Measurement and Geometry - General Mathematics Course

This unit covers measurement and geometry topics in Mathematics Standard Stage 4, Year 8. It includes key concepts, syllabus outcomes, teaching and learning strategies, and assessment tasks.

Running head: MEASUREMENT AND GEOMETRY
MEASUREMENT AND GEOMETRY
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MEASUREMENT AND GEOMETRY 2
UNIT OUTLINE
Subject: General Mathematics Course: Mathematics Standard Stage 4, Year 8 Number of Weeks: 4,
Unit title: Measurement and Geometry
Key Concepts/ Big Ideas The importance of this learning
 To identify any areas of stage 3 content that may
require to be reviewed so as to meet the
students’ needs.
 To comprehensively cover all mathematical
areas and solve problems related to measurement
and geometry topic
 Helps students develop the ability to recogniz
estimate measures and attributes of different
 Develop the ability to explore various concep
relationships
 Solve measurement and geometry related pro
mathematical strategies and formulas (NSW
(n.d.)a)
Unit context within Scope and Sequence/Purpose Syllabus Outcomes
The whole unit including working mathematically
(WM) – communicating, reasoning and problem
solving) and measurement and geometry (MG) –
length, area, volume, time, right-angled triangles,
properties of geometrical figures and angle
relationships (NSW Education Standards Authority,
(n.d.)b).
MA4-1WM: communicates, connects and interpre
ideas using suitable terminology, symbols and dia
Authority, (n.d.)c)
MA4-2WM: solves mathematical problems by app
techniques
MA4-3WM: uses reasoning to recognize and expl
relationships
MA4-12MG: uses appropriate methods to calculat
perimeters of plane shapes
MA4-13MG: uses appropriate formulas to calcula
quadrilaterals, and converts area between units
MA4-14MG: uses appropriate formulas to calcula
prisms, and converts volume between units
MA4-15MG: performs time calculations involving
zones properly
MA4-16MG: uses Pythagoras’ theorem for calcula
triangle, and also solves other related problems
MA4-17MG: categorizes, defines and uses proper
and determines congruent triangles so as to determ
lengths
MALS-20MG: recognizes time in contexts that ar
MALS-21MG: recognizes time and relates it in di
MALS-22MG: reads time and interprets it in diffe
MALS-23MG: measures and calculates time and d
MALS-24MG: organizes how to spend personal ti
scheduled activities
MALS-25MG: measures and estimates in everyda
MALS-26MG: identifies and uses units for measu
MALS-28MG: chooses and uses different units fo
volume and capacity of different shapes
MALS-29MG: uses formal units for calculating an
MALS-30MG: identifies, matches and categorizes
MALS-31MG: recognizes features of 2D and/or 3

MEASUREMENT AND GEOMETRY 3
different contexts.
Literacy Focus Numeracy Focus ICT Focus D
 Definition and
understanding of terms
such as triangles,
circles, polygons,
perimeter,
circumference, area,
volume, capacity,
angles and time zone
 Formulas for
calculating
perimeter,
circumference,
area, volume
and angles
 Conversion
between units
of length, area
and volume
 Estimating
time needed
for typical
day-to-day
personal
activities
 Using Excel for calculating area,
perimeter, circumference and
volume of different geometrical
shapes and/or objects
 Using online tools for calculating
area, perimeter, circumference
and volume of different
geometrical shapes and/or objects
 Preparing a daily personal
activities schedule
 YouTube clip
 Grad
 Indi
 Grou
Lesson Syllabus Content Teaching and Learning
Strategies including
assessment for learning.
Resources
Lesson
1
Evaluation and
measurement of length
 Pre-test including
quoting estimated
length of classroom
wall, height of shortest
and tallest student in
class, size of book, etc.
 Recap of what the
students learned in
Stage 3, particularly
about dimensions.
 Discussion with
students about the term
length.
 Explain how length is
used in everyday
activities and the
importance of
measuring length
 Give examples of
length measurements,
including perimeters of
 Meter rule and meter ruler
 Tape measure
 Standard lengths of class items
 Worksheets
 Exit slip
 YouTube clip https://www.youtube.com

