduce the other child's design on the geoboard.

On Pattern Blocks

With pattern blocks, one can create a design and another student can copy the design... 

or a student can make half a design and have the next student finish the design copying it symmetrically.
You can also use wooden blocks, Unifix cubes or any other math manipulative.

source: Mathematics Their Way, Mary Baratta-Lorton

Free Exploration of Math Materials: Introduction (Pre K-2)

One person's junk is another person's treasure, so when I have made up some homemade math manipulatives, we affectionately referred to them as "Junk" or "Treasure." I keep them in separate plastic containers and have kept the containers on shelves, or if I need the room, in a large bin. The shelves are nice because if they seem them, they tend to play with them more. They also begin to make their own collections and put them on the shelves to share. They tend to take more ownership of the materials in general if you let them be a part of the creating process, and if they have more ownership in general, they will be willing to work with the materials longer and more often. Some good materials to buy are patten blocks, Unifix cubes, multi-colored and shaped beads that can be strung, Cusesinare rods, Math-U-See blocks and geoboards (although these can be hand made). If you do not have any of these materials, do not feel you have to go out and buy them all. Just pick out one or two initially and then add to your collection as you go along. Many other math manipulatives can be bought at the grocery store, for example, very inexpensively or collected. Other materials to gather can be buttons, lids and/or bottle caps, stones, old keys, acorn tops or other natural items, glass counters, plastic "jewels," mixed color and shape macaroni, mixed beans, colored Popsicle sticks, foreign coins, etc. Be creative about what to gather. Things that have a particular category and yet have variations among them make the best math manipulatives.

On the first day, just let them explore and play with them any way they like. This is to explore the potentials and limitations of various materials, observe similarities and differences, and also have their curiosity satisfied so that when we use these materials for math activities they will be willing to do what is asked with them.

You will also need to need to establish some rules about their use. Once of my rules is that if they get them out, they have to put them back before they leave the table. Sometimes I limit the number of items they use on the table at once. Sometimes I limit how long they use a particular item, especially if it is new.

Other resources for gathering and using math manipulatives include Math Their Way and Treasure Boxes.
"For manipulative instruction to be effective, manipulatives must be:

*Basic to the instruction, not just an occasional add-on

*Used by students for exploring and modeling rather than by teachers for demonstrating

*Used patiently and consistently to allow time for processing and understanding

*Available in sufficient quantity to involve each student frequently and adequately

*Used before the textbook so that conceptualization depends on student thinking , not outside explanations

*Followed by student drawings that represent the concrete models as a bridge to symbols"

-Making Math Meaningful by Milt Uber Winter 2007 Charlotte Mason Educational Review from Childlight USA.
(re-posted from 7/18/08)

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