The Train Tracks Game

Who is it designed for?

Children who are beginning to develop understandings of repeating patterns as structures with a core that repeats and that these structure can be analysed and used to predict missing elements in that pattern.

The train tracks game is designed to move teachers and students away from the question of "what comes next?" and on to "what comes here?" type questions (Economopoulos, 1998). I came up with the idea of creating this resource after the tute in week 12 and considering the question "when would you encounter a situation which required you to discern a missing element in a pattern?" I thought, "maybe if the missing element was covered up by something." That was how I came up with the train tracks idea.

How do you play?

Form a simple repeating pattern with the train track cards (with the core containing no more than three elements).

Analyse the pattern with the children

"What kind of pattern is it?"

"How do you know that it is a repeating pattern?"

"Which part repeats?"

Form another simple repeating pattern but this time cover one of the tracks with the locomotive (as above).

Again, analyse the pattern with the children

"What shape is this locomotive standing on?"

"How did you work that out?"

*Note: When making patterns, make sure that the core repeats enough times for the pattern to be recognisable, e.g. A B C A B is not yet a repeating pattern.

Provide cards for a small group of children to make their own repeating patterns and cover one element of their pattern with the locomotive. Then they can invite each other to solve the missing element. It is important to give opportunities for the children to justify their answers by articulating their reasoning, including the rule that the pattern follows.

Alternative lesson idea:

The shapes on the cards alternate in colours and size. According to Taylor-Cox (2003), when teachers demonstrate repeating patterns with pattern blocks for example, the focus attribute seems always to be colour, which has meant that children often rely on colour to solve problems regarding repeating pattern. Children should be encouraged to construct patterns based on attributes other than colour. These train tracks allow this to occur.

Furthermore, the fact that the shapes alternate in colour and size also means that it can be used to teach how to analyse qualitative change. The train locomotive can be used to symbolise the function machine (Warren, Benson & Green, 2007) and I feel this is a helpful analogy to explain the idea of back-tracking.

Have a look at how this train changes the tracks after it goes over them.

Before & After






What would the train track look afterwards?


Or what about this train? Have a look to see what it does to the tracks after going over them.

Before & After

What could the track look like before if this is what it looked like afterwards?



After following the rule, and back-tracking, the following task would be to identify firstly the original rule, followed by the rule for back tracking (Warren & Cooper, 2005).

References:

Economopoulos, K. (1998). What comes next? the mathematics of pattern in kindergarten. Teaching Children Mathematics, 5(4), 230-233

Warren, E., & Cooper, T. (2005). Introducing functional thinking in year 2: a case study of early algebra teaching. Contemporary Issues in Early Childhood, 6(2), 150-162.