Sample unit Mathematics Stage 5 - STEM Pathway: Unit 5

NSW Education Standards Authority – Sample unit Mathematics Stage 5 - STEM Pathway: Unit 5 From Here to There Page 1 of 19

Stage 5: Mathematics STEM From Here to There Unit 5 sample program

Overview Duration

In From Here to There students will recall, re-learn and develop the following essential skills:

plot points accurately on a Cartesian plane using given coordinates

graph linear equations correctly using appropriate scale on both axes

identify and use trigonometric ratios correctly

use scientific calculator efficiently

In From Here to There students will develop the following essential STEM understandings:

mathematics allows us to describe the exact location of an object/landmark in a particular place using coordinates and calculate the distances between two points.

mathematical terminology and sketches allow us to communicate with precision in order to successfully navigate, create and use computer programs, survey the natural environment and constructions for the built environment, locate and track weather changes and predict the place and time of impact of crashed aircraft.

coordinate geometry and trigonometry together help in navigation for land, air and sea travel.

12 weeks

Outcomes

A student:

determines the midpoint, gradient and length of an interval, and graphs linear relationships (MA5.1-6NA)

uses the gradient-intercept form to interpret and graph linear relationships (MA5.2-9NA)

applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression (MA5.1-10MG)

applies trigonometry to solve problems, including problems involving bearings (MA5.2-13MG)


Language/Literacy STEM/VET

Cartesian plane, coordinates, length of an interval, distance between two points, midpoint and gradient of an interval

Sides of a right-angled triangle, Trigonometric ratios, angles of elevation and depression, bearings

This unit provides the opportunity for students to consider applications in:

Science: retail, business/revenue analysis, Geology: map projections, latitudes and longitudes, weather forecast, tracking hurricanes using GPS, astronomy

Technology: Digital media, programming, animation, scanning and photocopying

Engineering: Surveying, Optics, Navigation, Defence


Content Teaching and Learning STEM Resources and Stimulus

interpret three-figure bearings (eg 035°, 225°) and compass bearings (eg SSW)

interpret directions given as bearings and represent them in diagrammatic form (Communicating, Reasoning)

solve a variety of practical problems involving bearings, including problems for which a diagram is not provided

check the reasonableness of solutions to problems involving bearings (Problem Solving)

Activity: Students complete the activity: ‘Where am I?”: https://www.tes.com/teaching-resource/where-am-i-11417302, which is a bearings exercise to be completed in pairs.

Link to learning:

Students discuss: Which methods of transport are able to travel along exact bearings? What impedes those that cannot travel this way? How does this contribute to the efficiency of different transport modes? Hence, which professions make regular use of bearings?

Consolidation for learning and guided practice:

The teacher demonstrates a method for converting between true (three-figure) bearings and compass bearings (Teacher Note: For some students familiar with navigation, there

may be a need to clarify that in this context the term ‘true

bearing’ is not being used as a reference to bearing from ‘true

north’ as distinct from magnetic north – particularly if the activity is done in cooperation with the Science Faculty)

Students use the resource: ‘Picture this – bearings’:

https://www.tes.com/teaching-resource/picture-this-bearings-

11422455 . The teacher nominates a student to read each of the

‘stories’. Each class member translates the worded description

into a bearings diagram. Ideally this could be done on mini

whiteboards which students hold up to compare drawings.

Students revise using angle relationships to find unknown angles

by completing the worksheet: ‘Angles round a point’:

https://www.tes.com/teaching-resource/angles-round-a-point-

worksheet-6317913

The teacher presents the article: ‘How co-ordinate Geometry works in real space’: http://blog.askiitians.com/co-ordinate-geometry-works-real-space-five-practical-examples/

STEM: Ideally this activity would be done in cooperation with the Science faculty.

‘Make a homemade compass’: https://www.scientificamerican.com/article/steering-science-make-a-homemade-compass/

Develop the mathematics by adding three-figure and compass bearings to the device

Student discussion – Which of these forms of writing bearings makes most sense to them?

