Time Goes By So Quickly

Kristen decided to begin her unit on Measurement by starting with teaching them time.  Since there are only a few days before March Break she figured it was something that could be easily covered, and would not be hindered by the week off school.  This was her second lesson on elapsed time.  It was part of our FOS PLCs.  Therefore we did the lesson as a lesson study.

The minds on was giving the students a problem about finishing chores in time to watch a favourite t.v. program.  The students did a think-pair-share and also used the accountable talk strategy of repeating (in their own words) a strategy of someone else.  Here were three answers that were given:

Kristen then gave the students the problem.  It was taken from the curriculum document. 

They were reminded to check the Success Criteria before and after they started to make sure they were not missing any important pieces in their final answer.

Just before the consolidation, the teachers came together and decided what groups should present their work during the congress.  Three groups were chosen because they had done different strategies that were interesting and unique.  Some of the groups even tried to show their answer in more than one way just to see if they could. 

The teachers then left the classroom and headed back to the staff room to debrief.  They talked about making the action more of a parallel task where the students could chose between this problem and one that used slightly different numbers (e.g., ones that ended in 7, or 6) to allow for some DI for the class.  The group also talked about what some next steps could be for the class in the upcoming days to either help them build upon the concept of elapsed time, or to do as a culminating task.

The group broke into smaller groups to give some descriptive feedback to the students.  Here are some of their comments:

A Bansho was then created with all of the student work to showcase the different strategies that were used to solve the problem.  The group had some really rich conversations about the strategies and when to push students to try new strategies, and when to let them keep using a specific strategy.  Even in grouping the work for the Bansho, some of the work samples we felt could still be moved around and new groups could be formed, or bigger groups could be made.  Here are pictures of the finished Bansho and also of the specific groupings.

Strategy: Using words

Strategy:  Adding the times together.

Strategy:  Adding, but converting the units from minutes to hours and minutes.

Strategy:  Using a number line.

Strategy:  Writing out the time that each activity was finished in a "number line" type fashion.  These two pieces caused quite  a discussion in the group as we were not quite 100% sure where to put them...Are they just like a number line?  Are they something more?  Something less?

It was a great professional afternoon full of ideas, discussions, and rich learning for both the students and the teachers.  I highly recommend you take the opportunity to visit a demonstration classroom and be apart of a lesson study.  If you need help in finding one, please let me know and I will see what I can do.

Structural Safety

Peter wanted to do a lesson that he had done previously with the family of schools during a transitions workshop.  He made a few modifications to the question, and then decided to give it to his class as part of a final assessment for his measurement strand.

His three part lesson went as follows:

Minds on:  The students talked about what they would need to rebuild a building after it had been knocked down. 

Action:  The students worked on a problem that asked them to pick which support structure they should choose and why.  They were given a choice of a cylinder, a triangular prism, and a rectangular prism.

Consolidation:  As a class, the students talked about the "Pros" and "Cons" of using each shape.  This was recorded on the chart below.

The teachers in the group then headed back to the debrief room to debrief the lesson, and also do a bit of moderated marking.  Using the achievement chart as their guide they marked several piece of student work and gave some feedback to the students.  The discussions were really rich and really centered around why a mark would or would not be awarded.  Here is some of the student work, and how it was assessed:

Part 1 of the student "a"'s work

Part 2 of student "a"'s work.

Part 1 of student "b"'s work.

Part 2 of student "b"'s work.

The Rate of Things

Heather opened up her Grade 8 class to the PLC group for a great intro lesson on rate.  Her class has been looking at rate and ratio a little bit during their science class, but before she proceeded into the unit she decided to do a diagnostic lesson on what they already knew.  She started off with the following question as her minds on:

At first the discussion was going only based on observations about the numbers.  Then Heather moved the conversation into more about unit rates.  The students were able to share ideas freely, and as you can see in the picture made a mistake along the way, but quickly corrected themselves.  This was important to them so they could work on using justification skills and think about what makes sense.

For the action part of the lesson, she took a problem from the curriculum document and modified it to be more "2012" (substituting iTunes downloads for CDs).

When the students were done, three of them came and shared their work with the class.  The group of teachers in the lesson study chose the three groups because each of them used a different strategy to solve the problem, and all the strategies were different and unique in their own way.  Here were the three strategies:

This group made two charts (one for each type of download) and then found combinations that met the requirement of 130 downloads.

This group chose to find the rate in each package for one download.  They they went about finding what would be the best package to get for the 130 downloads.  They also did a bit of cross checking to make sure that they were on the right track.

This group chose to make a graph to visually show their findings.  The first picture shows how they came to their conclusions, but this second picture shows the graph. 

Here is a picture of what the board looked like at the end of the lesson:

After the students left the classroom to go to drama, the teachers de-briefed the lesson talking about what they noticed and where they would go next.  The group noticed that while the class is very good at figuring out the rate, they need some reminders to actually write the whole rate down (e.g, 33 cents per download).  This is a simple thing that can be reinforced when Heather co-creates her success criteria with the class for this unit. 

The teachers also practiced giving some descriptive feedback to the students.  Here is what they said:

Area and Perimeter, It's in the bag!

