Function machines are a superb way of getting your students to see patterns in related calculations and using the inverse operation. It also helps them think in more generalised terms about a number problem and can be used to introduce two-step calculations.
In its simplest form, a function machine might look like this.
The children are given a number of “inputs” on the left hand side of the function and have to calculate the “outputs” on the right hand side. The function they have to use is indicated at the top of the function machine (in this case, adding 6). This helps children notice what pattern emerges when the same number is added to a variety of starting points.
A more difficult problem might like look this:
In this example, the students need to recognise and use the inverse operation to work out what the inputs are.
The most challenging kinds of function machines look like this:
Here the object of the exercise is to identify the function from a given set of inputs and outputs, and encourages students to look for relationships between numbers. This can be made even more difficult by including two step problems (such as add 3, then mulitply 2).
1 & 2: Input value. This represents the range of input values that can be entered into the function machine. In this example, values between 1 and 10 will be used on the left hand side of the function machine.
3 & 4: Number of inputs. This controls how many inputs are listed on the left hand side of the function machine.
5: Number of steps. The number of steps involved in the function can be set to 1, 1 or 2, or 2. The more steps involved in a function, the more difficult the function machine is to solve.
6: Adding. If you want to include an add step, tick this box and enter a range of numbers to add to the input.
7: Subtracting. If you want to include a subtraction step, tick this box and enter the range of numbers to subtract from the input.
8: Multiplication. If you want to include a multiplication step, tick this box and enter the range of numbers to multiply the input by.
9: Division. If you want to include a division step, tick this box and enter the range of numbers to divide the input by. Please note that the division function is not available in whole number work sheets.
These tick boxes control how the function machine is presented to the student. Ticking and unticking these values varies how difficult the function machine is to solve.
10: Number In. This reveals the input.
11: Function. This reveals the function.
12: Number Out. This reveals the output.
Tip - when using the function machine worksheet, only the input values can be clicked on and changed.