A Math Toolbox
In Every Home

As teachers, we know the value of hands-on exploration with math manipulatives in school. We can extend the sense of discovery and empowerment into our students homes by helping them assemble math toolboxes to be enjoyed by the whole family.

About the Author Wendy Petti is the creator of the award-winning Math Cats Web site, author of Exploring Math with MicroWorlds EX (LCSI, 2005), and a frequent presenter at regional and national math and technology conferences. She teaches grade 4 math at Washington International School.

WHATS IN A MATH TOOLBOX?

What math tools do you find most useful in the classroom? Those tools will be most useful at home, too. Rather than purchasing expensive sets of Base Ten blocks, Cuisenaire rods, pattern blocks, counters, number tiles, and more, students and their families can create their own simple handmade versions of the math tools you use in school.

Handmade math tools can be created from...

Free Materials

• small or large boxes
• cardboard
• egg cartons
• styrofoam food trays
• plastic food containers
• magazine cutouts
• nature's manipulatives -- including twigs, leaves, nuts, berries

• stiff paper (cardstock or poster board)
• small food items: dried beans, cereal, marshmallows, uncooked pasta
  (Try tossing beans or pasta in a plastic bag with vinegar and food coloring to make manipulatives of different colors. You can write numbers on them, too.)
• toothpicks, popsicle sticks
• paper plates
• magnetic tape
• ziploc bags or disposable plastic containers

TYPES OF MANIPULATIVES

Many of our favorite math manipulatives can be cut from stiff paper, available for pennies per sheet from office supply stores and copy centers.

Base Ten Blocks and Cuisenaire rods use square centimeters as their smallest units. You can photocopy graph paper for younger children and encourage older students to measure their own grids. Planning how to make the best use of each sheet is a useful math challenge. Of course, students can look for other ways to represent hundreds, tens, and ones. How about dollars, dimes and pennies; or uncooked lasagna, spaghetti, and macaroni?

Stiff graph paper can also be used to make hundred squares, multiplication grids, and number tiles. You can make your own pattern blocks from stiff paper, too. You even can print or photocopy rulers, protractors, and number lines. Adding small bits of magnetic tape to the backs of paper manipulatives can multiply the fun as a refrigerator becomes a math playground.

Students can make practice clocks from paper plates and bobby pins. An egg carton makes a wonderful workstation for early multiplication and division work as children form equal groups of beans or other small objects. Children can create a play store with empty food containers or magazine food cutouts pasted onto small boxes or pieces of cardboard. Dont forget play or real money!

Students can organize their math toolboxes by keeping each type of manipulative in its own zippered plastic bag or disposable plastic container. The whole collection then can be stored in a shoebox.

USING THE MATH TOOLBOX

Don't overwhelm your students' families by presenting them with all the tools at once. Instead, you might have students add one new tool every few weeks.

Send home a few activity suggestions with each math tool. Each math tool supports a number of math concepts and skills at each grade level. Here are a few sample activities:

• Use Cuisenaire rods in grades 1-2 to add, subtract, and find missing addends:

  For numbers greater than 10 and less than 20, lay down an orange rod (10) and another rod end to end to make a "rod train." Lay other rods above them to match the length of the first rod train.
  For example: 8 + ? = 15
  

  

  
  We can see that 8 + 7 = 15.

• Use Base Ten blocks in grades 3-4 to explore multi-digit multiplication and division:

  As you write each step on your paper, show each step with the blocks. Trade 1 ten for 10 ones as needed; trade 1 hundred for 10 tens as needed.
  For example:
  

  

  
  
  In this partially completed long division problem, we started with 7 tens and 1 one, to be divided into 3 groups. We put 2 tens in each group, so we write a 2 in the tens column. In all, we've put 6 tens into the groups (3 x 2 tens), so we write 6 tens (60) below. We have 11 left (1 ten and 1 one). We will need to trade the ten for 10 ones so we can put 3 ones in each group (using 9 ones in all), and we'll have a remainder of 2. Our answer is 23 R. 2. We can see the proof!
  

  

• Use pattern blocks in grades 5-8 to explore fractions and percents:

  Create a design with mirror or rotational symmetry using triangles, rhombuses, trapezoids, and/or hexagons. Let a triangle have a value of 1. Make a chart to show the value of each shape. Ex:
  

  

  
  

  

  Be sure to visit Math Cats for more instructions on making and using a variety of math manipulatives and for links to other useful resources.

  BENEFITS OF A MATH TOOLBOX

  Collecting and creating manipulatives gives a feeling of ownership, independence, and resourcefulness. Students see that math is everywhere and that everyday items have hidden potential as math tools.

  A math toolbox can put hands-on math in the middle of family life and get families talking about math in meaningful ways. It involves parents in a new way so they can help support their childrens conceptual understanding as well as skill development. When hands-on math becomes part of daily life, families often find more and more ways to engage in real-life math explorations, inside and beyond the home.