STEM/VET:

Trust walk: Challenge students to think about the vast range of jobs where workers are entrusted with the safety of others.

Run a trust walk exercise with the class. (This might be done in cooperation with the PDHPE faculty.) Guiding students should use detailed verbal descriptions of the path. Later, blindfolded students are asked what descriptions they found most important/useful.

Teachers record student use of the language of location and movement and share back to students after the

https://www.tes.com/teaching-resource/where-am-i-11417302


https://www.tes.com/teaching-resource/picture-this-bearings-11422455


https://www.tes.com/teaching-resource/angles-round-a-point-worksheet-6317913


http://blog.askiitians.com/co-ordinate-geometry-works-real-space-five-practical-examples/


https://www.scientificamerican.com/article/steering-science-make-a-homemade-compass/





This article explains the use of coordinates in the real world. It also describes why it is the most important aspect of air travel.

In today’s world we rely on GPS to help us find the way. Students are asked to brainstorm what would help a person to find his/her way back home if they are lost and did not have access to technology such as a GPS or phone. Suggested brainstorm starters include the recollection of important features such as landmarks, buildings and signs.

Activity: ‘Finding your way’

Part 1

The teacher leads pre-task discussions about orientation and using a magnetic compass.

Students are given a map of the school’s neighbourhood, (obtained from Google Maps or the Street Directory).

Students find the bearing of nearest train station, shopping centre, primary school or other points of interest.

Part 2

The teacher prepares an enlarged copy of the school map. Students can use a map in their diaries if they have one, or could be provided with a copy each.

The teacher asks the students to point which way is north in the school grounds and mark it on the map.

Students walk around the school with compasses and mark features such as distinct landmarks, signs, trees or flagpoles on their sketch and note their directions/bearings.

Students brainstorm different elements they’d like to include, such as flagpoles, basketball hoops, soccer goalposts before they move outdoors.

Once back in class, students can mark/pin a small flag/note card on the enlarged school map to indicate the features they

discussion.

Science/Technology: Students with access to smart phones might compare a GPS app to compass readings.

Engineering/construction/ architecture:

Extension: Students might construct a scale model of the school including accurately located features.



mapped.

Post-task discussion:

The teacher explains that these important landmarks or signs could help a new student to find his/her way around the school. Similarly, people were using significant features to navigate for thousands of years before GPS used coordinates and bearing to identify locations.

Students discuss what would help pilots to navigate a commercial aircraft flying at 30 000 feet if GPS failed?

The teacher shows students a photo of an Aeronautical Chart that pilots use. Students discuss some of the features and markings on this chart, for example if they have to fly over the hills, they need to know exactly where they are flying and at what height they need to be flying.

Link to learning:

While doing the survey of the school grounds and marking landmarks on the map, students have used and discussed mathematical concepts of distance in a particular direction and positive and negative directions from a point of reference.

The teacher shows students a globe and talks about lines of Latitude and Longitude. Students should be able to comprehend and link the lines and directions, ie the lines of Latitude run horizontally and provide locations in east/west directions and lines of Longitudes run vertically and provide directions in north/south directions. Students could comprehend the link between various directions and use of Cartesian plane to locate a point.

The teacher challenges students to think about how a magnetic compass behaves close to the poles.



Consolidation for skill development:

The teacher explicitly teaches:

how to use standard tools to measure distances and angles/bearings correctly

how to locate/plot points on the Cartesian plane

how to measure the distance between the two points

the use of proper scale to locate different points on the Cartesian plane and convert to actual measurements.

Guided practice: school-based exercises and online worksheets could be used as resources.

plot and join two points to form an interval on the Cartesian plane and form a right-angled triangle by drawing a vertical side from the higher point and a horizontal side from the lower point

use the interval between two points on the Cartesian plane as the hypotenuse of a right-angled triangle and use the relationship gradient = rise/run to find the gradient of the interval joining the two points (ACMNA294)

Introduction to gradient: Students view the video: ‘2013 Cadbury Jaffa race down Baldwin Street’: https://www.youtube.com/watch?v=zYZCcABDuWE

According to Guinness Book of World Records, Baldwin Street in Dunedin New Zealand has a gradient of 35% or 1/2.86 which means the street rises by 1 metre for every 2.86 metre horizontal distance.

