Learn Reflective and Rotational Symmetry with Symmetry School for iPad

One of the great things about reviewing educational apps is having the opportunity to learn about various national curriculums used to design these apps. Two examples that I think are appropriate for today’s app pick include the Common Core Standards used by US educational institutions and the NSW Syllabuses used by Australian educational institutions.

The Common Core Standards for Grade 8 state that students should experiment with rotations and reflections. If you read the NSW Syllabus for Stage 3, you will find that students should be able to describe the effect when a two-dimensional shape is reflected or rotated. If you have juniors who are currently learning about symmetry, reflection, quadrants, and rotation, then you will find our app pick for today very useful.

A finished symmetry board.Symmetry School is an excellent learning tool to learn about reflectional and rotational symmetry

Reflective Symmetry

Symmetry School: Learning Geometry is a beautiful iPad app from Spraoi School which tries to help juniors learn how symmetry/mirroring and 90 degrees clockwise rotation work through games. Using basic geometrical shapes such as circle, triangle, square, pentagon, and hexagon, the app asks you to demonstrate your understanding on how these shapes would look like when they are mirrored or rotated.

The app has two game modes to choose from: Reflective Symmetry and Rotational Symmetry. Each mode also comes with three difficulty levels: Easy, Medium, and Hard. I would suggest choosing the Easy level of Reflective Symmetry if this is your first time playing.

In the Easy level, you will see a vertical line of symmetry dividing the 8×8 grids into two equal parts. You will see 12 objects of the same shape, four from each of the three colors, put randomly on the right side of the board. On the left hand side, you will see a pool of exact copies of these 12 objects ready to be dragged to the left side of the board. Your task is to arrange them such that they’re reflecting the objects on the right side of the board.

If this is your first game, you can also tap on the Show Me button to see an animation demonstrating the reflection process by flipping the right side of the board to fill in the left side of the board. Based on this visualization, you can start putting objects in their respective positions.

When you’re ready for more challenges, the Medium level adds a second line of symmetry that divides the board into 4×4 quadrants. The app will show up to 12 objects in one of the quadrants, and your task is to put copies of these objects in all the other quadrants by applying mirroring principles on both lines of symmetry. To make things even more challenging, the app gives you two shapes (circles and squares) and four colors instead of three to play with.

Finally, the Hard level randomly places the initial shapes in up to three quadrants instead of one. This mode also uses all five colors and five shapes. This provides quite a challenge even for some adults.

An easy level Rotational Symmetry.The app comes in two modes, each with three difficulty levels

Rotational Symmetry

The second game mode tries to teach how 90-degree clockwise rotation works. On the same 8×8 grid, you start with four objects of the same shape plotted in two adjacent quadrants. This can be treated as a tutorial for first timers. It helps new learners to visualize how the rotation should work. The Easy level also provides the Show Me button to show how the full 360-degree rotation works.

Once you get the hang of things, you can move up to the Medium level, which shows more objects in more shape and colors. The objects are placed in one of the quadrants, and you’re asked to put where the rotated copies should be in all the other quadrants.

In the Hard level, things are much more difficult even though you start with fewer objects spread across three quadrants. In addition to figuring out where an object would be located after it is rotated 90 degrees clockwise, you have to know how the rotation would affect its orientation as well. It’s not easy to imagine how triangles, pentagons, and hexagons would look like when they’re rotated.

A Hard level Reflective Symmetry game in progress.The app includes hints to help you when you are stuck

Parents Need to Know

Although this is a game, the app doesn’t show any visible timer while you try to solve a board. This allows you to focus on getting each piece correctly placed. Once the board is completed, the app will show you the number of moves and the total time you took to complete the board. You can then email the result if you want.

If you want to play another game, simply tap the replay button. It will reset the current board and show you a new board with the same difficulty level. You can also replay the game any time if you want to reset the current progress.

If you’re a teacher and you’d like to use the app in your class, there is a Flash version on the app on the developer’s website. This Teacher's Whiteboard Version allows you to play both game modes with all three difficulty levels on a web browser. To access to this version, you need to register with an activation code that is included with your app’s purchase. Simply go to the Info screen and look at the bottom right corner to find the activation code.

Finally, you can also try the Free Play mode to practice how reflection and rotation works. This mode allows you to drag any combination of colors and shapes onto the 8×8 grids to practice these concepts at your own pace.

You can review your performance at the end of every game.The game only shows your time and number moves at the end

Things I Like

I personally find the app an excellent tool for learning geometrical concepts visually through trial and error. The feedback is almost immediate. The UI does feel a bit serious, but it can also be considered playful at the same time thanks to the use of bright colors and dynamic shapes.

I really like how the app uses hints instead of giving out the exact location of where a piece should be. The app also provides different sets of hints for each game mode and difficulty level. To access these hints, simply tap the bulb icon at the bottom of the screen. Here are some examples of the hints that you will encounter in the Easy level of Reflection Symmetry:

  • Try mirroring all counters of one color at a time
  • Try mirroring all counters in one row or column at a time
  • Try to imagine folding the board along the mirror line
  • Try counting grid squares outwards from the mirror line

Practice your mastery of rotational and reflectional symmetry in Free Play.There is also a Free Play mode which lets you practice freely


Symmetry School: Learning Geometry is an excellent app that provides endless rounds of challenges to help kids perfect their mastery of reflection and rotational symmetry. Through the app, juniors can measure how well they are doing by assessing the time and number of moves they took to finish each challenge. The implementation of three difficulty levels also means that juniors can take their time and progress whenever they’re ready.

Symmetry School is available for iPad
Get it on the App Store: iPad

App was provided for our honest review.