Category Archives: Coordinate Grid

Following up with the Coordinate Grid

I have been meaning to follow up on this post for over a month now!

Over the first 6 slides, we saw so much great confusion when they were trying to figure out how to name the location of the point. We saw some students use measurements from the top and bottom of the screen, while others tried using some fractions. To get a picture of how students’ thinking changed from one grid to the next, I copied their responses from Desmos to this table in Google. In the table, each row is the same student’s response to describing the point location on each of the three different grids.

During the activity, we paused the students after the 6th slide and asked some volunteers to read their directions. After a few misses due to the fact they didn’t name a starting place or they counted squares instead of lines, we asked them to try re-writing some directions on the back of their paper.

We could tell they were finding the axes pretty necessary so after plotting the point successfully a few times as a class, we gave them some of the terminology and conventions for plotting and naming points in a coordinate plane.

This is the place where we thought we may run out of time but we wanted to give them a chance to plot some points that formed rectangles and look for patterns in the coordinates. I copied the things they noticed at the bottom of this table.

If they finished the work with their partner in Desmos, we asked them to complete two final questions about points that would connect to form a rectangle. We wanted to get a picture of which students were graphing them to find out and which were using what they noticed about the x- and y-coordinates. We knew this may be a stretch with some, given the amount of time we had in the class period, but I am always way to curious not to ask! Leigh was revisiting this work over the course of the next few days, so we were in no hurry to expect mastery at this point. It was great to see the mix of thinking about this:

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A Coordinate System

This standard in 5th grade always seemed like so much of a “telling lesson” for me.

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I never thought it was really addressed in the spirit of this standard in our curriculum, so I was typically like, “Here is what we call a coordinate grid. These are axes, x and y. We name the points like this…” and so on. It is not my usual approach so it always felt blah for me, for lack of a better word. I told them, they practiced plotting some points, and we played a little bit of Battleship (which was really fun).

Last week, I was planning with Leigh, a 5th grade teacher, and we spent a lot of time just talking about what we appreciate about the grid and how we can develop a sense of need in the students for it. Since they are in the middle of their 2D Geometry unit, we thought this could be the perfect place to plot points that connect to form polygons and look at patterns in the ordered pairs.

The questions we wanted to students to reason about through our intro lesson was:

  • Why a coordinate grid?
  • Why name a point with an ordered pair? 
  • Why is this helpful?
  • What structure do we see?

So, we created this Desmos activity. This was our thinking on the slides and the pausing points we have planned for discussion:

Slide 1: It is really hard to describe a location without guides or landmarks.

Slide 2: Note how difficult it is. Pause and show class the results.

Slide 3: It gets easier. Still need some measurement tool. Notice the intersection of axes.

Slide 4: Note it is a bit easier this time. Pause and show class results.

Slide 5: Much easier because of the grid. Still need a starting point. See it is the distance from axes.

Slide 6: Now it is much easier. Pause show class results. Would love to show all three choices side-by-side (don’t know if this is possible in Desmos).

~Pause~ Ask, “What names of things on the grid would make it easier to talk about the point’s location?” Give students vocabulary and ask them to revisit Slide 6 to describe the location to a partner.

Slide 7: Practice writing some ordered pairs.

Slide 8: Practice writing some ordered pairs.

Slide 9: Start to see some structure in the four ordered pairs of a rectangle.

We are ending with this exit ticket (with grid paper if they choose to use it):

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While we are not sure this is the best way to intro the grid, we thought it would generate some interesting conversation. Since we are teaching it tomorrow, there isn’t much time for feedback for change, but we would love your thoughts.