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Using symbols to build math skills

“I think we need to add some math activities to our schedule,” says Ms. Hudson, after the last 3-year-old has left for the day.
“You mean counting?” asks Ms. Jennings, her new aide.
“No, I’m talking about something more basic,” Ms. Hudson says. “Children have to understand that the word five stands for five things and that numbers follow a sequence. They must understand how to compare things like shape and size, make estimates, and measure length and weight.”
“How do we teach that?” asks Ms. Jennings.
“By asking them to observe and classify things, like who’s wearing sandals and who’s wearing athletic shoes. By setting up activities where they match or sort things, like sorting keys by size or shape. By seeing patterns, like the blue, yellow, and white stripes in a towel.”
“I get it,” says Ms. Jennings. “I thought math was math—you know, sitting down with pencil and paper and counting, adding, and subtracting. Now I can see that it’s more than that, and it’s everywhere.”

Early education teachers are often stymied when they try to develop math activities that don’t feel like drill-and-kill exercises. Too often they think math is paper-and-pencil number work and forget that opportunities for math experiences underlie activities in every area of the classroom.
A child as young as 2 years can generally identify the larger of two objects—the bigger block, doll, or piece of cake, for example. With experience and increasing cognitive skill, children are able to classify, order, rank, and evaluate relationships among objects.
With these expanding skills, we introduce patterns, charts, and graphs. By creating patterns and building charts, children enhance classification skills and one-to-one correspondences. In making charts and graphs, children use symbols to represent real objects. In all these activities, children collect and organize information, record it symbolically, and describe the information in mathematical relationships.
Children’s math skills grow through planned experiences and meaningful adult-child interactions. Consider your classroom’s learning centers—art, blocks, cooking, movement and music, and discovery. Integrate patterns, charts, and graphs as routine activities. The following activities offer suggestions.

Art
In the art center, children can use materials and activities to explore math concepts like classification, sequence, and symbol. A simple exercise in classification, for example, is to group similar items together, such as picking out all the yellow pencils from a pencil holder and putting them in a box.
An important math skill is seriation, the ability to arrange objects in order by size. A simple exercise in seriation is to line up crayons, pencils, or collage materials from longest to shortest, for example. A related skill, gradation, would be to arrange in gradual stages, as in sorting paint color chips from lightest to darkest.

Crayon sort
(ages 3 and older)
Here’s what you need:
crayons
containers, such as recycled food cans, margarine tubs, or small cereal boxes

1. Decorate the outside of the containers with the crayon labels or construction paper that matches the crayon color, as desired.
2. Give children a pile of crayons and invite them to sort according to color.
Variations: Invite children to sort pencils, paintbrushes, or colored paper squares.

Mosaic art
(ages 3 and older)
Here’s what you need:
colored paper
glue sticks
mural paper
scissors or paper cutter
photographs of mosaics and square tile patterns

1. Cut hundreds of 2-inch squares out of colored paper. A paper cutter makes this quick work. You can also buy precut, adhesive-backed paper squares at craft stores. Cut a length of mural paper and attach it to a wall near the floor.
2. Introduce the activity by talking about squares. Show the children that each piece of paper has four sides and four corners and that each side is the same length. All the pieces are the same size; there are many different colors.
3. Invite them to contribute to the mural by creating designs with the paper tiles.
4. With older children, reinforce geometry and spatial relationships. Show how a drawn 4-inch square can be filled with four 2-inch paper tiles. Challenge the children with larger and larger squares: How many paper tiles does it take to fill a 16-inch square or a 24-inch square?