Students can develop understanding of ‘steepness’ by watching the video: ‘Cycling up the steepest street in the World in New Zealand’: https://www.youtube.com/watch?v=a9uO3KCJImA

This video is about success while there are many others where people have failed, claiming it feels as one will fall off backwards.

Activity: ‘How steep is it?’

Part 1

Students investigate the steepness/gradient of the steps at home/school. They can also take the measurements of the ideal step.

Working in small groups, each group is assigned one ramp or

Engineering/construction/ architecture: When a ramp /staircase is built, the designer must calculate how far from the base it should start so as to reach the top safely with appropriate steepness for people to climb and hence, the number and riser height for the steps.

Some schools have access to a wheelchair. Students could deepen their understanding and connect this to the way they view construction by taking a turn navigating the school in a wheelchair. Are there areas they cannot access? Do they have to plan their route more thoughtfully than usual?

If a wheelchair is not available a stroller, trolley or any large, wheeled

http://syllabus.bostes.nsw.edu.au/glossary/mat/right-angle/?ajax

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

https://www.youtube.com/watch?v=a9uO3KCJImA



staircase within the school.

Students decide how to o measure the rise and run of the ramp/staircase o present information in a diagram o calculate gradient.

Part 2

Students research Australian safety standards for gradient of staircases and ramps and evaluate their group work against these.

Link to learning

Students will be able to relate the gradient to rise/run, ie the vertical distance with respect to horizontal distance. This relationship can then be presented on the Cartesian plane and gradient can be calculated using a right-angled triangle for the ‘rise’ and the ‘run’.



how to distinguish between positive and negative gradients from a diagram (Reasoning)

how to calculate gradient from a diagram

gradient presented as fractions, percentages and ratios

Guided practice: school-based exercises and online worksheets could be used as resources.

object could be used to test the accessibility of different areas of the school.

Extension: students could make a report on access at a local shopping centre. The report should include diagrams with measured or estimated gradients.

Engineering/construction industries: Special building materials are used for low-slope roofs, so a construction worker must know the slope of the roof before beginning the project. The slope of a road affects water runoff, so civil engineers and construction workers must plan accordingly. Most municipalities have rules regarding the minimum/maximum slope of their roads.

use the interval between two points on the Cartesian plane as the hypotenuse of a right-angled triangle and apply Pythagoras' theorem to determine the length of the interval joining the two points (ie 'the distance between

Activity: Calculating distances using Google Maps

The teacher briefs the students as follows:

The National Broadband Network is coming to the neighbourhood.

Technicians need to lay the cables around the streets and

Technology/electrical trades/construction industries:

Sketch an electrical or phone-line diagram of your house showing where the power or phone service joins from the street and access

http://syllabus.bostes.nsw.edu.au/glossary/mat/pythagoras-theorem/?ajax





the two points') (ACMNA214)

determine the midpoint of an interval using a diagram

use the process for calculating the 'mean' to find the midpoint, M, of the interval joining two points on the Cartesian plane

calculate the total length of the cable required.

Students discuss: ‘Does cable run down both sides of a street?’ ‘How does each house gain access?’

Using a printout from Google Maps or similar, select a section of the map representing the local area (note: an area with straight streets is required for simplicity).

Nominate three points on the map where the direct distance between points is a line that crosses through blocks. Students calculate the shortest direct route joining the three points and compare to the distance if they only travel along streets.

Students discuss reasons that the most direct path is not always the most practical or efficient one.

Link to learning:

To calculate diagonal lengths, students will recall and apply Pythagoras’ theorem. This understanding can be linked to the introduction of the distance between points formula.



problem-solving techniques/communication for the ways to find the distance between points when it is not horizontal or vertical

The use of right-angled triangles.

