Introduction

Working Mathematically: Communicating, Understanding, Fluency

Group Drawing + Table Construction (15 min) [NUM]

Start the lesson off by projecting a building plan of the school onto the whiteboard (an example is provided). Provide students with a copy of the school building plan and have them work in their table groups to construct a network diagram consisting of at least 5 vertices (including weighted edges). Afterwards, ask students the following questions:

• What do the vertices and edges represent within this network?

• What else could the weight values of the edges represent?

Students will then work backwards to construct a table using the weighted graph they have constructed. Monitor students' progress, and scaffold the table construction on the whiteboard if necessary (AFL). Ask the following questions to the students (AFL):

• Why do we not put a value in for matching vertices, e.g. A-A, B-B, C-C?

• Which buildings do not have a direct path between each other?

• What would this table look like if every building was directly connected to every other building?

• What would this table look like if there was a building that was not connected at all?

Body

Working Mathematically: Communicating, Understanding, Problem-Solving, Reasoning

House Floor Plan Drawing (40 min)

Students will be given a printed copy of an Example House Floor Plan and shown multiple different network diagrams on the whiteboard (draw before Body 2). Give students time to attempt to match the floor plan to one of the network diagrams. Poll the class by asking students to remember which network diagram they believe matches the floor plan, then ask them to close their eyes and raise their hand in response to prompts (AFL). Ask a student who correctly identified the matching network diagram to explain to the class why by redrawing it on the whiteboard (AFL).

Afterwards, instruct students to draw a house floor plan for a family who have just recently purchased their first plot of land. The floor plan must have at least: two Bedrooms, a Living Room, a Bathroom, a Kitchen and a Garage (it is up to students to decide if they want to include a hallway).

• Students will need to include length measurements in their house floor plan, and estimate the distance between rooms in the house for their weighted network diagram.

• Differentiation: students may optionally include additional rooms, such as closets, en-suites, pantries, foyers, dining rooms, ... (these will add additional vertices that students will need to manage).

Students will be given 30 minutes to work in their table groups to create an ideal house design, making sure they have included the minimum requirements set out by the family. Students should also draw an accompanying network diagram next to their house floor plan. Check students' work before assigning them the next task, and ask them to explain why their house design is ideal or efficient (AFL).

If students have finished early:

Using the floor plan they have created, instruct students to create a local area network (LAN) diagram for a computer in each bedroom and a gaming console in the living room, all of which are connected to the Internet through a router. Students can decide where the router is placed, but it must be connected to each device in the house via cables. As students are constructing their network diagram, ensure students have correctly drawn their LAN diagram, and ask students to justify the placement of their router (AFL).