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Math > Arithmetic


Better understand the role and function of prime numbers by substituting in game items for numbers with this quirky sandbox game.

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PlayMaker School


Little Alchemy is a creative sandbox game that challenges users to combine two “elements” (not periodic elements, but "things,” such as a brick or a cloud) to create as many new things as possible. The game starts out with four elements -- fire, earth, air, and water -- that, when combined, make new things (e.g. fire + water = steam). As more and more things are created, more and more possibilities become available. The objective of the game is to fill the library with all 360 possible things (more things are added as new versions are released). While things are fairly simple at the outset (e.g. fire, mud, rain, etc.), by the end of the game players can create complex, abstract, fantastical, and quirky things such as love, a surfer, or a lightsaber.

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Experience breakdown


Combine two elements and see how many new elements you can create.

Lesson plan Overview

Prime Factorization and Little Alchemy

At its core, Little Alchemy is a game that categorizes things by the elements that comprise them, allowing players to visualize what elements are needed to make up more complex items. For this reason, Little Alchemy can be used as an effective and engaging platform to teach students about prime factorization, since prime factorization centers around a similar concept of complex numbers and their elemental (prime) components.

Students start by simply playing the game and making as many combinations as possible. As they play, students make tree diagrams of their creations within the game, showing every element that went into making their "composite" items. By assigning prime numbers to the first four elements (fire, water, air, & earth) and multiplying accordingly up these tree diagrams, student effectively create factor trees from the bottom up -- and by engaging in this activity, students reinforce their understanding of prime numbers, how they relate to composite numbers, and factors, and have an opportunity to segue into learning exponential notation.


Students identify the prime numbers and assign each number to one of the starting elements (earth, air, fire, water).

Learning Objectives

● Identify prime numbers between 0-9.

● Convert a factor tree of Little Alchemy elements and items into a prime factorization tree.

● Conclude that composite numbers are made of factors, which can be further broken down into prime factors.

● Represent the prime factorization of a number as an equation (optionally in exponential notation).

LEsson Steps

STEP 1 Have students identify the prime numbers between zero and nine (2, 3, 5, 7) and assign each number to one of the starting elements (i.e. fire = 2, water = 3, air = 5, earth = 7).

STEP 2 Allow students to play Little Alchemy either individually or in groups, so that the library of elements and items becomes populated to several levels of complexity.

STEP 3 Take one of the more complex items (e.g. “life” or "volcano") and walk students through the process of making a tree diagram demonstrating all the elements that went into creating life. In this instance, life would be at the top of the tree, and at the bottom there would only be the four base ("prime") elements.

STEP 4 Apply the prime numbers to the elements at the bottom of the tree, then have students multiply up the tree until they reach the top (in our example, "life” would have a value of 1050).

STEP 5 Reverse this process by giving students complex item and its associated numerical value (e.g. "fireman" = 3150), and have them work down the tree to find its primary elements.

STEP 6 Optional: Have students write out the prime factorization in exponential notation.


Students create large factorization diagrams.


  • The number of prime factors will increase exponentially based on the apex item's level of complexity.
  • Final values will change depending on which numbers are assigned to the primary elements.
  • In the game, there may be several ways to create an item, and this is true in math as well (e.g. 3x10=30 and 5x6=30). However, because these alternate item recipes may not be numerically equivalent to one another, it is possible (and probable) for two different numbers to "inaccurately" be represented by the same item. Take care in which items and prime numbers you assign to students' work.
  • If desired, other primary numbers (larger than 7) may be assigned to the primary elements.


Common Core - Mathematics


Grade 4: Gain familiarity with factors and multiples.

CCSS.Math.Content.4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

ISTE NETS - Digital Age Skills

Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
Apply existing knowledge to generate new ideas, products, or processes 
Create original works as a means of personal or group expression
Use models and simulations to explore complex systems and issues
Identify trends and forecast possibilities 

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