NATIONAL QUALIFICATIONS CURRICULUM SUPPORT
Mathematics
Personal Mathematics
Advice and Guidance for
Practitioners
[NATIONAL 2]
This advice and guidance has been produced to support the profession with the delivery of
courses which are either new or which have aspects of significant change within the new
national qualifications (NQ) framework.
The advice and guidance provides suggestions on approaches to learning and teaching.
Practitioners are encouraged to draw on the materials for their own part of their continuing
professional development in introducing new national qualifications in ways that match the
needs of learners.
Practitioners should also refer to the course and unit specifications and support notes which
have been issued by the Scottish Qualifications Authority.
http://www.sqa.org.uk/sqa/34714.html
Acknowledgement
© Crown copyright 2012. You may re-use this information (excluding logos) free of charge in
any format or medium, under the terms of the Open Government Licence. To view this licence,
visit http://www.nationalarchives.gov.uk/doc/open-government-licence/ or e-mail
psi@nationalarchives.gsi.gov.uk.
Where we have identified any third party copyright information you will need to obtain
permission from the copyright holders concerned.
Any enquiries regarding this document/publication should be sent to us at
enquiries@educationscotland.gov.uk.
This document is also available from our website at www.educationscotland.gov.uk.
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PERSONAL MATHEMATICS (NATIONAL 2, MATHEMATICS)
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Contents
Introduction
4
2D shapes and 3D objects
5
Patterns and number relationships
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PERSONAL MATHEMATICS
Introduction
Advice and guidance for supporting practitioners in developing
learning and teaching strategies
The approaches suggested here will give practitioners support in developing
relevant learning experiences for learners covering this compulsory National
2 Mathematics unit, specifically in developing the ability to recognise and
use:
1.
2.
3.
basic 2D shapes
basic 3D objects
patterns and number relationships
in order to plan a range of everyday activities. They will also be able to :
4.
5.
6.
interpret information
communicate information
develop an awareness of chance and uncertainty
in order to make informed choices in real -life situations.
Learners will come to the National 2 Mathematics course with differing
levels of knowledge and skill. Some will move quickly through the units in
this course and others may take a few years to work through them or may
complete only aspects of some units. You will need
to assess the level of skill learners have and develop approaches and methods
accordingly.
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PERSONAL MATHEMATICS
2D shapes and 3D objects
Before practitioners support learners in
conducting shape or object searches in their local
environment, they may want to assess their knowledge about 2D shapes and
3D objects. There are quizzes and more ideas to be sourced on the internet if
you search for ‘2D shape’ or ‘3D object’.
It may be helpful to ask learners to make a poster of shapes or objects in
everyday life by searching through magazines and newspapers. This could be
a homework exercise or done in the classroom.
When practitioners are confident that learners can identify and name shapes
and objects in their environment, they could conduct a sear ch, one for shapes
and one for objects. Learners can take a digital camera along to record the
shapes/objects that are identified. If enough cameras are available learners
can work individually or in pairs. Practitioners may want devise a 2D shape
and 3D object tally sheet to keep a tally of the most frequently occurring
shapes and objects. These might be good sources for further discussion.
Practitioners could consider supporting learners in creating a slide show or
Clicker 5 talking book from their photographs, including naming and
describing the function of the shapes. For example:
‘We saw many rectangular doors. A rectangle is a good shape for a door
because it does not take up too much space and peo ple can fit through it
easily.’
‘A sphere is a good shape for a ball because it rolls in any direction. ’
There are also examples of shapes used in everyday life at
http://www.bbc.co.uk/learningzone/clips/.
These video clips may give practitioners ideas for further exploration,
including making 3D objects from 2D shapes (nets), investigating which
shapes are best for tiling and thinking about the function and purpose of 3D
objects in the world around us.
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Patterns and number relationships
Ideas for exploring simple number patterns have been presented
in Chapter 1. Practitioners can develop learning by supporting
learners in identifying the repeat number pattern in a sequence of numbers.
The calculator repeat function can be used to confirm pat terns and continue
sequences.
Practitioners may start by exploring shape patterns by supporting learners in
identifying examples both in nature and in man -made structures and objects.
Books, photographs and repeat patterned wallpaper and fabric can be us ed for
learners to get some ideas. Practitioners should explore the shapes in the
patterns and how shapes fit together.
Relevant video clips can be found on www.bbc.co.uk/learningzone/clips/.
These allow for discussion and further exploration of ideas.
One suggestion may be for learners to do a mini project on patterns in the
world around us. Learners can be given a topic, for example snowflakes,
trees, shells, ancient buildings, wallpaper, fabric patterns, etc, and can then
put these into a slideshow to share with others. Practitioners may want to
work with the art department in developing opportunities for learners to print
repeat pattern wallpaper or fabric.
It is important to allow for the option of group work and give as much
support as is necessary so that all learners are able to participate.
Another possibility is to work with the art department in exploring the
Fibonacci code or golden section sequence. This number sequence repeatedly
appears in nature. Practitioners can create a variety of learning experiences
based on this number series so that all learners can access learning at an
appropriate level, given the required support.
More information on the golden section can be found at
www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci.
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