Top Banner
Integrated K12 STEM Education: Unpacking the S, T, E and M in a Handson Design Activity Dr Bernardo A. Leόn de la Barra and Miss Sarah Lyden (School of Engineering and ICT, http://www.utas.edu.au/stem) University of Tasmania Australia 24 May 2014
44

egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

May 08, 2018

Download

Documents

letuong
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Integrated K‐12 STEM Education: Unpacking 

the S, T, E and M in a Hands‐on Design Activity

Dr Bernardo A. Leόn de la Barra and Miss Sarah Lyden (School of Engineering and ICT, http://www.utas.edu.au/stem)

University of TasmaniaAustralia

24 May 2014

Page 2: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

In this workshop, participants will be taken through the process of unpacking thescientific, technological, engineering, and mathematical concepts which are relevant tothe design and construction of a simple terrestrial vehicle built using low‐cost materials.

Ways on how to address the integration of trans‐disciplinary knowledge in the areas ofScience, Mathematics and Engineering in the context of this design task will beexplored. Participants will be able to identify the benefits of implementing this sort ofintegration in their own classroom settings.

The presentation will be pitched at the middle school grade levels (5 to 8) butsimplifications for earlier grades and extensions for later grades may also be outlined,respectively.

Page 3: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

STEM Integration in K‐12 Education: Key Contributions Come from the 

USA

Page 4: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

STEM Integration in K‐12 Education Video (3.5 min), March 2014

https://www.youtube.com/watch?v=AlPJ48simtE&feature=player_embedded

STEM Integration in K‐12 Education Report, March 2014

http://www.nap.edu/catalog.php?record_id=18612

Page 5: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Engineering Design in the USA’s Next Generation Science 

Standards

Page 6: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

The NGSS represent a commitment to integrate engineering design into the structure ofscience education by raising engineering design to the same level as scientific inquiry whenteaching science disciplines at all levels, from kindergarten to grade 12. There are bothpractical and inspirational reasons for including engineering design as an essential element ofscience education

It is anticipated that the insights gained and interests provoked from studying and engaging inthe practices of science and engineering during their K‐12 schooling should help students seehow science and engineering are instrumental in addressing major challenges that confrontsociety today, such as generating sufficient energy, preventing and treating diseases,maintaining supplies of clean water and food, and solving the problems of globalenvironmental change

Engineering Design in the Next Generation Science Standards (NGSS): Appendix I

http://www.nextgenscience.org/next‐generation‐science‐standards

Page 7: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Engineering Design in the Next Generation Science Standards (NGSS): Appendix I

Providing students a foundation in engineering design allows them to better engage in andaspire to solve the major societal and environmental challenges they will face in the decadesahead

In the K–12 context, “science” is generally taken to mean the traditional natural sciences:physics, chemistry, biology, and (more recently) earth, space, and environmental sciences

We use the term “engineering” in a very broad sense to mean any engagement in a systematicpractice of design to achieve solutions to particular human problems

Likewise, we broadly use the term “technology” to include all types of human‐made systemsand processes—not in the limited sense often used in schools that equates technology withmodern computational and communications devices. Technologies result when engineersapply their understanding of the natural world and of human behaviour to design ways tosatisfy human needs and wants

http://www.nextgenscience.org/next‐generation‐science‐standards

Page 8: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Interdependence of Science, Engineering and Technology Video [5.5 min](as explained by Paul Andersen, High School Science Teacher, Bozeman, USA)

https://www.youtube.com/watch?v=Be3G0IHO_4Y&list=PLllVwaZQkS2rtZG_L7ho89oFsaYL3kUWq

Page 9: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

The Engineering Design Process: 

NASA and Museum of Science (Boston, USA)

Page 10: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 11: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Engineering design process PD video series and educator guides http://www.nasa.gov/audience/foreducators/best/edp.html

Page 12: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

An Integrated STEM Perspective on a Hands‐On Car Crashes Activity

Page 13: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

“Understanding Car Crashes: It’s Basic Physics” Video [22 min], by Dr Griffith Jones

https://www.youtube.com/watch?v=yUpiV2I_IRI

“Understanding Car Crashes: When Physics Meets Biology” Video [24 min], by Dr Griffith Jones

https://www.youtube.com/watch?v=hi2FEyV2Z2E

Page 14: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

http://education.ufl.edu/gjones/files/2013/04/teachers_guidePhysics.pdf

http://education.ufl.edu/gjones/

More Teaching Resources from Dr Griffith Jones’ Homepage at the College of Education, University of Florida

http://education.ufl.edu/gjones/files/2012/09/teachers_guideBioPhysics.pdf

“Understanding Car Crashes: When Physics Meets Biology” Teacher’s guide for grades 9‐12

