Four Cube Houses: What is your point of view?
Name: _________________________________
Date: _______________
Statement of Inquiry
Through innovation and perspective, 3 dimensional views can be represented on a 2
dimensional plane . (Different views of prisms and solids formed from combinations of
prisms can be represented in drawings.)
Key Concept:
Perspective
Related Concept:
Representation
Global Context:
Personal and Cultural
Expression
Inquiry Questions
Factual-What is perspective?
Conceptual-How does perspective influence representation of 3 D shapes in a 2D plane?
Debatable-How might we determine which representations are most economical?
Task Outline:
Imagine you are architects who have just won a contract to build home sites on a new estate down the road from Linden
Park Primary School.
Your task is to find all possible combinations of four block (cube) houses.
You then need to cost your designs and produce a new housing estate poster showing where the houses will be
built and their total costs.
Design Brief: Four Cube Houses
Congratulations!!
Our company has won a contract to supply modular houses made of four cubes
to a new housing estate. The construction rules are:
 all cubes are the same size.
Cantilevers are not permitted
 all cubes touch face to face (not like in our logo).
 there are no 'cantilevered' structures.
 all the houses must be different, ( ie: cannot be transformed into each other by a simple rotation, reflection or
translation.)
1. Your task is:
 Design as many four cube houses as possible. Record the number of faces, edges and vertices for each model.
 Draw each house on isometric dotted paper.
 Work out the total construction cost of each design using these figures and record all working out:
o Floors:
- ground floor $3000
- first floor
$5000
- second floor $9000
- third floor $12000
o $1,000 for each square unit of external wall.
o $2,000 for each square unit of roof.
2. You now have an isometric drawing of each house design and its cost. On an A3 sheet of grid paper:
 draw the streets for the new housing development estate
 mark out 15 blocks of land and calculate their cost according to $10,000 for each square unit of land in the sub-divided
block
 redraw and cut out the isometric drawings and glue them to each block
 make sure the costing of the house and land package is written in as a 'price tag' (house price plus land cost)
 add commentary about the attractiveness and features of each house. See examples below:
This design keeps the resident fit
because the kitchen is on the top floor.
You save on lawnmowing costs with this
geometric beauty.
.

present the whole poster for class display.
3. Reflection:
What mathematical concepts were used in this investigation?
What mathematical techniques or methods did you use to complete this task?
How accurate are your results and how can you verify this?
Explain how the mathematics used in this activity connects to the real world.
4. Extension task for those who like a challenge
 Use x blocks to build a house worth $100 000.
 Show all calculations
B: Investigating patterns
level
0
Achievement level descriptor
Our task descriptors
The student does not reach a standard described by any of the descriptors below.
1–2
The student is able to:
i. apply, with teacher support, mathematical problemsolving techniques to recognize simple patterns
ii. state predictions consistent with simple patterns.
You have:
found and recorded some possible patterns that can be made
from four cubes to depict the cube houses with support
3–4
The student is able to:
You have:
identified and recorded some possible patterns that can be
made from four cubes to depict the cube houses
5–6
7–8
i. apply mathematical problem-solving techniques to
recognize patterns
ii. suggest how these patterns work.
The student is able to:
i. apply mathematical problem-solving techniques to
recognize patterns
ii. suggest relationships or general rules consistent with
findings
iii. verify whether patterns work for another example.
The student is able to:
i. select and apply mathematical problem-solving
techniques to recognize correct patterns
ii. describe patterns as relationships or general rules
consistent with correct findings
iii. verify whether patterns work for other examples.
You have:
identified and recorded many possible patterns that can be
made from four cubes to depict the cube houses
You have:
independently and confidently investigated, identified and
recorded all possible patterns that can be made from four
cubes to depict the cube houses
D: Applying mathematics in real-life contexts
level
0
Achievement level descriptor
Our task descriptors
The student does not reach a standard described by any of the descriptors below.
1–2
The student is able to:
i. identify some of the elements of the authentic real-life
situation
ii. apply mathematical strategies to find a solution to the
authentic real-life situation, with limited success.
You have attempted to

make a connection to the real world

describe the mathematics used in this activity
3–4
The student is able to:
i. identify the relevant elements of the authentic real-life
situation
ii. apply mathematical strategies to reach a solution to
the authentic real-life situation
iii. state, but not always correctly, whether the solution
makes sense in the context of the authentic real-life
situation.
You have stated

the mathematical techniques or methods you used to
complete this task

how accurate your results are and how the can be
verified

how the mathematics used in this activity connects to
the real world
with some accuracy.
5–6
The student is able to:
i. identify the relevant elements of the authentic real-life
situation
ii. select adequate mathematical strategies to model the
authentic real-life situation
iii. apply the selected mathematical strategies to reach a
valid solution to the authentic real-life situation
iv. describe the degree of accuracy of the solution
v. state correctly whether the solution makes sense in the
context of the authentic real-life situation.
Your responses provided a mostly detailed and accurate
description of

the mathematical concepts were used in this
investigation

the mathematical techniques or methods you used to
complete this task

how accurate your results are and how the can be
verified

how the mathematics used in this activity connects to
the real world
7–8
The student is able to:
i. identify the relevant elements of the authentic real-life
situation
ii. select adequate mathematical strategies to model the
authentic real-life situation
iii. apply the selected mathematical strategies to reach a
correct solution to the authentic real-life situation
iv. explain the degree of accuracy of the solution
v. describe correctly whether the solution makes sense
in the context of the authentic real-life situation.
Your responses provided a detailed and accurate
explanation of

the mathematical concepts were used in this
investigation

the mathematical techniques or methods you used to
complete this task

how accurate your results are and how the can be
verified

how the mathematics used in this activity connects to
the real world
MATHEMATICS
Levels
Achieved
Criteria B:
Criteria D:
Max 8
Max 8
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