Fractions in Action

Nichola Brandon, Year 4, St. Benedict's Primary School, Canberra

This is a story told in slide show chapters.

Following Days 3 & 4 of Working Like A Mathematician presented by Mathematics Centre at the request of the Catholic Diocese of Canberra Goulburn, Nichola planned and executed a unit on Fractions & Decimals. She selected activities from Calculating Changes, Maths300 and Mathematics Task Centre which are the major sources of the professional development. The slide shows are an edited version of a presentation to her colleagues on Days 5 & 6.

The slides will be more meaningful if you are familiar with the activities, so references are provided. Some will need membership access.

Slides in each show are timed to change each five seconds. You can also use keyboard arrows and left and right mouse buttons to move through each slide show. Ctrl L will expand the image to fit the screen.

Chapter 1: Chocolate Cake
Ten guests wait outside a 'chocolate restaurant'. Inside there are three tables at which they can choose to sit. They enter one at a time. Table A has one block of chocolate, Table B has two and Table C has three. Where will the guests sit to finish up with the most chocolate?
Reference
Maths300 Lesson 135, Chocolate Cake
Chocolate Cake (12 slides)
Chapter 2: Luke's Fraction Game
Six year old Luke invented this game. Students are in pairs. Each pair has a set of Poly Plug which they imagine to be a tray of biscuits. All the plugs are removed from the tray and placed in the bag. Pairs meet with other pairs and give them a fraction of a tray. Plugs given are secretly placed in the board and teams move on. A team is finished when their board is filled and they have no spare plugs.
Reference
Calculating Changes, Luke's Fraction Game
Calculating Changes, Fraction Game
Luke's Fraction Game (7 slides)
Chapter 3: Peg & Tape Fractions
The whole is a length of string, thin cord or sewing tape. Children are asked to estimate where a given fraction would be from one end then place a peg to record their estimate. Two or three children place different colour pegs. Who is closest to the fraction? How can we check?
Reference
Task 205, Peg & Tape Fractions
Maths300 Lesson 33, Fraction Estimation
Peg & Tape Fractions (14 slides)
Chapter 4: Columns, Rows & Fractions
Every rectangle can be thought of as a whole which can be partitioned into columns, rows or cells. Each of these divides the whole into equal parts. So a rectangle can be used to represent two fractions simultaneously (columns represent one fraction and rows the other) and the common denominator which links them is the partition represented by the cells.
Reference
Calculating Changes, Fractions, Plugs & a Calculator Calculating Changes, Columns, Rows & Fractions
Task 201, Rectangle Fractions
Maths300 Lesson 77, Rectangle Fractions
Columns, Rows & Fractions (13 slides)
Chapter 5: Rod Mats
Choose any Cuisenaire Rod. This is the whole today. A rod mat is made by lining up rows of all the other colours which fit the chosen rod exactly. The white rods will always work, so there will always be at least one other row to match the whole. The rows of rods of the same colour partition the whole into equal parts. Any rod mat can be used to generate many equivalent fractions and equations.
Reference
Task 202, Rod Mats
Task 203, Make The Whole
Maths300 Lesson 144, Rod Mats
Rod Mats (5 slides)
Chapter 6: Calculator Slido
Neither the decimal point, nor the place value columns move. The decimal point is always in the ones column and the columns are always in the same position relationship to each other. Digits slide left or right as a number is made 10, 100, 1000... times bigger or smaller - not the decimal point. This physical activity uses 'labelled' children as the columns and children holding digit cards as the numbers. When viewing the slides note how in this class the decimal point child works with the ones column child.
Reference
Calculating Changes, Calculator Slido
Calculator Slido (5 slides)
Chapter 7: Tasks
As part of the course schools were provided with ten sample tasks. Five were fraction based. Nichola used these as work stations with small groups. Reference links below are to the Task Cameo (if it has been created yet).
Reference
Task 136, Four Bead Mix
Task 177, Making Fractions 2
Task 203, Make The Whole
Task 222, Making Fractions 1
Task 240, Less Than Fractions
Tasks (9 slides)
Chapter 8: Assessment
In the photos below, Nichola provides samples of children's reflections following Luke's Fraction Game. She also submitted her own reflection on the six day course and, in part, wrote:
My practice has changed immensely! ... My low level students are now loving maths because they can get involved and can achieve! And my high flyers remain engaged because they can take the activity as far as they want to! ... I have changed my practice because it works! Students are forming connections, asking questions, using the language and challenging themselves! I have students coming up to me and saying "Miss, I never knew maths could be so fun!" ... It is amazing and IT WORKS!

   

You can find more about how teachers in this diocese approached the teaching of fractions in these two stories from Mathematics Centre:

Calculating Changes ... is a division of ... Mathematics Centre