On Similar Triangles

By Ashli Black

The fact that a line has a well-defined slope—that the ratio between the rise and run for any two points on the line is always the same—depends on similar triangles.
(p.12, 6–8 Progression on Expressions and Equations)

As students are building their understanding of dilation at the beginning of grade 8 in Unit 2 of the LearnZillion Illustrative Mathematics 6–8 Math curriculum, an activity asks students to dilate different quadrilaterals using a given center and dilation factor on a square grid. Here are the results of two of the dilations in that activity involving triangles: Continue reading “On Similar Triangles”

Why is the graph of a linear function a straight line?

By William McCallum

In my last post I wrote about the following standard, and mentioned that I could write a whole blog post about the first comma.

8.F.A.3. Interpret the equation $y = mx + b$ as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function $A = s^2$ giving the area of a square as a function of its side length is not linear because its graph contains the points $(1,1)$, $(2,4)$ and $(3,9)$, which are not on a straight line.

Continue reading “Why is the graph of a linear function a straight line?”

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