Length, perimeter and circumference | Stage 4 | Mathematics
Summary
Duration
Substrands: S3 Length (review), S4 Length
Term 3
2 weeks (5 lessons)
Unit overview
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Outcomes
Assessment overview
Mathematics K­10
MA41WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols
● MA42WM applies appropriate mathematical techniques to solve problems
● MA39MG selects and uses the appropriate unit and device to measure
lengths and distances, calculates perimeters, and converts between units
of length
● MA412MG calculates the perimeters of plane shapes and the
circumferences of circles
Content
Teaching, learning and assessment
Resources
Board of Studies NSW – Program Builder – pb.bos.nsw.edu.au
Program Builder contains NSW syllabus content prepared by the Board of Studies NSW for and on behalf of the State of New South Wales which is protected by Crown copyright.
1
Stage 3 ­ Length 2
Students:
This is primarily a review of Stage 3 content.
Convert between common metric units of length
(ACMMG136)
■ convert between metres and kilometres
■ convert between millimetres, centimetres
and metres to compare lengths and
distances
Have groups of students measure the same
objects’ dimensions using different units, then
compare as a class.
● explain and use the relationship between
the size of a unit and the number of units
needed to assist in determining
whether multiplication or division is
required when converting between units,
eg 'More metres than kilometres will be
needed to measure the same distance,
and so to convert from kilometres to
metres, I need to multiply'
(Communicating, Reasoning) Stage 4 ­ Length
Students:
Find perimeters of parallelograms,
trapeziums, rhombuses and kites (ACMMG196)
■ find the perimeters of a range of plane
shapes, including parallelograms,
trapeziums, rhombuses, kites and simple
composite figures
● compare perimeters of rectangles with
the same area (Problem Solving) ■ solve problems involving the perimeters of
plane shapes, eg find the dimensions of a
Practical: use centicubes (or similar), a specified
number of blocks represents a fixed area.
GeoGebra: students can drag rectangles to
change dimensions, they will need to recalculate
the area each time. Excel: enter a fixed area in
one column, then choose one side of the
rectangle to increase and use a formula to
Board of Studies NSW – Program Builder – pb.bos.nsw.edu.au
Program Builder contains NSW syllabus content prepared by the Board of Studies NSW for and on behalf of the State of New South Wales which is protected by Crown copyright.
2
rectangle, given its perimeter and the length
of one side calculate the remaining side.
Stage 4 ­ Length
Investigate the concept of irrational numbers,
including (ACMNA186)
■ demonstrate by practical means that
the ratio of the circumference to
the diameter of a circle is constant,
eg measure and compare the diameters
and circumferences of various cylinders or
use dynamic geometry software to measure
circumferences and diameters Using Excel to collect and evaluate the data, get
students to measure the “circumference” and
“diameter” of a variety of cylinders. Students
should create a formula for dividing the
“circumference” by the “diameter” in the top row
and autofill for all other rows.
Alternatively, for homework, ahead of time, get
students to each measure three different
cylinders (circumference and diameter) at home
and fill their results in to a GoogleDocs
spreadsheet. Results can then be analysed in
class on the whiteboard.
Google Docs
Insert ref to a sample spreadsheet.
■ define the number as the ratio of the
circumference to the diameter of any circle
● compare the various approximations for
used throughout the ages and
investigate the concept of irrational
numbers (Communicating) is used to
represent a constant numerical value
(Communicating)
Investigation using Google search or other, to see
what values/approximations for π students can
discover.
● recognise that the symbol Discussion that although irrational, this does not
mean that π is not constant.
Stage 4 ­ Length
Investigate the relationship between features of
circles, such as the circumference, radius and
diameter; use formulas to solve problems involving
circumference (ACMMG197)
Board of Studies NSW – Program Builder – pb.bos.nsw.edu.au
Program Builder contains NSW syllabus content prepared by the Board of Studies NSW for and on behalf of the State of New South Wales which is protected by Crown copyright.
3
■ identify and name parts of a circle and
related lines, including arc, tangent, chord,
sector and segment ■ develop and use the formulas to find the
circumferences of circles in terms of the
diameter d or radius r: Interactive whiteboard cloze passage exercise?
Return to GoogleDoc spreadsheet and class
discovery of π , try to encourage students to
develop a formula relating circumference and
diameter first, then extend to use radius.
● use mental strategies to estimate the
circumferences of circles, using an
approximate value of such as
3 (Problem Solving)
● find the diameter and/or radius of a circle,
given its circumference (Problem Solving)
■ find the perimeters of quadrants and
semicircles
■ find the perimeters of simple composite
figures consisting of two shapes, including
quadrants and semicircles
■ find arc lengths and the perimeters of
sectors
■ solve a variety of practical problems
involving circles and parts of circles, giving
an exact answer in terms of and an
approximate answer using a calculator's
approximation for Metalanguage
Evaluation
Board of Studies NSW – Program Builder – pb.bos.nsw.edu.au
Program Builder contains NSW syllabus content prepared by the Board of Studies NSW for and on behalf of the State of New South Wales which is protected by Crown copyright.
4
Perimeter, circumference, diameter, irrational number, quadrants, semicircles,
arc lengths, sectors, length/long, breadth/broad, width/wide, height/high.
Parts of circles (centre, radius, diameter, circumference, sector, semicircle and
quadrant) should be introduced in Stage 4.
Arc, tangent, chord and segment are introduced in Stage 4.
Board of Studies NSW – Program Builder – pb.bos.nsw.edu.au
Program Builder contains NSW syllabus content prepared by the Board of Studies NSW for and on behalf of the State of New South Wales which is protected by Crown copyright.
5
Syllabus images and equations
Board of Studies NSW – Program Builder – pb.bos.nsw.edu.au
Program Builder contains NSW syllabus content prepared by the Board of Studies NSW for and on behalf of the State of New South Wales which is protected by Crown copyright.
6
Board of Studies NSW – Program Builder – pb.bos.nsw.edu.au
Program Builder contains NSW syllabus content prepared by the Board of Studies NSW for and on behalf of the State of New South Wales which is protected by Crown copyright.
7