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.
The activities described in this resource will assist students to compare the sizes of collections. While the development of counting skills is occurring at the same time, counting is not a prerequisite for these activities. Comparing collections using grouping and correspondences will assist children to develop a broad sense of number and assist in developing counting techniques.
Classrooms should be equipped with a variety of materials suitable for counting, sorting, ordering and comparing. These should include collections of objects students are interested in handling such as readily available objects like plastic or wooden models, beads, seeds, blocks, pencils, card collections, acorns, marbles, paper clips, pegs; and commercially available collections of objects produced as counting resources.
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.
Classroom resources should also include some materials suitable for 'correspondence, structure and abstraction' activities. Some materials provide a conduit from the concrete of a collection of objects to some desired abstract ideas. Such materials are commercially available – multi-base arithmetic blocks for example – but in the early years linking blocks and icy pole sticks (pop sticks) or bamboo sticks and rubber bands adequately serve the purpose.
For children in the early years of schooling, much of the development of mathematical ideas will occur concurrently with language development. This will occur in the conversations teachers have with children and in how they describe and explain the activities. Children will encounter some words in mathematical settings and activities, and within these contexts some meanings of words will be refined for mathematical use aside from everyday use.
A vocabulary list is provided in Activity 1 that highlights the different words we use to express a similar idea and assume children will recognise the alternatives.
Teachers may add the following ideas to the collection of activities they use to develop counting concepts with their students.
Activity 1: Who has the most?
These tasks provide students with the opportunity to compare, order and make correspondences between collections, initially up to 20. Counting is an efficient method of comparing and ordering collections, but there is value in children developing other comparing and ordering methods.
In many cultures from the Asia region there is a presumption – often correct – that children will be able to count by the time they enter formal schooling. Children in all cultures collect tokens and trinkets of interest and significance to them. Often such tokens and trinkets have cycles of popularity.
Teachers should be open to using artefacts from, or used in, different cultures such as glass and wooden beads, like Japanese ohijiki, as well as matches, pop sticks and counters used in board games. The counting activities will be enriched by playing such games.
When objects are lined up in rows, the longer line will only be the larger collection if the objects are evenly spaced. A grid is a useful resource. Note too, that this idea has links with data representation. We could match the objects one-for-one and see who has any extras.
This activity should be performed with collections of both same-sized objects and differently-sized objects. In the latter situation, lining up the objects can be misleading. Clearly one-to-one matching or a grid assists.
Even if the children count accurately, at this age many still cannot answer the question: how many are there? Their response is to count again. Although the students may give the correct count and response they also need to know seven is more than six.
Activity 2: Comparing and corresponding
In this activity students will compare two sets of objects and establish a correspondence between them.
There are many opportunities for variations in this activity. Paired objects could include: cubes and images or Asia-brand cars; toy sedans and station wagons; boy and girl students; and, students and blocks and coloured tiles. Whatever association is used it needs to be carefully established and, in subsequent activities, varied.
For example when using boys and girls, they could physically form a line and identify if there are any extras. Alternatively, each boy and girl places a block in a row with each block representing a student.
Toy cars could be used to represent (model) the situation or use a cube to represent each sedan and a pop stick to represent each station wagon.
Alternatively, assign a student to represent a specific car; for example, a boy represents a sedan and a girl represents a station wagon or vice versa.
Activity 3: Ordinal numbers – Where's Yuki?
In this activity students use and extend their ideas about ordinal numbers beyond first, second and third. From an early age children are using ordinal numbers in everyday language situations: 'I want to go first!'; 'We had a race and I came second'. Where's Yuki? provides an activity where students have to identify the position of Yuki in the line-up and place the appropriate ordinal number cards – words and symbols as shown.
Activity 4: A game to practise numbers
In this activity students will play games using collections of objects to practise numbers. They will engage in ordering by flicking objects using the index finger to make a circle with the thumb and index finger.