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# Concrete Approaches to Abstract Mathematics.

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## Mr Mattock

on 20 September 2015

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#### Transcript of Concrete Approaches to Abstract Mathematics.

Algebra

Polydron sequences

Equations cups and saucers

Completing the square
Number
Jumping on a number line

Positive/Negative Cards

Ratio and sharing with Polydron and Counters

SSM

Hoops

Build a triangle

Hall based Vectors

Hall based bearings

Polydron shapes
Concrete Approaches to Abstract Mathematics.
Concrete Approaches to Abstract Mathematics
Me...

Singapore/Shanghai?

Mastery?

Variety!

Proportion and Multiplicative Reasoning

Cuisenaire

Measuring tools
Thank you
pgm@brockington.leics.sch.uk

goo.gl/l4UmA6

@MrMattock
Long term prediction

Highlight position-to-term relationship.

Promote natural argument, justification and reasoning.
Polydron
Practical Sequences

Colour, Shape, Perimeter.

Angle properties etc...
Two or more different colours

Ratio of one colour to another?

Scaling up/down
Cuisenaire
How many of one colour make another?

If I have 4 of one colour, how many of another colour do I need?

How many different relationships can be shown?
Measuring Tools
Tape measures - cm and inches

Luggage scales - lb and kg

Measuring jugs - pints and litres

Speedometer - mph and kph
Jumping on a number line
Positive numbers - jump forwards.

Negative numbers - jump backwards.

Adding - Face the positive direction

Subtraction - Face the negative direction
Positive and Negative Cards
One card showing a positive outcome or thing (with one each for each player)

One card showing a negative outcome or thing (with one each for each player)

If I give you a positive card, how do you feel? If I give you a negative card, how do you feel? If I take away a positive card how do you feel? If I take away a negative card, how do you feel?
Equation Cups and Counters
Start with counters under some cups (same number of counters under each cup).
Have some extra counters next to it.
Match this up to a separate pile of counters.
Move counters to show how many are under each cup.
Hoops
Two or three circles = Venn diagrams.
Using string - create a diameter. Radius. Chord. Demonstration of a cyclic quadrilateral. Demonstration of the Intersecting chord theorem.
Building a triangle
Different colours for different lengths and split pins.
Can you build...
an equilateral triangle?
an isosceles triangle?
a right-triangle?
a triangle with an angle
x
such that sin
x
= 0.5?
Completing the Square
Can be done with card - I actually prefer the image.
Completing the Square Video
http://www.veoh.com/watch/v1716790862S86Xhh?h1=The+Story+of+Maths+Part+1
Ofsted...
http://mrreddy.com/blog/2015/03/ofsted-and-mastery-of-maths-direct-from-jane-jones-hmi/
Data Handling
Cumulative Frequency in the hall

Calculating Mean
Ratio with
Polydron and Counters
Create a bar model using the polydron.

Share the counters as required by the problem
Hall based
Vectors
Set up little cones in the hall

Create some vectors as card arrows taped between two cones.

Where can they overlap
the cones?
Hall based
Bearings
Set up little cones in the hall

Use board sized protractors and balls of string/wool to measure/map out bearings.
Hall based
Bearings
Set up little cones in the hall

Use board sized protractors and balls of string/wool to measure/map out bearings.
Hall based
Cumulative Frequency
Set up measuring station in the hall for under 140, under 150 etc.

Pupils line up in size order.

Set up an axes on the floor.

Each pupil gets a bean bag.

They put their bean bag down on their position and heigh coordinate.
Calculating Mean
Use scales to find mean weights of sealed bags of objects

Move on to "If the mean of 8 apples is ... what is the total weight?"

Never teach "Add them all up and divide by how many there are."!!
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