Building Boldly

This activity uses the skills that students have developed in the activities on pages 8–9 of Geometry, Figure It Out, Level 3; Problem Two 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.
 

Answers to Activity

1. Using the top view:

a.

The smallest number is 7.

b. 

The largest number is 9.

2. Using the top view:

The smallest number is 11.

The largest number is 13.