Combined Grade Easy!

Andrea teaches a combined 4/5 class.  She is really lucky because her team was able to work their LOI position to help break the combined grade down into single grade periods for part of the day.  Each day Andrea gets to have 1 period with just the grade 4s and 1 period with just the grade 5s (They go off to Science/social studies during that period).  This has helped her to meet the needs of her class because she is able to teach math to them in both a combined grade and single grade setting.

Her class is currently studying multiplication and division.  For this lesson, the students would only be focusing on multiplication.  Andrea wanted to do a lesson where the students would have the opportunity to not only practice this skill, but also see that there are different strategies that they can use to help them solve these types of questions.  She decided to do her lesson as Bansho to help the students see all of the different strategies that the class was able to come up with.  Her lesson started with the whole class, then it was just the Grade 4s and then it was just the Grade 5s.

She started her lesson with the whole group by highlighting the learning goals and success criteria:

The students then did a math string to help draw out the strategies that they were currently using.  They were asked to mentally solve the problem first, and then do a turn and talk with their partner.  To help slip in some accountable talk, they they had to share what their partner's strategy was for solving the problem.

You can see how some students did multiplication by skip counting, or by using known facts to help them break the problem into smaller chunks.  Others used the "traditional" way of multiplying.  She even introduced them to the area model to show them a different perspective.

When the Grade 5 students left, the Grade 4s were given their problem and solved it.  What was interesting was that in terms of strategies, the Grade 4 students had many more strategies to draw upon that the Grade 5 students.  As a class they found this kind of interesting.

Here are the problems that they completed:

Here is what their different strategies were.  These pictures are of the whole group, not just the Grade 4 or Grade 5 work.  The strategies are broken out into very distinct groups.  There could have been a few that were grouped together, but Andrea wanted to stress to the group that there are multiple ways of getting an answer, and that all of them are correct - but we can all learn a new strategy in the process.



Once the students were done, they had a class discussion as to what strategy they would try next time and why.  It was interesting to hear from them what their "a-ha" moments were and what they took from seeing the strategies.  Here is what the lesson looked like as a Bansho when it was fully completed:

Another great example of how to multiply in more than just one way.

More Than Just Time

Michelle teaches a combined Grade 3/4 class.  She is nearing the end of her measurement unit and wanted to spend a few days working with her students on noticing the relationships between days, weeks, months and years.  She used a previous EQAO multiple choice question as the base for her lesson.  However, instead of it being a multiple choice question she opened it up to an open problem.  For her Grade 4 students, Michelle wanted to review what they knew about this concept and see what other strategies they were able to apply to help them solve the problem.  This concept is one that is really based in application.  Are the students able to apply what they know about the passage of time and the relationships between days to weeks and weeks to months?  And are they able to apply a strategy to help them show their understanding (e.g., adding, skip counting, fractions)?

Her lesson started off with the learning goal and success criteria clearly posted.

The students then were given this problem as their minds on:

They did a think-pair-share with their elbow partner to share what their thinking was.  Michelle then filtered in some accountable talk by having the students share the answer that their partner said.  This was recorded in blue on the chart to help illustrate the thinking on paper.

For their action the students did a similar problem as in the minds on: 

The students were reminded to use the success criteria to help them with their answer.  They also were reminded to show their work clearly and to explain their final answer.

When the students were done Michelle did a Bansho of the strategies that they used.  She had the students talk about what was similar in all of their answers, and had them name the strategy that they used.  In total the students were able to come up with 7 different strategies.  They were:

Michelle then had the students give each other some descriptive feedback on what they did well, and what they could do to improve. A great lesson with a lot of learning!

Learning To Add

Part of the Grade 2 number sense and numeration expectations are around being able to add and subtract numbers using a variety of strategies.  Steve's class has been working on using mental math as a strategy and he wanted to see what other strategies the students were using to help them add numbers together.

His lesson started off with a minds-on activity where the students had to talk about how they would go about adding three numbers together.  He did a think-pair-share activity where the students had to tell their partner how they would add the numbers together.  To help tie in a little more accountable talk, the students were then asked to share what their partners' strategy for solving the equation was.  "John" was asked why it was okay for his partner to move the 3 around in the addition sentence.  He told the class that because it is addition, it doesn't matter what order you add them in.  This thinking was recorded on the board to help with the upcoming problem.  Here are some of their strategies:

The students were given the following problem for their action part of the lesson: 

I went to the store and bought some stickers.  One pack had 14 stickers, one had 7 stickers and the last pack had 16 stickers.  Did I buy enough to give everyone in the class a sticker?

Working in pairs, the students quickly went to work adding the number together using different strategies.  What was interesting is that most of the students were successful in solving the problem, but didn't actually answer the question with a final sentence.  For some students they realized that the number they got was different than the number of students in the class, (the number of stickers purchased was higher than the number in the class) and they said that he didn't buy enough.  This was talked about with the whole class during the consolidation of the lesson.

For consolidation, the student's work was grouped together in a bansho to highlight the strategies that they used.  In total, the class showed 5 different ways of adding.

Pictures, Tally Marks and Tally Marks in groups of 10 (this was highlighted to get the students to think about groups of rather than just making groups of 5)

Adding by 1s and 10s is the "traditional" was of adding, and the final way was Using friendly numbers

For the group that used friendly numbers, they were prompted by the teacher in helping to explain their thinking.  Orally they were able to communicate what they had done, but were not quite able to record it on paper.  So when they became "stuck" the teacher recorded their thinking in pen for them and then they carried on from there.

As an "exit ticket" out of the lesson, the students were asked what strategy they would try next time they did addition.  What was great was that the students were keen to say "I used strategy x, and next time I want to try strategy y because..."  This shows that they are reflecting on their learning, and hoping to expand their addition tool kit.

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.

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.

Bansho Within A Bansho

For Lisa's lesson study she wanted to not only do a Bansho as a consolidation strategy, but also do her lesson as Bansho.  She teaches a combined Grade 2/3 class and wanted to do a parallel task that would allow for both grades to not only meet curriculum expectations but also do some problem solving as well.  So she took a question from a previous EQAO test and modified it to meet her needs. 

Her minds on involved estimating and measuring objects in the classroom using both standard and non-standard units. 





For the action she had the Grade 2 students (and any student on a modified IEP) do a problem where the students had to figure out how tall a student was.  For the Grade 3 students they had to use a reference of a door and a door knob to determine how tall a student was.

What was a great experience for this lesson study was that we went a little longer during the action, so we didn't get to consolidate right away.  The students finished up just as the recess bell rang.  What was great for the nine teachers in the room is that it allowed us the time to talk about the strategies that the students used to solve the problems, and where we would put them in the Bansho.  This is an opportunity that we don't always get when we are working in such a large group. Usually, the two or three people co-teaching get to have this discussion, but it is usually on the fly and usually done pretty rushed.  But today, the nine of us had about 15 minutes to sort through the work, move it around, and persuade others to see our reasoning behind our choice.

When the students came back we had them talk about what they noticed was the same in each of the groups and what they noticed was different.  They then gave their strategy a name and recorded it.  Here is what they saw:

Counting cubes to get her height.

Doubled checked by counting backwards from 18 to the door handle.  (They originally counted up from 9 to 18 to see how many blocks were left)

Drew a line to meet the door knob.



Used subtraction after they converted M to Cm

Here is what the finished Bansho looked like:

A great afternoon spent with a great group of colleagues learning from each other, and working towards improved student achievement.