Categories
Building Functions logarithms

Solving logarithmic equations

Selected by: Christopher Danielson

Question: What’s up with this? Why does this piece of student work matter? Does it?

Categories
Absolute Value Reasoning with Equations and Inequalities

Absolute Value Equations

What are these kids struggling with? What are they getting right? Are there interesting differences between the three different students whose work is shown?

Thanks again to Ms Miles (twitter / blog)  for the submission!

Categories
Absolute Value Distributive Property Reasoning with Equations and Inequalities

The Distributive Property of Absolute Value

Say something smart about the Distributive Property in the comments.

And thank Ms Miles (twitter / blog)  for the submission!

Categories
Vector and Matrix Quantities Vectors and Matrices

Perpendicular(?) Vectors

What’s the mistake? Why did the student make this mistake, in particular?

Thanks again to the tweeting and blogging Kate Nowak for this submission.

Categories
Vector and Matrix Quantities Vectors and Matrices

Perpendicular Vectors

Assignment: reconstruct what was going through the student’s mind as she solved this problem and, apparently, answered the problem with confidence.

This mistake has been brought to you by Kate Nowak, who blogs and tweets and stuff.

Categories
Building Functions Functions High School: Functions

Inverse Functions

What does the student know, and what does he misunderstand? How would you help?

Today’s submission comes via Christopher Danielson, who blogs at Overthinking my teaching.

Categories
Functions Interpreting Functions

Function Notation

How do you teach function notation? How would you help your students avoid this sort of mistake?

Categories
Complex Numbers Quadratic Functions The Complex Number System

Complex Roots and Quadratics

Here’s the work:

Can you make sense of it? What’s the cause of this mistake? How could you help?

Categories
Solving Trig Equations Trigonometric Functions

Solving quadratic trig equations

What’s the nature of this student’s mistake? Is it the sort of mistake that the kid would make given a linear equation to solve, or is the mistake particular to the trig context? How might you help the kiddo?

Categories
Arithmetic with Polynomials and Rational Expressions Rational Expressions Uncategorized

Multiplying fractions

In case you’re having trouble reading the kid’s work, and because the top of the question is cut off, I’m going to reproduce the problem in text below the image:

Question: What is the product of \frac{x^2-1}{x+1} and \frac{x+3}{3x+3} ?

Answer: \frac{3x^2-3}{3x+3}*\frac{x+3}{3x-3}

\frac{3x^2+9}{9x+9} \rightarrow \frac{1x^2+3}{3x+3}

 

The usual: What does he know, what doesn’t he know, and what would you do next?