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Learning area: Mathematics
Year level: Foundation
Country: Japan
General capability: Numeracy, Intercultural understanding

This learning sequence assists students to develop their ideas about the language and processes associated with comparing and ordering collections of objects. It supports the Australian Curriculum for Mathematics: Number and Algebra. 

The activities provide an informal means of comparing and ordering collections using correspondences.



Activity_4_landing_page_BigObjects for classroom activities

Acknowledgements

Image: AEF

Related resources

Activity 1: Who has the most?

In this activity, students will compare, order and make correspondences between collections from 1 to 20 including one-for-one, less and longest.

Task 1: Who has the most?

  1. Provide students with words and phrases as shown.
  2. Put these words and phrases in a prominent place so that students can use them.
  3. Pair the students and give each a different number of objects (perhaps from a country of the Asia region). Initially start with less than 10 objects, but later up to 20).
  4. Ask the following questions:
    • Who has more?
    • Who has less?
    • How could we find out?
    Suggestions:
    • Line up the collections. Who has the longest line?
    • Match the objects one-for-one and see who has any extras.
  5. Place the students in groups of three or more and ask the following questions:
    • Who has the most?
    • Who has the least?
    • How could we find out?

Task 2: Bigger Collections: Making stacks of 10

  1. Ask students to work in pairs and provide different sized sets of between 10 and 20 swap cards, pop sticks, marbles or small toys from a country of Asia; for example, ohajiki.
  2. Discuss which is the bigger collection.
  3. Ask the students to make stacks of 10.
Collections:
Two Three or more Other expressions
greater greatest odd even
more most next between
larger largest number count
bigger biggest how many? how far?
fewer fewest zero one
less least nine ten
small smallest ones units

Acknowledgements

Image: AEF

Activity 2: Comparing and corresponding

In this activity, students will compare two sets of objects and establish a correspondence between them by categorising and comparing objects of specific attributes such as height or colour.

Task 1: More sedans than station wagons in our car park?

  1. Ask the students to imagine the classroom is a car park.
  2. Assign a student to represent a specific car; for example, a boy represents a sedan and a girl represents an SUV or vice versa.
  3. Ask students to say whether there are more sedans or SUVs in the class. They could estimate this by:
    • looking around the class
    • lining up.
  4. There are a number of different representations of sedans and SUVs you could use. For example:
    • colour of hair (light/dark)
    • height (short/tall).

    Whatever association is used it needs to be carefully established and, in subsequent activities, varied.

Task 2: Comparing

  1. Allocate pairs of students different numbers of cubes and pop sticks.
  2. Line up the cubes and sticks. Which is the longer line?
  3. Ask students why they think there has to be even spacing.
  4. Give students sets of ordinal number cards.
  5. Ask them to identify specific positions of objects using ordinal numbers.

Task 3: More Japanese brand cars than Australian brand cars?

  1. Ask students to establish a correspondence between Japanese brand cars and, for example, coloured tiles; and a correspondence between Australian brand cars and, for example, cubes.
  2. Discuss how many cars there are in each line. Which has the most?
  3. Ask your students to suggest collections they would like to count, or investigate questions they would like to answer.
  4. If their collections have a cultural significance to them, ask them to explain why they are important to them.

Ordinal numbers: Place cards

1st 2nd 3rd 4th
5th 6th 7th 8th
9th 10th second to last
first second third
fourth fifth sixth
seventh eighth ninth
tenth last

Acknowledgements

Images: AEF

Activity 3: Ordinal numbers - Where is Yuki?

 

In this activity, students play a game of finding the position of 'Yuki' to practise and extend their ideas about ordinal numbers beyond first, second and third.

Task: Where is Yuki?

  1. Show students the photo above. What is her ordinal position in the line-up?
  2. For this activity, find a doll similar to Yuki and a collection of ten classroom objects according to the numbers of pairs of students in the class. Or use image cards as shown.
  3. For each pair, provide a table with three rows of ten empty spaces, based on the example below.
  4. Distribute the table to pairs of students. Ask students to place ten objects along the first row. Then ask students to place (or write) the appropriate positional word using the ordinal numbers – 1st, 5th, etc. – along the second row. Then ask students to place the appropriate positional word – first, fifth, etc. – below their corresponding ordinal numbers. 
  5. Act it out … engage the children in an activity that involves them finishing in an identifiable order. Ask the children to 'number off' in order: 'First', 'Second', 'Third', 'Fourth' and so on.
  6. Collaborate with the students to set up an activity challenge like the one presented above using classroom resources and artefacts.

Acknowledgements

Images: AEF

 

Activity 4: A game to practise numbers

In this activity students will use collections of objects such as cubes, tiles, blocks and ohajiki to play the Japanese game jan-ken-pon to practise numbers.

Task: The game

This game is played by two or more students. The players flick the pieces using the index finger to make a circle with the thumb.

  1. Players start with the same number of pieces on a flat surface.
  2. Players play jan-ken-pon to determine the player having the first turn.
  3. This player then spreads all of the pieces and indicates an imaginary line between a pair of pieces to indicate the piece intended to be hit by flicking one piece of the pair at the other.
  4. If a successful flick – a hit – is made, the player keeps the piece that was struck. Otherwise the second player takes a turn.
  5. When all the pieces have been won, students answer questions appropriate to the number of people in each group. For example:
    • Who came first, second, third, last ... ?
    • Who won more/the most pieces?
    • Who won fewer/the fewest pieces?

Acknowledgements

Image: AEF

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.

Ordinal words

  • first
  • second
  • third
  • fourth
  • fifth
  • sixth
  • seventh
  • eighth
  • ninth
  • tenth
  • last
  • second last

Other words and expressions

  • odd
  • even
  • next
  • zero
  • number
  • count
  • how many?
  • one
  • two
  • three
  • four
  • five
  • six
  • seven
  • eight
  • nine
  • ten (and beyond)
  • ones
  • units
  • between
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