Pythagoras’ theorem to calculate distance.

Differentiation:

Extension - the derivation of the distance formula from Pythagoras’ theorem.

Development:

The teacher explains that a junction box will be placed midway between two points on the map. Students locate the junction box

points within the house.

http://syllabus.bostes.nsw.edu.au/glossary/mat/mean/?ajax

http://syllabus.bostes.nsw.edu.au/glossary/mat/point/?ajax



using a ruler and marking the midpoint.

The teacher challenges students to develop a method of locating the junction box if they did not have a ruler but did know the coordinates of the two points.



how to determine midpoint using a right-angled triangle between points to change a diagonal distance into horizontal and vertical ones that can be halved

how to determine midpoint by calculating the mean of x and y ordinates of points

find the gradient and the

𝑦intercept of a straight line from its graph and use these to determine the equation of the line

Activity: Fuel costs

Students investigate the question: ‘What are the fuel costs for commercial passenger flights from Sydney to other NSW cities and does this depend entirely on the distance to be travelled?’, as follows:

Students discuss the possible variables and decide as a class how to get the best information to answer this question (for example, choose one aircraft).

Students research to find the quantity of fuel required by a commercial passenger aircraft to fly from Sydney to other major cities in Australia.

Students use an online tool to calculate the distance between Sydney and each city.

Students plot their findings as points on a Cartesian plane after discussion to decide on the independent variable.

Students consider whether the points can be joined with a straight line and hence whether the quantity of fuel changes in proportion to number of kilometres flown between major cities.

STEM/aviation industries:

Discussion: Are students aware of the different aviation courses that exist for NSW VET? What are the implications of modern flight for the types of careers or lifestyles students might have in the future?



Students discuss fuel that is used before a plane takes off i.e. the fuel will be used even for zero kilometres flown.

Students draw conclusions about how this fuel usage might be affecting the graph.

The teacher guides students to place an approximate line of best fit on their graph by joining two points that seem to represent the relationship between fuel usage and distance flown.

Students calculate the rise/run and continue the line to the y-axis in order to determine the equation of the line.

Students use the equation to predict fuel usage for a flight to Auckland, New Zealand.

Link to learning:

With calculations and graphs, students are guided to interpret the fixed and variable components of total cost and where these are represented in the graph and equation describing the situation. Students correlate the gradient with rate of change or, change depending on how much of the x-axis variable changes is a more challenging concept for students but the practical example of air miles can be used to develop their understanding.

(Note to teachers: developing the equation of a straight line from real data plotted on a Cartesian plane prepares students for later study of correlation and regression lines in statistical topics. Emphasis should be on the usefulness of obtaining an equation that can be used to make predictions.)



how to find the equation of a line

the importance of gradient and y-intercept in real life situations

how to find/interpret the equation of a line

how to understand trends and making predictions using the



graphs.

Guided practice: school-based and online worksheets could be used as resources.

Solve right-angled triangle problems, including those involving angles of elevation and depression (ACMMG245)

identify angles of elevation and depression

interpret diagrams in questions involving angles of elevation and depression (Reasoning)

(Note to teachers: students that have been on the recommended sequence of study for Mathematics STEM VET will have completed ‘Build Make Create’ in Year 9 and will be studying ‘From Here to There’ in Year 10. Students that have not previously studied Trigonometry will need to complete that learning before commencing with this development into angles of elevation and depression.)

Students review their trigonometry skills using the resource: ‘Trigonometry pile-up’: http://www.greatmathsteachingideas.com/2012/03/12/trigonometry-pile-up/ , which is a practice exercise to review and reinforce knowledge of trigonometric concepts and their applications to measure distances, correct use of scientific calculator and to emphasise the importance of not rounding off in the middle of the calculations.

Activity: ‘How high?’

Students measure the height of flagpole/football goal post or any other suitable point of reference, using the following procedure:

Students mark three points on the ground.

