Activity Instructions: 
The following game is a version of skip counting (by adding or subtracting increments).

1. All students are given 60 secs to write a sequence of numbers starting from a given number and using a certain increment, without using a calculator. For example, Year 2 may start at 25 and increment by 10. Year 4 may start at 3 and increment by 0.1.

2. After the time has elapsed, all students stand. One is chosen to start reading out their sequence. The teacher or a selected student writes the numbers on the board so that all can see.

3. Other students may challenge as the sequence is read out. If the person is incorrect, they sit down and the challenger takes over reading out the numbers in the sequence. The class, the teacher, or a calculator can adjudicate. Students remain standing if they still have numbers to offer to the sequence on the board.

4. A student can continue reading the numbers of their sequence until they are successfully challenged or the teacher calls on someone else. The last person standing is the winner.

Comments: 
Students who win too often can be handicapped by 5 seconds or more to allow others to become winners.

The teacher can start the sequences on the board if there are some students who need this assistance to start the game.

Number Trails has different challenges for different ages. It is a useful game format that can be used within the domain of whole numbers or extended to fractions and decimals and negative numbers. It can be used as an integral part of a lesson or to fill in a few minutes spare at any time of the day.

This is a good opportunity to let students know that there are more numbers than those they have studied formally without the pressure of being required to assimilate all the details. So longer decimals, or negative numbers may arise naturally. Discussion about various methods for predicting answers could draw attention to number patterns as well as basic features of notation. Students will look for patterns so that they can write numbers without calculating. As the numbers are written on the board, the students who sit down early get time to observe the resulting patterns, and use the constant addition facility of their calculator to check answers. Negative numbers might be 'discovered' by those using their calculators.

When decimals are used, there will probably be disputes over correctness: e.g. a sequence such as 4, 4.125, 4.25 (or 4.250) includes decimals of varying length, and those using a calculator may be able to offer alternative notation.

This simple game, a variation of skip counting, comes from Maggie Marriott of Sunshine East Primary School. The students love it.

Variations:
All four operations could be used with the same basic game format. Some sequences to try include adding or subtracting 2, 4, 5, 9 and multiples of 10 or multiplying/dividing by 10 or 2. The starting number, the operation and the increment or ratio could all be chosen by students who might seek to provide unusual/challenging possibilities.