Session Documents

Math and Making Open Conference Notes

 

5.  Research Questions and Priorities Maths through Making;  Using Making to Teach Math

Facilitator:  Noel Jackson

 

Up to age 7 years.

  • Number (up to 1000)
  • NUMBER LINE
  • Simple addition, subtraction,
  • Multiplication (2x,3x,4x,5x, 10x tables)
  • Simple division into parts
  • Shapes

Up to age 11 years

  • Larger numbers
  • NEGATIVE  NUMBERS
  • Tables up to 12x
  • Long multiplication
  • Long division
  • FRACTIONS
  • Decimals
  • Bar charts
  • Averages
  • TRANSFORMATION: 2D to 3D
  • STORY PROBLEMS

Up to age 14

  • Graphs
  • Cartesian coordinates
  • GEOMETRY INCLUDING PYTHAGOTUS THEORUM
  • ALGEBRA

Up to age 16

  • Trigonometry
  • Infinity
  • Vectors
  • PROBABILITY
  • Pre-calculus
  • Mechanics
  • IMAGINARY NUMBERS

Up to age 18

  • Calculus
  • Statistics
  • Functions
  • Proof

We didn’t spend so much time discussing the key areas for the older students so these areas would probably benefit for some further thought.

 

A key area identified was the development of MATHS SENSE which ran all the way through the progression , where students intuited a feel for what the answer should be.  It was felt that the peer-to-peer discussion inherent in making activities were particularly well suited for developing this ability.  Many maker activities will inherently develop maths sense but students would benefit from participation in activities where this was specifically encouraged.

We appreciate that the Noticing Tools developed at NYHSci are tackling some of the areas identified

 

FRACTIONS

We only had time to brainstorm on topic and selected Fractions as we thought we might be able to identify maker activities which did the job.

COOKING – any kind of baking where proportions could be changed or where a recipe given in parts had to be translated into measured quantities or adjusted to produce a different amount of product

  • Drink Mix (no cooking required)
  • Chocolate Chip Cookies
  • Microwave cakes
  • Pizza base – has the advantage that the finished product can be used for the traditional method of teaching fractions

STOP-MOTION ANIMATION – where a film is made frame by frame and each frame lasts a fraction of a second, production of the storyboard and then the film requires use of fractions to get a result that runs in real time.

DRUM MACHINE PRGRAMMING – Simple beatbox programmes play on a cycle and pleasing rhythms are made when the beats fall on fractions of the pulse.  Even stabs are fractional with a higher denominator than the main beat.

HAIR BRAIDS – braiding can be codified in terms of moving proportions of the hair to a new position

SCALE MODELS – measuring something and then producing a toy version . This idea very much depends on the facilities for building to hand for building the scale model.

  • 3D printing
  • Clay modelling to make a vacuum formed product (works for cars)
  • LEGO buildings

MAKING COLOURS – students use a colour chart to select the colourway they will use to decorate something they have made.  A given colour is expressed fractionally (eg ½ dark red, 1/8 dark blue, ¼ light blue, the rest white) and students are told that they are allowed so many mls of paint. They use syringes with the base colours to make up their pallets. A further sophistication is that if students are only allowed small volumes of each colour, they will need to come back and remix more paint to the same recipe. If they are successful, the different colours will match.

It was thought that the object that students decorated was something that they made following fractional instructions then this was the basis for a complete workshop.

BALLOON ANIMALS – students are shown how to make a balloon dog by dividing a long balloon into fractional parts for the nose, ears, neck, forelegs, body, hind legs and tail. They are then asked to use their imagination to create different animals by changing the proportions of the parts (long neck = giraffe, long body = dachshund etc.) they have to write instructions so that others can make the same animals, expression=ng each part as an appropriate fraction of the balloon length.