Categories
Negative Numbers The Number System

Arithmetic with negative numbers

Why is this mistake so attractive for students to make? If you saw this mistake in your classroom, what would your next step be?

Categories
Expressions and Equations Solving Linear Equations

Solving equations

Where did this kid go wrong? What does it reveal about his understanding of solving equations? What is your next step for him?

Categories
Rational Expressions Reasoning with Equations and Inequalities Solving Linear Equations

Solving equations with fractions

Where did the kid get 48 from? How would you help him, err, not get 48 in the future?

Categories
Distributive Property Expressions and Equations Simplifying expressions

Combining like terms

The mistake is clear. Why is this mistake so damned tempting, and how would you help?

Categories
Negative Numbers The Number System

Arithmetic with Negative Numbers

Here are the questions:

Here are the student answers:

What’s he messing up on? Focus in on #2.  How did he get 11 as his answer?

Categories
Reasoning with Equations and Inequalities Solving Linear Equations

Trouble solving linear equations

Clearly, the student’s work has more than one issue. But what issues doesn’t it have? What does the student clearly know that you could build on? What’s something that he clearly needs to work on, and how would you help?

Categories
8.EE.7 Solving Linear Equations

Backtracking

What does the student understand, and what does she not? How would you help?

Categories
F-IF.7 Graphing

“Can’t graph it. Too big a line.”

“The line’s too big.” So what? Why does this matter to the student, and what does this reveal about his understanding of graphing?

Categories
N-RN.2 Radicals

A classic: Subtracting radicals

This mistake is a classic in my classroom. What does the student understand about combining like terms, but what is the conceptual model that makes this sort of mistake so enticing?

Categories
8.EE.1 8.EE.4 exponents Feedback Scientific Notation

Scienfitic Notation

 

What does the student know? What are the student’s misconceptions? How would you help?