# MathTech Review: Sumaze!

Yuji Takahashi

Co-founder

Sumaze! is a free maths puzzle game developed by MEI and Sigma Network.

The game delivers a set of puzzles that encourage students to problem solve and build their procedural fluency with
various maths operations, including:

- arithmetic operations,
- arithmetic operations with negative numbers,
- exponentiation, and
- logarithms

Sumaze! also provides a digital interaction with maths that's a refreshing change from multiple choice questions and
typing answers into a textbox.

In this post we will cover the main elements of the game, its strengths as a learning activity, and how you can
use it in the classroom.

The aim of every Sumaze! puzzle is simple: move the player block to the goal.

The player block is blue and has a number on it. Students can move it up, down, left and right by swiping the
touch screen in each direction.

The goal is marked as a slot in the maze that has the same shape as the player block.

Gatekeeper blocks are green and specify a condition. A gatekeeper block will only allow the player block to pass
through if the number on the player block satisfies its condition.

Operation blocks are red. When students move the player block through an operation block, the number on the
player block is modified according to the operation.

The key game elements in a puzzle from Sumaze!

Although the aim of each puzzle is simple, it's not always easy to achieve. To finish a puzzle, students must
carefully select which operations blocks to use on the player block and think of the sequence in which to apply
them. This challenge, combined with the interactivity of the game, makes solving puzzles an engaging experience.

Let’s have a look at an example of a puzzle.

Here’s the puzzle from the 8th level in Sumaze!:

A puzzle from Sumaze!

Note the gatekeeper block (=10) in front of the goal. To finish the puzzle, we need to modify the player block’s
value from 1 to 10, so it can pass through the gatekeeper block and arrive at the goal. How can we do this?

Here’s an attempt:

An unsuccessful attempt at the puzzle.

This attempt results in an unsolvable state. With no more operations left, it’s impossible to modify the player
block's value of 6 to pass through the gatekeeper block (=10). At this point, your only option is to press the
refresh button and try again.

With some more experimentation (trying different sequences and observing whether you’re getting closer to the
gatekeeper block value) or some strategic thinking (i.e. working backwards), we can arrive at a solution to the
puzzle.

A solution to the puzzle.

One strategy students can be encouraged to use when tackling a Sumaze! puzzle is a tree
diagram. An example for the previous solution can be seen below.

A tree diagram made while working backwards.

A strength of Sumaze! is the way it provides opportunities for students to build both their procedural fluency
and their problem solving skills.

The puzzles in Sumaze! increase in difficulty as you progress through the game. This is pretty standard for
games. Unlike many maths games however, the increase in difficulty gradually forces you to adopt more strategic
approaches to solving puzzles.

Although students can solve the first few puzzles by brute-force experimentation, the puzzles later in the game
will require students to have some level of fluency with applying various operations to numbers.
As students progress even further, having fluency will no longer be sufficient to solve the puzzles.
If students wish to avoid spending countless hours experimenting by trial
and error, they will have to think deeper about the properties of the operations and numbers available to them
in the puzzle.

So how can you use Sumaze! in the classroom? You can use the app as a 30 minute in-class activity for students
to build their procedural fluency around arithmetic operations, logarithms or exponentiation, and build their
problem solving skills.

The novel interactions and the self-paced nature of the game, lends itself well for independent work.

You can also encourage students to build their reasoning skills by getting them to explain their
solutions to the puzzles to each other in small groups.

Because Sumaze! is a mobile app, using it as a class activity will be difficult if students do not have access
to mobile devices during class.

Accessing specific topics in the app will also be challenging. To get their players used to the controls of the
game, Sumaze! only has the arithmetic topic unlocked when players first start. As such, if
you want to get your students playing puzzles from other topics (i.e. exponentiation or logarithms),
they will have to play through the game, starting from arithmetic, to unlock the other topics.

Despite these shortcomings, there’s plenty to love about Sumaze!. It’s a refreshing maths puzzle game that can
help build your students’ procedural fluency and challenge them to think deeper
and more strategically about maths.

Sumaze! is free to download on both Android and iOS platforms.