Mean and Statistics — Year 5 Lesson Plan
National Curriculum: Mathematics KS2 (Year 5) — Pupils should be taught to complete, read and interpret information in tables, including timetables; to solve comparison, sum and difference problems using information presented in a line graph.
Overview
This lesson introduces pupils to the arithmetic mean as a measure of average and extends their statistical skills to include interpreting and drawing line graphs, completing tables and solving multi-step comparison problems from data. Pupils develop the ability to read and interpret data critically, explaining what data shows and what conclusions can be drawn. The lesson makes strong connections to real-world contexts and encourages mathematical discussion and reasoning about data.
Learning Objectives
- Calculate the mean (arithmetic average) of a data set and understand what it represents
- Compare two data sets using the mean and range to draw conclusions
- Read and interpret a line graph with an appropriate scale, answering questions about trends and change
- Solve multi-step comparison and difference problems using information presented in tables and graphs
Key Vocabulary
Suggested Lesson Structure
Present a scenario: five children each scored a different number of points in a quiz: 4, 7, 3, 8 and 8. Ask pupils: Is it fair to compare them to each other? What single number could represent how the group did overall? Introduce the idea of an average. Take suggestions for what average might mean. Display the three types of average: mean, median and mode (briefly). Explain that today the focus is on the mean. Use linking cubes: give pupils 4, 7, 3, 8 and 8 cubes in towers and ask them to make all towers the same height. Count how high the equal towers are. That is the mean: 6.
Formalise the method for calculating the mean: add all values, divide by the number of values. Model this with the quiz scores: 4 + 7 + 3 + 8 + 8 = 30; 30 divided by 5 = 6. Practise two more examples together. Introduce the range: highest minus lowest. Discuss why the range is useful alongside the mean: two classes could have the same mean but very different spreads. Then introduce a line graph showing temperature over a week. Model reading the graph, including interpolating between plotted points. Ask questions: What was the temperature on Wednesday? On which day was it coldest? What was the range across the week?
Pairs of pupils are given a data table (e.g. rainfall in a city over 12 months) and asked to: calculate the mean monthly rainfall, calculate the range, identify the wettest and driest months, and draw a line graph from the data using a prepared axis grid. Circulate and support. Check scaling decisions: pupils should choose a scale that uses the space well and is easy to read. Bring the class together to compare completed graphs and discuss any differences in scale choices and their effect on the appearance of the graph.
Pupils work independently on a set of data problems. Problem 1: Calculate the mean of five test scores and find what score a sixth pupil would need to raise the mean to a given value. Problem 2: Read a pre-drawn line graph and answer comparison questions including one two-step question. Problem 3 (extension): Compare two data sets using the mean and range and write a conclusion explaining which group performed more consistently and why.
Pose a true or false activity: display four statements about a data set (e.g. The mean is always one of the values in the data set — False; The range tells us how spread out the data is — True). Pupils discuss in pairs and then respond with mini whiteboards. Review each statement, addressing misconceptions. Ask pupils to summarise in one sentence what the mean tells us and why it is useful.
Common Misconceptions
- Pupils often believe the mean must be one of the values in the data set; use a simple example (e.g. the mean of 2 and 3 is 2.5) to show this is not the case
- Pupils sometimes add the values but forget to divide by the correct number of values, especially when there are missing values in a table; emphasise that the divisor is always the number of values in the complete data set
Prior Knowledge
Pupils should already be able to:
- Ability to add a set of numbers and divide by a single digit using mental and written methods
- Experience of reading bar charts and line graphs from Year 4 statistics work
- Understanding of scale on graph axes
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