Month: March 2013

“Prove the following conjecture: The sum of any 3 positive consecutive odd integers will be divisible by 3.”

Post author By mpershan
Post date March 31, 2013
1 Comment on “Prove the following conjecture: The sum of any 3 positive consecutive odd integers will be divisible by 3.”

First, I just love the question. Second: theorize! What happened to this student? What are some good signs in the student’s work?

Thanks to Bree for the submission.

Also: I categorized this under “Standards for Mathematical Practice.” Does anyone have another CCSS standard that fits this problem and work?

Geometry

“A square is never a rectangle.”

Post author By mpershan
Post date March 28, 2013
7 Comments on “A square is never a rectangle.”

The question below asked kids to state whether the given sentence is always, sometimes or never true. Then, they were asked to justify their response.

Suppose someone said this to you. How would you respond?

Many thanks to Tina for the submission!

Uncategorized

Help Canada with Percentages

Post author By mpershan
Post date March 27, 2013
2 Comments on Help Canada with Percentages

How would you help Alberta with population growth?

Many thanks to Evelyn Lamb for the tip! Many thanks to @MathUpdate for sharing the image!

Limits

Negative Infinity

$tina math precalc$

What’s the fastest way that you could help this student?

Thanks to Tina for the submission! Go check out her very exciting new and remarkable collaboration with some dude, Productive Struggle.

Expressions & Equations Feedback Middle School

Multiplication and Exponents

Post author By mpershan
Post date March 25, 2013

Dip into the archive and check out our other exponent mistakes. What do you notice?

Thanks to Julie for the submission!

Exponents Expressions Expressions Expressions & Equations Feedback

PEMDAS and powers

Post author By mpershan
Post date March 24, 2013

Question: Evaluate the expression $-z^{2} + x(3-y)^2$ when $x = 10$ , $latex y = -2$, and $latex z = -2$.

These submissions come from Julie, who posted about this stuff on her blog:

What happened? First, I HATE PEMDAS AND ANYONE WHO USES IT. This starts early, and students are already brainwashed by 6th grade when I get them. All of the GEMS in the world can’t seem to fix this. I hate PEMDAS because students see parenthesis and go into “I must do that first” mode, even when there is only ONE number inside the parenthesis. Just because it is in parenthesis, one number, for example (2), does NOT a group make.

Discuss her evaluation of the problem, and her next steps, either in the comments or at her place.

Feedback Trig Identities Trigonometric Functions