TASKS
We have just been focusing on the expectations of math.
Instead of typing these all up and going over them point by point,
Students have experiencing first hand what will be expected of them.
Most of the time, it has been through Thinking Non-Curricular Tasks at the vertical white boards
Which I will reflect on here in a bit.
One day we did a Number Talk to hit the expectations for Whole Group Discussions.
And one day we brought in the FISH! Philosophy to tie into our School Pillars and Growth Mindset.
Task 1: The Painted Cube Problem
Most students were able to complete the 3x3x3 problem.
More than half had a start or completed the 4x4x4 problem.
Few groups got to the 5x5x5.
And with time constraints on the following whole group discussion,
We did not even attempt the most abstract of them all, the nxnxn.
However, students got into the problem.
I could thinking occuring.
I was able to informally assess their understanding of volume and cubing skills.
Even though we were not able to bring the problem to completion,
Students were seeing patterns in how they could find short cuts as the cubes got larger.
--> No matter the size of the cube, 8 cubes will always have only 3 sides painted.
--> To find the number of cubes with no paint (these were unseen in the middle of the cube), one group found how many 1-sided cubes, 2-sided cubes and 3-sided cubes. Add these together and subtracted from the total number of cubes.
--> 1-sided cubes were always in the middle of each face and was always a perfect square which would then need to be multiplied by the six sides.
Time is definitely of the issue.
And this will require some playing around with.
This last week I was allowing 10 minutes for whole group discussions.
With the problems we were using, this seemed to be enough.
However, with these problems all being non-curricular,
Mastery or understanding may not have been achieved for all students.
This will definitely have to change when we start on grade level content!
Task 2: Four 4's
For this task, students just had to start playing with the problem.
It was a good problem for them to see that if you don't start and make a few mistakes
you will never get anywhere.
Students worked at their tables with horizontal whiteboards,
And when it came time for class discussion,
Students shared the ways they were able to arrive at solutions 1-30.
Multiple methods were discussed as students noticed expressions that were different than their's!
Another focus on this lesson was how the whole group discussion was critical to validating their learning
And also to understanding parts they had a struggled with.
Task 3: Palindrome Depths
This problem was definitely too long for the 42 minutes,
Which after explaining the instructions,
And allowing 10 minutes for a whole group discussion,
And another 10 minutes for Test Trainer at the end,
Ended up being more like 20-25 minutes of work time.
In this amount of time though,
Students started to find some patterns and relationships to make their task a little easier.
For example: if 14 was a depth-1 palidrome, than 41 would be one also.
In the whole group discussion, I shared how I had organized all my work
in a 10x10 grid with all the math problems and depths color coded.
We talked about how organizing our work can help with finding solutions and patterns.
Task 4: The Locker Problem
What a great problem to end our "Expectations Lessons" on!
After giving instructions using volunteers to "open" and "close" lockers for people 1-3,
Students headed off to the white boards, armed with tiles marked with an X on one side.
Some students chose to use graph paper,
And some students chose to record their process on the white board.
Only one group was successful in finding which lockers would remain open if there were 25 lockers.
But the problem ask which ones would be open if there were 100 lockers.
So when we went to whole group discussion,
We carefully analyzed each locker and which people would have touched it.
1:1
2:1,2
3:1,3
4:1,2,4
5: 1,5
6:1,2,3,6
By this point, some of the students were seeing that we were using factors,
Even if they couldn't correctly name the vocabulary word.
After the 6th locker with students yelling out who would have changed the status.
I looked around at the boards and noticed that no one had actually done this work,
So how were they getting the answers so quickly?
After that brief review,
We continued the process,
Looking for which lockers would remain open.
In most classes, someone observed it was the lockers with the odd number of factors.
Now we could move on
I created a t-chart with Locker Sequence and Locker # as the headings.
We placed the data we had found up to this point,
And students were quick to see either the addition pattern of the Locker #s
Or that the Locker # was simply the square of the sequence number!
Another shortcut!
Such a powerful problem to demonstrate modeling and looking for relationships!
So...the Building Thinking Classroom book suggest 3-5 non-curricular tasks to get students up and thinking.
With four tasks under our belt, I would say we have a good start!
RANDOM GROUPS
On the days that we used the vertical white boards,
Students drew a playing card that matched the number of the white board they were to go to.
By the last day I asked what they thought of this process.
Most students liked the randomness of it.
--> You never know who you will get
--> It's nice to work with a variety of people
--> I'm finding there are some I work really well with and some I don't
VERTICAL WHITE BOARDS
This was amazing to actually witness.
Students were working!
Each and every day.
They were thinking and solving math problems!
Just by standing.
Wow.
I did move a white board to get more distance between groups.
The moveable whiteboards seem to be working fairly well.
They stay in place, are easy to erase, and have enough room to get the job done.
Things I remembered to do, but need to be more consistent on.
1. Changing the marker to other students. I remember doing this one day. And then I did witness a student on a following day purposely hand over the marker to allow their partner to write as well! Small successes!
Things that went well
1. Allowing students to face struggle and then see the value of the whole group discussion.
2. Allowing students to struggle and being given permission to use the other boards as ways to get started.
3. Getting starting in the first five minutes with introducing the problem. After announcements and attendance, I just had the students stand around the cart or in a semi circle around the whiteboard or TV, as I gave the directions. We moved our curriculum's Test Trainer to the last 10 minutes and that seems to be working...we've only had a week, but no real issues during that time.
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