Pythagorean Theorem Right Triangles Similarity, Right Triangles and Trigonometry Trigonometry

30/60/90 Mistakes

Right Triangle Quiz Responses


This is fairly representative of the class’ work. What would your next step be with this class?

Area Circles Geometric Measurement and Dimension High School: Geometry Similarity, Right Triangles and Trigonometry

Area of a Circle, Minus a Square



Do you see the mistake? How would you help this student?

Distance Between Points Geometric Measurement and Dimension

The distance between (1,1) and (4,5) is 7


Expressing Geometric Properties with Equations Midpoint

“Find the midpoint between (2,5) and (2,396)”

What would you predict? Here are some twitter responses:

Here’s your answer key…

First Place:



Second Place:



Third Place


Area Geometry High School: Geometry Right Triangles

Using a bad base



I keep on seeing this in my Geometry classes this year. Tasked with finding the area of a right triangle, kids move toward the hypotenuse even if two of the other sides are given. Then they end up stuck looking for a height that they can’t find.

I’m pretty convinced — based on talking to kids and looking at their work — that this is all about how they see right triangles. These kids must be seeing hypotenuses as bases, and it must feel weird for them to treat the legs as bases. Or maybe instead it’s about the height? Maybe it feels strange to them to use a leg as a height?

Decimals Geometric Measurement and Dimension Surface Area and Volume

A decimal mistake

dylan image

Decimals are hard.

What would we even want the student to do here if he’s working in decimal? Like, how do standard multiplication algorithms handle something like a repeating digit?

That’s what I’m getting out of this mistake right now: the deviousness of decimal representation, and the way it can obscure numerical properties.

How about you? What do you make of all this?


Geometric Measurement and Dimension High School: Statistics and Probability Interpreting Categorical and Quantitative Data

Cylinder Scatterplot



1. This is a really cool question.

2. Gregory Taylor says he doesn’t know what the kid was thinking. Thoughts?

Geometric Measurement and Dimension Similarity, Right Triangles and Trigonometry

People Often Use Additive Instead of Multiplicative Reasoning


Area Geometric Measurement and Dimension Pythagorean Theorem Similarity, Right Triangles and Trigonometry

Base1 times Base2 = Area of Triangle



Lots to notice here, including the formula that the student is using for the area of a triangle.

Similar Figures Similarity, Right Triangles and Trigonometry

“They are not similar because you have to add different numbers…”




Another interesting instance where additive and multiplicative reasoning get entangled when working with similar figures.