Higher GCSE maths students are required to plot and interpret histograms with unequal class widths. Drawing histograms with unequal class widths are very common in GCSE maths papers.
Histograms look like bar charts but have important differences.
When grouping continuous data, it may be necessary to have different class widths if the data are not equally spread out. When class widths are not equal frequency density becomes the vertical axes.
I start the lesson by asking students to find a probability from a set of data in a grouped frequency table. I use this example to help students recap inequality notation and to discuss whether this is an exact or estimated probability. It is important to remind everyone that grouping helps to organise large samples of data but there is a trade off with accuracy when interpreting the results.
As we move on to the main part of the lesson I ask the class to think about how the table in the second slide is different to that in the starter. Students quickly pick up the class widths are no longer equal.
We discuss it may be necessary to use unequal class widths for data that are unevenly distributed and when we do so frequency is measured as the product of frequency density (vertical scale) and class width (horizontal scale).
When drawing histograms for Higher GCSE maths students are provided with the class widths as part of the question and asked to find the frequency density.
I work through the first example with the class plotting the histogram as we complete the table.
In the plenary students are challenged to complete a table and histogram by working out the scale of the frequency density axis. This task frequently appears in exam papers. I provide the students with a print-out of this slide, so no time is wasted copying it into books. Examiner reports state that those who understand frequency as measured by the area of a bar often go on to achieve full marks.
Here is an extract of an Edexcel examiner report for a similar question.
‘In general candidates appear not to be aware that the area of the bars of a histogram are the frequencies, evidenced by a lack of frequency density calculations.’
To ensure all students have enough time to complete the plenary I ask those who have finished first to additionally estimate the number of flowers that grew to between 5 and 8 cm tall. The most able students calculate this as a compound area of the bars on the histogram.
In the next lesson students practice finding the frequencies from histograms to calculate an estimate of the mean. As learning progresses we move on to using interpolation to estimate the median average from a histogram.
When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way. Mathematics Teaching and Learning Folder All teachers receive a folder […]
Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]
The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]