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Home Concept Builders Fundamentals: Relationships and Graphs Using Graphs Notes

Notes

The Using Graphs Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Concept Builder can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

Teaching Ideas and Suggestions

This Concept Builder is intended for early in a course but can probably be done at anytime that a teacher wishes to emphasize or re-emphasize the importance of graphs and graph interprettation. Any of the three activities in the Concept Builder could stand alone by itself allowing a teacher to pick and choose which activities are best for their students at any given time of the year. Ideally, the Concept Builder is suited for those teachers who begin the year with a unit or mini-unit on graphing and relationships. As with all our Concept Builders, Using Graphs makes for an excellent formative assessment of student ability to calculate slope, interpret graphs, and extrapolate outside the range of plotted values. We recommend using the activity only after students have been introduced to these concepts and skills and after they have had some guided practice.

 
 
 

This Concept Builder was intended as an in-class activity. It includes 13 different Question Groups divided across three different activities. Teachers using the Concept Builder with their classes should preview the activity (or view the Questions in the separate file) in order to judge which activities would be most appropriate for their students. Our summary of the three activities is as follows:
  • Calculating Slope: Question Groups 1 - 6; students perform slope calculations and identify the units on slope.
  • For Every ... : Question Groups 7 - 9; students perform slope calculations and identify the units on slope.
  • Predict! : Question Groups 10 - 13; students extrapolate to predict a value for the dependent variable that lies outside the range of collected data.
In order to complete a level, a student must correctly analyze each situation or Question Group at that level. If a student's answer is incorrect, then the student will have to correctly analyze a question from the same Question Group twice in order to successfully complete the level. This approach provides the student extra practice on questions for which they exhibited the most difficulty. As a student progresses through a level, a system of stars and other indicators are used to indicate progress on the level. A star is an indicator of correctly analyzing the Question Group. Once a star is earned, questions from that Question Group are removed from the cue of questions to answer. Each Question Group is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed a question from that Question Group and will have to correctly analyze two other questions before earning a star. A yellow box is an indicator that the Question Group must be correctly analyzed one time in order to earn a star. Once every Question Group in an activity has been mastered, the student earns a medal. The medal is displayed on the Main Menu. This system of stars and medals allows a teacher to easily check-off student progress or offer credit for completing assigned activities.

The most valuable (and most overlooked) aspect of this concept-building activity is the Help Me! feature. Each question group is accompanied by a Help page that discusses the details of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.
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