# Tilt-a-Graph

Explore graphing and angle measurement by tilting your smartphone—and then see how you can use a graph to tell a story.

20 minutes to prepare, 1+ hour for activity

### Tools and Materials

Facilitator Note

In this activity you’ll be using your phone as a tool to measure and record changes in tilt, and in the process exploring the relationship between graphs and the physical world.

This guide was written to support facilitators leading others through the activities, with the following expectations. While it’s not necessary to meet all of these expectations, they will help give you a sense of where you might have to adapt:

• Learners are at least 10 years of age.
• You’ll need 5–10 minutes prior to doing the activity to download the app on one phone.
• Both facilitator and learners are familiar with Science Journal and its Project, Experiment, Trial setup by going through the Getting Started activities.
• The facilitator has run through the activities prior to facilitating. If this is not possible, we hope that a facilitator will do the activity alongside their learners to better understand what is going on.
• The activity is designed to boost inquiry-based learning skills and scientific practices, not meet specific goals regarding the content.

### Set Up: Build Your Seesaw

Tip

This activity requires use of a seesaw with your smartphone. Below are instructions to build a simple version of a seesaw, but feel free to use one you have on hand or build one based on your own design. What is important for exploration is for the phone to be able to tilt all the way in either direction, so it can be both flat and almost vertical in both orientations.

1. Measure and draw two lines on a piece of chipboard using a ruler.

The lines should be about an inch (2 cm) apart and run down the middle of the chipboard’s shorter side. The two larger pieces should be the same size.

2. Cut the chipboard along the two lines, and apply tape so that each piece meets again. Fold the two larger pieces up to form a triangle.

Cutting rather than bending the chipboard allows you to fold it more easily. The smallest side of the triangle will form the base of your seesaw.

Tip

Because chipboard is thick, you might experience some difficulty cutting it. Use whatever resources you have (such as metal rulers or straight edges) to make these steps easier and safer for you.

3. Set your triangular base aside and collect your other piece of chipboard.

4. Cut your second piece of chipboard in half.

You can cut your chipboard in half in either direction (long or short side).

5. Tape one half of the cut chipboard to the base of the triangle.

This forms the wedge of your seesaw. It prevents the seesaw from tumbling as it tilts later on.

6. Tape a skewer so that it runs perpendicularly down the middle of the other half of chipboard.

You’ll be making this into the seesaw’s plank.

7. Cut two pieces, about one inch in length, from a paper straw.

8. Insert each end of the skewer into one piece of straw.

This forms the axle, the mechanism which allows the seesaw to tilt smoothly.

9. Tape the straw pieces to the ends of the top point of the triangular base.

It should now resemble a seesaw.

10. Tape the phone to the middle of the plank.

The middle of the phone should sit just above the center of the seesaw stand so that the top and bottom of the phone move up and down with the ends of the plank.

11. Open Science Journal and set your sensor to the Y-accelerometer.

The Y-accelerometer senses different kinds of movement. The seesaw limits that movement so that your measurement is only of tilt.

You’ll be using both graph and meter modes for this activity, which you can go back and forth between using the “i” icon in the top right corner of the sensor card.

### Try This: Test the Seesaw

Tilt your seesaw and observe changes. Find a partner and work together.

1. Try to reach a particular number in meter mode.

For example, can you make your meter read 2 m/s2? How about -6 m/s2?

Look around: What do you notice about the tilt of other seesaws that have reached the same number?

2. Now, try to make a graph with curves, straight lines, rounded edges, and sharp corners.

Have a partner observe how your seesaw is moving to make specific shapes or angles and describe it to you.

3. What is the highest positive value that you can make? What is the lowest value?

Talk with a partner about what you think these numbers mean.

Tip

Once you’ve tried the challenges below, feel free to create a worksheet of challenges using your own shapes or values for others to complete. At the end of this activity you can find a sample worksheet.

### Try This: Draw a Line Over Time

Measurements over time create lines—see if you can draw the lines below. (Some are tricky; it may take a few tries.)

1. Draw a straight, diagonal line.

Did you move fast or slow to do this? What position was the phone in when you started and when you finished?

2. Draw a curved, diagonal line.

How was your movement different this time?

3. Draw a vertical line.

Is your line perfectly straight up and down? Why or why not?

4. Draw a horizontal line.

Are there multiple ways to make this line?

5. Which one of these graph shapes is impossible to draw?

Try drawing each of them to find out. What makes it impossible?

### Try This: Scaling Triangles

Make triangles of various proportions and discover the relationship between speed, slope, and shape.

Tip

For this activity, the Record feature of Science Journal will be helpful. While in either graph or meter modes, use Record to document your observations and organize these trials into your experiments. Multiple recordings can give you a fuller look into your data.

To make a recording, press the red button to start and then again (it will be replaced by a gray square) to stop. Once you’ve finished recording, you’ll automatically be taken to Run Review, where your data is presented in multiple ways. Use the slider on the graph in Run Review to see particular values at a given time.

Tip

Record your graph only when you are ready to capture your data. It may help to find a partner to handle the recording while you do the tilting.

1. Draw a triangle in graph mode that looks like this and record your graph.

Did you perform a slow or fast tilt to make your triangle? At what position did the phone start and end? Was it ever flat?

2. Review your recording.

Scroll through to find values at certain times.

What value is at the first bend of your triangle? How about the top point? How much time is there between the first bend and the top point of the triangle? How about between the top and last bend of your triangle?

3. Now try choosing your own values to reach in meter mode.

Choose a small number, such as 2, then choose a higher one, such as 6, then return to the first number. Using meter mode, record your progress through the three values.

