Teachers Guide / Math Skills Development
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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.

ONLINE ACTIVITY: Visual representations of spatial
concepts are found on our Spatial Concepts pages.
The steps in developing math understanding are:
  1. Our children begin 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 .
  2. Development of rote counting (counting without understanding the value of the numbers)
    • Use number songs to familiarize children 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
    • Use nursery songs to practice counting on the fingers
  3. Development of 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 the child how many there are
    • Tell fairy tales and have the correct number of characters to count or act out the story and count the characters together
    • Set out three objects and have the children touch each object as they count it
    • Increase the number of objects to count as the 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 at lunch time, blocks, children in a center at free choice time
      Count clothes pins as you drop them into a wide-mouth jar
    • ONLINE ACTIVITY: Compare counting accuracy with Weebit Cuckoo's Automatic Fish Counter.
    • ONLINE ACTIVITY: Identify and count various animals with Animal Count.
  4. 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 the child count three items in a set and ask them "How many are there?" Put the objects in a line so they 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 see if he/she understands 4 as a total.
  5. Adding and subtracting items in a set
    • Use word problems to add and subtract - make them up yourself as you work with the child. You can introduce this idea in a small group activity with children acting out the problem. 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 the children tire of the game.
    • Have some counting bears out and let your child make up the story and count the bears as he/she increases and decreases it with the story.
  6. Classifiying objects - placing things that go together in sets.
    • Begin with objects that are alike in every way but one. For example, let the 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 the child classify by the number of holes
    • In the winter let the child sort by mittens or gloves
    • Place boys in one set and girls in another and count them
    • Keep a box of material scraps for sorting by size, color, shape, or texture
    • Other good sorting materials are: macaroni, shells, beans, seeds, rocks
  7. Comparing 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.
    • Look at 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
    • ONLINE ACTIVITY: Compare big, bigger and biggest rutabagas at the bottom of our Fun With Trains page. You can also compare the lengths of three trains.
  8. Ordering objects - placing objects in a series
    • Begin ordering by size using blocks, books, pencils, etc.
    • Use 2 objects at first and slowly add more
    • The child can also order by weight, length, nearness, fullness, etc.
    • Together, find the shortest pencil
    • Order 3 pencils from tallest to shortest
    • Order funnels by size across their mouth
  9. Estimating and predicting.
    • Use a jar with fewer than 10 objects and let the child estimate the total
    • Have the snacks piled on a plate and let the child estimate the number - show the cover of a book with an exciting picture and let the child predict what will happen
    • Have a small group of children predict what they will see on a field trip - write down what they say and later check to see if their predictions came true
    • Predict the weather for tomorrow
    • ONLINE ACTIVITY: Estimate how many monkeys or other animals will be needed to balance Marcus on a Teeter Totter.
  10. Patterning and sequencing - making a pattern by placing objects in a repeating sequence
    • Pattern blocks with preset patterns can be used
    • The child can create his own pattern
    • Work with the child and create a pattern for him/her to copy then let the child create a pattern for you to copy
    • Look for patterns in magazines cut them out and make collages
    • Use small animals and make patterns
    • String beads in patterns
    • Line children up in a pattern
    • Make patterns with paint
    • Glue objects to paper in a pattern
    • Make patterns with pegs and pegboards
    • Do vegetable prints
  11. Graphing (a form of voting or showing likenesses or differences graph and then count and compare results)
    • Favorite colors
    • Favorite animal
    • Birthday month
    • Predictions by the class individually
  12. Measuring
    • In the sand table do 2 trucks hold the same amount of sand? how many trucks long is the sand table?
    • At the water table measure volumes and predict whether 2 containers hold the same or different amounts
    • At any and all centers using materials found in the centers (children do not have to measure with rulers - a block, a piece of string, a jump rope will do
    • Measure the building
    • Measure heights of children and compare and order several children by height
  13. Recognizing and writing numbers. As children work with numbers they begin to recognize the symbol for each number. Eventually they will recognize the word for each number. Post symbols and words for numbers when possible.
    • Match cards with number symbols
    • Match number symbols to number words
    • Play number Bingo
    • Have number word cards in your writing center for a child to copy
    • Have simple connect-the-number pictures in the writing center
    • Look for number words or symbols in books and magazines
    • Make a number collage
    • Encourage the child to make and label his/her own sets
Counting Books can be excellent learning tools, too.
See our list of Great Counting Books. Learn how each one helps children build math skills.

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Copyright 1998, 2005, Susan Jindrich. All rights reserved. Revised 4/4/07