Reuse and attributions

Reusing this book

This book has been released under a CC-BY-NC 4.0 license.  That means that (with the exception of most videos, please see the note below):

  • You can share all of it, or parts of it, with others for non-commercial purposes.  This includes within your classroom.
  • You can modify any part of it for any non-commercial purpose.
  • You can reproduce parts or all of the work in other places for non-commercial purposes.
  • You must provide attribution as a condition of this licence.  See below for suggested attribution.
  • The book must not be used for commercial purpose.  If you do want to use it commercially, contact our copyright office for advice copyright@deakin.edu.au

Video reuse

Many of the videos in this book do not share the CC-BY-NC 4.0 license.  This is due to licensing arrangements with Getty images, whose images we have used in the development of many of the videos.  This means you are legally prohibited from downloading and/or modifying them.  You can still link to and embed these videos online, or show them in a classroom.  We have made the script and soundtrack of the videos available under Creative Commons, so that if you have the know-how, you can re-use those components of the videos under the terms of the licence.

However some of the videos (not containing Getty images) are licensed under Creative Commons.  These videos can be reused and modified.

We’ve listed the credits and license information of each video individually.  You can see these if you access the videos in Youtube.

How to attribute this book

If you wish to reuse the book or parts of it online, we suggest that you attribute the book as follows

Mathematical Reasoning and Investigation by Simon James, Chris Rawson, illustrated by Erin Cheffers, Deakin University (CC BY NC 4.0)

For a more formal reference (eg, if you wanted to put the book in a reference list), we suggest the following attribution (we have followed APA 7).

James, S., Rawson, C., illustrated by Cheffers, E. (2023). Mathematical Reasoning and Investigation (1st ed.). Deakin University. https://oercollective.caul.edu.au/mathematical-reasoning-investigation/

Image attributions

Banner attribution

All banners illustrated by Erin Cheffers, CC-BY-NC 4.0

Inline images attributions

The images and text produced by Deakin staff (Erin Cheffers, Simon James, Lea Piskiewicz and Matthew Griffith) are available under CC-BY-NC 4.0.  We have also utilised Freepik images from Flaticon which are available “free, for personal and commercial use with attribution.” You can access their licence summary by selecting “more info” under the licence information for each icon on their site or you can read the legal terms.

Front matter

house

Home icons created by Freepik – Flaticon

Plane icons created by Freepik – Flaticon

fence

Fence icons created by Freepik – Flaticon

open book
Reading icons created by Freepik – Flaticon
cup of coffeeCoffee icons created by Smashicons – Flaticon
two people laughing

Friends icons created by Freepik – Flaticon

computer screen

Computer icons created by Freepik – Flaticon

rubbish going into wastepaper basket

Rubbish icons created by justicon – Flaticon

The Hero’s Journey

handshake

Agreement icons created by Freepik – Flaticon

Spaceman moves around a planet, begins and moves through the following phases - call to adventure, meeting a mentor, crossing threshold, trails and failure, growing new skills, death and rebirth, revelation, finally changes, atonement, receive a gift, return changed

Lea Piskiewicz

described in text

Lea Piskiewicz

Graphic of the Huashan problem, described in text

Simon James

entry - mathematics - solution

Erin Cheffers

entry, conjecturing, reasoning, getting stuck, going back, solution, justifying solution, finding better or neater solutions

Erin Cheffers

People icons created by Freepik – Flaticon

Chess pieces

Chess icons created by Freepik – Flaticon

bee

Bee icons created by Freepik – Flaticon

house

Home icons created by Freepik – Flaticon

Store icon

Shop icons created by Freepik – Flaticon

train

Train icons created by Freepik – Flaticon

Fundamental concepts in mathematical reasoning

Rectangular glass cut into 9 pieces.

Matthew Griffiths

fish in fish tank

Matthew Griffiths

Tutor icons created by Eucalyp – Flaticon

coffee cup

Coffee icons created by Freepik – Flaticon

toll gate

Toll road icons created by Freepik – Flaticon 

badge

Sticker icons created by Tempo_doloe – Flaticon

numerator on top, vinculum is the line separating the top of the fraction from the bottom, and the denominator is on the bottom

Erin Cheffers

pizza slice

 

Pizza icons created by Freepik – Flaticon

Box icons created by Freepik – Flaticon

kangaroo

Kangaroo icons created by BZZRINCANTATION – Flaticon

car

Car icons created by Konkapp – Flaticon

Algorithms

image

Lea Piskiewicz

left: when green flag is clicked, if x position is less than 0 then say I'm on the right for 0.5 seconds. Right - same sequence, except the sequence is repeated forever

Screenshot from Scratch used under CC-BY-SA 2.0

 

Interpreting visual information

graph showing distance as a function of time

Erin Cheffers

straight line between distance and time

Erin Cheffers

Graph depicting the total cases of COVID-19 per 100,000 in its population over time. Compares several nations from the period of March 2020 to March 2022

TrautCC BY-SA 4.0, via Wikimedia Commons

Graph with two axes: vertical axis says 'total time it will take to finish the job' and horizontal axis says 'number of people picking strawberries'

Erin Cheffers

strawberry

Strawberry icons created by Freepik – Flaticon

 

Series of graphs showing a variety of different graph shapes.

