# Mr. Dreyer's Math Toys

These are some math toys I built with GeoGebra for my classes. They require Java. Sometimes you may need to *reload the page* a few times to see the buttons which launch the toys. Have fun!

## Algebra

### Slope-intercept form

This graph shows *y* = *m x + b*. Use the sliders to adjust *m* and *b*. It may be easiest to try to set them to "friendly" numbers. What do *m* and *b* represent on the graph? What are the coordinates of the red and purple points in terms of *m* and *b*? Why does each of those points lie on the graph of *y* = *m x + b*?

### Point/slope form

This graph shows *y* − *y*_{0} = *m* (*x − x*_{0}). Use the sliders to adjust *m* and *x*_{0} and *y*_{0}. What are the coordinates of the red and purple points in terms of *m*, *x*_{0} and *y*_{0}? Why does each of those two points lie on the graph of *y* − *y*_{0} = *m* (*x − x*_{0})?

### Standard form

This graph shows *A x* + *B y* = *C*. Use the sliders to adjust *A*, *B* and *C*. What are the coordinates of the red and purple points in terms of *A*, *B* and *C*? Why does each of those two points lie on the graph of *A x* + *B y* = *C*?

### Absolute value functions

Hit the button on the right to see a graph of *y* = *a* |*x-h*| + *k*. Play with the sliders to change *a*, *h*, and *k*. For example, when *a*=-2, *h*=3, and *k*=4, what is the slope of the right "piece" of the function in terms of *a*, *h*, and *k*? What is the vertex? What values of *a* make the vertex point down? Up?

## Geometry

### Hypothesis about angle and segment trisection

In class, some students hypothesized that in an isosceles triangle, rays drawn from the vertex to trisectors of the base trisect the vertex angle. In this experiment, drag the vertex to see the angle measurements change.

### Types of triangles

As you move the triangles around, the equilateral, equilateral, equiangular, isoceles and right triangles (green) stay true to form, while the others (red) may change

### Beyond CPCTC

From section 3.5 (p.125-126.) Sample problem 1.