2. Architectural Designs

• Three-dimensional blocks
• Three-dimensional objects such as jugs, bottles, boxes etc
• Blocks of all equal sizes, such as Lego blocks or wooden cubes
• Digital isometric drawing tool or isometric dot paper: PDF
• Grid paper: docx PDF
• Computer, laptop or tablet

This stage is designed to develop students’ visual images of geometric shapes. Students become architects to design a house that they would build in the suburb that they created in the previous stage, Urban Designs. Students will have the opportunity to explore the various perspectives of buildings and to represent them as two-dimensional patterns and vice versa.

Recap the learning from the previous stage, Urban designs. As a class, review the different views available on Google Map using an interactive whiteboard or screen. Engage students in a discussion about the differences between 'street view', when you are looking at the street or buildings from the front or side, and 'satellite view', which offers a top-down view of the streetscape or building.

Explore views of iconic landmarks around the world, such as The Great Pyramids of Giza, The Pentagon and Eiffel Tower. Prior to viewing these landmarks using the satellite view, encourage students to predict what they may look like from the top.

Explore object perspectives with students by playing a game of ‘What Am I’, using common household or classroom objects. Students select an object and draw the silhouette of its top view on one half of a piece of paper and the side view on the other half. For example:

Students cover the drawing of the side view, showing their peers only the top view diagram, then invite them to predict what the object may be. Students slowly reveal the side view to their peers as further clues to their guess.

Enable students to determine the top view of objects by encouraging them to invert the object onto a piece of paper so that the top of the object is against the paper. Guide students to draw a line around the perimeter of the object’s top so that an outline of the top is produced. Ask students to compare this outline with the top view of the object.

Extend students by challenging them to find objects which will have a different silhouette of the left and right view or a different top and bottom view to play this game.

1. From three-dimensional object to two-dimensional image

This activity gives students an opportunity to create their house designs, whilst developing their skills to visualise three-dimensional objects as two-dimensional shapes. It aims to encourage students to use metacognitive strategies to think about ways to complete the task and monitor their progress. This activity is inspired by the Four Cube Houses problem in the Maths Curriculum Companion (scroll to the bottom of the page and select the tab for 'Four Cube Houses').

Explain to students that since they have designed a suburb that they would like to live in, they are now going to design their dream house to build in that suburb. Facilitate a discussion about what rooms or features they would like to have in their dream house. Discuss which of these are essential spaces and which of them are useful spaces to have but not a necessity. You could create a class Venn Diagram to record these. 

Prompt students with a scenario as a context for the activity. For example:

'You are an architect, and you are going to build your house from cubes. Each cube will represent a room or space that you would like to have in your house. You will need to collect the number of cubes that corresponds to the number of rooms you would like to have. There are some building guidelines that you need to adhere to. Can you make two different house designs using these cubes?'

These are the building guidelines:

a) All cubes must be the same size.

b) The cubes must fit together, face to face.

c) The designs for each house must be different. If one house can be rotated to make the other, they are the same design.

d) The number of rooms that your house has must be between five and fifteen. That means you must have at least five and no more than fifteen cubes for each house.

Model how to create a design using the blocks, and then how to draw the building from the constructed design. Show students each view (top and each four sides) of the model and demonstrate how to draw each on grid paper. The building plan should show a top view of the building and the number of blocks in each position. For example:

Provide students with cubes of the same size to explore creating house designs. Once they have constructed their building, support students to draw the building plan from their constructed buildings. Encourage students to identify and draw the left, right, front, and back elevations on grid paper. Elevations are the views from different perspectives.

Guide students to make observations and connections between the left and right elevations as well as the front and back elevations. Ask students to put their drawings of the left and right elevations next to each other and ask them, “Do you notice anything similar about these two elevations?” The front and back elevations are symmetric, as are the left and right elevations.

Model how to draw a three-dimensional drawing of the initial house design on isometric dot paper, thus demonstrating another way to represent three-dimensional objects in two-dimensional perspective.

‘Drawing objects on isometric dot paper helps students to visualise three-dimensional objects in a two-dimensional perspective and engages them in both visual processing and visual interpretation. Isometric drawings show all three visible faces in proportion.’ Booker, G., et al (2014)

Support and scaffold students as they draw their own designs on isometric dot paper, as this can prove challenging for some students at first. Students could also use a digital isometric drawing tool.

Enable students by working as a group to design, build and draw each view of the house using square grid and isometric grid paper. Demonstrate how to label each face with the words ‘front’, ‘back’, ‘left’ and ‘right’, and to use this to guide the drawings. Encourage students to create their own buildings, using a reduced number of blocks if needed, and complete the task.

