KS4 Foundation Function Machines
Like many teachers I use function machines as an introduction to algebra, I often combine sequences and function machines by first introducing the sequence number as a letter, then move on to function machines.
The resources I use are listing below that include the extension resources that I always find essential. After my pupils have mastered 3 machines I introduce the letter 'x' and link this to the sequence number to show the machine can now predict any sequence.
Number Algebra 3
Starting on page 91 is a wonderful game for the introduction of function machines. I tend not to tell my pupils to write the comments as suggested in the book. But the game is won by the first pupil to predict the yellow number. The teacher knows the function, say 2x + 2 and then a pupil comes to the board and writes down the input, I, as the teacher, writes down the output. This continues until a pupil can predict the answers and they win.
The game can be continued whilst the class is engaged and competing.
Following this I use question A4 which slows down the whole class but this gives me the opportunity to introduce the extension material to those who finish first.
I then move onto page 93 B Function Machines and pupils copy the diagrams into their books with the answers. Pages 93 and 94 are used.
Function Machine
This is an extension resource to keep those who have achieved the activity busy and stretched whilst others finish off their activity. It is an excellent smartboard resource and ensure the flash file works on your school computer before using it. There are 10 questions as follows.
1) One simple function machine with addition
2) One simple function machine with multliply
3) Two inputs and two outputs with non algebraic multiple choice answers
4) 4 inputs and 4 outputs with algebraic multiple choice answers
5) Inverse simple function
6) Two stage and 4 input/output with multiple choice algebraic answers
7) Substitution using one substitution
8)Two stage and 4 input/output with multiple choice algebraic answers
9) Substitution using two substitutions and brackets
10) Pattern sequence - a bit tough usually and often not answered
Number Algebra 2
This is my second extension resource as the level is slightly higher. Begin on Unit 9 page 81 Function machines and use all the activities to 87 that gives plenty of questions to keep the most enthusiastic and capable pupil busy whilst others are completing the basic understanding. Inverse function machines are covered and some of the questions are sufficiently wordy to slow the majority of those who are being extended.
For any that finish the basic activity this is their second activity in lesson two.
Algebra Game
For those who have completed all resource this is my introduction to the words Expression, Equation and Formulae to ensure my pupils understand the difference between them. This is one of my favorite games as no maths is actually needed. Pupils move a cartoon character with a wheelbarrow using the computer's keyboard to catch the correct Expression or Equation or Formulae. There are 3 levels and pupils need to distinguish between them.