Monday, January 13, 2014

Fun With A Dot and A Line

Who would have thought a dot and a line would be so much fun?

[Update] Fun With A... series
Fun With A Sticky
Fun With A Name Tent

I gave my 6th grade students a pre-assessment a week ago Monday. They bombed on questions like this:

Here's today's launch (Round 1):
Me: We're going to have a little competition. Who can draw the best reflection of this point across this line in the middle of your paper?
I handed each student a paper with this at the top.

My kids we're doing some cool things as they attempted to reflect the given point across the middle vertical line. I'll recreate some of them for you.

Julio used a long pencil to line up the point and measured the distance from the point to the vertical line so he could put a point equidistant on the other side.

Jason measured in from the edges of the paper.

Silvana folded her paper down the vertical line and did something on the back.

I asked each group (of four) to pick what they considered the best "reflection" from their group and bring it up to the document camera. We first eliminated some contestants by eye-balling their point and narrowed it down to 5 reflections. I said,
"These all look pretty good, but I feel there's gotta be a more accurate way to determine who has the best reflection here. I need your help guys. How do you think we can determine the winner?"

They thought...

Student: "We can fold the paper over and see whose dot lines up with the first dot."

I try that, but they quickly see I have trouble making a good (accurate) fold.

Student: "Can we measure how far the point is?"

I ask: "What do you mean? Can you please explain?"

Student: "Like how far is each point from the line?"

Me: "Which line?"

Student: "The one in the middle that goes like this. [holds up arm in a vertical manner]

Me: "Let's do it!"

I grab my trusty blue stencil and line up the original. Students watch me measure the original point. 7 centimeters.

Me: Okay, looks like our winner has to be the closest to 7 centimeters. Let's find out.

We get down to two contestants. Anthony has 6.4 centimeters and Stephanie has 6.5 centimeters. Stephanie edged him out by 0.1 centimeters. However, I noticed his point was better aligned with the original... so I threw that out to the class. They settled for a tie.

Round 2
Okay, who can now draw the best reflection of the original point across the horizontal line?
Same rules: pick the best reflection from your group, but it can't be the same person as in Round 1. Our target: 3.2 centimeters.

For a long time, we had a tie between Miguel and Luis. Miguel's point was 3.0 centimeters from the line and Luis' point was 3.4 centimeters from the line. Then, here it came, the last contestant. Jason hands me his paper and I measure it to be 3.1 centimeters. OUR WINNER! Jason is our winner!

Queue the direct instruction and mathematical vocabulary. It became really annoying to keep saying this line and this line. We have already talked about the x-axis and y-axis, so it was easy to convince my students to use those terms. We went into some practice questions that looked like the first picture in this post:
I do, we do, you do!

And now we end class with our final competition: a double reflection. I'd like you to reflect it first across the y-axis and then across the x-axis. Who can draw the best double-reflection?

Fun with a dot and a line. That's an understatement. I think we all had A LOT of fun. Who would've thought?

I'm finding more and more success with these types of lessons. I've been trying to design lessons that have a simple visual, ask a simple question, are geared toward some type of competition and/or game, require students to keep each other accountable, students are checking the answers with me as opposed to me telling them the answers, and fun. I'm trying to keep a simple checklist going. How's this for a start? Anything else to add?

515 +1 dot


  1. Awesome activity! I'm going to be suggesting it to the Geometry educators at the school I work at.
    It's great how the activity forces students to develop a class criterion for precision which in turn facilitates their attention to being precise.

    1. Thanks Jeffrey. Let me know how it goes.

  2. Great activity, Andrew!

    After this activity, I'd have the kids reflect an asymmetrical shape, or one with only one line of symmetry, like the letter C, and see how they do.


  3. Excellent idea - need to keep this one in my pocket for transformations in a few months. Like it far better than any alternatives I've found! Have you found a good one to do for rotations? That always kicks my students' behinds. There are those who just *get* it, and others who just looked dazed and confused....

    1. Thanks Maria. Have I found a good one for rotations yet? Nope. I won't be addressing that with my sixth graders this year, but I would incorporate Fawn's idea here: use an asymmetrical shape or letter with only one line of symmetry, like C. Put it in quadrant one and do a contest for who can rotate it the best 90 degrees counterclockwise and so on.
      Im wondering if you could make some type of coordinate plane spinner. Kids could put the spinner on top of the item to be rotated? Hmmmm...

    2. For rotations, I have had success giving them patty paper to perform the rotation. I do one where I turn the patty paper and keep the paper still, and one where I turn the paper and keep the patty paper still. They soon figure out to get a glimpse of what the rotation would look like...just turn the paper.

  4. Nice activity! I'm looking at the pretest problem and asking myself if the problem should have a visual with the point already plotted. That way we have a better chance of understanding their thinking. I know many of my students wouldn't bother to create a visual for themselves. What do you think?

    1. Good question Mary. Our district test bank does not include coordinate plane with these questions. This drove me nuts. I have provided my students with a coordinate plane when working through these questions so they can create their own visual. Today, I pretty much forced them to use the coordinate plane on these types of questions. Use appropriate tools strategically, right? Many of my sixth graders aren't at such an abstract level of thinking to solve these questions without the visual. I say give them visuals... as much as possible.

  5. Great lesson! -- It'd be cool, after that assignment, to give them the same question but on a coordinate plane to discuss which is easier and why.

  6. Cool idea. I'd like to take this to rotations so students can intuitively see the coordinates switching and 1 coordinate becoming the opposite.

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  8. In a tough 8th grade class that already had a lot of experience with reflections, this lesson killed it. Couldn't have asked for more engagement and anticipation. I could have heard a pin drop during the second challenge, they were working so hard.

    Two interesting ideas that came up where to poke a hole in the middle of the original dot after it had been folded in half so they knew the center of the circle and the spot to put it. Another one was to draw lines down from the sides of the circle so they could get the diameter of the circle correct.

    #likeaboss #theythrewitontheground

    1. Right on!
      Thanks for sharing. I love the "poke a hole in the middle of the original dot" creativity.

      I'm curious if some students would categorize this as a foul? Should the class come up with and agree on a constraint or two? For example:
      •no poking holes in the paper