By completing this activity with my students...

...the student are teaching each other.

...the students are working together.

...the students know a problem well enough to teach it to someone else.

...the students are constantly self-assessing their knowledge.

...the students are completing many problems in a short amount of time.

...the students had a personalized study-guide.

#### Background:

I've been trying to teach my students how to solve compound probability problems that involve "OR". The process was going so slow. So many of my students needed one-on-one attention for these problems and I couldn't afford the time to give it to them. From this situation, the

*Problem Experts*activity was born...#### Getting Ready:

The largest class I have for Algebra 1B is 16 students. So I created 16 Probability "OR" problems. I decided that each students would get exactly one problem and become an expert on it. After I was sure each student knew their problem, they were going to pair off and teach/coach the other student on their problem.

On one paper I had each problem typed multiple times (as many times as would fit on the paper).

For instance: On one paper problem #1 was typed multiple times, on another paper problem #2 was typed multiple times, etc.

The problems were typed in a text box with the outline feature.

These papers were copied on colored paper!

I also created a packet for the students so, when they were finished they would have all their problems in one place. I created this document so that the problems would fit perfectly in the rectangles with the number. Their solution would be done to the right of the problem.

Then I took 16 envelope and wrote the numbers 1-16 on each envelope.

The goal of this activity is to become more confident in solving Probability "OR" problems. The goal is not to finish a certain amount of problems in a certain amount of time.

*I found one student copying from his partner and needed to remind him of our goals.

On one paper I had each problem typed multiple times (as many times as would fit on the paper).

For instance: On one paper problem #1 was typed multiple times, on another paper problem #2 was typed multiple times, etc.

The problems were typed in a text box with the outline feature.

These papers were copied on colored paper!

I also created a packet for the students so, when they were finished they would have all their problems in one place. I created this document so that the problems would fit perfectly in the rectangles with the number. Their solution would be done to the right of the problem.

Then I took 16 envelope and wrote the numbers 1-16 on each envelope.

#### Discussions to have before you begin the activity:

What makes a good coach. Here is yet another idea stolen from Square Root of Negative one. I will just direct you to her sight and have a look for yourself.

The goal of this activity is to become more confident in solving Probability "OR" problems. The goal is not to finish a certain amount of problems in a certain amount of time.

*I found one student copying from his partner and needed to remind him of our goals.

#### The first day of the activity:

As the students walked into the room, I handed them a random envelope with a number on it. Keeping with my warm-up activity (read about that here) they were instructed to sit so that the sum of them and the person sitting next to them was 17.

I handed each student enough copies of the problem that corresponded with their envelope number and instructed them to cut out each problem and place it in their envelope.

Next, take one problem out of your envelope and adhere it to the correct place in the packet.

Solve your problem. This is the step that took the most time, but was well worth it. I went to each student individually to make sure their problem was correct and that they could teach it to another student.

That was the end of day 1.

#### The second day of the activity:

As students came into the room they were instructed to sit with a partner. The students exchanged problems with their partner and adhered it to their packet.

As the students were completing their problems, I instructed them to coach each other and offer help without taking over.

Students would try to ask me a question, but I would turn the question back to their partner. After a while they figured out what I was doing and began asking their partner right away rather than me.

After each problem, the students has to place a dot next to that problem with colored pencils. If they needed no help to complete the problem, they drew a green dot, if they needed some help they placed a yellow dot, and if they needed a lot of help they put a red dot.

Once they were finished, they found a new partner and did the process all over again.

#### The end of the activity:

By the end of class the 2nd day, the students had completed about 7-8 problems. I noticed that as the period went on, they were getting fast and more accurate.

I did make a homework suggestion (strongly suggested): any problems that were marked as yellow or red should be completed again that night. This created personalized study guides.

#### Download the activity here:

#### What the students said:

Using my learning prompt poster:

"I was surprised by how I did all the problems by myself."

"After this session, I feel smarter."

"After this session, I feel that I can do these problems better now."

"Today I learned how to do the probability with the charts better."

"What I liked most about this lesson was that it was not just sitting copying notes, but we got to interact with others."

"After this session I feel a bit confused about the way probability works."

"One thing I am not sure about is the problems with the 2 dice being added."

"Today I learned how many times I could get something wrong and liked getting help."

"After this session I feel very confident about doing probability problems."

"Today I learned that a die has 36 dots on it." Hmmmm....

"I was surprised by how fast I learned how to do this. It surprised me how well I did also."

"Today I learned that I do need to write the formula when writing a problem."

#### Next time:

I copied the packet in white and the problems in pink. Next time, I think I will copy one of each problem in a different color, say green, so that the problem they are an expert on will be green and they can find it faster in their packet. I noticed a lot of students flipping their packets around, looking for their problem.

I mostly left it up to the students to find their own partner and it worked pretty well. However, next time I think I set up areas in my room. One area for working and one for finding a new partner. As the students come into the room, the seats will already be set up for pairing. When a pair of students are finished they will go to the waiting area to wait for another pair to arrive. With their new partner they can go back to the paired desks.

For my own sake, maybe next time I'll put a chart up on the board (tape a piece of paper to the board with colored pencils nearby) to see what students have done what problems. As they finish problems they can put their color on the chart. I'm thinking something like this:

This way I can see if there is a particular problem that the students are struggling with and also if any student is having a hard time, like student 2 above.

I mostly left it up to the students to find their own partner and it worked pretty well. However, next time I think I set up areas in my room. One area for working and one for finding a new partner. As the students come into the room, the seats will already be set up for pairing. When a pair of students are finished they will go to the waiting area to wait for another pair to arrive. With their new partner they can go back to the paired desks.

For my own sake, maybe next time I'll put a chart up on the board (tape a piece of paper to the board with colored pencils nearby) to see what students have done what problems. As they finish problems they can put their color on the chart. I'm thinking something like this:

This way I can see if there is a particular problem that the students are struggling with and also if any student is having a hard time, like student 2 above.

What is it about probability? My students are working on independent probability and having a time of it. I think I'll do this when we get to dependent probability if that is as much of a problem as independent probability has been.

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