Building boldly
This is a level 4 geometry strand activity from the Figure It Out series. It is focused on Interpreting plan views 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 plan views of cube buildings.
Building boldly
Achievement objectives
GM4-6: Relate three-dimensional models to two-dimensional representations, and vice versa.
Required materials
- Figure It Out, Levels 3–4, Geometry, "Building boldly", page 14
- multilink cubes
See Materials that come with this resource to download:
- Building boldly activity (.pdf)
Activity
This activity uses the skills that students have developed in the activities on pages 8–9 of Geometry, Figure It Out, Level 3; Problem 2 on page 20 of Problem Solving, Figure It Out, Level 3; and the activities on page 11 of Geometry, Figure It Out, Levels 2–3. You may find the teachers’ notes for these activities useful and you could use the activities as a warm-up.
The students could make models of the buildings and use trial and improvement to find the smallest and largest number of cubes, but there is a more efficient method. They can use the view from the top and write in the number of cubes in each column. For example, for question 1:
From this information, the students can answer 1a, again using the top view. For example, the bottom row has to contain one 3. A 3 in the left square works from both the side and the front.
A 3 in the second square works from the side, but it does not work from the front because the front can only have a maximum of 2.
The students can use the same sort of reasoning to fill in the other squares:
For 1b, the students can use the same method, but this time they are looking for the largest number of cubes:
The students could make models of the buildings with multilink cubes to check their answers.
1.
Using the top view:
a.
1 |
2 |
3 |
1 |
The smallest number is 7.
b.
2 |
2 |
3 |
2 |
The largest number is 9.
2.
Using the top view:
2 |
3 |
1 |
|
1 |
2 |
1 |
1 |
|
The smallest number is 11.
2 |
3 |
2 |
|
2 |
2 |
1 |
1 |
|
The largest number is 13.
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