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Increasingly difficult questions: Mean average – TES Maths Resource of the Week

To see all of the work I do for TES Maths, including Resource of the Week,  Inspect the Spec , Pedagogy Place, Maths Newsletters and Topic Collections, please visit the  TES Maths Blog here

What is it? I have long been a fan of David Taylor’s Increasingly Difficult Questions (IDQ) website , so I was absolutely delighted to see he had uploaded his wonderful resources to TES to share them with a wider audience. So, to celebrate, the least I could do was to choose one of them for Resource of the Week! The concept behind IDQs is so simple and yet so powerful. Students are presented with a series of questions on a given topic, but they get progressively more difficult. More than that though, as we can see in this example on the mean, they incorporate a wide range of other topics, allowing students to benefit from the positive effects of interleaving, whilst also starting to see maths as they connected subject that it is.

How can it be used? Increasingly Difficult Questions are ideal to use at the end of a topic unit. So, you have taught the basics of finding the mean from a list of data, and now you present your students with the selection of questions in this resource. As they work their way through the sheet, students are confronted with the challenge of applying their skills at calculating the mean when negatives, decimals and finally algebraic expressions are involved. The selection and progression through the questions is excellent, and the answers are even included too! Brilliant stuff!

Thanks so much for sharing Craig Barton

Download: Increasingly Difficult Questions – Mean Average View the author’s other resources

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This list is aimed at the lower end of KS3. The resources are suitable for pupils who have not learnt about averages before. I would suggest using the resources in the order I have listed them. The first 2 resources are good for introducing the topic, teaching it, giving examples and the pupils having a go at questions. The third resource does the same but from a functional point of view. The other resources are all interesting cross-curricular functional ideas to do with pupils that show them the relevance of averages. This unit of work could take 3 or more lessons, depending on how many of the cross-curricular resources you choose to use.

Handling Data 1

Quality Assured Category: Mathematics Publisher: Nuffield Foundation

Unit 2 pdf pages 17 & 18 make a good introduction to the topic of averages, followed by pdf pages 19-24 taking pupils through the mechanics of finding the mean, median and mode.

The assessment pack, pdf page 11 has a revision sheet on the 3 types of average, could be used as a starter, mini-plenary or homework sheet. Pdf page 19 is an extension sheet with problems to solve on the 3 averages. Pdf page 28 has answers to the questions in unit 2 and page 33 has the revision and extension sheet answers.

Quantitative Data

Quality Assured Category: Mathematics Publisher: Centre for Innovation in Mathematics Teaching

The Quantitative Data file pages 6-13 has examples and exercises on finding the mean, median, mode and range, followed by examples and questions on using these measures to compare data sets. The Outline Lessons Plan file contains suggested routes through the MEP resources for this unit of work. The Detailed Lessons Plan file contains suggested teacher questions and lesson timings to use when teaching this unit. The Teaching Notes file suggests three differentiated routes through this unit - lower ability, standard and extension. The Overhead Slides file pages 4-8 has large examples that can be projected onto a whiteboard to use in class. The Activities file page 2 has a couple of questions on calculating and using averages. The Mental Tests file has 3 differentiated mental tests on calculating averages. The Extra Exercises file pages 2-5 contains extra questions on calculating averages if you still need more.

What Is an Average?

Quality Assured Category: Mathematics Publisher: CensusAtSchool

This resource comes from the Census At School website. It is a good way of introducing the mean, median and mode to pupils for the first time. It also introduces pupils to using a spreadsheet for performing the calculations, so they can then analyse their results. Data is provided in a file, but you could also collect your own or go to the website to collect different data.

Issue 84: A Resource for the Classroom - Averages Mystery

Quality Assured Category: Mathematics Publisher: NCETM

Once pupils have understood how to calculate the mean, median and mode this resource will present a challenge to them. Pupils have to solve a set of clues to work out what the original data was. This is good for developing their problem solving and thinking skills and suitable for paired/group work.

Pixel Perfection

Quality Assured Category: Mathematics Publisher: cre8ate maths

Once pupils have grasped the basics of calculating averages this resource provides an interesting application in real-life for them. Pupils have to work out the optimum viewing distance from a TV, dependant on the pixellation of the screen. This resource gets pupils working interactively in groups, using their averaging skills. A suggested lesson plan is in the teachers notes file. The other files contain pictures of different degrees of pixellation for the pupils to investigate.

Helicopter Seeds

Another good resource suitable for when pupils have got the basics of calculating averages. A suggested lesson plan is included in the teachers file. Pupils make helicopter seeds, flight test them, record and analyse the data. This is done in groups. The pupils then modify their seeds, flight test them, record and analyse this new data and draw conclusions based on their findings which can then be presented to the class. There is a helicopter template and data recording worksheet provided.

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• Find The Median And Mean Averages And Range Worksheet For Ks3 Maths

Find the Median and Mean Averages and Range Worksheet for KS3 Maths

Five more questions that Clumsy Clive seems a bit confused on. These involve median and mean from sets of data, plus calculating the mean from a frequency table and estimating the mean from grouped data.

You can also throw a couple more questions in verbally (find the modal group etc) while discussing the answers and reasons why as a class.

KS3 Maths Curriculum Area

Statistics Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

Andy Lutwyche is a purveyor of mathematics and a producer of resources, more of which you can find on his TES shop . You can also follow him on Twitter at @andylutwyche .

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Resources you can trust

Comparing averages

A KS3-4 maths worksheet resource that can be used to practice concepts around comparing averages.

There are 3 questions, each following the same format:

• Find the mean, median and mode for a set a raw data
• Which would you use in a given scenario?
• Which gives the most truthful representation of the data?

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Year 2 Addition and Subtraction Fluency Question Worksheet Pack

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

5 April 2024

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A number of addition and subtraction activities suitable for children working on the Year 2 Programme of Study.

Fluency and some problem-solving questions covering the following objectives:

• To recall addition facts to 20 fluently
• To recall addition facts to 20 fluently and derive and use related facts to 100.
• To add and subtract numbers using concrete objects and pictorial representations
• To add and subtract a two-digit number and tens.
• To add three one-digit numbers.
• To solve problems with addition and subtraction.

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