### Learning Objectives

- Students will understand how to use the fill command to recreate polygons in three dimensions.
- Students will understand relative position.
- Students will determine area and volume of polygons. (CCSS.MATH.CONTENT.7.G.B.6)
- Students will solve problems involving scale models of geometric figures and reproduce scale models at a different scale. (CCSS.MATH.CONTENT.7.G.A.1)

### Guiding Ideas

Before beginning, students should be able to create ** player chat commands** and understand how to insert a

*. Knowledge of the xyz coordinate system would also be beneficial.*

**block fill command**Positive and negative coordinates place an object to the left/right, up/down, and forward/backward relative to the player.

Scale renderings of models can be created if given a scale factor.

Area is determined by multiplying length x width and volume is determined by multiplying length x width x height.

Block commands can be used to fill in three dimensions.

Block commands can be used to create solid or hollow structures.

### Student Activities

This activity can be completed by individual students, or by students working in pairs sharing the same world. Students will likely need scratch paper and a location to record their building dimensions and calculations. One option is to use the student portfolio available in * Minecraft: Education Edition*.

Students will investigate a model layout that contains three buildings of different size and a cactus. Their challenge is to create two scale models of this configuration. One reproduction should be created in area 1 using a scale factor of 1.5 (150%) and the second reproduction is to be built in area 3 using a scale factor of 0.5 (50%).

Area 2 contains the model that the students are to reproduce to two different scales, one larger, one smaller.

The buildings in area 2 have the following dimensions:

- 6 x 6 x 6
- 8 x 8 x 8
- 10 x 4 x 4
- the cactus is 4 blocks tall

The entire configuration sits on top of 20 x 20 x 1 grass blocks

Students will use the * blocks fill command* to complete the assignment. They should:

- determine the dimensions of the scaled polygon to be created and identify the block, then
(grass, acacia planks, acacia wood, or stripped acacia wood)**fill with**(current player position, or they could adjust the first and last coordinates to place front/back and right/left of their position)**from ~0 ~0 ~0**(representing the volume of the object to be created)**to ~x ~y ~z**

*Note that the * to coordinates* represent a position relative to the player and sometimes produce structures one block larger in each direction than desired. For example, creating a 10 X 10 X 10 cube sometimes requires players to enter ~9 ~9 ~9

Area 1 contains enough space to lay down a 30 x 30 x 1 grass area and area 3 can fit a 10 x 10 x 1 grass area. Each grass area can then accommodate scaled buildings and a cactus.

While working through this challenge, students should record:

- area on which the buildings are constructed
- dimensions of each building created
- volume of each building created
- height of each cactus
- photographic evidence of their scaled buildings

### Performance Expectations

Students will demonstrate their understanding of block fill commands by creating multiple polygons of various scaled sizes.

They will create a 150% scaled reproduction of the model and a 50% scaled reproduction.

They will accurately calculate the volume of each building.

They will accurately calculate the area upon which the collection of buildings sits.

As an extension, the teacher may challenge students to calculate the entire building zone (80 x 40, surrounded by a border of water) and then determine the amount of area not covered by grass blocks.

Students should be able to answer the following questions:

- How is a
useful?**blocks fill command** - What are the volumes of each 150% scaled building compared to the model buildings?
- What are the volumes of each 50% scaled building compared to the model buildings?
- How large is each build area?
- Predict the size of a 200% scaled model.