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Children know many math concepts through early play. As infants they know that they are small and their mother and father are big even though they do not know the words. Toddlers know that if they put one block on top of another, they will have two even though they do not know the words. They know that if they have 2 blocks and you have 10, you have more and they want them. Toddlers will often sort objects although we may not know the criteria they are using to form their sets. Very young children know the sequence of their day if there is a schedule to their day. They learn many concepts of number, size, shape, and weight during trips to the grocery store. When they enter preschool, children know many concepts in their own way of knowing.

The steps in developing math understanding are:

Begining to use and understand the language of math through our correct use of the words through the day. Some of these words are: tall and short, empty and full, near and far, first and last, high and low, in and out, few and many, light and heavy, all and none, hot and cold, same and different, more and less, pair, group, set, names of coins.

The development of rote counting
(counting without understanding the value of the numbers).
  • Use number songs to familiarize your child with the numbers repeated in order.
  • Finger plays which use numbers help teach the order of the numbers.
  • Count for fun during a spare minute of the day.
  • Related ONLINE ACTIVITY: See our list of recommended Counting Books.
Begining meaningful counting
(counting and understanding that the number 2 represents two objects and 4 represents four objects).
  • Begin with small sets of 2 or 3 and ask your child how many there are.
  • Tell fairy tales and have pictures of the characters to count or act out the story and count the characters together.
  • Set out three objects and have your child touch each object as they count it.
  • Increase the number of objects to count as your child becomes confident - when he/she is ready, they will begin to count without touching each object.
    Count golf tees - the child can make towers with them and then count them.
    Count bears, corks, farm animals, paint brushes, tables, books, each other.
    Count plates, forks, spoons, blocks, and shoes. Count all the time with your child.
    Count clothes pins as you drop them into a wide-mouth jar.
  • Related ONLINE ACTIVITY: Count Animals.
  • Related ONLINE ACTIVITY: Compare counting accuracy with Weebit Cuckoo's Automatic Fish Counter.
Begining rational counting
(counting and understanding that when you have counted the last item in a set, that number represents the total of the objects in the set).
  • Let your child count three items in a set and ask them "How many are there?" Put the objects in a line so your child will not count them more than once - practice with this will develop the understanding - be patient.
  • Once your child understands the total of three, add another object and help them understand 4 as a total.

Children should also have an understanding of the following math concepts when they reach kindergarten. These are not necessarily learned in this order.

Add and subtract items in a set.
  • Use word problems to add and subtract - make them up yourself as you work with your child. An example is: "Mario, Joseph and Cathy were walking to the store. How many children were walking? Mario's mother called him in. Now how many children were walking to the store? Sally and Ken came to walk with them. How many children were walking to the store?" You can go on and on until your child tires of the game.
  • Have some counting objects out and let your child make up the story and count the objects as he/she increases and decreases it with the story.
Classifiy objects
(placing things that go together in sets).
  • Begin with objects that are alike in every way but one. For example, let your child take a group of crayons and classify them by color.
  • Use a stack of plastic shapes and have them classify and sort by shape.
  • Use a bucket of buttons and let your child classify by the number of holes.
  • In the winter let your child sort by mittens or gloves.
  • Keep a box of material scraps for sorting by size, color, shape, or texture.
  • Other good sorting materials are: macaroni, shells, beans, seeds, rocks. Be sure to monitor the use of small objects.
  • Related ONLINE ACTIVITY: Sort Fall Leaves.
  • Related ONLINE ACTIVITY: Sort large and small fish into two bowls.
Compare objects
(looking at objects to decide which is bigger, smaller, darker, lighter, etc.).
  • Use the story of "Three Billy Goats Gruff" to compare the goats (ex. "Which goat is biggest? Which makes the least noise on the bridge? Which has the longest horns").
  • Use a crayon and a colored pencil and compare the width of line they make and the way it looks on the paper.
  • Make 2 block towers and compare their height and the number of blocks used to make each one.
  • Compare sounds made by different instruments.
  • Compare sizes of shoes in your closets.
  • Related ONLINE ACTIVITIES: Compare big, bigger and biggest rutabagas at the bottom of our Fun With Trains page. You can also compare the lengths of three trains.
  • Related ONLINE ACTIVITIES: Compare engine sizes with Railroad Conductor Bill in Locomotives Big and Small or Arrange animals by size .
Order objects
(placing objects in a series).
  • Begin ordering by size using blocks, books, pencils, etc.
  • Use 2 objects at first and slowly add more.
  • Your child can also order by weight, length, nearness, fullness, etc.
  • Together, find the shortest pencil.
  • Order 3 pencils from tallest to shortest.
  • ONLINE ACTIVITY: Arrange six animals according to size.
Estimate and predict.
  • Fill a jar with fewer than 10 objects and have your child estimate the total.
  • Pile some cookies on a plate and let your child estimate the number.
  • Show the cover of a book with an exciting picture and let your child predict what will happen in the story.
  • Predict the weather for tomorrow.
  • ONLINE ACTIVITY: Estimate how many monkeys or other animals will be needed to balance Marcus on a Teeter Totter.
Pattern and sequence
(making a pattern by placing objects in a repeating sequence.
  • Buy a set of stringing beads to use and create a repeating sequence for your child to copy (red-green-blue, red-green-blue).
  • Your child can create his/her own pattern for you to copy.
  • Look for patterns in magazines, cut them out, and make collages.
  • Make patterns with crayons. Have your child identify the pattern.
  • Glue objects to paper in a pattern.
  • Make patterns with cans in your pantry.
  • ONLINE ACTIVITIES: Arrange birds or pumpkins to make patterns or sequences).
  • Let your child help with measuring for recipes.
  • Let them measure bubble bath liquid.
  • Give your child some plastic cups or beakers to measure liquid in the tub.
  • Measure heights of your family and compare them.
  • Measure the length and height of a tricycle.
Recognize and write numbers. As children work with numbers they begin to recognize the symbol for each number. Eventually they will recognize the word for each number. Write the symbols (1,2,3) and words for numbers when possible.
  • Have your child match cards with number symbols written on them.
  • Have them match number symbols to number words (1 to one, 2 to two).
  • Play number Bingo.
  • Create simple connect-the-number pictures for your child.
  • Look for number words or symbols in books and magazines.
  • Have your child make a number collage.
  • ONLINE ACTIVITY: Count fish and point out displayed numerals on Weebit Cuckoo's Automatic Fish Counter.

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1998, 2018, Susan Jindrich. All rights reserved.
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