MEASUREMENT AND GEOMETRY 4
different geometrical
shapes
 Convert length
measurements from
one unit to another
 Conduct group activity
for measuring length of
different items in and
outside the classroom,
including length of
linear, circular, regular
and irregular objects
 Each group makes
presentation of their
findings.
 Allowing students to
ask questions from
their groups.
 Assessment task exam
 Self-reflection by use
of exit slip.
Lesson
2
Measurement and
calculation of area
 Discuss with
students about the
terms such as area
and Pi (π).
 Discuss different
units of area and
how to convert
between area units
 Develop and/or
derive formulas for
calculating area of
different
geometrical shapes
like square,
rectangle, triangle,
circle, cone,
trapezium,
parallelogram,
rhombus, kite, etc.
 Demonstrate how
to calculate area in
Excel
 Compare and
differentiate
between perimeter
 Worksheets
 Homework sheet
 Excel
 Calculators
 Pattern shapes
 YouTube clip https://www.youtube.com

MEASUREMENT AND GEOMETRY 5
and area
 Worksheet on
calculation of area.
 Convert area
measurements and
calculations from
one unit to another
 Assessment task
exam
 Homework sheet.
 Self-reflection.
Lesson
3
Measurement and
calculation of volume
 Discuss with
students about the
term volume.
 Discuss different
units of volume and
how to convert
between volume
units
 Develop and/or
derive formulas for
calculating volume
of different
geometrical shapes
like prisms, cones
and other solids
 Discuss the
importance of
uniform and non-
uniform cross-
sections when
calculating volume.
 Demonstrate how
to calculate volume
in Excel
 Compare and
differentiate
between area and
volume
 Worksheet on
calculation of
volume.
 Convert volume
measurements and
calculations from
one unit to another
 Calculators
 Worksheets
 Homework sheet
 Excel
 Exit slip
 Kahoot quiz
 Geometry pad

MEASUREMENT AND GEOMETRY 6
 Assessment task
exam
 Homework sheet.
 Reminder: exam to
be done in the net
lesson
 Self-reflection
Lesson
4
 In class exam
 Measuring and
calculating time,
area and
volume/capacity
 Provide exams
instructions
 Supervise the students
as they take the exam
 Collect exam sheets
after 20 minutes
 Recap about
measurement of length,
measurement and
calculation of area
and/or volume
 Explain how to
measure and/or
calculate length, area
and volume using
appropriate
measurement devices
and formulas
 Explain the relationship
between length, area
and volume
 Help students having
any query or difficulty
performing the
aforementioned
calculations
 Discuss answers to the
exam with the students
 Self-reflection
 Exam sheets
 Worksheets
 Calculators
 Excel
 Exit slip
 Pattern blocks
 Measurement materials
Lesson
5
Calculating time in 12-
hour and 24-hour time
 Adding and
subtracting time
manually or mentally
 Adding and subtracting
time using calculators
 Rounding time answers
to nearest hour, minute
or second
 Worksheets
 Calculators
 Desmos
 FluidMath

MEASUREMENT AND GEOMETRY 7
 Do time calculations
given in mixed units –
years, months, days,
hours, minutes and
seconds
 Activity: worksheet on
time calculations
 Guide students who
seem not to understand
how to calculate time
 Assessment task exam
 Reflection of students’
learning.
Lesson
6
International time zones  Explain the meaning of
international time zone
and how it works
 Give examples of
calculating time of
major cities across the
world
 Group activity:
spreadsheet based.
 Form groups of 4 and
explain the activity to
students
 Answer any queries
raised by the groups
 Give feedback to each
group
 Evaluate contribution
of every student in each
group.
 Group presentation.
 Provide helpful
feedback to every
group.
 Assessment task exam
 Reminder: exam to be
done in the next lesson
 Self-reflection.
 Spreadsheet activity
 Calculators
 Nearpod
 Worksheets
 Ext slip
Lesson
7
 In class exam
 Calculating time
in 12-hour and
24-hour notations
and calculating
 Provide exams
instructions
 Supervise the students
as they take the exam
 Collect exam sheets
 Exam sheets
 Calculators
 5 questions
 Exit slip
 Worksheets

