What's My Rule? Years 2 - 8

This game is sometimes played by drawing a computer on the board and pretending that the context had something to do with technology. If you have simple calculators that use Order of Operations (see Preferred Materials) you can use it with confidence as the 'computer' when playing this game. If you have MathMate calculators you can also use the two bracket (parenteses) keys, as in the example below.

Materials

• One MathMate calculator (for the teacher/leader)
• One Post-It note pad (for the teacher/leader)
• Blank worksheet for each student
• Blank graph sheet for each student
• Overhead transparency (or other enlargement) of one section of the graph worksheet

Procedure

Introduction

We are going to play a game today where I am the only one with the calculator. We are going to pretend that it is a Number Machine that has a secret rule. But it won't tell you its rule. All it will do is give you an Out Number if you give it an In Number to start with. Of course, we are only pretending, so I will have to press the buttons. So you know I am not cheating I will write the secret rule on one of these Post-It notes and stick it on the calculator while we are playing.

Write a rule on a Post-It note and dramatically stick it on the bottom of the calculator.

Playing The Game - Gathering The Data

OK, now you have to work out the rule on this sticker. You take turns to tell me a number, I pretend to be the machine, do the calculation and tell you the answer. Let's try a couple.

Ask one or two students to offer In Numbers and you calculate the appropriate Out Number, eg:

If the rule on the Post-It Note is Y = 2(X + 1) ... X is In and Y is Out ...
and you are given 5 you press [2] [ ( ] [5] [+] [1] [ ) ] [=] and tell the students the answer.

At first it may take some encouragement, but when the students realise that they are only gathering data and can't be 'wrong', they soon get into it.

Playing The Game - Organising The Data

After one or two guesses suggest that the students record on the worksheet the information they have gathered so far.

Interlude - Worksheet

Create your worksheet by:

• Saving it (right click or click/hold in Mac) and follow the instructions.
• Inserting the picture into a word processor.
• Copying it in this program to fill a page and adding any titles of your own.
• Printing it.

Back To The Lesson

Explain that when a student thinks they know the rule, they are not allowed to call it out. Instead they have to prove that they know it by telling you an In Number and predicting the corresponding Out Number. This has to be done twice in a row to show that it wasn't a lucky guess.

... that way others can keep thinking because you have only given them more data rather than told them the answer.

The first person to work out the rule in this way takes over the teacher's job and pretends to be the number machine.

Run the first game through.

Reflection

Look back over the In Numbers selected and ask:

If we played the game again, are there some In Numbers you could ask which give more useful information than others?

Play another game or two with a leader and the whole class, then try the game with student pairs. It is important to encourage recording of the In/Out pairs and to continue to encourage thought about the In Numbers to suggest.

It is also important to realise that students may be able to explain the same set of data in more than one way. For example, the rule above could be explained as:

Some teachers use such situations to introduce or reinforce the equivalence of algebraic expressions.

Interlude - Graph Sheet

Create your worksheet by:

• Saving it (right click or click/hold in Mac) and follow the instructions.
• Inserting the picture into a word processor.
• Copying it in this program to fill a page and adding any titles of your own.
• Printing it.

Back To The Lesson

Picturing The Rule

Remind students that the data they collect comes in pairs and use the graph OHT show how these pairs can be plotted by using the data collected in the first game.

Do you notice anything about these points on the graph?

Could you predict any other pair which might be on the graph.

Does this pair obey the In/Out rule for this game?

Emphasise that same set of data has produced both a number pattern and a visual pattern. Ask the students to plot the data for two or three more games from their recorded information. Encourage them to predict the shape of the graph.

Looking Back

With the background of the lesson set above students can be exposed to the process of Working Mathematically which involves working in context to:

• collect and organise data
• seek and see patterns
• make and test hypotheses
• record and communicate findings

Extensions

1. Provide the students with a worksheet of missing numbers that encourages 'thinking backwards' and using decimals.
2. Use rules which are non-linear, eg: Y = X x X.