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help students make and use
math manipulatives

 * What are some big ideas in the creation of math manipulatives by students? Creating manipulatives is empowering: It gives a feeling of ownership, independence, and resourcefulness. It can be a creative process. Students apply math skills when planning, measuring, and making efficient use of resources. The more they practice measuring precisely for meaningful purposes, the better they get at it. The process can build real world connections, with a sense that math is everywhere and that everyday items have hidden potential as math tools. Units of measurement are a convention, but students can measure creatively for their own purposes, creating their own units of measurement. Objects can represent one unit or a group of units (such as 10 or 100). Manipulatives can resemble a specific type of item or a specific value; they can also be an abstract representation. (For instance, a dime doesn't look like it is worth 10 pennies.) Students often engage in cooperative learning and sharing. Students of any age can make manipulatives, starting with cutting or decorating simple objects for counting and gradually moving up to complex measurement activities.

 * free and inexpensive materials for making manipulatives: free: cardboard styrofoam food trays from the grocery store plastic serving dishes refrigerator magnets from businesses (Cut them up and glue them to manipulatives.) small or large boxes AAA has free maps available at the end of the year. buttons A loop of thread stretched over two pencils (or a pencil and a toothpick) becomes a compass. nature's manipulatives - including twigs, leaves, nuts, berries inexpensive: paper (regular or cardstock or posterboard) small food items: dried beans (to be marked), cereal, marshmallows, uncooked pasta (Try tossing the pasta in a plastic bag with vinegar and food coloring to make manipulatives of different colors. You can write numbers on the pasta, too.) rubber liner plastic needlepoint material toothpicks, popsicle sticks optional magnetic tape ziploc bags

 * types of manipulatives: Base Ten blocks Cuisenaire rods pattern blocks tangrams number tiles (for + or x, using a hundred square or multiplication grid) counters number line, tape measure, ruler, yardstick and/or meter stick paper clock (use bobby pins for hands!) play money 3D cubes or Algeblocks (from stiff paper) dice play store with small boxes, magazine cutouts shape puzzles homemade measurement tools: A compass can be made from a loop of thread and two pencils. You can photocopy protractors, rulers and/or numberlines. Make fun stand-up manipulatives from cardboard cut-outs. Write numbers or draw pictures on them, or trim their edges to make people, animals, or objects.

 * What are some big ideas in students' use of portable handmade math manipulatives? Manipulatives are readily available any time, any place. Students have a variety of math tools at their disposal at any time. Using manipulatives helps students to visualize concepts: making the abstract concrete and helping students to transition from the concrete to the abstract. A given type of object can represent different values from one day to the next; students can assign and record these values with a key, and make a new key each day if they wish. When students have a packet of inexpensive, replaceable math manipulatives that they can use at school and at home, this promotes the home-school connection: It can put hands-on math in the middle of family life. (The refrigerator can become a math playground.) It can get families talking about math in meaningful ways. It involves parents in a new way so that they can help support the conceptual understanding as well as skill development. Families can brainstorm and use an endless variety of manipulatives. When hands-on math becomes part of daily life, families often find more and more ways to engage in real-life math explorations (for instance, during cooking or shopping). The manipulatives are available during the summer and in later years. Useful Techniques and Strategies: Think outside the box.(For instance, you can measure on an angle to adjust proportions as needed… a slanted 12-inch ruler will fit perfectly along 8 ½" paper for marking it in thirds.) Use graph paper with younger children; encourage older children to measure. Each student can design one small object, then gather these onto one paper and photocopy enough class sets to have plenty of manipulatives for all. A steel cookie sheet makes a handy surface for using magnetized manipulatives. Make slits in cardboard rectangles and stand them upright, supported by small pieces at right angles, or lay tiles of cardboard or thick paper flat on the table. Think About It: At what age can children make their own manipulatives? What degree of precision should we expect at different ages? Is it worth the time for children to make their own math manipulatives? Is it better to use templates or to create manipulatives from scratch?

 * Base Ten blocks Color and cut out your own Base Ten blocks and use them to illustrate addition, subtraction, multiplication, and division problems on a place value mat or board. Materials: graph paper, crayons, posterboard, glue, scissors (optional: magnetic tape) Color a few sheets of graph paper orange and glue them onto posterboard. Glue an uncolored half-sheet of graph paper, too. Cut the uncolored graph paper into square units. If you are using centimeter graph paper, each square will equal one unit. If you are using ¼" graph paper, each unit will be two squares wide and two squares long. Cut the orange sheets into 10-rods (one unit by ten units) and 100-squares (10 units by 10 units). Optional: Cut small pieces of magnetic tape and press a piece onto the back of each one-unit. Press two or three pieces onto the 10-rods, and place one piece in each corner of the 100-squares. Use magnetic Base Ten blocks on a metal board or a refrigerator; make a place value mat as shown and tape it to the metal surface. Use non-magnetic Base Ten blocks and place value mat on a desk or table. To add, set up each number on the place value mat. If you have more than ten ones, trade ten of them for one 10-rod. If you have more than ten 10-rods, trade ten of them for one 100-square. When subtracting, if you need more tens or ones, you can trade one 100-square for ten 10-rods or one 10-rod for ten ones. To multiply, set up groups of equal size and then regroup. For instance, to multiply 47 x 3, set up 3 groups of 47 (with 4 tens and 7 ones in each group), then regroup 20 of the ones into 2 tens to have 14 tens in all; then regroup 10 tens into one 100. To divide, split a large number into an equal number of smaller groups, regrouping as needed.

 * Cuisenaire rods: Color and cut your own magnetic Cuisenaire rods and use them to illustrate addition, subtraction, and multiplication problems. Materials: graph paper, crayons, posterboard, glue, magnetic tape, scissors Cuisenaire rods are rectangular rods of different colors and lengths. Use the side of a crayon to color half-sheets of graph paper matching the rods on the diagram. Glue each sheet onto posterboard. Cut each paper into strips of the right length along the gridlines. If you are using centimeter graph paper, each square will equal one unit. If you are using ¼" graph paper, each unit will be two squares wide and two squares long. Cut small pieces of magnetic tape and press a piece onto the back of each short rod. Press two or three pieces onto the longer rods. To add, make "number trains" of two or more rods end-to-end. Measure each train using orange 10 rods and one smaller rod if necessary. To subtract, start with a train of one orange rod and one smaller rod. Place a rod above this train, lined up with its right end. See what other rod is needed to complete the train. To multiply, make a train of one color and measure its length with orange rods and one smaller rod. You can also make one-color "rugs." Try to make two different rugs which have the same number of units.