Extend students by introducing building guidelines that challenge students’ thinking about building perspectives and to prompt problem solving. Some examples of building guidelines are:

• The top view of your building needs to be symmetrical.
• The top view of your building must not be a rectangle.
• The base of the building must not be more than 3 cubes by 2 cubes.

Encourage students who want an additional challenge to calculate the cost of building their house when prices are given. Examples of prices can include:

• $400 to paint each external wall of a room.
• $3000 to construct a roof over each room.
• $250 to install a window on each wall that is on the front and the back of the house.

2. Designing a floor plan

Explain to students that they will be exploring floor plans for houses. Invite students to use the classroom collaboration strategy, Think, Pair, Share to discuss what they think a floor plan is, and what features they might show. Facilitate a class discussion to share ideas, and record these on an anchor chart. 

Provide students with different examples of floor plans, which can be found on building company websites. Encourage pairs of students to select two or more different plans, and to record the key features that they can see on a floor plan. Facilitate a whole class discussion about the purpose and features of floor plans, and add these to the anchor chart. Ideas may include:

• a floor plan is a scale drawing at one level of a building that shows the top view
• it is like a map of the house
• architects use a floor plan to show what a room or building will look like
• a floor plan usually shows the measurements for lengths
• a floor plan indicates the room type and uses symbols to represent furniture and other items.

Introduce students to the context of the activity with a story, such as:

"Now that you have decided on the location of your house and designed its architecture, you need to draw a floor plan so that builders can construct your house. Draw a scaled floor plan of the ground floor of your house, assigning a room type to each cube you used."

Model how to draw the floor plan for the initial whole class design. Demonstrate how to draw to scale using square grid paper, including how to scale the rooms appropriately. Using the house design they created earlier with blocks, students visualise what the ground level will look like and draw a scaled floor plan for it, labelling the total length and width of the house. Support students to determine a suitable scale factor for their floor plan, such as 1 cm = 2 m.

Observe student drawings, prompting students as needed to ensure that they understand and apply the concept of using scales and legends in their drawing.

Enable students by encouraging them to remove the upper levels of their building (if there are any) and refer to each level of their model individually when drawing the floor plan. Simplify the scale that students use to 1 cm = 1 m.

Extend students by altering the scale factor, such as 1 cm = 2.5 m. Alternatively, set a length to a side of the building and have students determine the dimensions of each room when drawing their floor plan. For example, pose the problem:

If the length of the entire house from the front to the back is 26 m, what will be the dimensions of each room in your house?

3. From a two-dimensional view to a three-dimensional object.

Provide students with clues of building views and ask them to construct the building. For example:

I used cubes to construct a building and drew two elevations of my building.

Construct as many possibilities of what my building might look like using blocks or cubes and draw them on isometric paper. What will the view from the top look like for each building?

As students are constructing and drawing the three-dimensional building, encourage them to explain the reasoning for their answers.

Challenge students to create similar problems for others to solve.

Enable students by reducing the number of blocks or simplifying the design of the building. Initially, students should construct the building to match only one view, for example the front elevation. As students successfully complete this, model how to make modifications to the building so that it also matches the views from the side elevations.

Extend students by asking them to draw the elevations of the building if the perimeter is known. For example:

• if the perimeter of the front elevation is 14 cm when sketched, what could the side elevation be? What could the building look like?
• If the perimeter, when sketched, of the front elevation is 12 cm and the side elevation is 16 cm, what could the building look like?

Areas for further exploration

1. Calculating perimeter, area, and volume

Urban Designs gives students opportunities to draw plans on grid paper, resulting in a figure made from a combination of shapes. This can lead to discussion about the perimeter and area of shapes and how the perimeters and areas of composite shapes can be calculated. Students can also learn to calculate the volume of prisms from the three-dimensional construction they built.

Challenge students to use square tiles to create the top view of buildings. Challenge them to make designs with a given area and perimeter. For example, create a design with the area of 6 square units and perimeter of 14 units. This activity can also be completed with the Area Blocks activity.

The Brush Loads activity from NRICH Maths gives students opportunities to explore the surface area of buildings made from cubes.

Ask students how they can calculate the volume of their constructions. If the construction is a regular prism, how will they do so? If the construction is a combination of three-dimensional objects, what strategy will they use?

Revisit the success criteria of this stage:

• I can visualise three-dimensional objects from different perspectives
• I can visualise three-dimensional objects from two-dimensional patterns
• I can visualise two-dimensional patterns that can be made from three-dimensional objects

Provide a question prompt that allows students to demonstrate their understanding of these concepts. For example:

'Ahmed was shown the front view of a stack of cubes He used 18 cubes of the same size to create four building designs. What could the buildings look like? What might the other side elevations of each building look like?'

Enable students by reducing the number of cubes. 

Extend students by asking, “Can buildings have the same front and side elevations but have different floor plans?”

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