Multi-link Sequences

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!

Singapore/Shanghai?

Mastery?

Variety!

Proportion and Multiplicative Reasoning

Multilink

Cuisenaire

Measuring tools

Thank you

pgm@brockington.leics.sch.uk

goo.gl/l4UmA6

@MrMattock

Multi-link Sequences

Long term prediction

Highlight position-to-term relationship.

Promote natural argument, justification and reasoning.

Polydron

Practical Sequences

Colour, Shape, Perimeter.

Angle properties etc...

Multi-link Proportion

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."!!