Circles – forever going round in the loop

Have you had the same problem as me? I teach the vocabulary and characteristics of circles, to say a 12 year old, and then perhaps two years later we have the same bright youngster and introduce the concept of π. What went wrong they couldn’t remember what the difference is between circumference, radius and diameter? We really are struggling now, forget π, they can barely remember the names yet alone what they represent. Yet year after year we repeat the same mistake. I have developed these simple steps that have helped improve my success rate.

Colour

How often do we ignore the use of colour when teaching? Not only is it more cheerful than the usual drab black and white it is a great aid to memory. Not too many colours otherwise it starts to look like an explosion at a paint factory.

Circumference

I start with the circumference. I draw it, in say blue, and now right the name underneath. But write it with a huge blue circle almost swallowing the word explaining this is how you remember it because the first letter of circumference tells you what it is.

Diameter

We now move on to the diameter. Explaining what this is I draw my blue circle again but draw the diameter vertically in red. Now I point out that the word tells you what the diameter it is just the vertical in the D. Make sure you draw the D as a capital D.

Radius

At bit of human biology never goes amiss! I tell them the bone in the forearm from the elbow to the thumb side of the hand is called the radius. When drawing a circle on the board I explain that I have to keep my elbow steady in one spot and move my arm to draw the circle. A little demonstration helps. Next I introduce Homer Simpson, remember he only has 3 fingers. I draw a circle draw the radius and with great artistic license draw Homer’s hand waving at us showing his radius bone.

These ideas are simple, silly but they really help in children remembering the names and concepts.  I continue to use the colours and remain consistent with their use. I encourage the students to do the same it aids memory and understanding.

Does anyone else have a good tip?

Has anyone tried it and had success or failure?

Make a comment and share your thoughts.

Equations – your cut out and keep guide

Knowing what an equation is vital to progress in maths. This is a simple exercise in basic numeracy which can lay the foundations for future progress. and takes is a step removed from the normal worksheets.

Preparation

Give each pupil, or pair of pupils, as set of cards, five of them with numbers on two with the + sign, one with – on and one with = . Alternatively give them a sheet with the numbers and operations on and let them cut the cards.

Equation building cards

Instructions

Demonstrate how the cards can be used to make equations, the pupils will have the strong desire to call them SUMS but try to insist they are equations because one side equals the other. The students are to now make up as many equations as possible., they do not have to all the cards but cards cannot be repeated. Their results are to be written down. Perhaps give them a time limit the challenge is see how many they can make. Or ask for 20 equations to be made.

Extension

Change the numbers, increase the numbers or restrict them further.

Change the operations, add a multiplication sign or division.

Add a card with an x on it. The rules are now to make equations but they must have an x . They are then to record their results. They then swap their results with a neighbour. The partners have to mark each others.

What have you done to address this problem? Let me know.

What do you think? Please share your thoughts in the comments.

Number snap

To practice multiplication tables is vital. Parents are very keen for their children to learn multiplication tables so any activity that aids progression is always welcome. Here is a simple game that can be adapted to suit all needs or abilities; it is particularly useful for younger ones.

Preparation

Lest assume you wish to practice the three times multiplication tables, prepare 20 cards, some with the questions, some with the answers. Cut them up. I always prefer to put them on to card and make them fairly big.

The game

Each pair of pupils is issued with a set of cards. The cards are to placed face down on the table. They then take it in turns to turn up two cards, if the cards match, say 3 X 3 = and 9, then they get to keep the cards. If they don’t match then the cards are turned face down again. The game continues until there are no more cards left, the winner is the one with the most pairs of cards.

Advantages and benefits

This game is fun. It uses a multisensory approach to learning where the pupils see, here and do something connected with maths rather than being a passive observer. It also encourages collaborative learning.

An excellent book for activites and ideas is Key stage 2/3 Numeracy games by John Taylor



What do you think? Please share our thoughts in the comments.

Substitution: so what does it all mean?

Substitution: so what does it mean?

 

Substitution is taught every year and yet it is always causing problems. In particular when we ask a student to substitute a number into 2a then a².It is not the act of substituting that causes the problem but the understanding of algebra. Common misconceptions when substituting into a term happens time and time again. This activity helps to identify those that do, and do not understand, algebra particularly when those difficult areas of powers and brackets are used.

 

Step 1

A bit of preparation, but once done it is a resource that can be used time and time again. Each pupil needs a set of cards numbered 0 to 9. Make them big get them laminated, held together with an elastic band and stored in a cheap envelope.

 

Step2

Hand out a set of cards to each pupil or give them a set between two if you want a more collaborative approach. Write an expression on the board such as

 

2a

 

Emphasise that this is an expression not an equation. You may have to tell them what the difference is, again another big problem what is an expression, what is an equation.

 

Step 3

Now tell them a = 4, using the cards show the answer. Hopefully they will all demonstrate they know the answer is 8, if not you have an opportunity to rectify any misconceptions. Now put the following on the board

 

a²

 

Once again the same process is followed you can ask the class show me the answer. It is now some confusion occurs, some will give you the answer 16, others 8 again. Now is the opportunity to find out who understands and who doesn’t. Dependent on the answers it is up to you how you progress. Try other numbers and other powers. This quick simple exercise will inform your assessment and guide future lessons.

 

Extension

Once you have successfully rectified any problem with these issues, and it is a major problem to be solved if you want them to progress in algebra, you can now try something like these more challenging terms 3a² and (3a)². This starting activity will provide the basis for much useful discussion.

 

Substitution - do you know what it is yet?

 

Substitution: Do you know what it is yet?

 

Step 1

A bit of preparation, but once done it is a resource that can be used time and time again. Each pupil needs a set of cards numbered 0 to 9. Make them big get them laminated, held together with a elastic band and stored in a cheap envelope.



Step2

Write an expression on the board such as

3a

 

Emphasise that this is an expression not an equation. You may have to tell them what the difference is.



Step 3

Now tell them a = 4, using the cards show the answer. Hopefully the will all demonstrate they know the answer is 12, if not you have an opportunity to rectify any misconceptions. You can now progress depending as always upon the answers you receive, so for example you might want to put up the expression

2a – 1

 

You can continue with this exercise dependent upon the age and stage of the class.

Once again the same process is followed you can ask the class show me the answer. Where you go from here is up to you. You can continue with this exercise dependent upon the age and stage of the class. For example you can take this forward when introducing brackets, what is the answer to 2(x-1)? Or when you need to tackle the big problem that we all face of when many pupils become totally confused with the difference between x² and 2x?

 

This is an excellent activity for an instant assessment of what they have learnt. It ensures every child participates in the class and if you are in the UK it will satisfy some of the demands of the OFSTED inspection regime.

This activity was not thought up by me. I found it in an excellent book which is full of ideas, starters and worksheets that can be photocopied. It is not as dry as the normal text books or dare I say it teacher produced worksheet. The title is ‘Activities for Teaching Numeracy’ Year 7 algebra. The whole series is excellent and I have bought numerous copies over the years for departments I have run, oftenI have paid for them out of my own money, because I believe them to be so good.