BTC - Implementing When, Where, and How Tasks are Given (Ch. 6) and How to Weave Into Existing Curriculum

As we start with grade level content tomorrow,

I found myself turning to the book to review where and how I need to go.

We started introducing tasks while standing in the classroom last week,

So this seemed like a logical place to focus on this week.

This week we are going to work with integer operations,

Particularly, adding and subtracting integers.

I noticed during Test Trainer (a component of our online curriculum, MidSchool Math)

That this was an area of struggle.

And since positive and negative numbers are used regularly in 8th grade math,

Decided this was a great place to start.

So to get us started, I will have students standing around the whiteboard and go through the following scenarios...

Script:

Teacher: I spend 4 dollars at  Dollar Tree and 8 dollars at Kwik Shop, how much have I spent?

Teacher: I have 16 dollars and spend 5 dollars, how much do I have? 

Teacher: I am in debt 10 dollars but get paid 25 dollars, how much do I have?

Teacher: I am in debt 10 dollars and get paid 3 dollars, how much do I have?

These four scenarios can be represented with mathematical expressions that can be simplified to a single answer.

Write: -4 + -8 = ___ (-12)

Write: 16 - 5 OR 16 + -5 = ___ (11)

Write: -10 + 25 = ___ (15)

Write: -10 + 3 = ___ (-7)

After assigning random groupings,

Students will go solve integer puzzles from varying levels like the one below.

As part of this thinking process for how to introduce content,

I needed to think through how to marry my curriculum with these thinking strategies.

The following outline is what I came up with.

Math Simulator from MSM (Midschool Math)

Immersion Video - Addresses Ch. 6 of How and When to introduce the problem.

I will have students gather around the TV to hear about the problem for the day.

We will then shift to the whiteboard as students brainstorm how to solve the problem.

Once the task has been given,

Random groupings will be made.

Students will solve the problem from the Data and Computation Section.

Whole group discussion will follow

With the teacher sequencing the boards that will be addressed to hone in on the needed skills, common misconceptions, interesting strategies, multiple methods, etc.

If time, the Resolution Video will be shown. (This could be the intro for the next day as another input/retrieval opportunity for what was learned the previous day.)

Teacher Instruction (MSM component)

Prior to teaching this part of the lesson, the teacher will create leveled problems addressed in the teacher instruction section. Students will go to random groups to solve.  Consolidation from the bottom will occur during the whole group discussion.

Simulation Trainer (MSM component)

This can be done two different ways and I might experiment which way is most beneficial to learning.

1) Students do these problems on their own to check for understanding

2) Students work with table groups to continue the group think model for learning new material.

After completing the simulation trainer, students would write notes to their future forgetful self on the main ideas of solving the type of problem used in the simulation trainer.

Practice Printable (MSM component)

These are great Check for Understanding questions.  Would introduce the coding and would have random groups at the white boards solve as many as they need to before they believe they will be successful.

Add or complete their notes for their future forgetful self, based on their work at the vertical boards.

BTC Tasks, Random Groups, and Vertical WhiteBoards (Ch. 1-3) Reflection

TASKS

In the last week and a half since starting school,

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.

BTC - Day 2

Changed it up a bit today.

Instead of vertical white boards,

The white boards were horizontal on the tables.

We completed the four 4's problem today.

Students worked in their table groups,

Before sharing in the whole group discussion their answers for 1-20.

What I Observed:

1. More individual thinking today.  But it could have been the nature of the problem. We discussed that math takes on many forms and if someone wants some quiet time to first work on a problem, we will respect that.

2. The whole group discussion is vital for moving thinking.  As students shared their answers on how to get the various numbers, students were taking what they were learning from the others to help them complete expressions for the missing solutions.

3. During the hour that had only 70% of the students thinking yesterday, today 100% were on board!  Before we began the whole group discussion, I told them what I had observed and that I wanted their feedback as to why the change.  They came up with two ideas: 1) A different problem was used that might have been more engaging for them, 2) Different groups...or friends were not with friends this time.  This second observation was a perfect segway into making choices to be on task and work with others when the groupings match up best of friends.  Our conversation led to using self-control and doing the right thing in the moment.  We shall see how that translates down the road with future lessons.

Changes Made:

• We did not do random groups but worked as table groups.
• Used horizontal boards instead of vertical...to allow for more solutions to come through in the whole group discussion.
• Instructions were given with the students sitting down and there were lots more questions than I had yesterday when they were standing.
• Gave instructions from the south side of the room, but the whole group discussion was focused on the east side of the room.  Defronting?  Maybe????

BTC - Day 1

Today we did the random groups. (Chapter 2)

We defronted the classroom. (Chapter 4)

We gave a non-curricular task. (Chapter 1)

And did all of our thinking on vertical whiteboards. (Chapter 3)

And it flowed.

Really well.

Not only was it day 1 of BTC (Building Thinking Classrooms)

But it was the first day of school!

I gathered the class around my "go-dium" cart.

I had 3-D models of the various sized cubes.

I explained the problem and directed their attention to the board where it was written out

Should they have questions after I sent them to their NPVSs.  

Today's Task:

Picture a Rubik’s Cube. Now picture dropping it into paint so that it is completely covered. When the paint is dry, imagine breaking it apart into the smaller cubes. How many of the cubes have one face covered in paint? How many cubes have two faces covered in paint? How many have three faces covered in paint? How many have zero faces covered in paint? 

How could you predict the above for any size Rubik’s cube? 

What about a 4 x 4 x 4? 5 x 5 x 5? 6 x 6 x 6? N x N x N?

Thoughts:

For the most part,

I could already tell that more thinking was happening.

Maybe it was because it was the first day?

Maybe it was a please the teacher kind of thing?

Maybe they were actually intrigued with the problem?

Maybe they liked being able to think with others?

In one class, I noticed a lot of movement to the 3D figures.

Most of the conversation around this was on task.

However, movement created a blip in the bubble of thinking,

allowing space for other conversation to creep in.

In another class, only 70% of the class was in thinking mode.

It was my largest class.

The groups were fairly close together,

Allowing those not interested in participating to congregate together a bit.

Will need to figure out how to engage all 100%!

At the end of class, as a whole group, we talked about the benefits of using the others' boards.

I can only be in one place at one time.

If a group has a question,

It doesn't make sense to stop working until I can get to them.

By using the boards, groups can gain information on where to go after solving a problem,

Get unstuck if they are struggling,

And check their answers.

This was foreshadowing to mobilizing knowledge.  (Chapter 8)

We talked about the difference of just copying answers 

or figuring out who has the right answer if an answer doesn't match another group's board.

Day 1 Summary:

1. Lots of expectations woven into real life application.

2. Math thinking on the first day of school!

3. Non-intended intro to the concept of cubes.

4. Value of seeing the problem...drawing pictures...using our fingers...