“Understanding Car Crashes: It’s Basic Physics” Teacher’s guide for grades 9‐12

NSTA’s The Science Teacher, January 2013, pp. 32‐36

Page 15: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

http://www.utas.edu.au/__data/assets/pdf_file/0020/358310/stem_program_links_with_australian_curriculum_04_feb_2013.pdf

The hands‐on car crashes activity that will be presented in this workshop has been linked to the Australian Curriculum: Mathematics and Science (version 4.0). Full mapping details are 

available online in the following link

Page 16: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Typical Low‐Cost Materials Used in a 

Hands‐On Car Crashes Activity

Page 17: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 18: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Building and Testing Egg Crash 

Cars

Page 19: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 20: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 21: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

· Δ

12

2

Acceleration

Energy

Force

Friction

Gravity

Impulse

Inertia

Mass

Newton’s laws

Speed

Weight 

Key Science Concepts

Page 22: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Angles (in a triangle)

Average

Cosine

Distance

Graph

Hypotenuse

Inclination

Measurement

Outliers

Right angle triangles

Key Mathematics ConceptsParallel and perpendicular 

(force) components

Protractor

Pythagoras theorem

Sine

Slope

Speed

Stopwatch

Tangent

Vectors

Weight

Page 23: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Connections with Vehicle Safety Engineering Research

Page 24: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

http://www.physics.hku.hk/~phys0607/lectures/chap04.html

Safety Features in Modern Cars

Page 25: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Safety Cage

http://www.shattuckauto.com/Oakland‐Berkeley‐auto‐body‐blog/wp‐content/uploads/2012/10/Auto‐safety‐cage.jpg

Page 26: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Different Outside Views of a Crash Car Prepared by a 

Teacher

Page 27: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 28: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Different Inside Views of a Crash Car Prepared by a 

Teacher

Page 29: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 30: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Different Views of a Crash Car Built by 

Middle School Students

Page 31: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 32: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...
Page 33: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

Thank you and Safe Driving!

Page 34: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

1

Integrated K-12 STEM Education: Unpacking

the S, T, E and M in a Hands-on Design

Activity

Worksheets and supporting materials

Dr Bernardo A. Leόn de la Barra and Miss Sarah Lyden (School of Engineering and ICT,

http://www.utas.edu.au/stem)

University of Tasmania

Australia

24 May 2014

Page 35: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

2

Car Design:

Sketch car design below

Brainstorm:

Links with the mathematics curriculum?

Page 36: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

3

Egg-crash cars lesson plan (as used by the School of Engineering and ICT STEM Education and

Outreach Team)

TARGET GRADE LEVEL: 4 – 8 To cater for different age groups customise the theoretical focus.

KEY CONCEPTS: - Forces

- Newton’s Laws

- Engineering Design Process

LINKS TO AUSTRALIAN SCIENCE CURRICULUM: Foundation – (Physical Sciences) The way objects move depends on a variety of factors, including

their size and shape

Year 2 - (Physical Sciences) A push or a pull affects how an object moves or changes shape

Year 4 - (Physical Sciences) Forces can be exerted by one object on another through direct contact or

from a distance.

Year 7 - (Physical Sciences) Change to an object's motion is caused by unbalanced forces acting on

the object; Earth's gravity pulls objects towards the centre of the Earth

EQUIPMENT REQUIRED: - Crash Car Ramps & Brackets

- Crash Car Materials

- Eggs (Soft & Hard boiled)

- Balloon Car Materials for building a car/(egg enclosure)

- Example cars and Parachutes

- A big brick or something for the cars to crash into

- Stopwatch

- Glue guns

PREPARATION:

PRE-SESSION PREPARATION:

- Copy the chassis templates

- Ensure sufficient plastic wheels and axles are available

Page 37: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

4

SETUP AND ROOM ORIENTATION:

Get track set up off to the side where it won’t be in the way. Have example cars & parachutes ready

to show and all relevant car building equipment arranged on the desk at the front of the room. Setup

glue guns at the back of the room.

LESSON PLAN:

INTRODUCTION:

Ask the students what they know about forces. Put up the ideas they present on the whiteboard

and retain until the end of the session. Encourage students to present ideas and record all ideas on

the board.

A force is a push or pull on an object.

Rub your hands together. Do they get warm? Yes! This is because of the friction force.

Ask the students if they can think of any forces, in particular

o Pressure

o Gravity

o Friction

Pressure force – like a balloon – each side of the balloon is pushing in on the air inside the

balloon and forcing it out creating pressure forces.

Friction force – heat produced by two surfaces rubbing on each other. Friction turns kinetic

energy into heat energy.

