Activity Instructions: 
The computer game is self-correcting and so can be used for individuals, small groups or in a teacher-led discussion. Without the software, feedback needs to be given by the teacher or other class members. Young children will use only positive whole numbers (e.g. start with 1 and 100), older classes can use fractions, decimals or even surds!

1. The teacher or students write a pair of numbers on two blank cards. With a card each, two students stand up in front of the class, positioning themselves at either ends of an imaginary number line (smallest card on the left). The teacher then calls on a third student to write on another card, a number that is in between the pair and the student then stands between the two original numbers as if on a number line (i.e. standing at the correct position).

2. If a correct answer is given, one of the students on the ends sits down and hands their card to be reused by another student, who is called on to write a number between the new number and the earlier endpoint.

3. Continue as the number line is divided into smaller and smaller segments. Stop when interest wanes.

Alternative Equipment: A variation on this game that involves less student participation requires writing the numbers on the whiteboard, instead of students holding up cards. In this version, the teacher draws a number line on the board and the students write a number in between the smaller and larger number.

4. Tromp (1999) describes how he used this game in his classroom.

Comments: 
Beginning with integers and narrowing down to smaller intervals ensures that students realise decimals exist between all integers and not just between 0 and 1.

Use of the calculator to check whether an ordering is correct.
Ask students how they could use the calculator to decide whether a suggested number does lie between the given pair. For example, a smaller number subtracted from a larger number should give a positive number in the calculator display.

You may find that 'Money Thinkers' have trouble finding a 'number between' if the interval numbers contain two or more decimal places.

Some students have trouble with producing numbers of their own although can recognise the numbers if they were given to them. For example a student may not be able to produce a number between 0.3 and 0.4 although if given the number 0.35 they can recognise that this number does fit in between these boundaries. We have found that teaching models such as the MAB and especially the LAB have helped students produce their own numbers. By making the boundary numbers, then by using the materials, physically find a volume or length between the limits they can then convert the model to a number. These models, however, are restricted as they only extend to the thousandths place. Generalising beyond a few decimal places is important.

Variations:
If using decimals, ensure that the number pairs combine decimals of different length, integer and decimal pairs, and also that long decimals are included. Research shows one reason for students' misconceptions is that they don't encounter decimals of different lengths simultaneously as they learn about tenths, hundredths and thousandths in successive units.

Let teams of students write the number pairs for the game, as well as their correct order and 3 sample solutions. The teacher can take note of their familiarity with different types of numbers. Will any students in Year 4 write questions with negative numbers? Rather than disregard 'new' numbers which the teacher has not formally taught, this provides an opportunity for general discussion of where the new numbers fit into the overall scheme, without the added pressure of performing operations and getting correct answers. When presented in the context of a game, 'new' numbers (longer decimals, unusual fractions or negative numbers) may be more readily accepted by students.

Include surds or trigonometric ratios for Year 10 students.

Ask for a point that lies exactly midway between the given pair, or exactly one third of the way from the smaller to the larger. (Best done with a calculator, so that some pace and interest in the game is maintained.)

Number Between can be made into a team game with all teams creating say 3 number pair questions (with solutions) to give to the teacher. The teacher could choose a team to have a turn. Correct ordering by this team could score 1 point, with a further point for a correct number between. Other teams can challenge if they disagree with the solution, but must provide a correct solution to win 5 bonus points. (If a team challenges a correct answer, they forfeit 5 points from their score). The teacher is allowed to challenge an incorrect solution if no-one else does.