MEASUREMENT AND GEOMETRY 8
time of major
global cities
(international
time zone
calculations)
after 15 minutes
 Recap about adding
and subtracting time in
different notations (12-
hour and 24-hour
notations) and
international time
zones
 Explain how to add or
subtract time in both
12-hour notation and
24-hour
 Help students having
any query or difficulty
performing the
aforementioned
calculations
 Discuss answers to the
exam with the students
 Self-reflection
Lesson
8
Classifying triangles  Draw different types of
triangles on the board,
including equilateral,
isosceles, scalene,
acute-angled, obtuse-
angled and right-angled
triangles
 Explaining the
properties of each of
the triangles drawn
 Explaining how to
classify triangles by the
length of their sides or
their angles
 Activity: draw different
types of triangles on
board and ask students
to classify them and
give reasons for their
answers
 Assessment task exam
 Whiteboards
 Calculators
 Worksheets
 YouTube clip https://www.youtube.com
Lesson
9
Angle sum of a triangle  Show that angles of a
triangle add up to 180 °
 Show that angle of a
straight line add up to
180 °
 Calculators
 iPad Apps
 Homework sheets
 Whiteboards

MEASUREMENT AND GEOMETRY 9
 Show that alternate
angles are equal
 Give students some
problems by drawing
triangles on the board
with missing angles for
them to calculate. Help
those experiencing
problems
 Assessment task exam
 Geogebra
 Worksheets
Lesson
10
Parallel and transverse
lines
 Explain and
demonstrate parallel
lines
 Explain and
demonstrate transverse
lines
 Show how
corresponding angles
are equal
 Show how alternate
interior angles are
equal
 Show how alternate
exterior angles are
equal
 Show angle
relationship for
different pairs of
angles, including
vertical angles, linear
pair, corresponding
angles, same side
interior and exterior
angles, and alternate
interior and exterior
angles
 Assessment task exam
 Worksheets
 Tablets
 Whiteboards
 Flipgrid
Lesson
11
Measuring and naming
angles in parallel and
transverse lines
 Quick recap of what
was learnt in the
previous lessons
 Teacher hands out
worksheets on the
board
 Students copy the
diagrams drawn on
 Worksheets
 5 questions
 Calculators
 Whiteboard
 Geogebra
 Homework sheets

MEASUREMENT AND GEOMETRY 10
board in their books
then names relevant
geometric properties of
the diagrams and use
them to calculate
missing angles
 Handing over the books
with answered
questions
 Assessment task exam
Lesson
12
Properties of
quadrilaterals 1
 Explain how ESiM
program works and it
will be used in the
lesson
 Discuss properties of
rectangles using texts
and figures: show
YouTube clip
 Discuss properties of
parallelograms
 Calculators
 Laminated worksheets
 iPad apps
 Website
https://www.mathplanet.com/education/
of-parallelograms
 ESiM resources
 YouTube clip https://www.youtube.com
Lesson
13
Properties of
quadrilaterals 2
 Discuss properties of
squares
 Discuss properties of
rhombuses
 Discuss properties of
kites and trapeziums
 Calculators
 Laminated worksheets
 iPad apps
 Clickers
 Printable stuff
 Website https://www.dummies.com/edu
of-rhombuses-rectangles-and-squares/
Lesson
14
 In class exam
 Classify triangles,
determine angles of
triangles, calculate
and identify
relationships of
angles in transverse
and parallel lines,
and discuss
properties of
quadrilaterals
 Provide exams
instructions
 Supervise the students
as they take the exam
 Collect exam sheets
after 30 minutes
 Recap about types of
triangles, calculations
and relationships of
angles in a triangle,
calculations and
relationships of angles
in transverse and
parallel lines, and
properties of
quadrilaterals
 Explain how to classify
angles, calculate
 Exam sheets
 Calculators
 Exit slip
 Worksheets

