## 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.

## Wednesday, March 22, 2017

### Fishbowl... A @CPMmath Study Team Strategy

With one third of the school year left, I felt it was a good time to try out a study team strategy I had never done before: a Fishbowl. I remember doing it at the Academy of Best Practices at Seattle University and finally decided to use it. I think students needed a strong reminder of what the study team norms were.

So, I picked 1 group that seemed to work well together the day before, and a table next to them. I then asked the whole class to get their composition book and pencil and without talking surround the two tables. We were going to silently observe them use their study team roles to start and complete the first 2 problems of the lesson 8.2.2. I selected these because the first problem set is review of exponents from yesterday's lesson where they had to write the multiplying of power numbers in a simpler form. The second problem involved error analysis where the student correctly expanded the powers, but put addition signs between them and multiplied them out instead of writing them in simplified exponent form.

I asked students take notes on positive actions and actions the team could improve upon. After they finished, we would debrief right there, of course starting with the positives. Then we talked about what they could improve, and then they returned to their seats and I said now show that you can do it just as good or better!

In first period, here were my observations:

In second period, a student started reading right away, but skipped the introduction! In the other group, they started reading right away, but the introduction first. Group 6 moved on when they were done, and confirmed with their group that everyone was done. Group 7 moved on to the next problem, without going over the answers to 8-59. I observed some weren't finished, and didn't speak up. Group 6 moved on, but didn't write it in simplified exponent form. In the debrief, we saw how both groups started quickly. One moved on too quickly without making sure the group was ready. Also, group 6 didn't fully read the directions of writing it in a simpler form. This reinforced making sure you understood what the question was asking.

In fifth period, both groups started reading quickly. A suggested an idea. A also asked, "Are you done writing that down?" In the other group, M confirmed that they agreed with another group members idea. There also were no arguments about who wanted to read. One higher student didn't have the courage to speak up about disagreeing about the team's idea. C suggested an idea. One student said, "It'd be like..." which I mentioned in the debrief. as a good way to describe how you are going to write it, and to get confirmation from your group. When students shared, they said that A was dominating the discussion and not giving other team members a time to share their ideas, or use wait time. I talked about how as teachers we need to give students wait or think time, and students need to give each other time to think also. We also liked how there was some positive nervous clapping when they got an answer right and all agreed.

So, in conclusion, this is a great study team strategy. It's perfect to do when you feel like students aren't working together as well as they can and to remind students what the expectations are, by seeing what you should and shouldn't do.

Also, I thought it would put the other groups way behind, but they had heard the discussions before, so it made their start a little more smoother and efficient because they had listened to two different groups.

## Saturday, March 18, 2017

### Fraction Talks warmup @FractionTalks @mathletepearce

I can't take credit for the below image. I found it on twitter. It's located here and above under my Fav Problems. The variety of ideas and misconceptions with this problem make it a must-do warm-up in every classroom.
As you can see below, I treated it like a number talk. I had students share all their answers, without any reaction or judgment, and asked students to defend their answer.

As you can see in the top right, Juliana's idea was that there's 1 hexagon in the middle. But if there are 6 trapezoids on the outside, 2 of those trapezoids can be rearranged to make 1 hexagon. So 6 trapezoids would make 3 hexagons. Therefore she reasoned that 1/4 of the shape was yellow, because if the whole shape is 4 hexagons, only 1 of them is yellow.

Victor said that the yellow hexagon in the middle was 2 trapezoids, or 2 reds. So, if there's 6 reds on the outside, that's 8 total. Therefore, he said 2/8 are yellow.

I did want to acknowledge the wrong answer of 2/6, because that is the ratio of yellow to red, so there's something correct about that. It's just not the part/whole ratio that we are looking for when we say what fraction of the shape is yellow.

I also asked students how someone could say 1/7. They said they probably saw 1 yellow shape out of 7 total shapes. Students said you couldn't do this because they are not all the same sized shapes.

One student said 1/2 of the shape is yellow because a hexagon is half of a trapezoid... a good thought that wasn't extended though to the whole shape.

