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Many of these ideas were taken from a document which was the result of work on thinking skills by the Essex Leading Mathematics Teachers and Advanced Skills Teachers (Mathematics) group in conjunction with KS3 Numeracy Consultants.
1. Sorting Activities - Click here
This uses the basic skills of classifying, reasoning skills are developed as pupils have to justify their categories / pairs. Creative thinking will be encouraged when there is no right answer or more than one solution.
Possible Activities:
Working out a long e.g. algebraic problem cut up into steps for students to put into order.
Domino activities / loop cards / follow me cards on a variety of topics from %, fractions and decimals to expressions involving BODMAS.
Putting numbers, shapes etc. into a Venn diagram
E.g. A list of factors of 20 and multiples of 5 or multiples of 4 and 6 or square and triangular numbers.
Probability events giving the same probability
2D diagrams showing different views of the same 3D solid, could include nets of the solids.
Relationships e.g. between height and weight sorted into positive, negative, weak, strong correlation.
A game of Pelmanism e.g. a series of straight line graphs to be matched to an equation.
Often used at the start of a lesson as a quick starter. Pupils have to justify their choice of odd one out; ambiguous sets of numbers are useful in showing that there may be more than one answer. In this activity there are no correct or incorrect answers as long as pupils supply a correct justification.
Possible Ideas:
2, 33, 5, 9 and 35
2 is the only even number
33 is the only multiple 11
5 is the only odd prime
9 is the only non prime or the only square number
35 is the only multiple of either 5 or 7
(2x)2 2X2 4X2/2 4x2
Multiples, primes, factors, divide, square
Triangle, cuboid, straight line
Straight line graphs; parallel, not parallel, intersecting at the same point on the y-axis, this could be done graphically or with the actual equations
Standard form expressions
algebraic expressions e.g. x, 2x, 9x – 1, x2 + 2
Measurement / imperial units
Area/ volume/ length both units and formulas.
3. Maps from Memory - Click here
This task relies on students working in groups taking turns to look at a series of images for say 10 seconds. They then return to the group to share and record what they have remembered, adding to what previous groups members have seen, they should not know how many viewings they will have.
This will allow pupils to develop insight into part / whole relationships as well as planning for group co-operation. The choice of diagram will obviously be selected to match the ability of the group and could be used for revision or consolidation of a topic.
Possible Ideas:
A series of functions translated, reflected, enlarged or
reduced with their formulas (higher level GCSE)
Common graphs of key functions such as linear, quadratic, exponential, trig, with formulas to reproduce.
Written formal descriptions of shapes for the groups to reproduce as diagrams
Drawings of spinners with different probabilities.
A bus or train timetable with different starting times from the original station but common journey times so you could use the connection to fill in the gaps.
A series of dots alongside the points of the compass to identify relative positions.
A series of circles with radius, diameter, arc, circumference, tangent, sector, chord, segment identified by drawing and vocabulary.
Pupils are usually posed one big open question. The data is provided on small bits of paper, which allows them to be moved around as a solution is sought.
Possible Idea:
the following pieces of information are written on separate
bits of paper.
The distance from the x-axis is 5 squares
The distance from the y-axis is 4 squares
One of my co-ordinates is a prime number
He distance form the point (8,) is 5cm
One of my co-ordinates is a square number
The sum of my co-ordinates is 9
Y Value is greater than my x
This work relates to a 1cm grid.
What is my co-ordinate? What is the minimum number of statements you need to solve this and what are they? Now create your own puzzle.
5. The 5 W’s
What could this be used for?
Who might use it?
Where might it be used?
When would it be useful?
What are the dimensions?
Items form the cupboards or photos
An abacus
Slide rule
Log tables
Trundle wheel
Clinometer
3,4,5 triangle as a knotted rope
The examples above show some examples of activities, which promote thinking skills.
Hopefully they are
- Open and challenging
- Use prior knowledge
- Offer opportunities for group work.
Other Ideas:
True or False:
KS3 Statements
Answers
KS4 Statements
Answers
Simulation of the balloon
problem - deciding on priorities -
Click here
Crossing a river - Japanese IQ
Test -
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here
Spreadsheet that generate
Sudoku Problems -
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Top Tips -
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Thinking Words -
Click here
MindMap -
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Posters from the Leading in Learning Project (LiL) [Zip File
Save on your computer] -
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