## Monday, March 27, 2017

### @fractiontalks using @desmos activity by @ms_hansel Part 1

I saw Alison Hansel tweet out a super cool Fraction Talks Desmos activity she used with 4th graders after she posted some student work samples. I figured it would be perfect for my 6th grade math support class.

Now in a 53 minute period, I only got through TWO slides. And that's OK. It was a rich discussion. And we will definitely be returning to finish this activity at a later date!

I believe the images are from FractionTalks.com and she did the heavy lifting of selecting thought provoking images. This activity takes advantage of the sketch tool in a perfect situation. When working with these on paper, students can get lost in what they are subdividing shapes into. The beauty here is they can label, draw lines, and erase. Then they can describe their thoughts with words, submit to class, and see small sketches and explanations of their classmates.

I also used teacher pacing so students would be thoughtful and not just rush on to the next slide. I then PAUSED (big groan from class), asked for Chromebook screens to be almost closed to an acute angle, anonymize class responses, and review students work. Students were slowing it down by claiming work and shouting out it wasn't theres, so it went slowly as I had to remind students of my expectations.

MANY students made the following mistake on the first slide:

It is the classic mistake of seeing 4 shapes, and since 1 of the shapes is red, then 1 out of 4 shapes are red, or 1/4 of the shape is red. I asked students who disagreed why they did. Eventually they said that you can't compare them if they are not the same shape.

Then students saw the couple examples that were correct. They could see that these students had divided the other colors into triangles that were of equal size to the red triangle. My colleague had an interesting thought that some students might have said 1/4 because they were color blind and couldn't see the red and orange. I don't believe many students thought this or else they may have said 2/8 is red.

As we all know, the correct answer is 1/8. One student actually said 1/7, and I wanted to honor what was right about that. That student had described the part to part ratio, or in other words, there was 1 part red to 7 parts NOT red. This thinking is clearly further along than the 1/4 thinking.

Once we had discussed it in depth, we moved on to the next slide. Students felt much more confident and were much better equipped with strategies to succeed with this image. They immediately started dividing everything into triangles and said it was 3/8. Their explanations got A LOT better too.

And I love the anecdote about the student below here. He had come up with the answer, and kept disagreeing with all of the people that had put 3/8. I saved his for last to analyze.

So, I wrote 6/16 on the board, and 3/8 next to it. I asked the class, "Who is correct?" One student bravely raised her hand and said, they are both right. 6/16 simplifies to 3/8, because you can divide both numbers by 2. Mind you, students had worked on that skill in recent weeks but this student was able to articulate a context in which there would be a NEED to know how to simplify.

The rest of the activity has a few more sketches, and I believe uses the Card Sort feature to do some flag matching, but as I said, we didn't get more than 2 slides in, but it was a very rich discussion and I'd like to thank Alison for providing the link. I will definitely bust this out with my 7th and 8th grade math support during some free time at some point near the end of the year.