The Skate Park

In this activity, your students are helping Finley create a skate park! As they construct ledges and ramps, they’ll get to see volume come to life with real-world measurements.

Why Use the Skate Park Activity?

The Skate Park is about reinforcing volume concepts, and getting students to think about these concepts in a low-stakes, creative way, rather than a performance-based way. 

The Skate Park discusses the volume of a rectangular prism as length times width times height. It also introduces the volume of a triangular prism as half that of a rectangular prism of the same dimensions. Most specifically, it’s a visualization of the relationship between area of a flat shape, height of the extension of that shape into 3D space, and volume. 

The units used in the Skate Park are feet, square feet, and cubic feet. The measurements correspond to real-world measurements with 95% or more accuracy, varying only due to minute differences in how the device camera detects the physical environment. Therefore, this activity allows students to explore measurement as well as geometry. 

The Skate Park is not intended as an introduction to the concept of measurement in cubic feet, or how to calculate volume of a prism, but our simple interface may demystify the concepts in a way that paper and pencil struggle to express. It also gives the students more control over the shapes they are creating than activities with blocks do. 

This activity also holds inherent appeal for the students. Helping the character of Finley with something as cool as skateboarding is exciting! Moreover, the activity gives students the chance to move around and explore math while standing and walking, which is an exciting break from sitting at a desk.

What is in the activity?

This activity gradually scaffolds the information about how to build the skate park, before giving students a “sandbox”(i.e., an open-ended exploratory setting) in which to build their own skate obstacles. Here is a breakdown of what students are doing at each step of the activity.

1. Students learn how to connect dots placed on the floor of the space in a grid, by tapping one dot, dragging to the next dot, and letting go. This creates a Flat Rail, a basic skate obstacle, which Finley will demonstrate.
   Math Concept: Connecting two dots to form a line segment. 

2. Next, they will learn how to create a 1ft³ unit cube. They will connect four dots on the ground to make a square, and see that it is 1ft². Then, they will learn how to drag the shape off the floor and into the third dimension. This is done by pressing in the center of the shape and dragging up on the screen until the app shows that the volume is correct. This creates a ledge that Finley will jump over on their skateboard. 

Math Concepts: A unit square being used to form a unit cube, the relationship between height and volume for a rectangular prism, real-world illustration of 1 foot measurements.

Math Question, before forming the ledge: What kind of shape could you make out of these dots?

Math Question, after forming the ledge: How high did Finley have to jump to make it over the ledge?

3. Third, the students will learn how to create a ramp, a triangular prism. This time, there are six dots on the ground. The student is again tasked with creating a rectangle by connecting the dots, but they can make it either a rectangle with an area of 1 ft^2, or one with an area of 2 ft^2. This rectangle will serve as the bottom of their ramp. 

Before we move on, let’s talk through WanderMath’s decision to construct the bottom of the ramp as a rectangle, and how that impacts the math visualization. The formula for the area of any prism is (base) times (height). For a triangular prism, that means (length times  width times  ½) times (height), because the triangle is considered the base. In our activity, we do not consider the triangle to be the base, we consider one of the rectangle-shaped faces as the base, and the triangular faces are considered part of the height (rectangular bottom, triangular sides). This is because it is much easier to visualize that what you are building is a ramp when it looks like a ramp as it is being raised out of the ground. If a triangle was the base, the entire shape would have to be rotated in space in order to look like a ramp, and it would be harder to visualize “height” as being actually related to how high the ramp would be when Finley skates on it. Therefore, we state the formula for volume of a triangular prism as (length of base) times (width of base) times (height)x(½). 

Now, the student will see how their choice of the size of the rectangular base impacts the volume. Finley tells the student that they need the ramp to use 1ft^3 of concrete. If they started with the smaller base, their ramp must be 2ft tall to fulfill this condition. If they started with the larger base, their ramp only needs to be 1ft tall. The way that they construct the ramp in the 3rd dimension is almost the same as the way they constructed the ledge. Instead of pressing in the middle of the rectangle, though, they will need to press on the edge, to drag that edge up and thereby create a triangular prism. The student can drag up on whatever edge they’d like to create the ramp, so not every student’s ramp will look the same, even though they have the same volume.

Math Concept: Volume formula for a triangular prism, different shapes that have the same volume, relationship between volume for a rectangular prism and triangular prism, commutative property of multiplication

Math Question, before forming the ramp: How big do you want the base of your ramp to be? Which one do you think will use more concrete: your ledge or your ramp?

Math Question, after forming the ramp: How much concrete did your ramp actually use- more or less than you thought it would? Was your ramp taller or shorter than you thought? How much concrete would a ledge with the same length, width, and height use?

4. Finally, the students will put all of what they’ve learned together to create the skate park. With a 4×3 grid of dots (which takes up 3ftx2ft of floor space) and 6ft^3 of concrete to use, the students can freely create ledges and ramps of many different base and height configurations. In order to create any shape, they must draw a rectangle, but for any rectangle, they can either tap in the center to make it a ledge, or on the edge to make it a ramp. There are many, many different configurations. Some configurations are not possible, due to Finley not being able to safely skate when two obstacles border each other. 

Math Question, before starting: What obstacles do you want to have in your skate park? How tall do you think they’re going to be?

Math Question, after finishing: What was the tallest obstacle in your skate park? What was the obstacle with the largest volume? What was the obstacle with Finley’s coolest trick?

5. When they’re done, they can double tap Finley to finish the Skate Park!

What’s Not in the Skate Park Activity?

The Skate Park only covers volume for rectangular and triangular prisms. It also covers the volume of a triangular prism in a slightly different way than extending a triangle into the third dimension, which may be different from other ways of talking about volume. Rather than phrasing the formulas (length x width x ½) x (height), we phrase it as (length) x (width) x (height) x (½). This provides greater connection with the formula for volume of a rectangular prism, but less connection with the formula for area of a triangle.

The measurements in the game are accurate within several percentage points of one foot (less than 1 inch), but due to differences in device cameras, cannot be guaranteed to be as accurate as a ruler or tape measure.

Other ways of measuring volume, such as liquid displacement for irregularly shaped objects, are not part of this activity.

Suggested Classroom Integration

The Skate Park is useful as a jumping off point for a larger discussion about volume and measurement. Questions you could ask the students might include:

• How do you know how much concrete it takes to make a ledge?
• Which one takes more concrete, a ledge or a ramp?
• There are many different ledges that could all use the same amount of concrete. Why do you think they all look different?
• If Finley was human-sized, how much bigger do you think the ledge and ramp would be? How much more concrete would they use to build?
• If Finley wanted to paint the obstacles a new color, how would you help them figure out how much paint to buy?
• If the base of a ramp was a triangle, not a rectangle, would that change how you calculate the volume?
• Ask students to take a screenshot of their finished park to show to the rest of the class, and talk about how they made it. 

Helpful Tips for the Skate Park

Measurements are displayed as the student draws the 2D shape, as well as when they are dragging up to create volume. The units used in the Skate Park are feet, square feet, and cubic feet. 

If a student is having trouble connecting the dots on the floor’s grid, remind them that the dots must be connected in the shape of a rectangle. 

If a student is having trouble making a ramp, remind them to drag up from the edge of a rectangle, not from the center. 

If a student’s finger goes in front of the camera, the AR will start to lag and not function properly. It may be best to use a case that has handles or a grip, so the student’s hands are not tempted to stray in front of the camera.