Tag Archives: reasoning

Explaining “Explain”

Here is a released question from Smarter Balanced (I even answered it!!!):


Ok I lied. ¬† That was an edited version of a Smarter Balanced question – here’s the original:

ExplainingExplain1Now all of a sudden my answer doesn’t seem sufficient anymore ūüôĀ ¬† Here’s my best guess at a popular student answer:


This word “explain” is keeping me up at night lately. ¬†In this problem I’m not sure adding the word explain to the end gains us enough to warrant it. ¬†To achieve Common Core we can’t just throw the word “explain” after every problem we did last year and call it a day. ¬†By the way I’m not saying that’s what the Smarter Balanced Consortium did on this particular problem. ¬†But this use of the word “explain” does bring two things to mind:

1. ¬†It’s hard to explain your mathematical reasoning without access to drawing diagrams.

2.  If we ask students to explain something Рit should be something worth explaining.

With respect to #1 Рmy focus this year has been on explanations through multiple representations.  Basically I have students make connections between diagrams, tables, graphs, mathematical symbols, and written descriptions.  I feel underwhelmed asking students to explain with just a typed explanation.  I want explanations to look like this:


In the student work above Рimage if it was only the conclusion.  Look at how much would be lost.

There are certainly better answers to the rectangle problem from Smarter Balanced than I offered up here.  I actually really like the problem itself, I just do not think having them explain it gains us much versus just solving it.

It’s hard to explain the word explain. ¬†It’s a word that only makes sense to me until I try to explain it.


The Description:

Teach/Pair/Share is my structured version of a pair/share.  It is structured more formally that the regular pair/share in that I have to be prepared to do the Teach/Pair/Share, whereas I can just have students do a pair/share at anytime without slide preparation.  The Teach/Pair/Share fits into #reasoning because it requires the students from group A to teach those in group B.

For the Teach/Pair/Share I have make sure each student has a partner, put those rows closer together, one row is group A, the other is group B.

Intially I will have one of the groups take notes, say group A, and the instruction for group B will be to listen.  I tell group B to just listen Рand I make sure they do not have a pencil in their hand, because I do not want them writing anything.  Then I have group A take notes and help me solve the problem.  Once we have the whole problem on the whiteboard, I erase it, and switch the slide.

Now it is time for group A to teach group B, and for group B to take notes on what group A is telling them.  It is critical to be circulating at this point.  Randomly choose a group and ask the student in group B how to do the problem. If they explain it correctly, thank the group A students for great teaching, and the group B student for great learning.

Now repeat the same steps with jobs reversed.  At the end I have one problem that everyone needs to do.  I typically google translate the instructions into a language no one knows, and then I act upset when the students do not initially know what to do.


These are a listing of hastags that I use to catagorize my lessons plans.  Each catagory represents a different style lesson plan.  My instructional goal is typically to make sure that I use each hashtag at least once a month.  The goal of this blog is to share all the lesson plans that I use under each hashtag.

My detailed lesson plans are my Keynote slides. ¬†But along with those, I make a quick, calendar-style overview to me a general idea of what I am doing. ¬†It’s on this calender where I place the hashtags at the bottom of each day. ¬†This allows me ¬†to quickly look back at what I have been doing, and know whether of not I am differentiating. ¬†For example, here is two weeks worth of my lesson plans in geometry. ¬†Notice that I can quickly see whether or not I have differentiated my instruction, without having to analyze each specific lesson plan. ¬†The hashtags allow me to get a quick sense of what I have been doing, and what I have not been doing.


*Notes –

-The term “perplexity” is being used as described by Dan Meyer here