Students measure the distance to the base of the flagpole and the angle of elevation of the top of the flagpole from each of those points.

Students record measurements on diagrams while ‘in the field’.

Students return to the classroom and with teacher guidance, students use the distance and the angle of elevation to calculate the height of the flagpole.

Science: Why take measurements from three points and not rely on one? Remind students of scientific method and the questions of how many experiments need to be conducted before you decide you have proof of something?

Engineering extension: Create a tool to perform a function, in this case, a homemade clinometer.

http://syllabus.bostes.nsw.edu.au/glossary/mat/angles-of-elevation-and-depression/?ajax

http://syllabus.bostes.nsw.edu.au/glossary/mat/angles-of-elevation-and-depression/?ajax

http://www.greatmathsteachingideas.com/2012/03/12/trigonometry-pile-up/




Differentiation:

Structured - Provide students with a clinometer or allow estimations of angle of elevation. Provide students with diagrams of predetermined objects and students add correct labels and measurements while in the field.

Extension - Students devise their own method of measuring angle of elevation given a selection of possible tools such as protractors, string, weights. Students create and label their own field diagrams.

Guided practice: school-based and online worksheets could be used as resources.

Differentiation:

Structured - diagrams are provided and the required angle is marked on the diagram.

Extension - include problem-solving questions where diagrams are not provided.

applies trigonometry to solve problems, including problems involving bearings

find the lengths of unknown sides in right-angled triangles where the given angle is measured in degrees and minutes

find the size in degrees and minutes of unknown angles in right-angled triangles

solve a variety of practical

Activity: ‘Do degrees matter?’

Equipment: Compass, ruler and A3 paper per student.

Students draw diagrams from worded descriptions of bearings and distance travelled given the scale of 1 mm represents 1 km. The bearings should only differ slightly in order to demonstrate that a small change in degrees becomes a significant difference in final location. For example: o A plane flies on a bearing of 045° to land at an airport 150 km

away. Another plane leaving from the same place flies on a bearing of 050°and lands after flying 150 km. Use your scale diagram to measure the final distance between the planes.

o A ship sails on a bearing of 170° for 250 km while another sails the same distance on a bearing of 175°. How far apart

Science and Engineering:

Activity: Students make paper planes or gliders.

Mark two lines on the ground about half a metre apart as the landing zone and another to be the launch line.

Allow students to practice and adjust their model until till they can land within the Landing Zone.

Investigate the effect of wind on the landing point. Wind can be



problems involving angles of elevation and depression, including problems for which a diagram is not provided

interpret three-figure bearings (eg 035°, 225°) and compass bearings (eg SSW)

interpret directions given as bearings and represent them in diagrammatic form (Communicating, Reasoning)

are they?

Students research: ‘What is the longest direct commercial passenger flight?’ ‘How many kilometres?’

Students calculate: What scale would be needed to show that flight on an A3 page? If the pilot made an error of 5 degrees in his/her bearings at take-off, how far off course will the plane be by the end of its flight?

Link to learning:

Students have revised scale, worked with mixed units and practiced accurate use of protractors. The teacher explains that as distances increase the impact of a few degrees difference in bearings becomes exaggerated. The teacher asks students to consider the accuracy that would have been required to land modules on Mars.



how to draw diagrams to represent this information

how to use the diagrams to calculate the distance to be travelled

how to enter and interpret degrees and minutes with a scientific calculator.

Guided practice:

school-based and online worksheets could be used as resources

use of scientific calculator.

Differentiation:

Structured - diagrams are provided and the required bearing is marked on the diagram with compass divisions to assist students locate right-angled triangles. Limit compass bearings to N, NE, NW, S, SE, SW, E and W and limit true bearings to the equivalents of these.

generated by using a fan and locating it one side of the flight path. Note the change in the landing point with and without the wind.

Investigate the effect of the wind when the fan creates headwinds and tailwinds.

