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Mathematical Development

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 maths understanding are:


Step 1
Beginning to use and understand the language of maths 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 .


Step 2
The development of rote counting (counting without understanding the value of the numbers). You can u
se number songs to familiarise your child with the numbers repeated in order.

For example:


1 2 3 4 5

Once I caught a fish alive

6 7 8 9 10

Then I let it go again.

Why did you let it go?

Because it bit my finger so

Which finger did it bite?

This little finger on my right.




Step 3

Begin 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 bears, corks, farm animals, paint brushes, tables, books, each other.

    Count plates at lunch time, blocks, count all the time with your child.

    Count clothes pins as you drop them into a wide-mouth jar.

Step 4

Beginning 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 - practising this will develop their understanding.
  • Once your child understands the total of three, add another object and see if he/she understands 4 as a total.


Step 5

Adding and subtracting items in a set.

  • Use word problems to add and subtract - make them up yourself as you work with your child. An example is: "Adam, Jo and Davar are on a bus, but then Jo gets off the bus at the park. How many people are now on the bus?  Marco and Ali get on the bus.  How many people are now on the bus ?" 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.

Step 6

Classifiying 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 colour.
  • 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, colour, shape, or texture.
  • Other good sorting materials are: macaroni, shells, beans, seeds, rocks.

Step 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 (eg: "Which goat is biggest? Which makes the least noise on the bridge? Which has the longest horns?").
  • Use a crayon and a coloured 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 home.                                                                                                                                                

Step 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.
  • You can also order by weight, length, nearness, fullness, etc.
  • Together, find the shortest pencil.
  • Order 3 pencils from tallest to shortest.


Step 9

Estimating and predicting.

  • 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.



Step 10

Patterns and Sequences - 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.
  • Glue objects to paper in a pattern.
  • Make patterns with cans in your pantry.

Step 11


  • 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 bath.
  • Measure heights of your family and compare them.

Step 12

Recognising and writing numbers

  • As children work with numbers they begin to recognise the symbol for each number. Eventually they will recognise 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.



Severn Primary School

Severn Primary School

Severn Road, Canton, Cardiff, Wales, CF11 9DZ