N&A Teaching ideas

Ideas, activities and resources

Here you should find a wealth of resources that can be used by you and your students for teaching this topic. The resources at the top of the page are activities and investigations aimed at creating a stimulating and engaging environment in the classroom. With these activities you can create opportunities for students to really explore the Mathematics they are studying and discover some of the ideas for themselves!

These lessons need to be backed up with practice activities and so below there are links to worksheets aimed at practising the skills learned and to some short tests. There also some IB style questions, some note taking tasks and an end of topic test!

There is also a section called 'The Internet Guide' which provides a brief guide to some of the best related internet items that students could use to back up there studies.

Sets of Numbers

This activity involves exploring the very nature of numbers and asks students to start to classify them themselves, compare their means of classification with each other and the 'Sets of Numbers' as they are defined. Hopefully having done this activity some meaning is added to the sets.

Exactly!

What in our world is known exactly? The vast majority of the numbers we use to describe and explain the world around us are rounded or approximated. This activity gets students to explore that idea and understand its significance and the need to know how to do it! Students practise rounding.

Percentage Error

The concept of relative error is really very important and can really mess with our minds when presented in different contexts. How can a bigger error be less significant? In this activity students get a little taste of why this relativity is important and how it can be used or misused to confuse us.

Big and Small Numbers

This activity is about the purpose of scientific notation, its advantages and the ability to manipulate numbers in and out of scientific notation. There are some videos as an opening to discussion, clarification of notation and then students are asked to do some research.

Rogue Trader

This activity invites students to go back in time and invest some serious money in currency! Then they get to track the progress of their investment over time to see how wise it was! Using a great historic database of currency exchange rates, this is really possible and is a great context for practising currency exchange.

Buying and Selling

This is a little activity to encourage some thought about buying and selling rates using the excellent currency converter from OANDA. The activity extends to encourage some thought about commission.

Visual Sequences

Building visual representations of arithmetic sequences can really help to understand their structure and the associated formulae. This activity aims to do just that and lead to the discovery of the formulae in question! more...

Arithmetic Sum

Students use their intuition, some multilink cubes and a nice bit of geometry to prove and understand the formula for the sum of an arithmetic sequence. This follows on nicely the visual sequences activity above.

In the Money

A long lost relative wants to share their riches with you! Students are asked to choose between 4 ways of receiving their cash and given only a couple of minutes to do so. The subsequent task helps them understand the wisdom of their choice by introducing the idea of exponential growth compared to linear. This is a good opportunity to go from arithmetic to geometric sequences.

Dr Who

Geometric sequences as geometrical objects. Students consider animations involving repeated enlargements and try to reconstruct them. It gets really interesting when the common ratio becomes negative

Quick Ideas

The following is a list of ideas for teaching that are either quickly done or not yet fully developed into resourced activities.

Which sequences

This is just the first part of an idea I am playing with which is a  little activity on arithmetic sequences for now. Which of these sequences will have the term 80? How do you know? Which term will it be?

Speed!

How fast is Usain Bolt running when he runs the 100 meters? Students look at different speeds and convert them into different units in attempt to understand them. Use this Split times link from speed endurance to look at how the speed varies over the course of the race. There are also results from previous winners.

SI Units

Do a research activity that helps students to understand the tools that are used to measure the world around us. The aim is to become familiar with the units used and how to interpret them and change between them. There are always more units out there than you think!

Swine Flu and You

Inspired by this article Arithmetic eases Swine Flu from Marcus du Sautoy's Sexy Maths series, have a think about how the spread of diseases can be modelled by exponential functions and/or geometric sequences.

Human sequences

This is a brief activity where students are given cards with each card being a term in a sequence. They have to arrange themselves to make the sequences. This can be a great activity for greeting people moving around the class. Here is the first draft of an Human Sequences activity sheet to go with this which includes a challenge sequence to order.

Compounding Calculator

Get students to create a spreadsheet that will calculate the value of an investment for some given variables. the more general the spreadsheet the better. For example, it would be great if you could vary all of the inputs and see the calculation change accordingly! For an example, complete this Compounding Calculator spreadsheet so that it solves the problems posed!

Money Lender

It could be fun to set up some kind of pretend money lending organisation that could be run over a long period of time. The context could be engaging and the calculations required would be useful.

See Also....

The Internet Guide

This page is designed to be a brief guide to some of the best related Internet items on this topic that students could use to back up their studies.

This page contains a growing list of videos freely available on the internet that could be used to help the teaching of this module. Each video comes with a brief explanation of how and when it may be used. It may also link to an activity on the site

N & A Practice

This page has a variety of tasks designed for practise and revision.

Worksheets

This page links to a series of focussed worksheets for this topic. The worksheets consist largely of 'Practise Questions' but most finish with more open ended questions to extend. Ultimately, students need to be able to answer questions from a variety of topics and contexts, but often it is necessary to spend some time focussing on particular skills whilst still in the process of learning them. The worksheets are clearly titled according to the particular sub-topic and come complete with answers.

Revision Notes

This is a series of 'Fill in the Gaps' notes that I have created to help students keep useful records of the course. The rationale is explained in more detail on the 'Exams and Revision pages. Essentially the aim is bridge the gap between Students making their own notes on a blank canvas and being given detailed notes that they did not create.

Tests/Assessments - Planned!

This page will contains some assessments for use with this module

Short Tests

These are just a few short tests aimed at testing smaller subdivisions of the topic with IB style questions. The more exposed students are to past paper style questions, the more familiar they become with them and hopefully the more adept they become at handling them. The tests can be used for '30 minute quizzes' as the topic is taught.

End of Topic Test

Here is a 1 hour long end of topic test made up of 'IB style' questions that cover the syllabus items from this topic. This is a great opportunity to create a real IB exam experience.

Quick Test

There are hundreds of past paper questions and exercises available for this purpose and the challenge is trying not to reproduce questions and to put together collections of questions that serve your purpose. The 'Quick Test' series (there is one for every module) was written with an end of course revision day in mind but could be used at any other time as well. This page links to the quick test for Number and Algebra and there is a link to the document itself as well.

Quick Test

There are hundreds of past paper questions and exercises available for this purpose and the challenge is trying not to reproduce questions and to put together collections of questions that serve your purpose. The 'Quick Test' series (there is one for every module) was written with an end of course revision day in mind but could be used at any other time as well. This page links to the quick test for Number and Algebra and there is a link to the document itself as well.

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Comments 2

Lois Bennett 11 August 2017 - 09:29

Hi Jim,
I have just used the Visual Sequences and Arithmetic Sum. The Sum activity is pretty brilliant, the visual sum being the area of the terms. Thanks.
But the picture is misleading. The first four terms are 1,4,7,10 and they are shown as 1,5,9,13? Just change the pic please.
Keep dreaming, we all benefit!
Lois Bennett

Jim Noble 15 August 2017 - 16:47

Hi Lois! Thank you... does it work too for another time if I just change the general formula to Un = 1 + 4(n-1) ..... I am just away from home at the moment and looking for a quick fix.... thanks for spotting....


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