- Students will understand how to use the agent destroy obstacles command to create two water conduits.
- Students will understand how to use a repeat loop.
- Students will use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane (CCSS.MATH.CONTENT.8.EE.B.6)

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

The agent can be used to generate a “line” with different slopes.

Students can compare similar triangles to explain why the slope is the same.

Students can derive the equations y = mx for a line through the origin and y = mx + b for a line intercepting the vertical axis at b.

This activity can be completed by individual students, or by students working in pairs sharing the same world. Students will need to generate two similar triangles on graph paper that they wish to recreate in Minecraft before entering the world.

At the spawn students will interact with a villager to determine their challenge. Each student, or pair of students, is to use their agent to dig two tunnels (conduits) from the water holding tanks on the mountain, through the mountain and into a reservoir on the other side.

The player agent will begin in the empty pool on top of the mountain, and with player instructions, dig a conduit with a rise and run previously determined in class.

Students will then instruct the agent to build a second conduit near the first using an equivalent rise and run.

The result will be two similar triangles (one larger, one smaller) with the same (negative) slope. With this information students can derive the equations y = mx for a line through the origin and y = mx + b for a line intercepting the vertical axis at b.

Agent commands students may likely use include the following:

- agent [destroy obstacles] <true>
- agent move [forward, down] by (num), where the number is the rise or run.

Students should also wrap the commands within a loop:

- repeat (num) times do, where the num is equal to the number of repeats required before the agent exits the other side of the mountain.

Once the two conduits are completed, students may break the red sandstone blocks holding back the water in the tanks. Water should then flow into the pool and then down the two conduits and into the village reservoir.

Students will demonstrate their understanding of** destroy blocks command** by coding their agent to build two conduits with negative slope.

They will use a ** loop command** to demonstrate their understanding repeating actions.

They will code their agent to create two equivalent triangles with the same (negative) slope.

Students should be able to answer the following questions:

- How is a destroy blocks command useful?
- How can the slope of a line be the same if the rise and run are different?
- How can you determine x and y in both triangles?