Building on composite functions
I can expand my thinking on composite functions to consider a more efficient way to write composite functions comprised of many functions.
Building on composite functions
I can expand my thinking on composite functions to consider a more efficient way to write composite functions comprised of many functions.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- A composite function could be many iterations of one original function
- To write this in function notation would be cumbersome
- There is more efficient notation that can be used in these circumstances
Keywords
Iteration - Iteration is the repeated application of a function or process in which the output of each iteration is used as the input for the next iteration.
Common misconception
Pupils are very familiar with exponents but the introduction of 'subscript' notation may confuse them. For example, they may think $$x_2$$ must be a function of $$x$$ because $$x^2$$ is.
Use of language helps. When talking through an iterative formula like $$x_{t+1}=8x_t +6$$ say, \"The next $$x$$ value is equal to eight lots of the current $$x$$ value plus six\" whilst pointing at it. Get pupils to do the same back to you.
To help you plan your year 11 maths lesson on: Building on composite functions, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Building on composite functions, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Iteration unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
$$\text{f}(4)$$ -
$$-2$$
$$\text{ff}(4)$$ -
$$16$$
$$\text{fff}(4)$$ -
$$-38$$
$$\text{ffff}(4)$$ -
$$124$$
$$\text{fffff}(4)$$ -
$$-362$$
$$\text{ffffff}(4)$$ -
$$1096$$
Exit quiz
6 Questions
£500 invested, 2.5% interest -
$$y_{t+1}=y_t\times1.025, \ y_0=500$$
£500 invested, 12.5% interest -
$$y_{t+1}=y_t\times1.125, \ y_0=500$$
£250 invested, 2.5% interest -
$$y_{t+1}=y_t\times1.025, \ y_0=250$$
£250 invested, 5% interest -
$$y_{t+1}=y_t\times1.05, \ y_0=250$$
£500 invested, 5% interest -
$$y_{t+1}=y_t\times1.05, \ y_0=500$$