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
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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?

Dot,
515 +1 dot