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Mathematics Year 5: Function Machine Introduction This lesson encourages children to look at the relationship between pairs of numbers, using the concept of a function machine to do this. Although this is not a new idea it still forms the basis of an excellent maths lesson This lesson uses a program that can be downloaded from: http://www.standards.dfes.gov.uk/numeracy/publications/ Click on Teaching Resources and in the left hand menu window change the subject to ‘mathematics’ (leave the other two boxes reading ‘all’). Scroll down the list and click on Function Machine. Resources • One PC and an interactive whiteboard or data projector for whole class work • Children will need paper and pencil to help them note the relationships that are being suggested. Some children may need access to a calculator Previous learning The children should be able to carry out simple arithmetic calculations. They should be able to apply a set of rules to a particular number and to work out which rule applies to all of the other numbers. Learning Objectives • To understand the relationship between input and output • To hypothesise what the relationship might be • To recognise that initially one of several rules might apply, but that only one is true in all cases. What to do A function machine applies a rule to an input number and produces an output. For example, if the input number is 6 and the output is 12 then any of these rules could apply: Add 6 Double Halve and add 9 Treble and subtract 6 etc. However, if the children try another input – for example 8 and the output is 13, then they should find that only one of these rules now holds true. This lesson is centred on looking at number pairs and deciding the correct relationship between them. At the start of the lesson the teacher can choose the complexity of the ‘rule’ – which they may want to keep hidden from the rest of the class. This can vary in difficulty from ‘adding a single digit number’ to ‘halve and subtract a single digit number’. The teacher chooses this option from an initial menu page (or the computer can choose a rule at random – which then puts the teacher at the same disadvantage as the children!). There are 8 single step and 5 two-step rules to choose from. The teacher (or a child coming out to the interactive whiteboard) types in an input number and the computer displays the output number. There can then follow some discussion as to what the class think the computer might be doing with this number. It will be useful to have a conventional whiteboard on which the different ideas suggested could be written down. Once a rule has been determined, the children have to predict the answer to any input before the ‘activate’ key is clicked. At this stage they are practising their mental arithmetic skills whilst also trying to determine whether the rule is correct or whether they need to predict a new one. Note that even if the rule is only ‘add 8’, the inputs can be three digit numbers, negative numbers or decimal numbers – making the program quite challenging for some children. The rule can be revealed at any stage by clicking on the ‘reveal program’ button. Differentiation © ictopus ltd
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Maths Y5: The Function Machine June 2008
As this is a class activity it is not easy to differentiate the task, although if children are working in pairs with the classroom assistant then an appropriate choice from the menu can be made depending upon ability. For those children that can handle these concepts quite easily, they might like to try the ‘Bounce’ program on this website (http://www.mape.org.uk/activities/index.htm . ‘Bounce’ is a freely downloadable program. This program is also about number relationships, but the children will also need to be familiar with the concept of the highest common factor. The role of ICT Children can themselves play the part of a function machine. One child might, for example, be the ‘adder’ and another child the ‘doubler’. However, using a PC is much quicker and allows the children to concentrate on the mathematics being demonstrated. Changing the rule is very simple and the computer will not make mistakes! Follow-up suggestions There are several ways to extend this program, namely: Introduce negative numbers as possible inputs. Discuss the value of zero as an input – is it a useful number to use? Revise commutative operations - if we add 6 and double, is it the same as doubling and adding 6? Take the resulting number pairs (input, output) and plot them on graph paper - what do the children notice about the shape of the graph. Introduce the idea of inverse functions – provide the children with the output number and ask them to work out the corresponding input number (they can then use the program to check their answers). Assessment The children should consider the difference between a random approach and an approach based around a systematic method. On average how many input numbers did it take to discover the rule? Did they get better with practice? Which part of the activity did they find the hardest; calculating the output or determining the rule? Does the computer ever produce a false result, and, if not, why? Is it harder to perform the inverse operation? The more able pupils can test themselves by visiting this site: http://www.subtangent.com/maths/ty-fn-machines.php They are offered 10 questions, although a basic knowledge of algebraic notation will help (i.e. do they know, for example, what 3n + 6 means)
This lesson idea was first published as part of the Becta Direct2U subscription service for teachers, (c) Becta, 2005-2006
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lessons2go
Maths Y5: The Function Machine June 2008