Bead trade
(ages 5 and older)
Here’s what you need:
flour
cornstarch
salt
paste food coloring
small pitcher of water
measuring utensils
spoons
bowls
index cards
zip-top plastic bags
toothpicks
string
fine-tipped markers

1. Put the flour, cornstarch, and salt into separate bowls with measuring spoons. Nine tablespoons of flour, 6 tablespoons of salt, and 6 tablespoons of cornstarch will make about one cup of bead clay when mixed with water. Adjust the quantity of ingredients to the number of children in the group. Make a rebus chart or recipe card for the children to follow. Label plastic bags with children’s names.
2. Introduce the activity by telling children they will be able to wear a graph on their necks. They will make beads to represent themselves and then trade the beads with classmates. At the end of the project, every child will have a necklace with beads that represent all the members of the group.
3. Invite the children to consider the beads they will make. Ask about color, shape, and decoration.
4. Show and then encourage the children to measure the flour, cornstarch, and salt into a plastic bag. Close the bag to mix the ingredients.
5. Open the bag and add water, 1 tablespoon at a time. After each addition of water, close the bag and knead the dough. The resulting dough should feel like commercial play clay—not too wet but not crumbly.
6. When the consistency is satisfactory, show how the food coloring can be added by dipping a toothpick into the desired color and spreading it on the clay. A tiny bit will make an intense color. Knead again.
7. Invite the children to shape their beads. Talk about how the bead is a symbol of the child. Tina’s beads may be in the shape of a ball, while Jeff’s beads may look more like a rolling pin. Have children make enough beads to give every child in the group. Poke a toothpick through the center of the finished bead for stringing.
8. Let the beads dry for three or four days. Some children may want to make only a few beads at a time. Remind them to keep their plastic bags tightly zipped; the dough will keep for about a week.
9. When the beads have dried, talk again about the beads as symbols. Invite children to use markers to decorate them in a personal, distinctive pattern.
10. When all the beads are decorated, let the children trade beads and string them into a necklace.

Blocks
Unit blocks and other construction toys are perfect tools for investigating pattern, classification, sequence, and one-to-one correspondence.

Same or different?
(ages 3 and older)
Here’s what you need:
plastic locking bricks
lengths of cord
construction paper
scissors
black marker

1. Cut the cord into three 3-foot lengths. Tie each into a circle.
2. Gather a basket of construction bricks in a variety of colors and sizes.
3. Spread the cord circles on a work surface. Make three small signs designating the sorting attributes—yellow, red, and green, or bricks 1X1, bricks 3X3, and bricks 4X4, for example.
4. Invite children to separate the bricks according to specific attributes.
Variations: Challenge older children to identify more than one attribute at a time for their sort: red 1X1 bricks, green 4X4 bricks, and yellow 3X3 bricks, for example.

Chart towers
(ages 3 and older)
Here’s what you need:
n same-sized blocks (unit blocks, homemade milk carton blocks, or plastic locking bricks)
chart paper
construction paper
scissors or paper cutter
glue sticks

1. To prepare for the activity, gather blocks of the same size. Cut construction paper into 2-inch squares.
2. Introduce the activity by telling children to make block towers and paper towers. The towers will have the same number of components but won’t be the same size.
3. Ask children to divide into pairs. One child will build a block tower, and the other will construct a tower of paper in a one-to-one correspondence.
4. After the two towers are completed, reinforce the concept by counting (with the children) the number of components in each tower. Draw two columns on the chart paper and label them paper and block. As you count, make a tally mark in the appropriate column. Write the number at the bottom of the chart.

Block patterns
(ages 3 and older)
Here’s what you need:
unit blocks
large open floor space

1. Introduce block patterns with a demonstration. Choose several blocks and arrange them in a pattern on the floor. Make sure the blocks are touching.
2. Talk with the children about the pattern: “Our pattern starts with a long block (double unit). Next to it is a half circle and then two short blocks (single units).” Encourage the children to name the blocks as you point.
3. Challenge the children to cooperate in continuing the pattern with more blocks.
4. Encourage the children to continue the activity on their own. Ask, “Can you think of other patters to make?” “Can you think of other materials we could use to make patterns?”

Deconstruct and chart
(ages 4 and older)
Here’s what you need:
unit blocks
chart pad
black marker

1. Invite children to construct a building with unit blocks. Make several block shapes available but avoid dictating the design.
2. Prepare the chart pad by drawing columns—one for each of the block shapes used in the construction. Draw an outline of each shape across the top of the pad.
3. At the end of the activity time, gather the group and talk about the difference between destruct and deconstruct.
4. Invite the children to deconstruct the building. As each block is removed, draw a tally mark in the appropriate column.
5. Ask the children to estimate the number of blocks used and then count the tally marks. Talk with the children about the results, using words like more, less, equal, match, tally, and total.