Gravity force – the force of the earth pulling you in towards the centre.

Ask students what they know about engineering and engineers. Based upon their responses provide

a brief introduction to engineering. Explain that engineers design things to make our lives easier.

Explain the types of engineering that we are involved in. Tell the students that today they are going

to be engineers.

SESSION ACTIVITIES:

PART 1: EGG CRASH CARS

BUILDING THE CAR:

1. Tell the students that today we are going to make a vehicle that will be traveling down a

steep incline. (Indicate the ramp at the back of the room) Their job as engineers today is to

design and construct a car that will protect an egg when travelling down the incline.

2. Ask students to identify some of the safety features in cars that save people in crashes –

such as seatbelts, airbags, crumple zones, etc. (We will be looking at these things in more

detail as the session progresses)

Page 38: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

5

3. Provide students with the simple templates and get them to get out and construct their car.

If they complete this quickly encourage them to decorate as they go. Also provide them

with 2 green axles and four white wheels to attach to their car at this stage.

THE ENGINEERING DESIGN PROCESS:

1. Explain to students that what we will be doing today will be using some of the steps of the

engineering design process.

2. Draw the engineering design process up on the board and explain to students that we have

identified the problem – protecting the egg and we now need to brainstorm, design, build

and test our solutions.

THE DESIGN CHALLENGE:

1. Tell students that the rules of the design challenge today are:

a. They can use any material that they can find/we can provide them with

b. Wheels must roll, and not slide down the track

c. We need to be able to easily check the egg at the end of the track and remove it

d. Once the car starts down the track you can’t touch or correct its path

2. Ask students to design what they want to do with the car on a piece of paper first then

collect equipment to complete this. Give students approximately 30 – 40 minutes to

complete this task.

TESTING THE CARS:

1. Gather all students around the testing ramp. Test each car going down the ramp. Only

place an egg in each car just before it is going down the ramp and instructors are the only

people to handle the eggs.

2. Record how many eggs break.

Page 39: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

6

UNDERSTANDING THE MOVEMENT OF THE CARS:

1. Get students to return to the tables and discuss some of the things that worked well and

why. Also get them to identify the forces acting on the car.

Important concepts to convey:

− Concept of force due to gravity and how it generates acceleration down an incline.

The driving force comes from gravity.

− Concept of inertia: an object’s ability to resist a change in linear or angular velocity.

This is the reason we need to wear seatbelts!

2. Newton’s laws: Who has heard of a very famous person called Sir Isaac Newton? He has

three laws which are known all around the world.

• 1) Nothing will happen to an object until a force is acting on it.

• 2) F = ma: [we can talk about this in respect to gravity and propulsion]

• 3) every action has an equal and opposite reaction

3. For older students and more advanced groups consider the force diagram below:

4. Ask the students if they know what energy is.

Energy (comes from Greek) is a physical quantity that describes the amount of work that can be

performed by a force. For instance, if you lift something up then you are doing work, so the object

will gain energy. This is called potential energy. When something is moving it also has energy. This

is called kinetic energy. Other forms of energy are things like sound, heat, etc. Remind them that

energy is only ever converted it is not created or destroyed.

Page 40: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

7

5. Ask the students what energy changes they think are taking place as the car travels down

the ramp. Draw a picture up on the board and indicate energy changes as the car moves

down.

Basically, the energy change is from potential to kinetic to sound and heat (when the car stops).

Include more detail for older students.

IMPROVING THE CARS:

1. Return to the engineering design process and explain to students that we are now up to the

redesign stage. Engineers may redesign a solution many times until they find the best

solution.

2. Explain that this time we will have a steeper incline and go from a higher point up the ramp,

so everyone will probably need to make some modifications to their car to protect the egg.

Also as an added challenge say that if none of the eggs break going down the track then we

will run an egg down by itself so that they can see what happens.

3. Give students 10 – 20 minutes to redesign.

TESTING THE CARS AGAIN:

1. Once again gather all students around the testing ramp. Test each car going down the ramp.

Only place an egg in each car just before it is going down the ramp and instructors are the

only people to handle the eggs.

2. Record how many eggs break. If no eggs break put a single egg down the ramp by itself to

show the students what happens.

CONCLUDE ACTIVITY:

1. Return to desks and get students to explain what was happening with the cars and the ideas

that worked well. Get them to explain to us what forces are and what energy changes were

taking place. Ask if they have any further questions about their cars, forces, inertia, energy,

etc.

