Category Archives: Algebra

139. Maths Roast

We’ve all seen the question about using a worded problem to work out the cooking time of a chicken. So dull and in many respects irrelevent – cook books & websites don’t write a big description. This is more like real-life:

Extract from the ‘Reader’s Digest Cookery Year’

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Butcher’s label – no cooking instructions

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Equipment
Pictures of labels from fresh meat* (actual labels are a hygiene hazard) – you might want multiple copies
Some cookbooks or tables of temperatures for cooking
Cards saying ‘Delicious’ or ‘Food poisoning!’
Calculators
*Be aware of pupils’ beliefs regarding meat – you don’t want to cause offence

Activity
1. Give out the cooking instructions & labels from the meat, ensuring the actual type of meat is on them.

2. Get pupils to decide how they want to cook their meat. You may also want to specify the cooking method to ensure variety in the,solutions.

3. Pupils calculate the appropriate times.

4. Each person (or group) presents their answer to a group (or the class). The other pupils hold up ‘Delicious’ if they agree or ‘Food poisoning!’ if they disagree. This can lead to a discussion as to why.

5. This can then be extended to look at writing formulae for cooking times.

Vegetarian Option
This task is easily adapted for any vegetarian recipe where weight is important eg Roast squash.

Don’t forget all the work on time and unit conversion that can be included!

130. Banging your head against a y-axis

Confession time!

I like teaching co-ordinates.

I like teaching plotting graphs.

But …..

Getting pupils to draw axes drives me up the y-axis.

 

Right now I can sense people shaking their heads – why are you doing co-ordinate plotting if they can’t draw axes?

 

The problem is that they can draw axes, but for some pupils it takes about half an hour to get lines drawn with a ruler, axes marks equally spaced, lines (not gaps) numbered. For other pupils, their particular SEN means it’s a struggle using equipment. Should I be penalising pupils because they are slow to draw axes, when I know they’ll work brilliantly if I give them axes?

 

So I’ve put together an A4 sheet of axes. There are two identical sets: the x-axis goes from 0-10, the y-axis goes from 0-18. There is also space to write name and Question number so you can keep track of who has done what. I know there are many websites that will generate these for you on demand, but I’ve just used what was available to me at the time to make something that works for my pupils.

 

You can download it from TES resources here.

128. Book of the Week 1

If you haven’t had a chance to take part in the rather excellent ‘How to Learn Maths’ online course at Stanford University, led by Jo Boaler – don’t worry!

 

Get reading the rather brilliant book ‘The Elephant in the Classroom’ instead. You’ll find yourself going ‘Yes, I know what you mean!’, ‘I’d never thought of that …’ and ‘I need to try this out’, before you’ve even finished it.

 

119. Inequalities Trashed

My colleague Jane introduced me to ‘Tick or Trash’ worksheets and they are just brilliant!

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The basic idea is you have a table with three columns. The middle column is the question, either side are the solutions of fictional pupils. I called mine Kirsty and Kyle as I don’t teach anyone with those names. One solution is correct, one isn’t. Your students must decide who is right and why. They must then decide where the other pupil went wrong.

The worksheet I’ve put together is about inequalities. It covers using a numberline, solving a linear inequality with the unknown on one/two sides and dealing with a negative. There is also a QR code linking to a short YouTube clip (not mine) on solving inequalities. Download it here. The basic colour coded answers are available too. Note: the files are in docx format.

This is an ideal activity to use with the Validator concept. I would give my peer Validator the answer sheet to refer to, but the explanations would be down to the students to gauge if they understood.

95. Quadratic puzzles

To an experienced mathematician, factorising a quadratic (with real roots) is a little number puzzle, into which the algebraic terms fall gently into place.

To a secondary (high) school student of middling ability they can be algebraic torments conjured from the darkest recesses of a fevered genius’ imagination. Impossible!

This year I have introduced factorising with no mention of algebra, equations, solving or factorising. My class are at least C grade students who have convinced themselves they are no good at algebra. We started by considering this puzzle:

What values of a, b, c &d make this multiplication grid true?

bc = 1
ad = 30
ac + bd = 13

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The solution is fairly straightforward:

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Once they got the hang of this kind of puzzle, I compared it to the grid method for expanding double brackets. I asked them to think about what the brackets could be if I gave them the values for bc, bd, ac & ad.

Finally the stabilisers were taken off. I asked them what the brackets were if I gave an algebraic form of the number puzzle. First we considered:

bc = X squared co-efficient
ac + bd = X co-efficient
ad = constant

Once it clicked that this was just a fancy number puzzle they were flying. I was really impressed by their positive attitude and willingness to try.

You can download a set of questions (and answers) here.

71. Algebra with a dash of probability

If you are on the Ikea Family mailing list you may have got a booklet with this a few months ago:

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It’s basically a decision spinner in the form of a hexagonal prism. On the reverse you are asked to customise it:

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Being a maths geek I thought about writing algebraic expressions. You can customise the difficulty for individual pupils.

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All the pupils do is roll a standard die and the prism. Then they substitute that value into the expression.

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You can increase the difficulty by using a variety of non-standard dice.

Construction
All you need is a strip of card – say 12cm long and some tape.
Rule off every two centimetres, fill in the gaps, fold and stick.

Probability
There are two probability questions to consider:

Bias
Is the roller fair?

The Ikea one wasn’t due to the cardboard flaps weighting one side. Over-enthusiastic taping could have a similar effect.

Outcomes
How do you know when you have had all the possible combinations of number and expression?

This could be a nice way to think about listing outcomes and sample space diagrams.

Once you start thinking of ways to use these dice rollers, it is amazing how many topics you could cover.