Math Skills – Representation

There are several foundational math skills that are core to an understanding of math. One is the idea that a number symbol can be used to represent a number of objects. The digit 5 is a way to describe 5 books or 5 balls.


Kids can represent a number first with objects (three blocks can represent the three people in the family, or the three goldfish crackers), then pictures, then words and symbols.

  • Recognize written numbers 1 – 5 (by age 3)
  • Identify numerals 1 – 20 by sight. (by age 5)
  • Can read the words for numbers, and match them to the symbol. (kindergarten)

Help them practice

  • When a child is less than three, simply work with them on visual discrimination – encouraging them to look for details: I-spy games, or draw out really simple “spot the difference” games. This will help them someday tell the difference between a 6 and a 9.
  • Help them start to understand symbols and that the same symbol can have the same meaning in different contexts: press the up arrow when you want the elevator to go up, press the triangle to play the video on YouTube or on the DVD player.
  • You can also teach them how to count on their fingers.

After age 3 or so, start working on actual numbers, working first on 1 – 5. The more places they encounter the symbols where they have meaning the better.

  • Use masking tape to make numbers on the floor and hop from one number to the next.
  • Put magnet numbers on the fridge, in order.
  • Make number symbols with play-dough or draw them in a tray filled with salt or flour.
  • Play with home-made number blocks.
  • Count five objects, write the number, write the word – helps them see how these things are all relate.
  • Make number cards 1 – 5. when you count some objects, they need to find the number card that matches your total.
  • Have them color in pictures of the number.
  • Use one of many apps that allows children to trace numbers and letters.
  • Point out the numbers on signs wherever you go.

Wait till they’ve really mastered 1 – 5 before you do more. When we rush them, they don’t fully internalize information. Being patient now will give them a richer understanding for their future. Once they’ve mastered that, keep doing similar techniques, just with more numbers. First, from 1-10, then 1 – 20, then 1-100. And so on.

Image credit: From, marked as free to share and use.


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