The Foundations of
Measurement
Kaye Treacy
Awareness Test
• How many passes does the team in white make?
©Foundations of Measurement
Kaye Treacy Nov 2016
2
What measurement skills do adults need?
Australian Core Skills Framework Level 3:
Mathematical knowledge
and skills: measurement
and geometry
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©Foundations of Measurement
Kaye Treacy Nov 2016
Applies knowledge of properties of 2D and 3D shapes to describe and draw
everyday objects, including constructing common 3D shapes
Measures, estimates and calculates length, perimeter, mass,
capacity/volume, time, temperature and simple area (for
rectangular areas only, using A = L x W, or estimates area of a
non-rectangular shape by counting squares)
Identifies and estimates common angles, e.g. as a rotation with a full turn =
360° and recognition of right angles as 90°
Converts between routine metric units by applying
understanding of common prefixes, e.g. milli, centi or kilo
Uses distance, direction, coordinates, simple scales, labels, symbols and keys to
read and use everyday maps and plans
First Steps in Mathematics
Diagnostic Task
What is this students’
misconception?
©Foundations
4 of Measurement
Kaye Treacy Nov 2016
pp21-22
First Steps in Mathematics
Diagnostic Task
Out of 700 students:
Almost half of Year 5 students,
a third of Year 6 and
a quarter of Year 7 and 8 students
said the leaf was 7 cm long!
©Foundations of Measurement
Kaye Treacy Nov 2016
p136
5
Australian Curriculum
Using units of measurement
YEAR 6
• Connect decimal representations to the metric system (ACMMG135)
• Convert between common metric units of length, mass and capacity
(ACMMG136)
• Solve problems involving the comparison of lengths and areas using
appropriate units (ACMMG137)
YEAR 7
• Establish the formulas for areas of rectangles, triangles and
parallelograms, and use these in problem-solving (ACMMG159)
YEAR 8
• Choose appropriate units of measurement for area and volume and
convert from one unit to another (ACMMG195)
YEAR 9
• Calculate areas of composite shapes (ACMMG216)
©Foundations of Measurement
Kaye Treacy Nov 2016
Foundation Mathematics
Unit 1 page 214
©Foundations of Measurement
Kaye Treacy Nov 2016
Foundation
Mathematics Unit 1
Practice Exercise
©Foundations of Measurement
Kaye Treacy Nov 2016
Mathematics: Foundations Unit 1
Length Mass and Capacity
1.3.1 identify and discuss situations which involve using length, mass and capacity measures
1.3.2 determine whether an estimate or an accurate length, mass or capacity measurement is needed in everyday situations
1.3.3 choose appropriate measuring tools to solve everyday problems involving length, mass and capacity
1.3.4 use informal units of length, mass and capacity, (e.g. hand span, stride, cups) to estimate, measure and compare the size of
everyday things
1.3.5 develop and use a sense of size of commonly used standard length, mass and capacity units. e.g. 1 cm, 1 m, 500 ml, 1 L,
500 gm, 1 kg to estimate in familiar situations
1.3.6 understand standard units are divided into subunits and recall commonly used relationships such as, 1cm = 10 mm;
1m = 1000 mm; 1L = 1000 ml; 1kg = 1000 gm
1.3.7 choose
standard length,
or capacity calibrated
unit is appropriate forscales
everyday contexts
1.3.8
usewhich
a variety
ofmass
simple
to measure and
1.3.8 use a variety of simple calibrated scales to measure and compare length, mass and capacity to the nearest whole number.
compare
length,
mass
and
capacity
to
the
nearest
whole
number
1.3.9 add and subtract whole number length (including perimeter), mass and capacity measures, to solve everyday
measurement problems
1.3.10 determine whether an answer is reasonable by using estimation and the context of the problem
1.3.11 communicate solutions (oral and written) consistent with the language of the context
©Foundations of Measurement
Kaye Treacy Nov 2016
Kitchen Scales
How much does the coffee weigh?
What do the lines mean?
Which lines are numbered?
Which are un-numbered?
©Foundations of Measurement
Kaye Treacy Nov 2016
Kitchen Scales
What do the lines/dots mean on
these scales?
©Foundations of Measurement
Kaye Treacy Nov 2016
Understanding magnitude of units
Brainstorm other items that fit into the benchmark categories.
©Foundations of Measurement
Kaye Treacy Nov 2016
Metric Relationships
Diagnostic Task from:
Knowing What they Know
p 45-47
Sandra Year 9
What is this students misconception?
What does she need to learn?
©Foundations of Measurement
Kaye Treacy Nov 2016
Length, mass and capacity units
In a group of 3:
Write a list of all of the length, mass and capacity metric units that you know.
Order them from smallest to largest.
What is the relationship between units as you move from smallest to largest?
Draw a diagram to illustrate this relationship to students.
©Foundations of Measurement
Kaye Treacy Nov 2016
Length, mass and capacity units
What is the base metric unit for :
• length
• mass
• capacity
What is the standard metric unit for :
• length
• mass
• capacity
©Foundations of Measurement
Kaye Treacy Nov 2016
metre
gram
litre
metre
kilogram
litre
Foundation Mathematics Unit 2
Page 234
We can move in either direction from one unit to the next.
Moving from right to left, each place is ten times larger, or x 10.
Moving from left to right, each place is ten times smaller, or ÷ 10.
This connection to place value is helpful when converting from one unit to another.
To convert 1 metre into centimetres, break it into 10 equal sized pieces then break these
into 10 equal sized pieces to make centimetres.
• One metre is equal to 100 centimetres.
1
©Foundations
of
Measurement
• One centimetre is
of a metre.
Kaye Treacy Nov 2016
100
Foundation Mathematics
Unit 2 page 237
©Foundations of Measurement
Kaye Treacy Nov 2016
©Foundations of Measurement
Kaye Treacy Nov 2016
©Foundations of Measurement
Kaye Treacy Nov 2016
Mathematics: Foundations Unit 4
4.3 Application of the Mathematical thinking process
• Interpreting the task and key information
• Choosing the mathematics
• Using the mathematics
• Interpreting the results in relation to the context
• Communicating the solution
©Foundations of Measurement
Kaye Treacy Nov 2016
Foundation Mathematics Unit 4
Page 157
When solving everyday problems
involving measurement we work
through a decision making process
as outlined in the flow diagram.
Sometimes we work through the
thinking process in the order
shown.
Sometimes we need to jump a step
and come back to it later.
©Foundations of Measurement
Kaye Treacy Nov 2016
Use the mathematics to solve the problem
Interpret the task and key information
Interpret the results
Choose the mathematics
Choose the mathematics
Choose the mathematics
Choose the mathematics
©Foundations of Measurement
Kaye Treacy Nov 2016
Foundation Mathematics Unit 4
The degree of modelling and scaffolding will be dependent on students.
… the goal is for students to learn to independently apply the mathematical
thinking process.
©Foundations of Measurement
Kaye Treacy Nov 2016
Foundation Mathematics Books
The Foundation Maths books are designed to help students to learn to
become more numerate … to help older students to learn the mathematics
content they may have missed before.
… all students can learn mathematics provided they are supported to move
from practical examples which connect with what they currently know and
understand through to more abstract examples.
©Foundations of Measurement
Kaye Treacy Nov 2016
The Foundations of Measurement
[email protected]
treacymaths.com.au
©Foundations of Measurement
Kaye Treacy Nov 2016