Noticing Subtleties…Reflection

So I wrote this post yesterday, and today we tried it out.

The purpose was to give students an opportunity to notice the subtleties in the language associated with three different mathematical scenarios they may need to represent.

We read each scenario out loud and then asked the students to compare and contrast each problem type with their table partner.

Some students began by discussing the similarities and differences of the contexts…noticing subtleties 1

Others began by making a list of what they noticed on the back…You can see that this student paid attention to more of the mathy parts~understanding what was meant by a one-variable versus a two variable equation.

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And then you’ll see below where students were able to make sense of each scenario and the math required.  However, the first student used an equation in two variables for the first scenario and created a table to find the solution.

We didn’t get to the whole class conversation part of this lesson…I want to talk about each problem type and how to recognize the differences.  Notice that two of the students above wrote the equation for the two variable scenario, but the third student created a table.  I think we need to talk about why that is.  Also, I think I may want to do three more scenarios that would produce equations in standard form, to see if they would recognize the differences then.

I definitely think that this was a useful exercise and would do it again.

One little shout out…one student pulled out their phone because they wanted to check out the equations for the third scenario on their Desmos app!!!



My first year out of the classroom was 2010.  I was talking to a colleague today about a type of assessment I used to do in my classroom.  I called it an un-quiz.


This is a variation of a typical multiple choice quiz, except that I asked for a WRONG answer. Along with the wrong answer choice, the students had to give a reason why it was a wrong answer.  (Be sure that your wrong answer choices provide valuable information!) This allowed me to see how they reasoned about wrong solutions, language they used, AND the students had multiple means of showing their knowledge.

I haven’t used this strategy in a while…if you do something similar or try it for the first time, I’d be interested in hearing about what you think.


My Favorite Formative Assessment Tasks

I’m a little late…but, here’s my week 2 “My Favorite” post for the Explore MTBoS blogging initiative.


The Charles A. Dana Center out of The University of Texas at Austin has put together a great set of tasks for eliciting student thinking.

One of my favorite tasks that I have used with 8th graders (for years) is called Mosaics.

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Because we spend time making sense of the patterns from the Visual Patterns site, this task works well as an independent assessment task.

I particularly like question one in that it asks students to represent the problem in at least three ways–they are not told how to represent the problem.  I like to see if they will use a table, graph, etc.

Also, it’s interesting to see how different students “see” the pattern growing and how they choose to show that thinking.

And my FAVORITE piece of student work for this task incorporated the independent use of “noticing…”


Here is a link to additional student work from this task.  We’ve used this task, along with the student work, as part of our back-to-school professional development on using a examining student work protocol.

Dana Center tasks are not a free resource…but you can find some sample items for free. Doing a Google search for Dana Center Algebra 1 Tasks will yield these results. You can purchase a book of these tasks here, or on CD here.

Thinking about Feedback

There have been some really great posts lately about how teachers are giving feedback on assessments.  You could read this post here by Nathan Kraft or this post here by Fawn Nguyen.  Also, there is a great Teaching Channel video on highlighting mistakes as a grading practice for you to watch here.

All of these posts show the power of the highlighter.

A strategy that I started using last year involves the highlighter…but in a different way.

Problem-Attic  is a resource I’ve been using to create weekly assessments.  I wanted to figure out a way to help students to be more independent in identifying and revising mistakes.

I decided to turn each problem from the assessment into its own one page station where I highlighted important features and made notes of important think-abouts.  For the most part…these related to common misconceptions or careless errors.

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Students then had the opportunity to work around the room and read the “hints” that were provided in order to revise their work.  Some of my hints were probably too “hinty,” but it was a starting point for a process that I was working out.

I did this with 8th grade-on grade level students.

Students reported liking the process–and were able to figure out their errors independently of me.

I’m hoping to refine this process this year.

A Favorite Activity: Create-A-Quiz

This is part of a challenge to blog weekly for the school year.  See other posts at #MTBoSChallenge.


I missed yesterday’s link up to share a favorite game or activity…and @luvbcd already shared one of my favorite games SKUNK.  See her post here.

One of my favorite things to do towards the end of learning about a topic is to have the students “Create-A-Quiz.”  The most important part of this assignment is that they MUST make it a multiple choice quiz.

I talk about quizzes and tests with the students and ask them how they think the multiple choice questions are created.  We discuss how the common errors/misconceptions are used to create the WRONG answer choices.  We go over a few examples of how this might be done…focusing on all of the different ways students might respond for a particular question.  Then, I have them work with a partner to make their 4 question multiple choice quiz.  They, of course, must have the correct answer marked for me so that I know they understand the question themselves.

I often use some of the student-created questions as quiz problems and name the authors on the assessment.

I love this activity because the students are focusing on the errors that might occur while using a ton of math talk to come up with the question and the multiple responses.  I think it would be a nice extension to have students come up with multiple select items for their quiz as well.