Tag Archives: investigation

211. Hidden Rectangle problem

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Cool vectors can be exciting! They can describe the motion of a particle, they can represent the acceleration of a rocket, they can tell you about the angle an impact takes place at!

3D axes

Uncool vectors describe lines, they can intersect, they could be perpendicular, they could even describe skew lines in three-dimensions. Not quite as exciting. It isn’t difficult to see that revising standard C4 vectors can be a tad dull. How about an investigation? An investigation without an obvious answer. A question so simple that the answer is a single number. It’s the steps in between that make things interesting…

  • I asked my A-Level class to find the area of a rectangle … simple so far, how is this worthy of C4?
  • The rectangle is bounded by four vector equations … ok, points of intersection, line segment length, bit of Pythagoras there
  • The vector equations are 3D … ooh, that makes it a bit harder
  • There are eight equations to choose from … that’s mean, that means finding the angle between lines, checking for skewness, identifying parallel vectors
  • There are plenty of ‘red herrings’ … now that is just unfair (great!)

The solution to the problem is a simple surd. If you do ‘Crack the Code’ or ‘Locked Box’ problems you could use the digits under the square root sign as your padlock code.

You can download the worksheet and teachers notes here: C4 Vectors Hidden rectangle (pdf)

Depending on the engagement/ability of the students this could take between 20 and 40 minutes. It would also make an easy to assess homework.

185. I’ve lost a Dime

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I haven’t actually lost a dime, rather I’m missing a Dime – specifically the second Dime probability pack. It was a great teaching resource for experimental probability from the first school I taught at. Unfortunately it is no longer available, although it is listed on the Tarquin archive site. Each student had a plastic tube with different coloured beads, a related experiment card and a record card. They could investigate the meanings of key vocabulary, carry out repeated trials and use this amazing graph paper, designed by Geoff Giles, to record results:

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The graph paper works a little like a bagatelle or pinball machine. You start at the top ‘pin’. A success means move along the line to the next pin on the right, a fail means move to the left. You always move in a downwards direction. The more trials that are recorded, the further down you go. When you reach the bottom you will have carried out 50 trials and will be able to read off the experimental probability as a decimal. I found this blog (medianchoices of ict) with links to the Nrich website and interactive probability graphs. The graph paper from the Nrich site is here: RecordSheet.

 

Activity

I decided to recreate the old Dime investigation sheets:
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Students start by explaining what their experiment is and define what is a success/fail. They give the theoretical probability as a fraction and decimal, then predict the number of successes in 100 trials.

 

Students then carry out their experiment, recording their results in the tally chart and graph. After 50 trials, they write down the fractional experimental probability of success using the tally total and the decimal probability from the graph – hopefully they are the same! Students then reflect on their work and consider how to improve their results.

Download the worksheet here: Experimental Probability investigation

Sample

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154. When will I need to work out the area of a circle?

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Answer:
If this is your crop on your farm!

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This is center pivot (or central pivot or circle) irrigation. The area which is watered is pretty obvious. There are plenty of images on the internet and sites full of statistics.

I could imagine this making a good research homework. Apart from simply working out the fertile area, you could look at volume of water used – you could even work out the optimum size and number of circles for maximum coverage!

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.

91. Scouting for Symmetry

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This week a relative joined the Scout Association in Wales. I knew that welsh scouts wore ‘Y Ddraig Goch’ (The Red Dragon or Welsh Flag) on their uniform. I didn’t know they wore it on each sleeve, symmetrically:

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This gave me the idea for a symmetry homework.

If you look at the uniformed services and uniformed youth movements, how often does symmetry occur in their badges? Do some badge styles occur in several associations? Are some images deliberately stylised to make them symmetrical? Are repeated emblems always placed symmetrically on either side of a uniform?

Pupils could also design their own symmetrical class reward badges.

From a pastoral point of view, this would be a nice way to celebrate younger pupils’ interests outside school.

61. St George’s Day Investigation

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Here is a quick St George’s day area investigation for the 23rd April.

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What size cross must be drawn for the areas of red and white to be equal?

Assume the flag is a rectangle and the strips of the cross are the same width.

KS2/3: investigate by counting squares or working out areas.

KS3/4: extend to an algebraic solution if appropriate

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