Page 41: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

8

Links with the Australian Mathematics Curriculum:

Foundation:

Measurement and Geometry

Location and Transformation

o Describe Position and Movement

Year 1:

Measurement and Geometry

Using units of measurement:

o Measure and compare the lengths and capacities of pairs of objects using uniform

information units

Shape:

o Recognise and classify familiar two-dimensional shapes and three-dimensional

objects using obvious features

Year 2:

Measurement and Geometry

Using units of measurement:

o Compare and order several shapes and objects based on length, area, volume and

capacity using appropriate uniform informal units

o Compare masses of objects using balance scales

Shape:

o Describe and draw two-dimensional shapes, with and without digital technologies

o Describe the features of three-dimensional objects

Statistics and Probability

Data representation and interpretation:

o Identify a question of interest based on one categorical variable. Gather data

relevant to the question

o Collect, check and classify data

o Create displays of data using lists, table and picture graphs and interpret them

Year 3:

Measurement and Geometry

Using units of Measurement:

o Measure, order and compare objects using familiar metric units of length, mass and

capacity

Shape:

o Make models of three-dimensional objects and describe key features

Location and Transformation:

o Identify symmetry in the environment

Geometric Reasoning:

o Identify angles as measures of turn and compare angle sizes in everyday situations

Page 42: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

9

Statistics and Probability

Data Representation and interpretation:

o Identify questions or issues for categorical variables. Identify data sources and plan

methods of data collection and recording

o Collect data, organise into categories and create displays using lists, tables, picture

graphs and simple column graphs, with and without the use of digital technologies

o Interpret and compare data displays

Year 4:

Measurement and Geometry

Using units of Measurement:

o Use scaled instruments to measure and compare lengths, masses, capacities and

temperatures

o Compare objects using familiar metric units of area and volume

Shape:

o Compare the areas of regular and irregular shapes by informal means

Geometric reasoning:

o Compare angles and classify them as equal to, greater than or less than a right angle

Statistics and Probability

Data representation and interpretation:

o Select and trial methods for data collection, including survey questions and recording

sheets

o Construct suitable data displays with and without the use of digital technologies,

from given or collected data. Include tables, column graphs and picture graphs

where one picture can represent many data values

o Evaluate the effectiveness of different displays in illustrating data features including

variability

Year 5:

Measurement and Geometry

Using units of Measurement:

o Choose appropriate units of measurement for length, area, volume, capacity and

mass

o Calculate the perimeter and area of rectangles using familiar metric units

Shape:

o Connect three-dimensional objects with their nets and other two-dimensional

representations

Geometric Reasoning:

o Estimate, measure and compare angles using degrees. Construct angles using a

protractor

Statistics and Probability

Data representation and interpretation:

o Pose questions and collect categorical or numerical data by observation or survey

o Construct displays, including column graphs, dot plots and tables, appropriate for

data type, with and without the use of digital technologies

Page 43: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

10

o Describe and interpret different data sets in context

Year 6:

Measurement and Geometry

Using units of Measurement:

o Solve problems involving the comparison of lengths and areas using appropriate units

Geometric Reasoning:

o Investigate, with and without digital technologies, angles on a straight line, angles at

a point and vertically opposite angles. Use results to find unknown angles

Statistics and Probability

Data representation and interpretation:

o Interpret and compare a range of data displays, including side-by-side column graphs

for two categorical variables

Year 7:

Measurement and Geometry

Shape:

o Draw different views of prisms and solids formed from combination of prisms

Statistics and Probability

Data representation and interpretation:

o Calculate mean, median, mode and range for sets of data. Interpret these statistics in

the context of data.

o Describe and interpret data displays using median, mean and range

Year 8:

Statistics and Probability

Data representation and interpretation:

o Investigate techniques for collecting data, including census, sampling and observation

o Investigate the effect of individual data values, including outliers, on the mean and

median

Year 9:

Number and Algebra

Linear and non-linear relationships:

o Graph simple non-linear relations with and without the use of digital technologies

and solve simple related problems

Measurement and Geometry

Pythagoras and trigonometry:

o Investigate Pythagoras’ theorem and its application to solving simple problems

involving right angled triangles

o Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a

given angle in right-angled triangles

o Apply trigonometry to solve right-angled triangle problems

Page 44: egg crashes ppt latest - University of Tasmania, Australia | …€¦ ·  · 2015-01-05simplifications for earlier grades and extensions for later grades may also be outlined, ...

11

Year 10:

Number and Algebra

Linear and non-linear relationships:

o Solve problems involving linear equations, including those derived from formulas

o Explore the connection between algebraic and graphical representations of relations

such as simple quadratics, circles and exponentials using digital technology as

appropriate

Measurement and Geometry

Pythagoras and trigonometry:

o Solve right-angled triangle problems including those involving direction and angles of

elevation and depression

Statistics and Probability

Data representation and interpretation

o Use scatter plots to investigate and comment on relationships between two

numerical variables