Offline resources
Physical resources
Using concrete resources is one of the best ways to really develop mathematical understanding. We start teaching concepts and ideas using physical representations of numbers. Any item at all can be used to represent numbers. The learning comes in understanding and assigning value to an object
In school,we generally use base 10 and counters to represent numbers, as we can share an understanding of the "rules" for these representations.
We also use a wide range of physical items to represent number.
Below are fantastic ways to really broaden your child's understanding of maths.
We would love to see the most interesting representations of different numbers, and the explanations!
Be creative and experiment with different types of objects
Pegs are fantastic way to start representing number
All the pegs are the same colour and shape, so each peg represents the same.
If each peg is worth one, there there are 6 pegs on the line. This is called 1-1 correspondence counting, and it how we learn to count and begin to represent number.
It can be taken further though: what if each peg represents 10? Or 100? Or 7?
This way, even simple pegs can be used to represent a range of numbers.
These plastic game pieces can easily be used to represent number.
As with the pegs, each piece could represent one, allowing for 1-1 correspondence counting. Or, each piece could represents 100, 5 or even 30.
The fact there are different colour pieces opens up more possibilities: could the blue pieces represent one, the yellow 20 and the red 5?
This is a more sophisticated form of representation as it requires more information to be known. creating and explaining the "rules" of a representation is a fantastic activity to build mathematical skill, understanding and confidence. It can also be fun!
Marbles are fantastic to represent number.
Again, they allow 1-1 correspondence. They can also have different values depending on their colour, opening up lots of possibilities for representing number.
Taking representation further, could the size of the marble link to the value it represents? Do bigger marbles always have to represent more? Why?
This is a superb way into a much more in depth understanding of representation
Printable base 10 material
Base 10 cut outs.pdfPrintable place value counters
Place Value Counters.pdfLower school Place value grid.pdfLower School place value grid
US Place Value Chart.pdf