Understanding Proportional Relationships with the Proximity Data Game

In the Fall as Middle School and Algebra 1 teachers look for activities to develop students’ understandings of proportional relationships, they may turn to measuring scale diagrams or using springs. One of KCP Technologies’ new online Data Games called Proximity offers a new option for teachers to help students learn about proportional relationships.

In Proximity, you shoot a ball toward a target–the closer you get, the higher you score. Try it here! To shoot the ball: click on or touch it, drag away from the target, and release.

Most computer games generate data, but they go unexamined and disappear when the game ends. But notice when you push the ball here that the data dynamically update in the graph and the portion of the table shown. Students learn that analyzing this data is the key to success in Data Games!

Students playing Proximity generally develop intuition that a proportional relationship exists between how hard the ball is pushed and how far it travels. Some students get really engaged in trying to score big just using trial and error as they figure out how hard to push. And they can achieve some modest success with this informal approach, perhaps unlocking the second level of the game. But it’s very difficult to advance to the third level, which we recommend Middle School and Algebra 1 teachers set as a goal, using only this method. We’ve designed the Data Games so that students really need to analyze the data and apply their math skills in order to succeed.

There are various strategies students might discover they can use to their advantage. Students might examine the table, shown below, and see a common ratio between push and distance, which they can then use to determine the amount of push needed for each future desired distance. Our student worksheet for Proximity also asks students to think about what the distance would be for a push of 0.

Needing to know the desired distance prompts students to use the onscreen ruler to measure the distance from ball to target. The game provides scaffolding for those players who don’t catch on to the value of measuring distance, offering a prompt if the ruler hasn’t been used for the past 60 seconds.

We chose to use a whole-number proportional constant in the first level of Proximity so that students could more easily discern the type of relationship that exists. In higher levels, decimal constants are introduced, and students generally find examining the graph to be a more useful strategy. They observe the data points fall on a line which passes through the origin. The gear menu allows students to create a movable line on the graph, which you can try below. The equation for the line is provided, and when you drag the line to fit the data, the equation updates dynamically. Students can then see that the line passes through the origin, and its slope is the proportional constant they need to determine push, given distance. (Bouncing the ball off the side walls creates points that do not all fall on the line like this, a good piece of data complexity for students to grapple with, or avoid by not bouncing.)

These beginning Algebra skills are not easy for many students, but game-based learning can motivate them to develop their understandings. Data Games are not designed to be so thrilling for kids that they’re going to throw away their Wii games at home, but they engage students at a high level during math class to improve their skills with data analysis.

Teachers can use Proximity and the other Data Games to help students master the Common Core State Standards for Mathematics involving data analysis. You can find the games and teacher resources supporting their classroom usage free on our website at play.ccssgames.com. These resources for each game include: short videos introducing the game and its data analysis tools to students; a video for teachers; a student worksheet; and teacher facilitation guidelines, including Common Core State Standards alignment. Free registration is required to access the materials.

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