MEASUREMENT AND GEOMETRY 11
missing angles or side
lengths of triangles,
establish the
relationship between
angles in a triangle or
transverse and parallel
lines and recognizing
different quadrilaterals
 Help students having
any query or difficulty
performing the
aforementioned
calculations
 Discuss answers to the
exam with the students
 Self-reflection
Lesson
15
 Line of symmetries  Definition of line of
symmetry
 How to determine
if a shape has a line
of symmetry: show
YouTube clip
 Apply folding test
to demonstrate line
of symmetry of
different shapes or
objects, including
equilateral triangle,
isosceles triangle,
scalene triangle,
quadrilaterals
(square, rectangle,
rhombus, kite and
irregular
quadrilaterals).
 Group activity
 Explain the activity
and respond to any
queries raised by
the students.
 Allow each group
time to complete
the activity
 Each group
presents their
results
 A4 papers
 Worksheets
 Exit slip
 YouTube clip https://www.youtube.com

MEASUREMENT AND GEOMETRY 12
 Provide helpful
feedback to each
group.
 Self-reflection
Lesson
16
 Rotational symmetry  Definition of
rotational
symmetry
 How to determine
if a shape has a
rotational
symmetry: show
YouTube clip
 Use A4 paper to
demonstrate
rotational
symmetry of
different shapes or
objects, including
equilateral triangle,
isosceles triangle,
scalene triangle,
quadrilaterals
(square, rectangle,
rhombus, kite and
irregular
quadrilaterals).
 Establish the
relationship
between line of
symmetry and
rotational
symmetry (number
of rotations before
the shape returns to
its original
position).
 Group activity
 Explain the activity
and respond to any
queries raised by
the students.
 Allow each group
time to complete
the activity
 Each group
presents their
 A4 papers
 Worksheets
 Exit slip
 Google slides
 Homework sheets
 Interactive whiteboards

MEASUREMENT AND GEOMETRY 13
results
 Provide helpful
feedback to each
group.
 Self-reflection
Assessment Task Exam
Stage 4, Year 8
Lesson 7
Marks: 20
Time 15 minutes
Q1. Jane work up at 5:55 a.m. to go for jogging. She came back at 5 minutes to 7 o’clock. How
long was her jogging session? (Give your answer in 12-hour notation).
a. 1 hour 10 minutes
b. 1 hour 50 minutes
c. 50 minutes
d. 45 minutes
Q2. It took Tom 45 minutes to complete his homework. If he started at 3:30 p.m., at what time
did he finish the homework? (Give your answer in 24-hour notation)
a. 4:15 p.m.
b. 0414 hours
c. 16:15 p.m.
d. 1615 hours

MEASUREMENT AND GEOMETRY 14
Q3. A plane departed from an airport at 2310 hours Monday night. The journey took 8 hours.
When did it arrive the destination? (Give your answer in 12-hour notation).
a. 0710 hours Tuesday morning
b. 7:10 a.m. Wednesday morning
c. 7:10 a.m. Tuesday morning
d. 1910 hours Tuesday night
Q4. The current local time in City A is 8:30 p.m. What is the time in City B if its local time is 3
hours behind City A? (Give your answer in 24-hour notation).
Q5. A train left town A at 8:15 a.m. for town B. After travelling for 3 hours 45 minutes, it
developed a mechanical problem that took 30 minutes to fix. The train continued with the
journey for 6 hours nonstop. At what time did it reach town B?
ANSWERS WITH THE MARKING CRITERIA
Question 1, 2 and 3
Criteria Marks
Correct answer for question 1, 2 and 3 9 marks (3 marks each)
Question Answer
1 c
2 d
3 c
Question 4
Criteria Marks

