Teaching Secondary Mathematics Using NRICH Resources

Age 11 to 18
Article by Charlie Gilderdale and Alison Kiddle

Published October 2014.

This article is part of Enriching the Secondary Curriculum.

We'd like to take you on a tour of the Secondary NRICH site...

We will invite you to have a go at some NRICH activities and reflect on how you might use them in the classroom, so have some paper and pencil handy.

We will also offer advice on how to choose suitable tasks for your classes, and point you in the direction of articles that will support a pedagogy based on teaching mathematics using rich tasks.

Who is this page for?

Secondary mathematics departments, teachers of secondary mathematics, and mathematics advisors.

If you are a secondary mathematics department, you could work through these resources together and discuss how to integrate some of these ideas into your schemes of work and teaching strategies.

Of course, you don't have to wait for the rest of your department to join in... there is plenty to gain by working through this material on your own. Blogging or tweeting can be a great way of connecting with like-minded teachers.

Mathematics advisors may want to use the material on this page to introduce teachers to NRICH.

Let's start with a problem.

Have a go at M, M and M. While you are working on the problem, think about:

What mathematical content knowledge are you drawing on?
What mathematical skills are you using?
Which students might you use this task with?
How does this task differ from those you might normally use?



Once you've had a go at M, M and M, and had a chance to think about the questions above, take a look at the Teachers' Resources. Teachers' Resources can be accessed from the sidebar on the top left of the problem page.

You may have noticed a link to Unequal Averages as a Possible Extension to M, M and M.
Were you tempted to have a go? Try it now!
Many of our problems can be linked together to form a sequence of lessons. The Teachers' Resources draw attention to these links.

Now take a look at Pair Products. While you are having a go at the problem, think about the questions above again. Again, take a look at the Teachers' Resources to see how we suggest a lesson could be structured.

These rich tasks can be used to replace more traditional exercises often found in textbooks. They offer an opportunity for students to consolidate their understanding of averages and expanding brackets in a more engaging way. The repeated practice needed to build fluency is done for a purpose, rather than for its own sake.

There are many more NRICH tasks that can be used for consolidation purposes. Take a look at our Secondary Curriculum pages. See if you can find the three problems you have worked on so far, and have a look at some of the other problems in the same sections. Think about whether you might use each problem as a consolidation task.

Now let's take a look at some tasks that can be used to introduce new ideas to a class.

Have a go at the problem Tilted Squares. You can print off some dotted paper from our Resources page.

Once you've thought about the problem, take a look at the Teachers' Resources, where you will find some video footage showing the NRICH team working with a class on the problem.
You can also watch the videos and read our thoughts about the lesson in the article Tilted Squares - Teaching Using Rich Tasks

We think Tilted Squares is a great way to introduce students to Pythagoras's Theorem. It only requires prior knowledge of finding areas of squares and right-angled triangles, and offers students the opportunity to discover the Pythagorean relationship for themselves. The proof follows naturally.
Another couple of examples of introductory tasks are Factorising with Multilink and Cyclic Quadrilaterals. Again, once you've had a look, see if you can find the problems on the Curriculum Mapping Document and have a look at some of the related tasks.


Other useful links:

NRICH Resources for Every Occasion highlights NRICH tasks that can be used for a variety of purposes in the classroom.

Models for Teaching Mathematics in which Alan Wigley invites us to take a closer look at the curriculum we offer to learners of mathematics. He questions whether it is the job of the teacher to make it easy for students.

Angle Measurement: an Opportunity for Equity in which Paul Andrews attempts to establish a principle of worthwhile mathematical activity for all pupils. 

Post-16 Curriculum has links to a selection of NRICH tasks suitable for older students.

The Lower Secondary Students' page
The Upper Secondary Students' page

I've Submitted a Solution - What Next? describes how the NRICH team select solutions for publication on the site.

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