Above is the overview of this week's and next week's number talks.
As you can see one answer was 5.6 with no bar over it. Henry explained the traditional way using long division with a decimal. Jennifer showed how the remainder is the numerator and the divisor was the denominator of the mixed number. Tommy multiplied by the reciprocal. I really like Patrick's way. He knew 18 / 3 is 6. So, 1 divided by 3 is 1/3. 6 minus 1/3 is 5 2/3. I also honored someone who counted up by 3's on their finger and got 5 groups of 3 being 15. I also illustrated how an array of dots would look when grouping them into groups of 3 and having 5 groups.
On Monday in all 3 of my 8th grade classes I did a participation quiz. If you have students work in groups and have never done this, you must do it. Notice how group 1 got off topic and the task manager didn't get the group back on track. I noticed group 2 had no one working ahead. Group 3 a teammate asked another if they were good. In group 4 I clarified shaded is positive and unshaded is negative. When it's unshaded the red side of the tile would be facing UP.
I absolutely love Justice's method here. He said 18 / 3 is 6. 15 /3 is 5. So, 17 / 3 must be 5 and 2/3, because 17 is 2/3 of the way from 15 to 18.
I like how group 5 verified what part of the problem they were on. Group 1 had to re read the problem to make sure they needed a negative sign. Group 2 was discussing how regions affect the sign of a tile. In group 7 I wanted them to speak up when they saw a group member not using the tiles as tools. I also recognized a person for being brave enough to tell their group they didn't get it.
We discussed 2 ways of representing an expression. -(y-2) is huge. In this class I was surprised they didn't have the shaded y and the unshaded unit tiles both in the negative region, I always try to make sure I have that representation displayed.
I like how one student here just wrote the division problem as an improper fraction in their head then figured out it's mixed number. I like how this class said 5 remainder 2 and 5.2. This is a common misconception that the remainder is the decimal. I notice we didn't show the way the repeating decimal was found in that class period. I also brought in a strategy from 2nd period into the 5th period discussion because I liked it so much (Justice's in the bottom right).
5th period is right after lunch and is a class that I constantly have to remind to stay on topic. The participation quiz might be necessary more often with this group. Group 2 noticed one of their diagrams had all unshaded tiles. Someone from group 1 told their teammate to do their work! Group 1 asked a question when they were all stuck, which was good. A student in group 3 asked a question that started with "What's the difference between..?" to clarify how a group of algebra tiles were represented. As you can see group 8 was talking about their siblings when I walked by. When some students have tiles in their hand, they stop writing, so I reminded a student their to put the tiles down when drawing their diagram.
This was a great conversation in 6th grade math support. We talked about how it didn't make sense to regroup when subtracting 18 from 21. One student explained they counted up 3 jumps from 18 to get to 21. Another said, no way that's not how I did it! They started at 21 in their head, and counted back until they got to 3 after 18 jumps back. I think by illustrating it on the board I hope to get to them that some strategies were better in certain situations.
We had no wrong answers to discuss in this class. I liked when a student added 1 tenth or 0.1 to 8.9 to get 9. Then added 7.48 to get 16.48. Then subtract 0.1 for 16.38.
2 students in this class really know their place value because one separated .48 into .4 and .08. Another way was decomposing the decimal.
Here we reviewed how to 3 situations represented zero and how to represent it with symbols. They also reviewed the 2 ways to make zero.
Here Vivian divided 600 by 30 to get 20. Then divided 43 by 30 to get 1 13/30. Then added those together. One student added 17 to 643 to get 660. Then 660 divided by 30 is 22. Then they subtracted the 17/30 to get 21 13/30. This is the one class where no one gave a decimal answer.
Here we showed how the negative sign is distributed to each term in the parentheses.
Here we honored the mistake of multiplying 27 by 2 and getting 51. Then dividing 51 by 3 to get 16. The process is correct, except they should have gotten 54 when they multiplied. One student said 27 divided by 3 is 9. So, that's 1/3. Double 9 to get 18, which would be 2/3. Another student discussed cross cancelling or simplifying when multiplying fractions.
I liked how this student quickly illustrated the 3 legal moves. It was pretty simple and to the point.
I liked how someone here thought of 2/3 as an equivalent fraction with a denominator of 27. Therefore they thought of Giant One in their head to multiply 2/3 by 9/9 to get 18/27, so 2/3 of 27 must be 18, the numerator.
One student was able to do improper fractions in their head. In this case it's quite a laborsome process. I liked when a student rounded 7 2/3 to 8. Then added 3 and 5/9. Then subtracted 1/3 which is 3/9 from that to get 11 2/9.
In 6th grade math support we did a number line activity. At first, students thought that the single digit decimals were the smallest and closer to 0. Double digit decimals were closer to 1 here. One student correct 1.0 so it was right under 1, because they said you can add a point zero on the end and not change it.
Here you can see a misconception of 4/5 being between .5 and .6. Students couldn't explain why that was not correct. Students correctly identified .90 as being close to 1.
Then a student moved the .01 to the left of .1. They said if you compare the tenths place, 0 is less than 1, so it has to be smaller. This was a huge jump and turning point.
I told students they could use extra clothespins to pin any decimals that were equal or equivalent. Eventually a student pinned .20 to .2. They said that they had the same number in the tenths place and the zero at the end didn't change it. I reiterated that 2 is 2/10 or two tenths as they said. .20 is 20/100 or twenty hundredths, which simplifies to 2/10.@TTTPress @mr_stadel @MathProjects eventually 6th graders made connection double digit decimals were not always bigger than single digit pic.twitter.com/sHu0pYmE37— Martin Joyce (@martinsean) October 1, 2016
This student below really understands proportional relationships, but I ended up taking a bit off for the explanation because passing through the origin is not sufficient to be a proportional relationship and their 2nd reason didn't make it clear to me.
This S nailed one of @hpicciotto 's problems. Used it on sbg assessment. Suggestion for followup anyone #mtbos ? pic.twitter.com/bxbwaY4wWb— Martin Joyce (@martinsean) September 27, 2016