MEASUREMENT AND GEOMETRY 15
Provide correct answer 3 marks
Provide wrong answer 0
Sample answer:
8:30 p.m. – 3 hours = 5:30 p.m.
Convert 5:30 p.m. to 24-hour notation by adding 12 hours = 5:30 + 12 = 1730 hours
Question 5
Criteria Marks
Provide correct answer 3 marks
Provide wrong answer 0
Sample answer:
8:15 a.m. + 3 hours 45 minutes = 12:00 pm
12:00 p.m. + 30 minutes = 12:30 p.m.
12:30 p.m. + 6 hours = 1830 hours (or 6:30 p.m.)
Justification
This unit outline, lesson plan and the associated assessments have prepared for the
subtopic measurement and geometry in the Mathematics section of the New South Wales
Mathematics Standard stage 4, year 8 syllabus. The unit outline has a total of 16 lessons of one
hour each. It ensures seamless integration of content that the students learnt previously and the
one they will be learning. This continuity helps students to apply the mathematics knowledge
and skills they acquired in previous units in this new stage of learning (Loosli, Buschkuehl,
Perrig, & Jaeggi, 2012); (St Clair-Thompson, Stevens, Hunt, & Bolder, 2010), because their

MEASUREMENT AND GEOMETRY 16
memory already has previous knowledge (Kroesbergen, van't Noordende, & Kolkman, 2014).
Adequate focus was also put on both literacy and numeracy knowledge and skills. Literacy
focuses on developing students’ knowledge, understanding and skills related to the topic and
enables them to engage and communicate the learnt ideas easily and confidently (Education
Review Office, 2012). Literary focus also aids in boosting the reasoning capacity of students
hence being able to solve more complex mathematical problems (Forster, 2009). Both literacy
and numeracy skills are essential for students to perform well in Mathematics and also in other
subjects (Office for Standards in Education, Children's Services and Skills, 2015).
I chose the topic of measurement and geometry because it is a fascinating topic
considering that it is applicable in everyday life. We make measurements of length, area, volume
and time every day. Different aspects of measurements and geometry are almost everywhere.
When you look around, you will see lines, shapes, angles, curves, line segments, etc. This
implies that principles of measurement and geometry are very essential in everyday life.
Additionally, the knowledge gained in this topic will be useful in tackling various mathematical
problems hence it is an essential background even for other topics to be learn in the stages and
years ahead.
The mode of teaching and learning has also significantly changed over the years and use
of information and communication technology (ICT) is very essential today (Montrieux,
Vanderlinde, Schellens, & De Marez, 2015). One of the major benefits of ICT is that it helps
students relate what they learn in class with real-life scenarios. ICT also makes both teaching and
learning to be more fun, (Cox, 2015), offers varied teaching and learning styles (Learning Portal,
2018), enhances knowledge retention, improves engagement and boosts collaboration between
students (Savvidis, 2016); (Nocar & Zdrahal, 2016). The various resources used ensure that

MEASUREMENT AND GEOMETRY 17
students understand the topics and also relate their applications in day-to-day real situations. The
main challenge faced when preparing this lesson plan was how sequence the lessons. However,
that was solved by following the sequence recommended in most teaching guidebooks.
Works Cited
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Benefits of Technology in the Classroom. Retrieved September 25, 2018, from
http://www.teachhub.com/benefits-technology-classroom
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Literacy and Mathematics in Years 9 and 10: Using achievement
Information to Promote Success. Wellington: Education Review Office.
Forster, M. (2009).
Literacy and Numeracy Diagnostic Tools: An Evaluation. Camberwell, Victoria:
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MEASUREMENT AND GEOMETRY 18
NSW Education Standards Authority. ((n.d.)b).
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geometry/
NSW Education Standards Authority. ((n.d.)c).
Stage 4 Outcomes. Retrieved September 25, 2018, from
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Key Stage 3: The Wasted Years?
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