Saturday, January 28, 2012

4 Ways to Develop Preschool Math Skills at Home

Learning About Same and Different

Before beginning to work with numbers, preschoolers develop math skills that involve discrimination. Simply put, this means knowing what objects are the same and what objects are different. Children learn to sort, classify, sequence and create patterns long before they begin counting. Using real objects, talk to your child about what is the same and what is different. Objects that a child can hold onto are called, “manipulatives” by teachers.

Working with manipulatives gives children a concrete example of “the same” and “different.” For example, offer a child two square blocks that are the same in size and shape, but a different color. Talk to the child about their likenesses and differences. Another example would be to offer a toddler two oranges and an apple. Talk to the child about which one is out of place, odd or doesn't belong. Explain to the child that this is “different.”


Sorting and Classifying

preschool blocks
Matching, sorting and classifying help children build their logical thinking and math skills. Use clear containers and scrap items from around the house to encourage sorting. This is a wonderful opportunity to recycle materials for games. Used plastic containers and bowls can be washed and reused as storage bins. Small plastic cups, or tin soup cans can also be used as sorting containers. Below is a list of items that can be fun for children to sort or classify by color, size, or shape:
  • Blocks
  • Buttons
  • Cars
  • Shapes cut out of scrap material
  • Crayons
  • Cereal
  • Socks
  • Pencils
  • Coins
  • Silverware
  • Flash Cards or Playing Cards
  • Photocopied Pictures of family members


Patterns and Sequencing

Another important preschool math skill is patterning and sequencing. After children have learned to recognize shapes, they can next learn to put these shapes into predictable patterns, such as a-b-a-b, or a-b-b-a, a-b-b-a. One way to teach preschool shape patterns is with hands-on manipulatives. String a pattern of beads with a child. String the pattern yourself, as an example, then ask the child to duplicate the pattern.

Popcorn, berries, buttons, candies, blocks, pasta, cut-out shapes, and ink stamps all make excellent manipulatives for building preschool shape patterns. These do not all need to be strung on a string. Stamping the pattern on paper, or gluing the objects in a pattern on paper will work. Another idea is to simply lay out the objects in order on a table and ask the child to repeat the pattern with their own objects. This patterning by example will help your child to develop critical preschool math skills.


Learning Directions and Sequencing (Teaching Prepositions)

Spacial directions and locations also help a child develop preschool math skills. Preschoolers need to learn the meaning of directional words, such as up, down, inside, outside, front, back, near, far, over and under. These words are sometimes referred to as prepositions because they describe the location of objects.
A terrific game for developing the awareness of direction or location is the game, “I Spy.” Say you see something and give clues about it’s location using prepositions. For example, "I spy a red object outside the window. This object is under a tree."

Preschool math skills can be encouraged at home by learning shapes, identifying same and different, sorting, patterning and learning spacial directions. Many of these activities can be done with little to no monetary investment. Simply talk to your child, play games with your child, and making math skills an important part of your daily routine.



  • Photo of preschooler with blocks by jessicafm.
  • "Help Your Child Get Ready for Math." Continental Press. 2005. Elizabethtown, PA 17022.


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How to Teach Number Conservation

These activities are typically done at the beginning of the Kindergarten school year to ensure the child understand the concept before moving on in math.

Counting Counters for Number Conservation

DSCA3981Materials: Blue and red counters, or other math manipulatives.
  1. Put 5 red counters in a line. Directly below the red counters, line up 5 blue counters.
  2. Help the child to count the red counters, pointing to each red counter as the child counts outloud. When the child is finished say, "Yes, five. There are five red counters," to reinforce the total number of red counters.
  3. Help the child to count the blue counters, pointing to each blue counter as the child counts aloud. When the child is finished say, "Yes, five. There are five blue counters," to reinforce the total number of blue counters.
  4. Talk to the child about both groups of counters having the same number.
  5. Now, space the blue group of counters wider apart. Ask the child if both groups still have the same number. If the child does not understand that both groups still have five counters. Count with the child to show them that the spacing does not change the total number in each group.
  6. Repeat this game often beginning with various groups of numbers, for example, start with 2 groups of 4 chips or 2 groups of 3 chips. Arrange the groups in similar patterns and then space the blue chips farther apart. Each time asking the child if there are more blue chips, or the same number.


