140. Cut out the Quartiles

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Quartiles on cumulative frequency graphs are such easy questions when you get ‘it’. The hair pulling, nail biting wrong answers you see on exam papers make you wonder if you’ve ever taught the topic. Time for the scissors again …

Activity
This activity demonstrates in a practical and visual way how to set up the quartiles on a graph.

Equipment
Printed cf graphs
Rulers
Scissors
Glue
Coloured pens

Task
1. Cut out the area to the left of the graph. Leave a column of graph squares next to the y-axis, for scale. Cut exactly to the top of the curve.

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2. Fold the graph in half, parallel to the x-axis, with the maximum value just touching the axis.

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Repeat the half fold again
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3. Fold along the x-axis. Unfold – you’ve just divided the graph into quarters. This should reinforce that y-axis is split into quarters.

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4. Stick down the axes. Place a ruler on the fold lines and join the ends of the folds to the y-axis.

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5. If you fold the graph forward you get this:

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6. Put a mark at the end of each line and continue with a dotted line. Discuss what proportion of the data each line represents and label it.

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7. Fold the graph back and mark in the vertical lines. Solutions,can now be read from the x-axis.

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8. The interquartile range can also be highlighted and calculated.

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Review
This activity covers a fair few learning styles and creates a visual/memorable resource,in their books. Since using it, the number of pupils who quarter the x-axis has dropped significantly. I hope it works for you.

139. Maths Roast

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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!

138. Kandinsky Combinations!

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This week I gave a talk to a group of PGCE/Schools Direct associates about innovation and ‘keeping it fresh’. One of my points was you should ‘Keep the good ideas and bin the rubbish/pointless ones’. This is one of my ideas I kept – first used in the late 1990s!

Background
Wassily Kandinsky was an artist, born in Russia in 1866. He died in France in 1944. He is credited with being the first artist to explore purely abstract work. Researching him is a nice homework task which can add to the final work.

Farbstudie quadrate mit konzentrischen ringen

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This work has been reproduced thousands of times -you can see it everywhere from student bedrooms to upmarket coffee shops. The original was completed in 1913. It roughly translates as colour study squares with concentric circles.

Investigation

You will need:
Squared paper (or plain)
Coloured pencils or pens

1. Show the class the painting and discuss how the colours are arranged.

2. How many ways can you colour in one square with one colour? 1

3. How many ways can you colour in two concentric squares with two colours? 2

4. Repeat for three colours and ask for predictions. The usual prediction is 3, the answer is 6.

5. Repeat the process and ask them if they can see a pattern forming. Encourage them to be methodical.

The colour patterns form a set of factorial numbers. Finding out about factorials could be a good extension task.

After the work is completed you’ve potentially got a great wall display, a cross-curricular link to art and an understanding of combinations/factorials.

Variation
This also looks rather cool done with concentric equilateral triangles or hexagons on isometric paper.

136. Quiz-Its

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Here’s a simple starter/revision activity. All you need is Post-it notes.

Hand out Post-its as the class arrive.

Once they have got their things out they each write four questions on a topic of your choice. Encourage them to make the questions challenging. Once that’s done tell them they need to write the answer lightly in pencil on the back.

Stick all the Post-its on a table or wall.
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Everyone then collects a Post-it (or Qwiz-it) to answer (not their own).

Once they’ve answered, they can check their answer. If the answers don’t match, who is correct? Why?

This can lead to discussions about question-style, methods, misconceptions and understanding.

135. Book (& Website) of the week 2

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If you are on Twitter, you may have heard of the perfectly titled @MathsBookClub. If not, let me explain.

People were asked to nominate their favourite Maths related book (Fiction or Fact).

People voted and the most popular was chosen.

The winner was: ‘Alex’s Adventures in Numberland’ (‘Here’s looking at Euclid’ USA) by Alex Bellos.

Just like a “meet down the pub bookclub” there will be an online discussion on Wednesday 23rd October. Except with this bookclub, the author has offered to join in! Very cool!

To join in the mathematical literary fun either follow @MathsBookClub on twitter, visit the mathsbookclub website or do both!

(Support your local Library. If that’s not possible then click on the book for a link to the paper version on Amazon.co.uk; ebook also available)

134. Revising around in Circles

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Ah … beloved GCSE students. Why does revising feel like I’m just reteaching a topic for the Nth time?

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I’ve been trying some new ideas out on my GCSE group. One of the more popular ones ideas, for an unpopular topic, were these Circle Theorems fact cards. Students were given four cards with a diagram and an open question, for example: What is special about angles ABD and ACD? In the gap, they had to answer the question. They soon realised that the answers they had written were the theorems that they’d learnt. Their solutions had popped into their heads, without being bogged down by number stress. They could then try number questions, referring back to these fact cards if they got stuck.