Inspired by dance, Choreo Graph invites youÂ to explore graphs and coordinate geometry to choreograph a characterâ€™s dance moves or create an interesting scene with moving parts. Choreo Graph uses your own photos as the raw material for your animations while noticing rotation and translation.

Take a digital photo, cut out multiple parts, connect them, and then animate them. Like other movie editing software, Choreo Graph uses keyframes. At each point in the keyframe, youÂ can manipulate line graphs (Graph Controller) to set the angle of each individual cut out. YouÂ can also move pieces on screen, building up a graph of translation through time. When the animation is played, the parts rotate and translate smoothly from one keyframe to the next. Â You control the complex motions of yourÂ animation through the manipulation of the graphs.

The screen – or stage – in Choreo Graph where youÂ build and animate includes layers of mathematical visualizations that can be toggled on or off. By showing or hiding a coordinate grid, dynamic coordinates, and angle measurements, youÂ can call up precisely the data youÂ need to choreograph yourÂ moves. These visualizations also provide a broad spectrum of curriculum touch points for educator.

### Whatâ€™s Going On?

The primary concepts that youÂ will explore are rotation and translation. Along the way, you’llÂ develop fluency in reading and using graphs.

### Rotation

In some lesson activities, youÂ can create a dance with pics of themselves or their friends, teachers, family, pets, etc. Each body part will be programmed to rotate throughout the animation and youÂ explore direct connection between the angle measurements they program and the resulting animation. Sometimes the results are not what youÂ expect at first. Since you can attach rotating parts to other rotating parts, the motion can become rather complex very quickly. But if youÂ want their animation to work out – practice, play, and figure until the graphs achieve the effects youÂ envision, to get that crazy dance move just perfect.

### Translation

Itâ€™s simple to slide parts around onscreen, but these simple actions open up ways to investigate mathematical concepts such as linear equations, slope, coordinate translations, systems of equations, distance formula, etc. Turning on the dynamic coordinates and the grid can turn the coordinates into powerful tools to define the translations in yourÂ animation. Some Choreo Graph activities invite youÂ to use such nomenclature as: [(x-h), (y-k)] where h is the horizontal distance traveled on the coordinate plane, and k is vertical. Those are precise directions of motion from A to B.

### Working Through Misconceptions about Graphs

In using Choreo Graph, youÂ canÂ discover how to interpret graphical representations of these rotations and how translations guide animated figures. Exploring the graphs of the rotations addresses a common misconception of graphsâ€”that the graph of an event is the same as a picture of the event.

For instance, by creatingÂ symmetric motions, youÂ invariably confront this misconception. To have both arms go up symmetrically, one of the arms will be rotating counterclockwise, and the other will be rotating clockwise. The clockwise rotation is a decreasing angle, so as the arm goes up, the graph goes down. To make arms on either side of a animated character go up, youÂ have to build graphs that go in different directions.

Choreograph activities are good opportunities for students to refine their understandings of how graphs can relate to real-world situations, and to develop fluency in interpreting graphs. These activities can also provide rich opportunities to discuss misconceptions and start to dispel them.

### Math in the Real World

Choreo Graph invites you to to use yourÂ imaginations and create impossible motions such as a dancer with every body part flying apart and twirling around onscreen. However, there is also great potential to create direct representations of motion in our real, shared world. Dances that approximate actual dancing, boats on the sea navigating a map, vehicles driving through a city, objects flying through the air, molecules floating into place in a solution, planes flying over buildings. YouÂ can approximate all these motions in Choreo Graph, using translations, rotations, and graphs.

### Language

As youÂ engage with Choreo Graph, youÂ might notice thingsÂ like, â€śWait, that angle is too much,â€ť or, â€śthatâ€™s not steep enough,â€ť or, â€śthose two birds should intersect here not there.â€ť The mathematical visualizations encourage youÂ to start to insert mathematical thinking into yourÂ animations because youÂ care about achieving effects that match yourÂ vision. This kind of analytical language becomes part of the creative process.

### Tutorial

Here is a brief tutorial to get you started in Choreo Graph.

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