Surface Area....Trying It Out

Anthoula was part of our Grade 6 lesson study a few weeks ago and she really liked the activity that she saw.  She had set a personal goal for herself of trying to do more small group problem solving, and thought that the lesson she saw in Brian's class would be a great place to start.

For her minds on, she had the students brainstorm a definition of what surface area is.  Then they co-created a list of steps to take in order to successfully find out the surface area of any shape.

For the action, the class was divided into small groups based on their abilities.  Each group was given a box and the students were each assigned a task to do based on the box.  The tasks were:  create a net, justify what polygons are in the figure, find the area of each face and finally find the surface area of the box.  They then had to give an example of when they would need to use surface area.  The students were reminded to refer to the success criteria that is being created when working on their activity.

Here are some samples of the students work.

 

To consolidate the lesson, Anthoula offered each group descriptive feedback on what was done well, and what could be changed to help make their answer better.  For some students, she even allowed them the opportunity to reflect on what they could have added (based on the success criteria) to make their answer stronger.

An Amazing Thought!

Diana opened the doors to her combined Grade 5/6 class for a lesson study with some teachers in our FOS.  She is just about to start her next unit on multiplying and dividing and wanted to get a sense of where her students were.

For the "Minds On" part of the lesson she asked them to use mental math to divide a number.  The students were each given some think time, and then used the "turn and talk" strategy to share what they were thinking with a partner.



After they had time to think and talk, a few of the students shared their answers with us.  The writing in black was their initial thinking.  However, one of the students came up with a hypothesis of how they think that they could do a "trick" that would work on all of the numbers (that was crossing off the zeros).  So the writing in red is a reflection of the class "testing" the hypothesis.

Because it is a combined grade, Diana gave both the Grade 5's and 6's the same problem, but changed the numbers to be more appropriate for the grade (93 for Grade 5, 186 for Grade 6).  The class had to solve a division problem about dividing a set number of marbles equally among 3 students.  As the students were working, all of the teachers who were observing used the assessment for learning tool to keep track of what strategies they noticed that the students were using.  The students also completed a "Star and a Wish" statement at the bottom of their work.  The "Star" was what they thought they did well on, and the "wish" was one thing that they still needed help with.  When the students were done, Diana selected three of them to share their work with the class.  She chose them based on the different strategies that they used.  As they shared their work it was put on the board and notes were made along side of it to record the thinking / learning.

Here was the first sample of work that was chosen:

Diana picked this student's work because they used the strategy of drawing the marbles (all 93 of them) and then grouped them into groups of 3.  Once they were all in groups of 3, she then counted the groups and used that number as the number of marbles each person would get.  If you notice the "wish" this student wrote it says that they "wish" to do division in a different way than just drawing pictures.  What great insight, and a great way to self regulate and identify what they need help with.

This is what we identified as the student talked:

You can see how she orally talked about what she did, and that she has a small misconception when decomposing 93 into friendly numbers. 

Here is the second example of student work:

This student really surprised us.  When they were working we all noticed that they had divided their work into three parts, and then used tens and ones to decompose 186 marbles into 3 equal groups.  This was a little more sophisticated than the previous student sample, but what we quickly learned, what that we saw on the paper wasn't exactly what the student was thinking when they solved the problem.  Here is the picture of what they told us they did:

The student started by saying that he broke the number into 6 and 180.  They then divided the 6 into 3 and got 2.  Therefore they put the two "ones" into each of the groups they had drawn.  Here is where things got AMAZING....They then said that they thought of 180 as 18 because it was an easier number to work with.  They divide the 18 / 3 and got 6.  But they knew it wouldn't be 6 ones, but 6 tens.  So they added the 60 + 2 and got 62.  Therefore they made sure that each person got 62 marbles.  They then used the 10s to represent each ten in the 60.  To double check their work, they then added up 62+62+62 and got the final answer of 186.  Everyone in the room was blown away!  The student was pretty happy when they saw this.  What was thought of (originally) as a simple answer turned out to be much more in depth.  In fact, the oral descriptive feedback that was given to this student was to put all of their thinking down on paper, just like they had described it to us. 

The third strategy was also quite a bit different than the other two:

This student's work was chosen for two main reasons.  The "main" reason being that they had used a highlighter to underline key information in the problem.  Being in Grade 6, this is a key strategy that can help students when they write the EQAO and also as they move along in their math career.  The second reason was because they had successfully used traditional long division as a way to solve the problem.  They then used multiplication as a way to double check their answer. 

