Category Archives: Problem Solving

80. Sunshine and constructions

Here is a quick consolidation/revision/application task for constructions, which involves very little preparation. If the sun isn’t shining you could always adapt this for indoors.

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Equipment
Chunky chalk (look in your local pound shop)
String
Straight edge and tape measure or just a metre stick
Usual classroom textbook/notes

Task
A company has sketched out a set of new signs and it is your job to accurately draw them without a protractor. The task is differentiated by sign design.

Sign 1
Made from a rectangle and two equilateral triangles.

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Sign 2
Same as sign 1, but with a border of constant width

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Sign 3
Made from a rectangle, an equilateral triangle and a right angled isosceles triangle.

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Sign 4
Same as sign 3, with a border of constant width.

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Skills used:
Constructing an equilateral triangle (1,2,3,4)
Constructing the locus of a moving point (2,4)
Bisecting an angle (3,4)
Constructing a perpendicular bisector (optional in all cases)

Activity
Once the signs are allocated, each group must present a plan to the teacher on how they will draw it. They may use their notes, textbooks and smartphones (if your school allows this).

When the groups are outside, they can easily increase their understanding by moving on to the next design or developing their own arrows.

Examples of work

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Health Warning!
These signs, when viewed from the end, can look rather like rockets. All I will say is:
rockets + construction arcs + pink chalk + teenager boys’ level of humour= ….

75. Factorisation Forest

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MrNussbaum.com

I found this brilliant website via Pinterest. It is a great way to practise prime factor decomposition and it allows pupils to either be creative or use a timed challenge.

I particularly like the fact that you can generate as many base and power boxes as you want, as opposed to similar games where you are given a rigid structure to complete – pupils are allowed to try their answer and be wrong, rather than see their answer doesn’t fit and just give up.

67. Banquet Challenge

Anyone else end up getting out the pencil and paper when you try to figure out the instructions on a supermarket ready meal banquet?

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Some companies take you through the cooking process step by step. Others tell you how to cook each individual part, but not how the timings overlap. It occurred to me that this creates a nice Functional Skills/Time problem. You could even develop this into a critical path analysis problem.

Example: Mexican Banquet

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Microwave
Chicken & vegetable mix: 2mins 30secs
Tortillas: 20secs
Chilli: 5 minutes

Oven
Potato wedges: 15mins
Quesadilla: 10mins

Question
If you want to eat at 7pm, what time should you start cooking?

What time does each item go on?

Assume that only one item can be put in the microwave at once, but the oven can fit more.

61. St George’s Day Investigation

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

If you like this post why not follow Maths Sandpit on twitter: @Ms_KMP

60. Special Offer 3

You know, once you start noticing odd logic in special offers, you notice them everywhere. I’m collecting all the ones I find with the aim of creating a numeracy/ mental arithmetic/ problem solving board. I hope it will start some good discussions – especially if I throw in some good value offers too.

Two 300ml pots of double cream:

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But 2 x 300ml = 600ml

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Like this particular places says “Every little helps!”.

52. Special Offer 2

I think you’ll agree that this is a pretty good offer:

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A total saving of £7.94.

How about this one?

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I know these are meant to be mix and match offers, but the numbers are just funny.

(PS: I hope the discount algorithm on the till system doesn’t automatically apply the offer price if you buy two of the second toy.)