It is essential to have plenty of objects for sorting and counting, plastic counters, and packs of digit cards 0 to 9 to use in various ways. Dominoes and dice are useful for number games.
Many children find it a lot easier to explain their thinking if they have equipment available to touch and move so that they can describe their actions rather than trying to formulate abstract thoughts. These objects also provide images that make it easier for children to follow the thinking of others and to recall situations that they have experienced before.
A bead string is a practical resource usually made up of ten groups of ten beads in two or more different colours. Sometimes they are grouped in fives. It provides a useful connection between two important aspects of number: the cardinal (separate counting objects) and the ordinal (numbers arranged on a number line).
It is important to draw children’s attention to the groups of ten beads in alternate colours and ask questions such as ‘Is there a quick way of locating numbers on a bead string?’
Pegs and pegboards are useful for modelling the representation of quantities. Pegboards are usually made of either a 5 × 5 or a 10 × 10 array. This is helpful when children are learning to count in fives or tens. A pegboard is also a useful model when teaching complements to 10 and 100. Pegboards are very powerful models for exploring number patterns such as square numbers, triangular numbers, prime and composite numbers. Children can be given more than one pegboard to ‘join together’ so that they can explore larger numbers.
There is usually a good variety of structured sorting toys in Key Stage 1 classrooms. These can be sorted by colour, size and sometimes other attributes. Examples include plastic sorting dinosaurs, sorting animals, teddy counters, people sorts and pet counters.
However children should also work with non-structured objects for sorting and classifying, for example shells, leaves, buttons, items of clothing such as gloves, socks etc. They learn to sort and classify by observing and discussing the similarities and differences between objects. In order to do this, they must first develop their powers of observation and be able to identify properties, characteristics or attributes of a variety of objects. You can start with young children by setting up a 'blue' table on which is displayed various blue items. Ask children to find something that belongs on the table because it is also blue.
What this looks like in the classroom
Beads, counters and other counting objects can be used to support mathematical concepts and skills such as quantity, counting, sorting and classifying. They can also be used to explore pattern. Children can use beads and counters to represent quantities of numbers. For example, they can be
- given two piles of beads and asked to identify which pile has more beads and which has fewer beads
- asked to make piles of counters that have the same amount.
Counting objects can be used to develop counting skills and the concept of the conservation of number. For example, children can:
- touch or move beads or counters as they are count forward in ones
- count a group of beads on a string by moving them along the string from one end to the other
- count a group of counters, move them and then count them again
- be asked to show particular quantities of beads and counters, such as two beads or three counters.
Take a tin and some counters or beads. Ask the children to close their eyes. Drop the beads into the tin slowly but loudly one at a time and ask the children to count in their heads as you drop them in. Stop at four, for example. Ask the children how many beads are in the tin.
As with counters, pegs can be arranged in different ways on a pegboard to represent numbers. To begin with children can place the pegs in any order on the board. Later on children should be encouraged to work more systematically when building up numbers.
Beads and counters can also be used to develop sorting and classifying skills. For example, ask children to sort and classify a pile of beads or counters according to colour, size or pattern.
Bead strings help children to visualise numbers on a number line and see how numbers can be partitioned into tens and ones.
For example, counting 12 beads on a bead string starting at the beginning of a group of beads shows the children that 12 can be made up of 10 and two: