Crazy cubes
This is a level 3 geometry activity from the Figure It Out series. It is focused on interpreting and drawing representations of cube patterns and identifying the pattern in a series of cube buildings. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Interpret and draw representations of cube patterns.
- Identify the pattern in a series of cube buildings.
Crazy cubes
Achievement objectives
GM3-4: Represent objects with drawings and models.
NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Required materials
- Figure It Out, Level 3–4, Geometry, "Crazy cubes", page 4
- multilink cubes
- copymaster of isometric paper (Isometric paper CM)
See Materials that come with this resource to download:
- Crazy cubes activity (.pdf)
- Isometric paper CM (.pdf)
Activity
Activity 1
This activity requires students to view 3-dimensional models made from multilink cubes, make the models, and practise drawing models on isometric paper (Isometric paper CM). Drawing the models on isometric paper is quite a challenging task, but it follows on from the activities on pages 6 and 10 in Geometry, Figure It Out, Level 3.
If the students record their findings for question 1 on a chart as shown in the answers, it makes it easier for them to look for patterns and to predict the next model in the sequence. As noted in the answer for question 3, the difference generates triangular numbers. (This activity connects to the algebra strand.)
Activity 2
Some students may have difficulty working out the various layers of the isometric drawing in this activity. The following diagram of the layers may help.
- Stage 5 will be 41 + 50 + 26 + 10 + 2, and so on.
As an extension, the students could also use the models in both activities to draw views from different perspectives such as the front, top, and side. This task can help them to visualise and draw 3-dimensional models. It also makes them realise that cubes can be part of a model but cannot always be seen in a drawing. Alternatively, given a drawing of different views, the students could create the 3-dimensional model.
Activity 1
1.
Practical activity. A table is a good way to organise the information:
Hour |
Number of cubes in crystal |
Difference |
|---|---|---|
1 |
1 |
|
2 |
4 |
3 |
3 |
10 |
6 |
2.
a. Practical activity. The crystal should look like this:
b. The crystal has 20 cubes at hour 4 and 35 cubes at hour 5.
3.
When the crystal is made with cubes, the difference between the number of cubes in each stage is a triangular number.
So a note to Cecily could read:
Dear Cecily,
The crystal pattern is growing a little more each hour. In the first hour, the crystal grew by three cubes. In the next hour, the crystal grew by six more cubes, then by 10, and then by 15. I think the pattern is triangular.
Yours sincerely
signed
Activity 2
1.
Practical activity
2.
63
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