Rod Mats

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

The thrust of this task is the generation of mathematical conversation about fractions in a visual and kinaesthetic context. Spoken words are converted to written words and written words are converted to symbols. The task first highlights that In order to use fraction language in a situation you must: know what the whole is be able to show that the whole is partitioned into equal parts One these criteria have been established, deciding which fraction language is based on counting the number of equal parts to make the whole. In the photo: pink rods show two halves make the whole red rods show four fourths (quarters) make the whole white rods show eight eighths make the whole Student responses to Q. 2 need to indicate that they recognise all of these aspects. Note: Over time, encouraging the writing sequence of: two thirds 2 thirds 2/3 helps students to understand the purpose of the different messages given by the two numbers that make each fraction. Since fractions make no sense without the whole, in Question 3 students would need to either state that brown is the whole or include it in their drawings, something like: which shows: one eighth + three eighths = four eighths or two quarters or one half which shows: one eighth + one quarter - 3 eighths = ... The answers to Questions 4 and 5 depend on the students' choices, so will vary. Questions 6 and 7 open the iceberg of this task. Any rod (or collection of rods, say blue joined to dark green) can be the whole. Each new whole produces a new rod mat and a new discussion and recording session. Over time, students' understanding of fractions and facility with fraction operations develops soundly. This task is a partner with Task 203 Make The Whole.

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.

This task can only be converted to a whole class investigation if you have a rod set for each pair. Multiple copies of these can be ordered from the Distribution Manager at Mathematics Centre. Once you have the resources it may be best to use the activity for a few minutes each day two or three times a week over several weeks. Just choose a different whole each day then: Threading the activity through the curriculum in this way is more reflective both of the history of how fractions developed and were understood and the view that learners need time and challenging experiences to construct their own learning. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 144, Rod Mats.

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 Rod Mats task is an integral part of: MWA Number & Computation Years 3 & 4 MWA Number & Computation Years 7 & 8 The Rod Mats lesson is an integral part of: MWA Number & Computation Years 5 & 6 MWA Number & Computation Years 7 & 8

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