Drawing Circles to Teach Conservation of a Number

Materials: Paper and PencilDSCA3982
  1. Begin by drawing 2 groups of 4 circles on a sheet of paper. Draw the first group going down. Draw the second group going accross.
  2. Point to the first group of circles and ask, "How many circles does this group have?" Write the number by the group if the child answers correctly. If the child does not answer correctly, help the child count the circles.
  3. Point to the second group of circles. Ask the child, "How many cirlces does this group have?" Write the number given by the group or help counted, if needed.
  4. Direct the child to the number written by each group. Explain that each group, regardless of placement, has the same number.
Repeat the activities above as many times as necessary until the child develops a clear understanding of conservation of a number (the number of items in a group stays the same regardless of placement). If the child struggles, try the activities with a smaller number of objects (two or three) then move up to groups of five objects. Once a child has mastered the concept of number conservation, the child is ready to move on to "one to one correspondence," also known as "counting with meaning." To learn more about teaching one to one correspondence, see more by this author below.

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Teaching One to One Correspondence in Kindergarten

The concept of one to one correspondence is introduced as a precursor to counting with meaning. When children begin counting, they can often sound off the numbers from memory without giving it much thought. This is called "rote counting." Assigning meaning to the numbers, by helping the child understand that the number 1 represents one object, number 2 represents 2 objects, etc. Before, counting with meaning can be taught, children will need to understand how to match groups of equally numbered items, or one to one correspondence.


How do you know if you should teach One to One Correspondence?

If a child counts objects skipping over ten of them as they count to 3, you will know that they are having trouble assigning meaning to numbers and need to understand one to one correspondence. If a child can already count with meaning, they already have a good grasp of one to one correspondence.


Be Fair!

Have the child pass out something to everyone in the room, for example a plate. Before you begin, tell them to, "be fair and make sure everyone gets a plate." If the child can not do this, model it for him/her and keep practicing until they can give one object to each person. Other ideas for objects that can be passed out are: toys, cups, candy, napkins, forks, pencils, pieces of cake, etc.


Counting Groups of the Same Number

Materials: 6-10 household objects.
Count out a group of objects. They can be forks, spoons, counters, quarters, pennies, or anything that you have around the house. Begin by counting out a small group of 3 objects. Place them in front of the child as you count. Now ask the child to repeat what you did. See if the child can count on a second group of the same objects. If the child can not do it, model the counting out of the second group, then start over and ask the child to do it after being shown. In this activity the groups of objects should be identical. For example, a group of 3 pennies and a second group of 3 pennies. After the child is successful, move on to larger groups of objects.


Dice Drawing Game

Materials: Paper, pencils, small round objects
Draw 2 squares on a sheet of paper. Ask the child to place one counter on each square. Counters are small round manipulatives used to teach math, if you don't have counters you can use any small round objects that are identical in shape or size, such as dimes or raisins. You can also draw the circles onto the squares, but this may be more difficult for some children. If the child cannot place a counter on each square, model the activity and then ask the child to repeat it. Once the child has mastered this activity, put more dots on the squares to make "dice." See if they can place equal numbers of dots on each square die that's been drawn.


Matching Games to Teach One to One Correspondence

Materials: Reusable cans, yogurt containers, or plastic bottles with the top cut off, markers, construction paper, straws.
You can recycle materials to make your own one to one correspondence games at home. Use empty bottles, cans, or yogurt cups to make containers. Cover them with construction paper. Place dots one through 5 on the front of the containers. Have the child practice one to one correspondence by putting the correct number of straws in each container. For example, a container with 5 dots, should have 5 straws placed in it. Other household items such as craft sticks, spoons, or forks can be used in place of the straws. A similar game that can be used to teach one to one correspondence with dots is the parking garage game. Use old milk cartons to create "garages" as seen in the photo. Place dots on the top of each garage and have the child drive the correct number of cars into each garage. DSCA3978
Once you have mastered teaching one to one correspondence with objects, children will be ready to learn to count with meaning. This concept is typically taught in kindergarten, but the bsic principles can be used with any child.

Photo Credits: HS Schulte

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