 One of the reasons why Minecraft is such a powerful learning tool is how easily it can be used to visualize math concepts. The first time I saw the game being played it was clear to me that I could use the blocks in the game as hands-on math manipulatives. In this article, there will be quick lessons on:

• building fractions
• equivalent fractions
• comparing fractions
• multiplying fractions
• finding fractions on a number line
• finding a missing number using a ratio comparison

All of these structures are super easy to build and will help you and your students learn how to control and move in the game. These lessons are specifically designed to assist new to Minecraft teachers with simple ways they can use Minecraft: Education Edition to teach the concepts involved with exploring fractions. Before you let your students into the game, build these structures in front of the class and have a discussion about what is going on with the structure. Have the students do the math on paper as you build the models. Once you have gone over the structure, have the students build 3-5 problems, then incorporate free play time in the world. Fraction Models (related video) Let’s start with creating fractions in Minecraft. Start by building a tower out of glass and solid blocks that matches the fraction you are trying to explore. The solid blocks represent the numerator, and the total number of blocks represent the denominator. For example, in this picture we have a model of ⅓ and ⅖ . To make solid blocks stand out, use blocks with dark edges (like jewel blocks and polished stone), so you can see each individual block. As you can see in this picture, blocks without dark edges (like wool blocks) make it harder to tell how many blocks there are in the measurement.

Ratio Walls (related video) The concept of equivalent fractions is often a difficult concept to for students to fully grasp; luckily there is Minecraft. To make a ratio wall start with building a fraction model. Next, skip a space and build the same model but put two of them next to each other, then three, then four, and so on. When you look at the long side of wall, you will see a fraction in the unreduced form. However, when you move the camera to look at the short side they will all demonstrate the same reduced form of the fraction. Here are two pictures that show ratio walls for ½. The first picture shows ½, 2/4, 3/6, 4/8, 5/10 and 6/12. The second picture illustrates the ratios walls from a different angle. All walls in the second picture also show ½.

Demonstrating Inequalities (related video) Inequalities (also known as greater than or less than) build off the concept of ratio walls. To start, build the two fractions you wish to compare with about five spaces between them. Next, ask your students which one is bigger. During the number talk, point out how they both have different number of total blocks or “denominators” and how this shows that it’s not a fair comparison. Therefore, the students must find a number that both “denominators” multiply into. Lastly, expand the fraction models into a ratio wall with an equal number of blocks and simply compare the amount of the solid blocks to find the larger fraction. The two pictures compare ⅕ and ¾ . The first picture shows the reduced form. Notice how the denominators are not equal, however 4 and 5 fit into 20. The second picture shows how ⅕ can be expanded into 4/20 by multiplying the fraction model by 4/4 and how ¾ can be expanded into 15/20 by multiplying the fraction model by 5/5.

Multiplying fractions in arrays (related video) Let’s demonstrate ⅗ x 4/6 by using our fraction models and the formula for an area - length times height, LxH=A. Start your equation in Minecraft by building a length of ⅗, followed by a height of 4/6. Next, find the numerator by completing the rectangle with the solid blocks and find the denominator by completing the rest of the rectangle. The total number of blocks represent the denominator.

Fractions of a Number Line (related video) To examine how fractions fit on a number line, start by building a number line. To do this, start by choosing how many parts make a whole. Use two kinds of blocks: one for whole numbers and one for fractions of whole numbers. As you can see in the picture, the red block represents 0, the diamond block represents whole numbers, and the gold block represents parts of a whole. The denominator is 4 as every fourth block is a diamond. This number line goes from 0 to 3. After the number line is complete, the next task is to add points onto it. For example, after creating the number line explained above, I asked my students to find the points ½, 1 ¼ , 5/4, 8/4 and 2. The students marked the points by placing a block on top of the number line. They noticed some points have more than one number representing them, for example 1 ¼ and 5/4 land in the same spot and so do 8/4 and 2. This is another way to illustrate the concept of equivalent fractions.

Crafting Ratios  Learning how to craft items in survival mode is an engaging way to introduce ratio comparisons to 5th and 6th grade students. Step 1: Find the Ratio (related video) Look at this picture illustrating the stairs crafting recipe. On the left side of the picture you will see a 9-square crafting grid with six stone blocks inputted in the shape of a stair. On the left of the arrow there is a smaller box with a picture of a stair with the number 4 underneath. That means for every 6 stones you put on the crafting table you will receive 4 stairs, creating a ratio of 6:4. Step 2: Find and Solve a Ratio Comparison Once you have the ratio you can ask questions like “How many stones will I need to gather to create 12 stairs?” Now just set up the problem like this (6/4=s/12), solve for stones (s=18), and test to see if 18 stones will give you twelve stairs! Step 3: Creating your Test Go into a survival world and gather the 18 stone the ratio comparison indicated you needed (if you don’t have a crafting table make one). It should look like this picture. Divide the 18 stones into the 6-square needed for the crafting recipes, and you will notice that there are 3 in each square because 18/6=3. Also, the output has a 4 and 3x4=12, the total number of stairs we wanted. Helpful tip: The same crafting recipe works on a number of different blocks. For example, you can craft stairs with wooden planks, stone, and sandstone too. There are a lot of great tools for math out there, but few are as unique in capturing students’ imagination like Minecraft. Not only does it make math visual - it presents math in a tangible way, creating something you can play with. For more lessons, please check out the Mathcraft website and while you are there, feel free to sign up for the Mathcraft Wiki.

Jim Pike is the upper elementary teacher at Sycamore School in Malibu, California and the Director of Game Based Learning at CodeRev Kids Learning Center. Jim has been teaching with Minecraft for 4 years and uses the game to teach everything from math, film, and biology to coding and video game design. When Jim is not teaching he enjoys surfing, ice hockey and designing cheese burgers.