Make The Whole

Task 203 ... Years 2 - 8

Summary

This is a game built on the same idea as Rod Mats, but it is not necessary to explore that task first. The materials provided are limited to the situation of Orange being the whole, but they also model how to construct a similar game using other rods as whole. The rules of the game might take a little extra oral explanation, but students quickly see that they make sense.

Rod Mats is the starting point for all of the slide shows on the Picture Puzzles Number & Computation C menu where the problem is presented using one screen, two learners, concrete materials and a challenge. The five puzzles use five different wholes which between them include families of fractions based around 8ths, 9ths, 10ths, 15ths and 18ths. You can also read the story of how one teacher used the 10ths Picture Puzzle (Orange is whole) in a Year 6 class.

Teachers wishing to build a curriculum unit around Fractions are likely to find Nichola Brandon's article Fractions In Action worth researching.

Materials

A collection of rods as described on the card
A collection of cards for Orange as whole

Content

concept of a fraction
recording fractions in words and symbols
equivalent fractions
addition and subtraction of fractions
multiplication of fractions by a whole number

Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

Before the game begins:

The 'orange rod is whole' card must be placed where it can be seen.
Each player must have an orange rod as reference.
Each player must have selected a secret card.

The rules now give each player choices in what to do with the card they pick up on their turn.

Once the whole is made by one player, the finished whole and its parts have to be sketched and a statement has to be said and written about how the whole was made. The iceberg of the task comes when you ask the students if what they have made could be written another way. For example if the whole was made in this way:

one tenth + one half + one fifth + one tenth + one tenth = one whole

then this could also be written as:

three tenths + one half + one fifth = one whole

Another part of the iceberg is to ask students to make a set of cards for the same game with a different whole. The pack provided has 10 one tenth cards, 5 one fifth cards and 2 one half cards.

This task is a partner with Task 202 Rod Mats.

Whole Class Investigation
Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.
The task is best converted to a whole class experience if you prepare cards for different wholes and have sufficient rod sets. Card masters are easily prepared using the table facility of a word processor. Masters are printed and laminated as in the task.
Make The Whole does not have a matching lesson in Maths300, but its partner Rod Mats does. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 144, Rod Mats. Also Maths300 Lesson 191, Fractions & Fraction Charts, is concrete, visual and language-based. In particular, the software presents symbolic challenges which can be worked out with materials or with a 'brain picture', by seeking the whole in the way experienced both in Rod Mats and Lesson 191.

Is it in Maths With Attitude?
Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
The Make The Whole task is an integral part of:

MWA Number & Computation Years 3 & 4

MWA Number & Computation Years 7 & 8

Follow this link to Task Centre Home page.