This learning sequence is designed to assist students to recognise, read, represent and say whole numbers. Students learn that there is a sequence to numbers, and a counting process that applies irrespective of language or culture. They develop skills in using and recording number sequences.
These activities have connections with figurate numbers. For example 3 is a triangular number because three counters can be arranged in a triangular shape. Similarly 4 is a square number and is a commonly used arrangement on objects such as dice. One-to-one correspondence, which underpins the counting process, is also embedded in many of the activities.
These activities will require a variety of counting artefacts (animal models, beads, seeds, counting frames, cubes, marbles, blocks), paper or cloth bags, numeral cards and number word cards.
The activities highlight the place value ideas that cross language and cultural boundaries.
Many young children begin formal schooling being able to say number names in the correct sequence but are unable to count and answer the question 'How many …?' Certainly, being able to say and sequence number names is part of counting but not the only part.
The following activities are ideas that teachers may decide to add to the range of activities they use to develop counting concepts with their students.
Activity 1: Pebbles in a bag
When we count, we are establishing a one-to-one correspondence between the objects we are counting and the number names. The last number we say is the count of the set of objects. It is the answer to the question 'How many?'
The bag and pebbles – let’s call it a counting bag – can help to develop young children’s concept of counting. A bag containing four pebbles (counters, cubes or artefacts) may be used to represent (that is, be the count of) the 4 children in the class with red hair, the 4 noticeboards in the classroom and the 4 children who travel to school by bus. This helps to develop the idea of four-ness. That is, four apples, four pencils, four students, four cubes and so on all have a common attribute … their four-ness.
In ancient cultures (and possibly still in some present-day cultures) herdsmen were not interested in the actual number (that is, naming the actual number) of animals in their herds. Their counting system seldom extended beyond three or four. After that they referred to whatever they were counting as many. But they were interested in maintaining the number of animals they had, and checking that they had them all in their herd or flock. One way to keep check of the number of animals was to place one pebble for each animal in a bag. It does not matter how many pebbles are in the bag as long as there is one for every animal and no more. This is what we call one-to-one correspondence and is an essential component of counting.
Activity 2: Counting in Asia
Depending on the classroom resources available teachers may ask students to represent their collections using other means.
In Western cultures children represent the numbers 1 to 10 using the fingers on both hands … firstly 1 to 5 and then an extra 1 to 5 on the other hand. Asian children learn to represent the numbers 1 to 10 using one hand. A common form (sometimes with small variations) is the set of Chinese finger signs.
Chinese finger counting uses only one hand. In some cultures the number 10 is represented by a clenched fist.
Activity 3: Addition
Counting bags can be used to introduce the idea of addition by combining the collections; that is, by combining the contents of the counting bags. Where bags are involved in the activity, some students might find it necessary to open the bags, count the contents of a bag and then continue the count; that is, count on.
These activities are also useful to add to 10 and beyond.
Activity 4: Subtraction
Classrooms should have a variety of collections of artefacts. Children might be given the opportunity to suggest the type of artefacts they work with and to use artefacts they have made. Artefacts might be models such as animals or cars; blocks; collections such as collector cards or trinkets; or objects used for counting in other cultures such as pebbles, acorns or marbles.
Teachers should take advantage of opportunities to introduce counting artefacts from other cultures. The artefacts could be selected to reflect the different cultures represented in the class. Japanese chopsticks, glass beads and marbles (called ohajiki); Chinese chopsticks, counters or miniature dolls; or goods from other countries are types of artefacts that may be used in counting activities.