Myths about teaching can hold you back
- Year 11•
- Higher
Approximating solutions to equations
I can use iteration to find approximate solutions to equations.
- Year 11•
- Higher
Approximating solutions to equations
I can use iteration to find approximate solutions to equations.
These resources were made for remote use during the pandemic, not classroom teaching.
Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
Lesson details
Key learning points
- You can rearrange an equation in order to carry out iteration
- This process finds an approximate solution to the equation
- This process is carried out until the outputs are the same to a given degree of accuracy
- Efficient use of the calculator makes this process much faster
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
To find a solution to a given degree of accuracy an iteration can just be rounded.
Several successive iterations need to round to the same value to a given degree of accuracy. If in doubt efficient calculator use means many iterations can be generated easily until confident that a digit is fixed.
To help you plan your year 11 maths lesson on: Approximating solutions to equations, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Approximating solutions to equations, 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
Prior knowledge starter quiz
6 Questions
Q1.What is 0.0647399 rounded to 2 significant figures?
Q2.What is the value of the expression $$x^3 +3x-12$$ when $$x=2$$?
Q3.For which values of $$x$$ are we able to evalate the expression $$\sqrt{6-2x}$$?
Q4.Use the iterative formula $$P_{t+1}=2.5(P_t-50)$$ with $$P_0=200$$ to find the value of $$P_4$$. Write down your full calculator display.
Q5.Using the iterative formula $$x_{n+1}=10-4(x_n)$$ with $$x_0=1$$ which of these is the value of $$x_8$$?
Q6.Using the iterative formula $$x_{n+1}=\sqrt{10-2(x_n)}$$ and $$x_0=3$$ match up the iterations with their values.
$$x_1$$ -
2
$$x_2$$ -
2.449489...
$$x_3$$ -
2.258543...
$$x_4$$ -
2.341561...
$$x_5$$ -
2.305835 ...