We Need More Drawing in Math Class

I worked with a 6th grade student in our In School Intervention classroom today.  I do this every day.  A boy had been assigned a set of pages from a workbook and had begun the work on his own. From what he had already completed, I could tell that this student had a strength in math. He was unsure of what he had done, so he was looking for validation from me.  We looked at this next problem together:

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He said, “so you gotta subtract right?” I said, “yes you do, but that’s if you’re looking for the answer. This is asking you to write an equation.”

He began to write y = x – 14.

I talked to him about variables, and how many unknowns were in this problem and he could tell that there was only one.

I asked him to draw a picture of the situation.  Here is what he drew.

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HMMMM….(maybe they’ve recently worked on area and perimeter???)

I then asked him to reread the problem and prompted him to draw the house and the airport.Screen Shot 2016-05-17 at 5.56.08 PM

He drew the line between the house and the airport, and I had to do some questioning to get him to realize it represented the distance of 29 miles.  We reread the problem and I asked him about the 14 and how he would represent that on the drawing.

He thought to himself for a moment and then began drawing the tick marks.  I could tell that he was counting them.  He labeled the 14th tick mark and the 29th, and then circled the 14.

I drew the bracket and asked him what that would represent.  He said with a questioning tone, “the remaining distance?” Thinking for a minute, he then said, “oh I know…would it be 14 + x = 29?”

We did one more problem together that we represented with a drawing, and then I left him to be independent in the rest of his work.

He came over to show me one of his drawings and the equation he had written:

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(In a previous part of the problem they were told there are 150 seats in coach seating.)

We high-fived!


Teaching students how to create math drawings is a valuable sense-making tool that can be over looked in math class.  I know numerous reading language arts teachers that ask students to draw pictures to portray what’s going on in a story.  We need more of that in math class.

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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.

noticing subtleties 2

 

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!!!

 

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.