Sarika is currently working on Measurement with her students.  They have spent a few days on time, and have moved into area and perimeter.  She has her Learning Goals and Success Criteria up for her class to see.  She also has a chart which shows some math vocabulary that the students will be using for this unit:

For the lesson study in her classroom, she decided to do a lesson on area and perimeter with her students.  Here is what she did:

For the minds on, Sarika showed the class this picture and asked them to figure out the area and the perimeter of the garden:

You can see that the class quickly gave her both the formula for area and perimeter and also substituted in the values to help them find the area and the perimeter.

She then gave them this problem for their action:

She worried that the problem was too open for her students.  However, as a group we discussed the pros and cons of having a problem so open.  The group agreed that in having it as open would be a good way to help the students justify in a way that they felt comfortable with.  This also stopped us from seeing a lot of "they should go with this one because its the biggest" type justification.

For the consolidation of the lesson, Sarika originally had decided to do a Bansho with her students.  However, as a group, the teachers decided that it would be better for the students to get the time to discuss their thinking and what else needed to go into their answer in order to really help them justify their reasoning as to why they think the garden they chose was the best.  Justification is a really hard thing for students to do.  They are good at writing " I think they should pick C" but the "because...." is something that they tend to leave out.  They are able to do it when you ask them orally, but the stuff that is in their head, does not always make it onto paper.

Here is the work that Sarika's students did.  You notice that they did not use the colour black or yellow.  This is because yellow is really hard to see, and black becomes the "editing" pen.  As you look at the work samples the black writing is what the students added to their work as they were presenting it to the class.  This is a great way for the students to see how sometimes just adding a bit more appropriate details really helps to make their answer that much better.

This group struggled to get going, but really had some great ideas as to why they picked the gardens that they did.  It goes to show that students will always surprise you with their thinking!

After the lesson was over the group headed into the staff room where they had a great discussion about the student work and gave some descriptive feedback to each group.  Sarika is planning on giving the work back to the students so they can learn from the feedback and apply it to the next problem that they do.

Everybody Add and Subtract Now!

The afternoon Grade 2 PLC asked to look at different strategies they could use to teach addition and subtraction to their class.  The group had some great discussions about the pros and cons for teaching the different strategies and also for ways to try the strategies out in the classroom.  One discussion was about how great it would be to divide up some of the strategies to make them be "must covers" for different grades.  This way, as the students progress through the grades and into higher numbers in addition and subtraction they would already have some strategies in place, and be able to add strategies to their tool kit.  See which of the strategies you are familiar with, and see which ones will be added to your tool kit.  If you want to learn more about addition and subtraction strategies I highly recommend reading "Young Mathematicians at Work:  Constructing Number Sense, Addition, and Subtraction" by Cathy Fosnot.  You can get the book from Pearson.  The ISBN is: 0-325-00353-X

 

Birthdays Lead To Multiplication?

Zahra teaches a combined Grade 1/2 class.  Her Grade 1s have been doing addition and subtraction and her Grade 2s have been learning about making equal groups leading up to multiplication.  Drawing on a problem she had done with a previous class, Zahra decided to do an activity involving birthday candles on a cake for the PLC lesson study.

For her minds on she used magnets and a picture of a cake to have the students represent different ways to put 6 (and then 12) candles on a cake.  She recorded their thinking beside the cake on the dry erase board:

Because it is a combined Grade 1/2 Class Zahra chose to do a parallel task type question.  However, instead of letting the students choose what task, she assigned one for each grade.  They now had to find different ways to put candles on a birthday cake:



When the students were done it was recess time, and as they headed out to play, the teachers at the lesson study headed out into the hall to Bansho the work that was done.  We chose to do this on our own and not with the children only so that we could have more time to talk about the work that we were noticing, and see the progression of strategies that the students used.  Here is a picture of what the finished Bansho looked like:

As a group, it was easy to put the strategies at the outer most ends of the Bansho down.  They were very clear in what they had done, and where it was along the spectrum of strategies.  However, where we had some of the best professional dialogue was around what pieces went into the middle of the Bansho and why.  We found ourselves really looking at what was on the paper and really comparing it to other examples of work.  We looked for what was similar and what was different in pieces.  As well, we discussed what we considered more sophisticated, and what was not as sophisticated and why.  We also found ourselves really looking at the math and not the right answer.  While yes, the right answer is part of the bigger picture, knowing how they got there and being able to work that out is almost a bigger part of the picture.  After much discussion here are our final strategies that were decided upon:

Used counters - not yet able to move past the manipulative onto paper

This strategy was to draw pictures to represent the candles.

Pictures and numbers to "talk" about what the pictures mean.

Making Equal Groups (not always the correct number as per the question, but equal groups)

Used pictures, number and started to use the terms "groups of"  The group decided to call this "Making Groups With Proof"

Multiplication

What we found interesting was that within the multiplication group we had several different "styles" of multiplication.  Here are some of the "styles"

Making Arrays (Grade 2 expectation)

Using "groups of" as well as repeated addition and a multiplication sentence.

Groups, Addition and Multiplication

A great morning filled with professional dialogue, discussion and idea sharing.  Thanks to all who participated.