I had to take a picture of this one because all day this was the only person who thought of it this way. The student said you can make the whole shape triangles, and a hexagon is 6 y yellow triangles, and there would be 24 triangles total, so 6/24 is yellow.

Every period I mention the way I see it if no one has said it yet, which is noticing the shape is symmetrical, and if you cut it in half you have 1 yellow trapezoid out of 4 total trapezoids, for 1/4.

More images like this can be found on fractiontalks.com. We have also worked in some of the flag matches from that site which are pretty awesome and cross curricular.

This blog post was inspired to by a video @mathletepearce made and the conversations on Twitter that followed.

### 8.SP.4 IM Task 2 way frequency table student survey samples & rubric

I wrote a blog post for NCTM about the lesson used. I also have an idea about how to score the assignment using a rubric and already want to label the columns independent variable and the rows dependent variable so students know why they are totalling the columns for the relative frequencies.

This post will have my reflection notes, the scoring rubric that I'd love feedback to improve, and some interesting student work samples of varying levels of understanding.

I have improved the survey assignment template with the following: each question is labeled. The independent and dependent variable are labeled on the table and in the hypothesis example sentence. I also added to the conclusion by adding "Therefore if ________________________, you are more likely to ___________________.
My hypothesis was...correct or incorrect? conclusive or inconclusive?"

I also discussed this lesson with some colleagues from my FAME program and one had a great suggestion! An alternative to calling out students name for yes yes, no no, yes, no, or no yes votes you could ask the class who play a musical instrument? If yes, line up in a column on left side of room. If no in a column on the other side of the room, parallel to the rest of the class in the other line.

Then when you ask the next question, do you play a sport? Those groups separate into different corners of the room. For example yes can step forward, no can step back. You now have the four quadrants of the 2 way table and you can visually see how much bigger the group of students may be that play an instrument and a sport, compared to the students who play an instrument and no sport. I want to try this next time.

To help me make a rubric, I looked at each classes results and separated them into piles: 1 pile if they didn't finish the survey or filling out the two way table (only 2 or 3 students per class), another pile if they got the hypothesis, conclusion, and relative frequency percents. Then a middle pile if they were missing the fractions & percents and/or their conclusion.

My rough rubric was students earned a 4, or A if they had their column totals, fractions, percents, hypothesis stated, questions clear, and a conclusion using the data as evidence. Students got a 3 if they were missing the percents or conclusions. A 2 was earned by not stating their hypothesis and hypothesis. A 1 was given to students who completed the survey and filled out the table, a 0.5 if they attempted, and a 0 if I didn't receive the assignment.

Some students did not complete the fractions or relative percents because they were reading the wrong row or column or didn't understand how to do it in general.

Note to self, I need to put that rubric as a small footer to the assignment sheet so students know what I am looking for and could make it easier to grade by marking the grade with comments on the rubric.

Above is my reflection notes with items I wanted to mention in this blog post.

This student nailed the concept and even had time to decorate it a bit. Her hypothesis was correct, if you watch cartoons you have an 88% chance of watching Spongebob.

This student mixed up their conclusion a bit. Great survey idea. His hypothesis was correct. What he meant to say I believe is of the 20 people who are 49ers fans, 17 are also giants fans. I also see that his joint frequencies don't add up properly to his marginal frequencies, so there's some type of miscalculation going on here.

Good work and conclusion, just missing the percents to support the conclusion.

This was interesting... The above picture is 2 students who had one of their questions be do you like to read? What's shocking is the results are different. To me, this means either some kids changed their answers as the class progressed, or they answered the question differently based on who was asking them the question. I am not sure.

A socioeconomic question that had no surprises. Stellar work. Actually, just noticed that they made a mistake with the top right joint frequency of 7, which should have been 7/7 for 100%.

Good work here.

This was interesting. 31 students were asked if they liked school. 20/31 said they didn't like school. Of those 20, 1 of those kids wanted to be a teacher!! Shocking! I'm very curious who this student is. What was surprising also was that of the 11 kids who liked school, none wanted to be a teacher.

This student had a great hypothesis and survey. Just made a mistake when calculating the relative frequencies. They used the total student surveyed as the denominator rather than the total students who were born in the U.S. of 26.