Adapted from The Language of Functions and Graphs (1985) by Shell Center for Mathematical Education (this version modified by Deakin University and licensed under CC BY NC 4.0 with permission from Shell Centre for Mathematical Education).

 

 

Sequences and progressions

cow

Cow icons created by surang – Flaticon

planets in orbit

Universe icons created by smalllikeart – Flaticon

shrub

Shrub icons created by Flat Icons – Flaticon

1+1=2

Sum icons created by Smashicons – Flaticon

population

People icons created by Freepik – Flaticon

graph

Line chart icons created by Freepik – Flaticon

geometric progression image

Simon James

Measurement

ruler

Ruler icons created by Freepik – Flaticon

folded clothes

Clothes icons created by Vitaly Gorbachev – Flaticon

whiskey

Whiskey icons created by Freepik – Flaticon

Decking

Floor icons created by Good Ware – Flaticon

Shoe

Shoes icons created by Flat Icons – Flaticon

cheetah

Cheetah icons created by Flat Icons – Flaticon

microchipMicrochip icons created by vectorspoint – Flaticon simplify icon (three arrows converging)

Simplify icons created by Freepik – Flaticon

wristwatch

Watch icons created by Freepik – Flaticon

quiz buttons

Quiz icons created by Freepik – Flaticon

code on screen

Code icons created by Freepik – Flaticon

summary report

Report icons created by Freepik – Flaticon

thought bubble

Thinking icons created by Freepik – Flaticon

Geometry

image

Simon James

similar triangles

Simon James, Erin Cheffers, Lea Piskiewicz

sine, cosine, tangent

Lea Piskiewicz

Pythagorean dissections

David EppsteinCC0

 

polyhedron (cube with dotted line from front bottom left corner to back top right corner)

Lea Piskiewicz

image

Simon James

3D geometric shapes - elipse rectangle and trapezium

Erin Cheffers

pyramid

 

Pyramid icons created by Freepik – Flaticon

Graphs and networks

Konigsberg Bridge

Erin Cheffers

Bridge icons created by photo3idea_studio – Flaticon

generalising

Creativity icons created by Eucalyp – Flaticon

graph

Simon James

graph

Simon James

graph

Simon James

graph

Simon James

complex graph

Simon James

image

Simon James

image

Simon James

image

Simon James

network icon

Algorithm icons created by Becris – Flaticon

figure described in text

Simon James

image

Simon James

image

Simon James

Relationship icons created by Becris – Flaticon

marine animals in a network

Simon James

A network

Simon James

A network

Simon James

a network

Simon James

Probability

Chance icons created by ultimatearm – Flaticon

dice

Dice icons created by Freepik – Flaticon

ticket iconTicket icons created by Nikita Golubev – Flaticon tree diagram

Erin Cheffers

basketball into net

Basketball icons created by Freepik – Flaticon

venn diagram, 1 on the left circle, 4, 6 on the right circle, 3,5 in the overlap and 2 outside any circles

Lea Piskiewicz

venn diagram - forgets to validate in 1 circle, ticket inspector checks ticket in the other circle

Simon James

two circles, on within another. In the outer circle 'forgetful man forgets to validate ticket' and the inner circle 'forgetful man is fined'

Simon James

 

Simulation

leaves

Leaves icons created by cahiwak – Flaticon

coin

Coin icons created by Freepik – Flaticon

dice

Dice icons created by Freepik – Flaticon

balloons

Birthday icons created by Freepik – Flaticon

playing cards deck

Deck icons created by Nikita Golubev – Flaticon

seats in plane

First class icons created by Flat Icons – Flaticon

bell curve, details described in text below

Erin Cheffers

woman's height being measured

Tall icons created by kerismaker – Flaticon

coin toss

Coin toss icons created by SBTS2018 – Flaticon

histogram described below

Simon James

Simon James

comparison of normal distributions of crocs (right) and sharks (left)

Erin Cheffers

animal shelterVeterinary icons created by Freepik – Flaticon skewed distribution histogram, long tail

Erin Cheffers

Histogram stepping down a hill

Erin Cheffers

bar graph

Graph icons created by Freepik – Flaticon

License

Icon for the Creative Commons Attribution-NonCommercial 4.0 International License

Mathematical Reasoning and Investigation Copyright © 2023 by Deakin University is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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