Embedded Files
Summary
Summary
Lesson Goals
Lesson Goals
By the end of the lesson, students should be able to:
By the end of the lesson, students should be able to:
Explain the benefits of analysing real-world networks
Construct and draw network graphs from simple scenarios (friendships and acquaintances)
Use network terminology to describe network graphs
Explain the effects that vertices with high or low degree have on real-world networks
Syllabus Content
Syllabus Content
N1.1 Networks
Students:
identify and use network terminology: vertices, edges, paths, the degree of a vertex, directed networks and weighted edges
solve problems involving network diagrams AAM
recognise circumstances in which networks could be used, e.g. the cost of connecting various locations on a university campus with computer cables
Working Mathematically
Working Mathematically
Identify and explain the significance of real-world networks (Understanding)
Identify appropriate vertices and edges from descriptions of social networks (Understanding, Fluency)
Represent networks in graphical form given worded descriptions (Communicating, Understanding)
Describe the features of a network diagram using the terms degree and connectivity (Communicating, Fluency)
HW: Explain the benefits & disadvantages of highly connected networks (Understanding, Reasoning)
Resources
Resources
Ball of Twine (or String, see Introduction)
Whiteboard, Whiteboard Markers (see Body 1)
A4 Paper, Sticky Tape, Coloured Markers (see Body 2)
Index Cards (see Exit Task)
Strategies Used
Strategies Used
Class Brainstorm
Class Practical Activity (Twine)
Group Practical Activity (Network Building)
Higher-Order Questions
ICT Research Task
New Vocabulary
New Vocabulary
Simple Network
Simple Network
A network with no multiple edges or loops.
Connected Network
Connected Network
A connected network is a network where all vertices can be reached from any other vertex by travelling along edges, i.e. a walk can be made from one vertex to any other vertex.
Lesson Details
Lesson Details
Orientation
Orientation
Working Mathematically: Understanding
Homework Recap (5 min)
Address last lesson's homework: students write their researched real-world network examples on the whiteboard. Select students to share what they wrote and the benefits of analysing their example network.
Introduction
Introduction
Working Mathematically: Communicating, Fluency, Understanding
Class Twine Activity (5 min) [LIT]
Before the lesson begins, prepare a ball of twine. As students enter the classroom, instruct students to form a circle in the middle of the classroom (clear space in the middle of the classroom first by moving tables to the sides).
When ready, give the ball of twine to one of the students. Instruct them to throw the ball to someone they know in the circle (but it cannot be the person next to them) while holding the other end of the ball of twine. Students will continue this process until everyone is holding a part of twine (remind students to hold onto their part of twine tightly as the ball of twine is thrown around).
As a class, discuss what they have just created (linking back to terminology used in Lesson 1) (AFL). Let students know that they have created a social network, where each person represents a vertex and the string connecting each person represents the edges. Additionally, explain to the class what simple networks and connected networks are (using the Introduction activity as a context).
Follow-up questions (AFL):
What did it mean for two of us to be connected by twine?
How connected is everyone in the class?
What would an unconnected or low-connected class network look like?
Suppose two of us were not directly connected to each other. How are we indirectly connected?
What do people with high or low numbers of connections represent?
Body 1
Body 1
Working Mathematically: Communicating, Fluency, Understanding
Class Whiteboard Mapping Activity (20 min)
Once students have sat down at their tables, select 3 students who do not know each other well to come to the whiteboard, give each a marker, and have them each draw their own network with the people they know in the class on the whiteboard (limiting it to 5 depending on the class size). Once finished, have the students return to their seats.
Ask each table group to visit the whiteboard and draw a line connecting two students if they know that a person on the board knows another person on the board (but are not connected already). Repeat this process with each table group until students are unable to connect students together.
As a class, discuss how networks might help us in drawing and understanding social connections. Discuss whether, and why or why not, the whiteboard drawing is similar (in any way) to mutual friends on Facebook (AFL).
Example Whiteboard - Details
Example Whiteboard - Details
Photo and Activity taken from Students map their social network by Matthew Kushin
Body 2
Body 2
Working Mathematically: Fluency, Communicating, Understanding
Group Drawing/Construction Activity (25 min)
Provide each student with A4 paper, sticky tape and coloured markers. Instruct students to write the names of the 5-10 people they last spoke to, and to spread out all around the page (differentiate the number of people per table). Instruct students to create a social network diagram with those 5-10 people, drawing a line between two individuals if they know each other. Monitor each table and ensure students understand the task (AFL).
After students have completed their diagrams, instruct students to pair up with the person next to them and see if they can make any new edges between the two diagrams. Instruct students to use sticky tape to combine the 2 A4 paper together. Student can then group up with another pair and repeat the process, combining their papers together.
See: Group Questions (AFL)
Group Questions
After a table group has finished creating and combining their network diagrams, provide them with the following questions (to apply to their final network diagram):Group Questions
Suppose information (e.g. a rumour, news, misinformation) is passed on from one individual to every other individual they have talked to in the last hour (or day). How long would it take for the entire network of people to hear this information?
Suppose you fell sick and unknowingly transmitted your sickness to everyone you have talked to in the last hour (or day). How long would it take for the sickness to spread throughout the community? How could we prevent the sickness from spreading?
What is the effect of vertices with high and low degree numbers in networks like these?
Explain how social networks (e.g. Facebook) suggest 'Mutual Friends'.
At most, how many connections away are you from any other person in the network? What If your network extended to the entire world (see Six Degrees of Separation; Oracle of Bacon)?
Conclusion
Conclusion
Working Mathematically: Communicating, Fluency, Understanding
Think-Pair-Share (5 min)
Ask students to recall a real-world (or fictional) example of a social network (AFL). Could include the following:
Family network (relatives, close friends)
Friends (offline and online)
Fictional TV shows, movies or books (characters)
Sports (teams/players)
Local communities
Actors/Actresses
Select students to describe whether their network examples are highly connected (i.e. each individual is connected to many other individuals) or somewhat isolated (i.e. individuals only know 1 or 2 other individuals, or none at all) (AFL).
Homework/Follow-Up
Homework/Follow-Up
Remind students to update their Trip Log (Simple Network, Connected Network) (AOL).
Students complete one of the following tasks at home and hand in their response at the start of the next lesson.
Construct a network diagram of a real-world (or fictional) social network and provide context (e.g. what is the network, what do the vertices and edges represent). Add any additional insights (e.g. about the level of connectivity of the network).
Browse https://oracleofbacon.org/ and summarise your findings for the class
Supplementary resources: Among the Oscar Contenders, a Host of Connections; and Constellations of Directors and Their Stars
Read through the following article about physical/social distancing and summarise your findings for the class
Browse https://fatiherikli.github.io/post-truth/ and summarise your findings for the class
Supplementary resource: https://ncase.me/crowds/
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