4. Make multiple recordings in meter mode reaching these same three numbers.

As you make recordings, notice the position of the phone and the speed of your tilt. Is it easier to reach your numbers after a few trials?

5. Review all of your triangles in Run Review.

Compare the graph shapes, from the first step in which you drew a triangle to the recordings you made reaching your three numbers. How do the graph shapes compare? How does their data compare? Scroll through to explore the data between corners.

### Try This: Squiggle Along Axes

Draw squiggling lines to explore the relationship between data points and axes.

Tip

In these challenges, start by using the 0-line to draw your graphs. This will give you greater space for movement as you explore.

1. Draw a graph like this.

What movements do you have to make to accomplish this?

2. Draw a graph like this.

How has your movement changed to make this shape? How about your position?

3. Draw a graph like this.

What do you notice about the squiggle shapes above the x-axis, and below it? Are they the same? Make a recording and then use Run Review to compare the numbers at each peak and valley of your squiggle.

4. Draw a graph like this.

How would you describe the movements needed to make this graph to a partner who wasn’t able to see this picture?

5. Try recreating the above graphs with a different value for the x-axis.

What happens when you change the line to 2? -5? What challenges do you come across by changing the x-axis line?

6. Which of the above graphs best describes the weather where you live?

Which parts of the graph shape you’ve chosen support your case?

### Try This: Talking Shapes

Describe position, speed, and direction to collaboratively draw shapes.

1. Find a partner and take turns drawing these shapes.

Observe and talk about what ways you need to move the phone to create each one. How does speed change the shape? What positions does the phone move to and from as you draw? In which direction is the phone moving as shapes form? Are you and your partner making the same movements when drawing each shape?

2. Write down the ways you can change a graph.

Some examples of what you might write: “tilt top of phone slowly up,” “move from -5 to flat,” “make a downward spike.” Are there any common words you and your partner can use to describe the speed, direction, and position?

Tip

You can record your graph as you draw each shape to notice some useful details, such as the values at the corners of the shape.

3. Using the record function in Science Journal, draw this graph as best as you can. You may need to do a few practice tries.

Have a partner write down the movements you are making to draw the shape in a list of steps, using as much detail as possible.

4. Switch places and roles with your partner, and draw a “new” shape.

Read off the list of movements starting with the last step and going backward while your partner follows the prompts to draw a new graph.

5. Compare your graphs.

How do they compare? Do you see a resemblance between the two graph shapes?

6. Next, try drawing your own graph shape without your partner seeing and give them prompts to recreate it.

You can reorder the steps you’ve already written down, or make them up.

### Try This: Create a Graph, Tell a Story

Use data and inferences about graphs to make a story rich with detail.

Tip

You can do this activity by yourself or with a partner.

1. Create a graph shape either in Science Journal or on a piece of paper.

You can give this graph as much variation as you would like.

2. Choose your y-axis.

Think of something to measure that will move up or down—call this variable y. If your y moves below zero, then the y value becomes negative. What things can you have less than zero of?

Is your y measuring snow storms? Puppies? Voters? How much ice cream you’ve eaten? This graph can be personal, whimsical, or serious—it’s up to you.

3. The x-axis should be time. Define how much time is covered in your graph.

In Science Journal, the x-axis is time, and moves from left to right. Time is commonly used for the x-axis, but how much time is represented in the graph can change dramatically.

Is your x-axis one hour? One day? Your entire lifetime?

4. Using these details, write the story of the graph.

How does the shape and position of the graph through time help to provide more information in your story?

5. Share your graph’s story. Invite others to make inferences.

You can make all kinds of guesses about what happened at different points in the graph’s story. Did a holiday season lead to an increase in the number of puppies in a neighborhood? Has climate change affected the frequency of snowstorms in the arctic? Did ice cream consumption increase because it was summer? The shifting shape of your graph can tell (or just hint at) all sorts of stories.

### What’s Going On?

Data—often represented as graphs—is the bread and butter of science. To reach a scientific conclusion of any kind requires observation and measurement—ideally, careful, repeated observation and measurement. The data collected becomes evidence that may (or may not) support a conclusion.

Knowing how to read a graph is an invaluable skill, because just like words, graphs can mislead, as well as tell hidden stories. And like all skills, learning to read graphs requires practice, practice, practice.

No matter your math level, a few basic terms and rules of thumb will help you learn to “speak” in the language of graphs. While by no means an exhaustive list, this will help get you started:

Title: Any formal scientific graph has a title that follows a “Y versus X” format, as in “Number of Hot Dogs Eaten versus Time.”

Axes: The x or horizontal axis is generally time or a variable that you directly controlled. The y or vertical axis is the quantity you measured, and which changed as a result of changes in x.

Scale: The scale on a graph is the range of numbers used to label the x and y axes. Watch out for tricky scaling—for example, a scale that starts at something other than zero can fool your eye into seeing small changes as big ones.

Maximum: A maximum is a peak on the graph. A graph may have several relative maxima, but only one absolute maximum.

Minimum: A minimum—surprise—is a valley (or negative peak) on the graph. A graph may have several relative minima, but only one absolute minimum.

Slope: The steepness of an increase or decrease is called the slope. Mathematically, it is defined as the change in y divided by the change in x, and it can be either positive (increasing), negative (decreasing), or zero (flat).

Shape: A graph that’s a straight line (that is, having a constant slope) is called linear. Curves have changing slopes and are called nonlinear. Nonlinearity includes a wide world of possible mathematical relationships that may or may not be familiar—quadratic, cubic, exponential, logarithmic, and so on. A graph that waves up and down in a regular rhythm is called periodic.

### Going Further: Make a Worksheet

Create your own challenges for others to try.