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.

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