1. Describing Unique Buildings Supplies: Cubes, Grid paper, Dot paper, Isometric Dot Paper, Mira Labsheets 3.1, 3.ACE

2. Finding all the possibilities. Base Outline Front Right ViewFront View Construct the building Draw the base plan How many different buildings can be made from this set of building plans (Draw a base plan for each) labsheet 3.1

3. 1. Of the different base plans you made in Problem 3.1, are there any squares with numbers that do not change? If so, identify the squares with numbers that always remain the same. Connected Mathematics, Ruins of Montarek, p.41

4. 1. Of the different base plans you made in Problem 3.1, are there any squares with numbers that do not change? If so, identify the squares with numbers that always remain the same. Connected Mathematics, Ruins of Montarek, p.41 Base Plan Front 1 1 1

5. 2. Look at the different base plans. Connected Mathematics, Ruins of Montarek, p.41 a.What is the least number of rooms for any building? b.How many different buildings can be made from the least number of cubes? c.What is the greatest number of cubes used for any of the buildings? d.How many buildings can be made from the greatest number of cubes? a.11 b.2 c.15 d.1 with 15 cubes

6. Minimal Buildings & Maximal Buildings From previous work you may have notice that there can only be one UNIQUE Maximal Building but there were many Minimal Buildings.

7. Find a minimal building and the maximal building. Base outlineFront viewRight view Bldg 1 Connected Mathematics, Ruins of Montarek, p.42

8. Find a minimal building and the maximal building. Base outlineFront viewRight view Bldg 2 Connected Mathematics, Ruins of Montarek, p.42

9. Find a minimal building and the maximal building. Base outlineFront viewRight view Bldg 3 Connected Mathematics, Ruins of Montarek, p.42

10. Create a set of building plans where the minimal building is the same as the maximal building. Connected Mathematics, Ruins of Montarek, p.42

11. The minimal building is the same as the maximal building. Connected Mathematics, Ruins of Montarek, p.42 Base outlineFront viewRight view

12. A mysterious building. (looking for a minimal building and the maximal building) Base outline Connected Mathematics, Ruins of Montarek, p.43

13. A mysterious building. (looking for a minimal building and the maximal building) Front view Connected Mathematics, Ruins of Montarek, p.43

14. A mysterious building. (looking for a minimal building and the maximal building) Right view Connected Mathematics, Ruins of Montarek, p.43

15. A mysterious building. Connected Mathematics, Ruins of Montarek, p.44 How might this maximal building be used.

16. Complete Labsheet 3.ACE