This learning sequence that includes number games assists students to develop confidence with whole numbers. The games (and recording the numbers involved) highlight number patterns and relationships between numbers. The games provide a stimulus for discussions about the observed patterns and the testing of simple student conjectures. The games and activities may be adapted for use with older students.

The number grids, 1–100 and 0–99, can be used to generate number cards and are useful for many other mathematical activities. There are significant benefits in students having their own copies and a bag of counters to keep a personal record of the number patterns they create in class. These can be photographed to create a permanent record of the patterns or to contribute to a class project on these themes. The number grids may be used in conjunction with an interactive white board or digital projector for whole-class activities.

There is little preparation required to do these activities in class.

The games can be played by any number of children: a small group or the whole class. The games are easiest to play if the students are in a circle or a line so that they know their physical order and when it is their turn to respond.

Playing games like sam-yuk-gu and its variations gives an opportunity to explore, refine and extend the students' use of mathematical language. Involving students in counting games and recording the patterns engages students in discussions beyond the immediate focus of the activity.

The teacher can introduce or use new terms such as odd, even, multiples of, factors, groups of and common multiples. By using counters to record number patterns on number grids students begin to establish a visual sense of number sequences in addition to saying the number word sequences.

#### Activity 1: Sam-yuk-gu

*Sam-yuk-gu* is a Korean children's counting game popularised through a Korean television program. It is well known to Australian teachers as buzz or whiz, or even buzz*-*whiz. It involves replacing numbers in counting with a clap of the hands according to a number rule established before play begins.

The number of variations in playing this game is limited only by the imagination of the teacher and students.

The game can be played with younger children who are unfamiliar with terms such as factors/multiples/groups of*. *In this version the teacher can use number flash cards during the counting sequence for the numbers that require a clap of the hands. At this level, to familiarise students with the game, the flash cards could replace any numbers in the counting sequence rather than follow a rule. They could include different representations of numbers such as figurative pictures, dice faces, playing card numbers and so on.

Vary the game by counting:

- groups of three, starting at 30
- groups of three, from 30 going backwards
- from any starting point such as 8 or 13
- groups of 5, or any other number
- odd numbers
- even numbers.

Teacher can extend the game by:

- nominating two or more numbers in the rule; for example, 2 and 7
- adding actions; for example, clap hands on multiples of 3, stamp feet on multiples of 7
- playing any of the above backwards
- combining skills; for example, clap hands on multiples of 3, stamp feet on multiples of 5, say 'buzz' for numbers containing a 7. Such a game would go like this: One, two,
**clap**, four, **stamp**, **clap**, **say buzz**, eight, **clap**, **stamp** … twenty-six, **clap** and **say buzz**, twenty-eight, twenty-nine, **clap** and **stamp** …

#### Activity 2: Counting by ones

In this activity students will use objects, toys or number cards for 1 to 20 made from the 1–100 number grid. Students count on by ones. The whole class can do this together or students can take turns to say the next number.

#### Activity 3: Skip counting

In this activity, students will practise multiplication using number cards, the 1–100 number grid, the 0–99 number grid and plastic counters.

#### Activity 4: Counting frames, abacus and number boards

In this activity students will use a variety of counting aids in the classroom, including some from Asia. They will take turns to use the materials and record the patterns.

The abacus has a long history as a calculating device. It comes in various shapes and forms. The top section of an abacus is called 'heaven' or the upper deck.

The Japanese abacus – soroban – has one bead on the top deck and four in the lower deck.

Both forms of abacus are used to perform base 10 calculations by moving the beads towards the centre beam. They can be used to represent numbers and are useful aids when discussing number representation and place value.