Manipulatives
Of all classroom materials, manipulatives offer the most options for classification and pattern work. Collections of buttons, keys, coins, marbles, balls, counting bears, postcards, jar lids, hardware, leaves, shells, playing cards, stones, feathers, and plastic animals invite sorting by one or more attributes. For example, children can sort a collection of balls by color, use, hardness, and size. They can also order the balls by size and hardness.
Place coins, counting bears, buttons, or other items in one side of a balance scale. Encourage children to estimate the amount to put in the other side of the scale. Use the terms more than, less than, and equal to.
Teach children how to sort materials before putting them away. Provide appropriate boxes, baskets, and bins to make this housekeeping chore easy, fun, and satisfying.

Picture sort
(ages 2 and older)
Here’s what you need:
tray or clean pizza box
6 plastic lids, 2-3 inches in diameter, from dairy product containers
duplicate pictures of familiar objects, such as a chair, flower, cup, tree, shoe, and dog, cut from old magazines or catalogs
glue
scissors
clear, adhesive-backed vinyl
zip-top plastic bag for storing pictures

1. Glue a picture to the inside of each lid. Cover the picture with clear vinyl. Glue the outside of the lids to the tray.
2. Cover the duplicate pictures with clear vinyl.
3. Invite children to match the pictures to the ones in the lids.
Variation: Glue circles or squares to the inside of each lid: one in the first, two in the second, and so forth. Cut out other circles or squares and have children place the appropriate number in each lid. For older children, glue printed numerals in each lid. Have children place the appropriate number of beads, buttons, paper clips, washers, coins, marbles, or pebbles in each lid.

Music and movement
Music is a combination of patterns of notes put together in a particular rhythm or beat. Use music and body movement activities to reinforce repeated patterns and classification by attribute.

Streamer music
(ages 2 and older)
Here’s what you need:
cardboard tubes from paper towels or gift paper
ribbon
tape
scissors
two recordings of music each with a different tempo, such as a quick march and a soothing lullaby
large open space

1. Make streamers by cutting 2-foot lengths of ribbon, and taping several to one end of a cardboard tube. Make less expensive and less durable streamers using crepe paper. Make one streamer for each child in the group.
2. Introduce the activity by inviting children to listen to two types of music. Ask them to move their bodies to show the tempo of the music.
3. Invite children to use a streamer as they dance to the music. Talk with the children about how the streamers dance to the rhythm just as they do.

Find the beat
(ages 4 and older)
Here’s what you need:
rhythm instruments in a basket

1. Gather children, and introduce the song “B-I-N-G-O.” Tell the children you’ll sing the song twice: once with just their voices and once with instruments.
2. Lead the children in singing once through.
3. Share the basket of rhythm instruments and ask each child to choose one.
4. Tell the children that they will change the usual way the song is performed. Typically, at the refrain, the singers substitute a clap for the letters B-I-N-G-O, adding one clap for each verse. Instead of clapping, the children will play their instruments. For example: first refrain: shake instrument, sing I-N-G-O; second refrain shake instrument, shake instrument, N-G-O; and so on.
Variations: Use the same technique in songs that have clear beats. For example, “Boom Boom, Ain’t It Great to Be Crazy,” “There Was a Man and He Was Mad,” or “Fooba Wooba John” all in The Silly Song Book.

Conducting
(ages 4 and older)
Here’s what you need:
cardboard
black marker
scissors
rhythm instruments

1. Prepare for the activity by making patterned direction cards for playing rhythm instruments. First inventory your instruments and make a shadow template of each kind. Trace the shape of the instrument on cardboard and cut it out.
2. Use the templates to draw patterns that direct children how to play particular instruments. For example, one card may indicate two drum beats, one tambourine shake, and two drum beats.
3. Invite children to take turns being the rhythm band conductor, showing the cards to the group and directing the playing.
Variation: Encourage the conductor to give additional directions like loud, quiet, fast, or slow.

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