Based on observation on their model’s flights, students discuss whether pilots need to adjust their direction of flight accordingly to compensate for wind at altitude.

Discuss the impact of wind on flight speed and how pilots adjust for this.

(Adapted from NASA Education resources)

Science and Technology/information and digital technology industries:

Data entry and analysis and creation of digital presentations of information is a growing field of employment opportunity for current students.

Students can look at the data that is available for pilots and other aviation professionals on the ‘Aviation Weather Service Site’: http://www.bom.gov.au/aviation/, or

http://www.bom.gov.au/aviation/



Extension - include problem-solving questions where diagrams are not provided.

the ‘Australian Bureau of Meteorology site’: http://www.bom.gov.au/ and consider the number of people employed to gather, sort and turn the data into a form that is interesting and useful for the general public.

sketch linear graphs using the coordinates of two points (ACMNA215)

determine that parallel lines have equal gradients

construct tables of values and use coordinates to graph vertical and horizontal lines, such as

x = 3, x = −1, y = 2, y = −3

identify the x- and y-intercepts of lines

graph a variety of linear relationships on the Cartesian plane, with and without the use of digital technologies

determine whether a point lies on a line by substitution

Activity: ‘Flying in formation’

The teacher uses the STEM/Aviation stimulus as an introduction

Students use the resource: ‘Flying in formation – introduction to parallel lines’: https://www.tes.com/teaching-resource/flying-in-formation-introduction-to-parallel-lines-11443543

Students consider flying in tight formations through images and linked videos of birds, people and planes. Track running is given as a secondary stimulus to get students thinking about the importance of parallel lines.

The teacher guides students to define parallel lines and sketch graphs and give equations for lines parallel to those given in the worksheet.

Link to learning:

Students consider real-world examples of parallel lines before formally graphing horizontal and vertical lines, to prepare for sets of lines with the same gradient.


The teacher ensures students can correctly use their calculators in order to complete tables of values from which to graph a linear function, as follows:

Students consider a table of values for horizontal and vertical

STEM/aviation industries: Watch the video: ‘Australian Air Force Roulettes’: http://video.airforce.gov.au/play/3102 and the ‘Wings of Illawarra Air Show’: http://video.airforce.gov.au/play/4657.

Question: What is the most important thing for a pilot to know while flying in tight formation? (Note to teacher: If students do not arrive at the answer themselves, guide them towards, ‘knowing where the other planes are’.)

http://www.bom.gov.au/

https://www.tes.com/teaching-resource/flying-in-formation-introduction-to-parallel-lines-11443543


http://video.airforce.gov.au/play/3102






lines.

Students discuss: Does 𝑦 = 7 look like an equation or the

answer to an equation? [class vote]. What about 𝑥 = −2? [class vote]

Students complete the worksheet: ‘Special cases for tables of values – Part 1’: https://www.tes.com/teaching-resource/special-cases-for-tables-of-values-part-1-11401553

Students watch the video: ‘How do you make a table of values for a linear equation’: http://www.virtualnerd.com/pre-algebra/linear-functions-graphing/equations/introduction-linear-equations/generate-table-values-example as a ‘flipped learning’ lesson.

Students develop their understanding that coordinate pairs for points on a line can be generated from equations, and hence ‘work’ when substituted into equations. This understanding is then used to determine whether a point lies on a line by substitution.

Students use the resource: ‘Which one doesn’t belong?’: http://wodb.ca/index.html as a ‘warm up’. As described on the site, solutions are not provided and multiple correct answers are possible. The challenge is to be able to justify your answer. (Note to teachers: Developing student capacity to look critically at a set of information and determine similarities and differences is beneficial to many mathematical processes. This is further enhanced by asking students to articulate their thinking and decision-making. In the learning that follows, students will be asked to check their answers for anomalies and hence identify potential errors in their workings.)


that points that satisfy an equation or fall on a line ‘belong’ to the relationship described by that equation and graphed by that line. o students test a set of points to identify the one that does not

belong to the given equation.

