What's My Rule? Years 3 - 6

Summary What's My Rule? is a classic which appears in many forms and is sometimes called Number Machines or Function Machines. In this version the calculator is used as the 'number machine' that delivers OUT numbers for a suggested IN numbers. The game can be played with the whole class or in small groups. It provides skill practice in number and problem solving in pattern and algebra. What's My Rule? is included in Maths300, as Lesson 34, with the addition of a great piece of software. Suitable for threading. Materials One calculator for the teacher/group leader One sticky note pad for the teacher/group leader One calculator between each pair of students (to support conversation) Note: You may have to be careful about order of operations if the children are using their calculators to discover the machine's rule using trial and improve. For example if the rule is + 2 x 3 and IN = 6 , an order of operations calculator will give the answer 12, but a 'non-order' calculator will give the answer 24.

Procedure Introduce the activity as a game between the children and your calculator. Tell them that you will pretend to be the calculator and they can use their machines if they want to. Explain: It might help you to record information during this game. and suggest they sketch up an IN/OUT table like the one you draw on the board. IN OUT         We are going to play a game today where we pretend my calculator is a Number Machine with a secret rule. It won't tell you its rule. It will only give you an OUT Number after you give it an IN Number. So I can remember what rule to use I will secretly write it on one of these yellow notes and stick it on the calculator where you can't see it.

Content data: collecting, recording, displaying data: interpretation equations: creating/solving graphing number pairs mathematical conversation operations - whole number order of operations pattern generalisation pattern interpretation pattern recognition problem solving recording - written using brackets

Begin with rules like: Three times the IN Number plus 5 Dramatically write a rule on a sticky note and affix it to the bottom of the calculator. Ask for an IN Number. Press the buttons theatrically to work out the corresponding OUT Number. (You can undoubtedly work it out in your head without the calculator, but the theatre adds to the fun. What was the IN Number for the OUT number displayed here?) Now you keep giving me IN numbers and I will tell the OUT number from the calculator... Partners take turns to offer an IN Number and you return the OUT Number. ... you can 'prove' to me that you know the rule by telling me an IN number AND its OUT number.

If they are correct this process doesn't reveal the answer to others and the game can continue.

• The game can be played regularly with the aim of becoming better at working out the rule. Recording is essential to developing this proficiency, as is the mathematical conversation. In addition the game encourages mental arithmetic.
• Use the team which guesses correctly to assist for the next game. That way the successful team is 'removed' from the challenge and a different team must be first next time. The assistants help decide on a rule and check the teacher's button pushing by calculating in their heads.

Reflection

• After each game look back over the IN Numbers selected and ask if there are some which give more useful information than others.
• Also ask students to explain in words the pattern that allowed them to predict the IN/OUT pair. It is important to realise that students may be able to explain the same set of data in more than one way. For example, a student might describe the rule as 'double IN plus 2', whereas your sticky note might state 'add 1 to the IN number, then double'.
• How have we been working like a mathematician?
  Highlight the aspects of the Working Mathematically Process which involves working in context to:
  • collect and organise data
  • seek and see patterns
  • make and test hypotheses
  • record and communicate findings

Extensions

1. If the children can describe and write the rule in words, then the words can be 'shorthanded' and eventually symbolised to become an expression like: y = 3n + 5 as in the picture above ('n' stands for any IN Number).
2. Remind children that the data they collect comes in number pairs and use an overhead transparency, or graphing on an electronic white board, to show how these pairs can be plotted. Use the data collected by one of the pairs and predict data points from the plot. Check the new pairs by using the children's rule.
   • 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.
3. Try some non-linear rules such as Y = X x X.
4. Try some of the rules using decimal IN numbers. Ask the children to calculate in their head/on paper first, then check with their calculator.
5. When the children have discovered a rule, take the opportunity to set some backwards questions like:

   What would be the IN Number corresponding to the OUT Number of ...?

6. Explore Backtracking, Maths300 Lesson 19.

Return to Calculating Changes Activities