Materials to Support the Numbers and Operations Standard
Mathematicians consider the numbers and operations standard to be the most important of the standards for the early years (Clements, 2004). Operations include not only addition, subtraction, division, and multiplication but also “counting, comparing, grouping, dividing, uniting, partitioning, and composing” (Clements, 2004, p. 17).
Counting
Children typically begin counting by memorizing the number words. Depending upon the environment, this may begin as early as the age of 2 (Clements, 2004). However, number words are more difficult than other words for children to learn due to their function as a grouping rather than an individual item. Numbers are also a concept rather than a noun (Mix, Huttenlocher, & Levine, 2002).
To count items successfully children must understand one-to-one correspondence or that there is one number word for each item they are counting. They must learn to keep track of items as they count them and to tag or count each item only once. It is often easier to do this if children touch each item they are counting. Finally, they must understand that the final number that they count represents the number of items in the collection. This concept forms the basis for all future work with numbers and operations (Clements, 2004). When you assess children’s understanding of numbers, it is important to look at each of these steps. By doing so, you can determine what skills the child will need to work on to progress to the next level. For example, Sabrina could count by rote to 10. She recognized small sets (up to four) without counting them. However, if the set was larger, she seemed unable to determine how many items there were. While observing Sabrina counting money in the dramatic play area, the teacher noted that Sabrina did not tag each coin as she counted it and therefore recounted several of the coins. The teacher demonstrated how to organize and tag the coins to count them.
One-to-One Correspondence
It is easier for children to use materials that are less abstract for one-to-one correspondence. Therefore, teachers should first provide real objects, then cutouts, then pictures, and finally symbols and patterns (Charlesworth, 2005). Following are several materials that you could place in the math center to assist in developing one-to-one correspondence.
- Outline game—Outline interesting items and place the outline and the items in a box. Children can match each item to the correct outline.
- Match groups of items—For more advanced one-to-one correspondence, create matching games of items that go together (fork and spoon, nut and bolt, and mitten and hand).
- Pegs and pegboards—These come in a variety of sizes, so they can be chosen based upon the fine motor development of the children in the group.
- Jars and lids—Collect a variety of different types of jars with matching lids that children can put together.
- Cars and garages (as in the opening scenario)—Initially children might drive a car into each garage. As children become more proficient with one-to-one correspondence, this task can become more difficult by adding a different number of dots to each car and the corresponding garage allowing children to match the dots. Finally, numerals can be added to the cars, which are then matched to the dots on the garages. To make the task self-correcting, add matching colored dots to the bottom of the car and the top of the garage.
Recognizing Numerals
Following are materials that you can add to the math center to help children recognize numerals.
- Objects with numerals, including calculators, adding machines, playing cards, magnetic numbers, and puzzles.
- Games where children match numerals. For example, use two old calendars that have similar size grids. Cut one apart and place magnetic tape on the back of each number. Attach the intact calendar to a cookie sheet or magnetic file cabinet. Children can match the appropriate number to the intact calendar. For another simple-to-create game, take a deck of cards and cut the top and bottom apart. By using a different type of cut for each card, the cards can be self-correcting.
- Sandpaper numerals. Add a blindfold that children can use if they wish. Children can feel the number and try to guess which numeral it is. Make sure to add dots to the other side of the card so children can check their answers.
- Play dough, clay, or wire for children to use to form numbers. You can add a spinner to add interest. The child spins the dial to determine which numeral to create.
- Numerals from burlap or other textured surface glued on a card. Children can place paper over the numeral and make a rubbing.
- Number sewing cards (write a numeral on burlap with black permanent marker; use a large sewing needle and yarn to sew around the numeral) (Brown, 1982).
- Beanbag toss. Children throw a beanbag and then identify the numeral that the beanbag lands on. Include the numeral, number name, and dots to meet the developmental needs of more learners. When children have mastered the numerals, they can throw more than one time and add the results.
Writing Numerals
You can assist children to learn to write numerals by providing the following materials:
- Zip-lock plastic bags filled with hair gel or other items for a transitory writing slate. Children can write numbers and then erase them and start over.
- Laminated number cards to trace or use as a model for writing numerals.
- Lined and unlined paper and different types of pencils and markers to use for writing numbers.
- Individual number books with a numeral on each page and materials such as stickers, stamps, pictures, or cutouts for children to use in completing their book.
- Old calendars with large squares that children can use to practice writing their numbers (Seefeldt & Galper, 2004).
Counting and Matching the Correct Number of Items to the Numeral
There are many materials you can add to your center that allow children to practice identifying numerals and matching these to the correct number of objects. Following are a few suggestions:
- Materials where children actively manipulate the objects they are matching to the numeral. For example, they might place golf tees into predrilled holes in a wooden numeral or the correct number of gems into a bowl.
- Number games. When children are exposed to number games, they make significant gains in numeracy compared with children who do not have this opportunity (Young-Loveridge, 2004). Games should have an element of chance to keep them interesting and to prevent only the most skilled children from winning. Some appropriate games include Go Fish with a deck of cards, Math Bingo, Candy Land, Dominoes, Number Concentration, and Chutes and Ladders.
- Number books. Researchers have found that using number books is also associated with larger gains in numeracy skills (Young-Loveridge, 2004). When you add counting books, make sure you also add props so that children can actively manipulate them as they read the book. For example, you might add flannel pieces or pretend pieces of fruit to manipulate when reading The Very Hungry Caterpillar.
- Fishing game. Add string to a dowel with a magnet at the end. Create fish from cardboard and add a paper clip to their mouth. Write a numeral on the side of the fish. Children draw a card with a number of dots and then “catch” the fish with the correct numeral. To make it easier to find the correct fish, fish with larger numbers can be larger.
Adding to or Taking Away
One experiment found that children as young as 3 can add and subtract sets up to 10 by first predicting and then counting (Zur & Gelman, 2004). To assist children to add and subtract, provide the following materials:
- Objects from songs, finger plays, or books that stress addition or subtraction. Teachers can introduce these activities during circle time and then place the props in the math area for children to use. For example, if telling a story involving a baker who added ingredients to create different dishes, you could add both the baker’s hat and the flannel board pieces to the math center (Zur & Gelman, 2004).
- Cuisenaire rods that children can use to create equal combinations (for example, two 5 cm rods equal one 10 cm rod). Cuisenaire rods are wooden, colored manipulative sticks, ranging in size from 1 to 10 cm, that children can use for a variety of math activities.
- Addition and subtraction games. Play games with two dice. Children add the dice and move that many spaces on the game board.
- A money center. Based upon the children’s developmental level, challenges can be created. For example, “How many different ways can you find to equal a nickel, a dime, a quarter, or a dollar?
View Full Article
© ______ 2010, Merrill, an imprint of Pearson Education Inc. Used by permission. All rights reserved. The reproduction, duplication, or distribution of this material by any means including but not limited to email and blogs is strictly prohibited without the explicit permission of the publisher.
Celebrate Memorial Day! Worksheets and Activities About American History 
May Workbooks are Here! 