https://www.tes.com/teaching-resource/special-cases-for-tables-of-values-part-1-11401553


http://www.virtualnerd.com/pre-algebra/linear-functions-graphing/equations/introduction-linear-equations/generate-table-values-example



http://wodb.ca/index.html



the conditions of 𝑥 and 𝑦 intercepts, including the value of 𝑥 at

the 𝑦intercept and the value of 𝑦 at the 𝑥intercept. o the teacher asks students whether this is a rule to memorise

or a thing they can see will always be true. o students practise substituting zero for 𝑥 and 𝑦 to find

intercepts.

how to sketch graphs from two points, usually the 𝑥 and

𝑦intercepts.

Guided practice: school-based and online worksheets could be used as resources, such as:

Worksheets: ‘Graphing from function tables’:

https://www.worksheetworks.com/math/geometry/graphing/function-table-graph.html

‘Linear equations worksheets’: https://www.mathworksheets4kids.com/equations/linear.php

compare and contrast equations of lines that have a negative gradient and equations of lines that have a positive gradient (Communicating, Reasoning)

use graphing software to graph a variety of equations of straight lines, and describe the similarities and differences between them, e.g.

y = −3x, y = −3x + 2,

y = −3x, y =1

2x,

Activity: ‘Design an aircraft hanger’: https://www.tes.com/teaching-resource/design-an-aircraft-hanger-11429791 (Potential assessment activity)

Students are given a design brief for an aircraft hangar and aircraft specs are provided in a graphic.

By plotting the extremities of the plane on a Cartesian plane, students provide the equations that define the front-on edges of their walls and roof sections.

An extension question challenges students to re-think the original brief for an improvement to their design.

Differentiation:

Structured - Print a front-on image of an aircraft for students to

STEM/aviation industries/tourism:

Show students video of an aircraft aborting landings such as ‘B747 very late go around!’: https://www.youtube.com/watch?v=MW7AbEwxmTw&feature=youtu.be (Select video showing the aircraft approaching from the left.)

Students sketch the flight path from a side-on view. Label positive and negative gradients. Decide whether the landing or approaching path was steeper.



https://www.mathworksheets4kids.com/equations/linear.php

https://www.tes.com/teaching-resource/design-an-aircraft-hanger-11429791


https://www.youtube.com/watch?v=MW7AbEwxmTw&feature=youtu.be




y = −2x, y = 3x, x = 2, y = 2

(Communicating)

graph straight lines with equations

in the form 𝑦 = 𝑚𝑥 + 𝑐 ('gradient-

intercept form')

recognise equations of the form

𝑦 = 𝑚𝑥 + 𝑐 as representing

straight lines and interpret the 𝑥-

coefficient (𝑚) as the gradient,

and the constant (𝑐) as the 𝑦-

intercept, of a straight line

match equations of straight lines

to graphs of straight lines and

justify choices (Communicating,

Reasoning)

cut out and stick onto a blank and unlabelled grid in order to

locate wing and tail tips. Guide students to transfer

measurements from the graphic onto the axis. Using a ruler,

students draw an aircraft hanger around the plane and label

each line with positive, zero or negative gradient.

Link to learning:

Students in Stage 5 may not yet have considered shapes as being constructed from line segments and hence, not be aware that every side has its own equation if the shape has a location in space (ie, if it is real).



how to interpret the ‘gradient-intercept’ form of linear equations

𝑦 = 𝑚𝑥 + 𝑐

how to graph straight lines with equations in the form 𝑦 = 𝑚𝑥 + 𝑐

the vocabulary required to justify choices when matching equations of straight lines to graphs of straight lines.

Guided practice: school-based and online worksheets could be used as resources, such as:

‘Graphing from function tables’:

https://www.worksheetworks.com/math/geometry/graphing/functi

on-table-graph.html

Develop understanding of positive and negative being distinct from steepness.

Students could role-play communication between pilot, and flight crew in time with the video playing.

Students consider the reasons for and implications of go-arounds. What are the costs of making this decision?

http://syllabus.bostes.nsw.edu.au/glossary/mat/gradient/?ajax




Assessment strategies

Activity: Calculating the length of the NBN cable required

Research: Australian safety regulations of the steepness of ramps/staircases

Worksheet: Triangle pile-up

First Hand Investigation: Paper Aircraft/Glider Activity

Topic test: Short answer and multiple-choice test.

Student self-evaluation: Students rate their own development through this unit – their understanding and skills, their application to learning and

working mathematically. Students discuss these with one another and then with teacher 'For Learning' in order to identify their readiness to move

on to the next topic and personal learning objectives they might set themselves for the next topic (eg participation in class, completion of

homework, developing skills).

Resources overview

URLs of linked resources:

Teaching and Learning URLs of linked resources

‘Where am I?”: https://www.tes.com/teaching-resource/where-am-i-11417302

‘Picture this – bearings’: https://www.tes.com/teaching-resource/picture-this-bearings-11422455

‘Angles round a point’: https://www.tes.com/teaching-resource/angles-round-a-point-worksheet-6317913

‘How co-ordinate Geometry works in real space’: http://blog.askiitians.com/co-ordinate-geometry-works-real-space-five-practical-examples/

Video: ‘2013 Cadbury Jaffa race down Baldwin Street’: https://www.youtube.com/watch?v=zYZCcABDuWE

Video: ‘Cycling up the steepest street in the World in New Zealand’: https://www.youtube.com/watch?v=a9uO3KCJImA

‘Trigonometry pile-up’: http://www.greatmathsteachingideas.com/2012/03/12/trigonometry-pile-up/

‘Flying in formation – introduction to parallel lines’: https://www.tes.com/teaching-resource/flying-in-formation-introduction-to-parallel-lines-

11443543

‘Special cases for tables of values – Part 1’: https://www.tes.com/teaching-resource/special-cases-for-tables-of-values-part-1-11401553





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

https://www.youtube.com/watch?v=a9uO3KCJImA






Resources overview

‘How do you make a table of values for a linear equation’: http://www.virtualnerd.com/pre-algebra/linear-functions-

graphing/equations/introduction-linear-equations/generate-table-values-example

‘Which one doesn’t belong?’: http://wodb.ca/index.html

‘Graphing from function tables’: https://www.worksheetworks.com/math/geometry/graphing/function-table-graph.html

‘Linear equations worksheets’: https://www.mathworksheets4kids.com/equations/linear.php

‘Design an aircraft hanger’: https://www.tes.com/teaching-resource/design-an-aircraft-hanger-11429791

‘Graphing from function tables’: https://www.worksheetworks.com/math/geometry/graphing/function-table-graph.html

STEM Resources and Stimulus URLs of linked resources

‘Make a homemade compass’: https://www.scientificamerican.com/article/steering-science-make-a-homemade-compass/

‘Aviation Weather Service Site’: http://www.bom.gov.au/aviation/

‘Australian Bureau of Meteorology site’: http://www.bom.gov.au/

‘Australian Air Force Roulettes’: http://video.airforce.gov.au/play/3102

‘Wings of Illawarra Air Show’: http://video.airforce.gov.au/play/4657

‘B747 very late go around!’: https://www.youtube.com/watch?v=MW7AbEwxmTw&feature=youtu.be

Sites showing careers that use maths:

Plus Magazine – career interviews: https://plus.maths.org/content/Career

Get the Math: http://www.thirteen.org/get-the-math/

Teacher Evaluation of Unit



http://wodb.ca/index.html


https://www.mathworksheets4kids.com/equations/linear.php




http://www.bom.gov.au/aviation/

http://www.bom.gov.au/




https://plus.maths.org/content/Career

https://plus.maths.org/content/Career

http://www.thirteen.org/get-the-math/

http://www.thirteen.org/get-the-math/

Documents

Sample unit Mathematics Stage 5 - STEM Pathway: Unit 5