After the students had each shared their work a highlights sheet was created with some tips for them to remember when they continue through the unit.  These highlights can be added to and also can be used to help co-create success criteria.

When the lesson was over all of the teacher's headed out to a break out room where we discussed some ways that we would change the lesson to make improvements upon it.  Most of our discussion was around changing the minds on to reflect division more than multiplication.  We also discussed the merits of doing a pre-assessment "cold" (like we did here) or "warm."  The morning ended by giving some descriptive feedback to several students in the group. 

Overall, we had a great professional morning together - Thank you Diana for helping to make that happen.  (The lesson plan and AfL chart is available on our wiki)

Lesson Study In Grade 6

Brian opened up his Grade 6 classroom to several teachers in our family for a lesson study.  The group of teachers each had a clip board and were assigned a group to "watch."  The lesson was done in three part lesson format.  Here is a copy of what the lesson looked like:

For the "action" part of the lesson each group was given a box as their example.  Each person in the group was also given a job card to use which gave them a specific task to complete as part of the whole problem.  Here are some examples of different students working on their part of the problem:

As the groups worked, the teachers made notes and observations about the group they were watching.  They also got to walk around the room and look at other groups work as well.  They all agreed that the hardest part was not talking to the students, but merely observing them and taking note of their thinking.

For the "consolidation" of the lesson each group presented their findings and then justified how they knew they were correct.  The teacher who had observed that group then offered oral descriptive feedback as to how they could improve for next time.  Another teacher would the scribe this feedback down onto the students work.  It was a great opportunity for the students to not only recieve feedback orally, but also was a great chance for a teacher to practise giving feedback.

The student's work was then hung up in the staff room to encourage discussion amongst staff, and to showcase the great work that the students did.

A great morning was had by all!  Thank you Brian for opening up your classroom!

What a Graph Could Mean

Brian's Grade 6 class has been reviewing the "text features" of a graph.  They have also been talking about how graphs can be used to display data that represents a small group of people, or a large group of people.

His Minds On was getting his class to look at a graph (Via the ELMO) that had no "text features" on it.  They talked about what was missing and then gave examples of what they might be.  Brian recorded these things on an anchor chart to be used as their unit carries on.

For the Action part of the lesson, the students used the same graph, but came up with their own ideas as to what the graph could be about.  Some of them choose topics that were important to them (e.g., how much homework students got per grade) and others that were a little more worldly (e.g., the number of people in a union).  Once they came up with their topic, they then came up with all of the key elements of the graph (title, lables, key, scale, etc.) and also created 3 questions that could be asked of their graph.  One question was a true/false question, a second question was a multiple choice question (with 4 choices) and the final question was a more open question that could fall into a Level 3/level 4 range on a Q-Chart.

To consolidate the lesson Brian had the students look at all of their graphs and talk about what was similar and what was different.  They also talked about what questions were easy to make, and about what questions were hard to make.  They also talked about why the graph looked the way it did - and that it lent itself to going from smallest to biggest. 

The work on display with the expectations covered on the pink piece of paper.

Type of Job and Amount Paid

Number of Ice Cream Scoops Sold Per Day

Recycling Rates by Province

Popular Ice Cream Flavours At The School

Homework Given By Grade

Number of Employees Per Union

Using The Walls To Improve Students Strategies

Arpine's Grade 3 class was about a week into their unit on Patterning and Algebra.  She was finding that the students were always using pictures as a way to communicate their thinking.  They had been exposed to different strategies (like using a number line) but were always going back to drawing a picture.  Not only is the strategy not varied, it also was taking them a lot of time to complete their work!

As she headed to her class one day she noticed the work of Brian's Grade 6 class posted on the wall.  She stopped and had a look at what they were doing.  They too were doing Patterning but had shown different strategies in their answers.  So she decided to take her class down the hall to look at the wall before she gave them their next problem.  This is what they saw:

The "Wall" of student work.

A brief explanation of what they achieved in the lesson.

One sample of how the students found the pattern.

A second example.

When the students went back to their class something happened.  They wanted to do what the Grade 6 students did.  They now had seen different ways to find patterns, and wanted to demonstrate their thinking in a different way.  Here is a sample of the work Arpine was getting before looking at the "wall"

Here are samples of some of the different strategies that she go after the walk:

These students decided to try a number line.

This student attempted to use tally marks to help show their thinking.

To consolidate this lesson, they then created an anchor chart with the strategies that they could now use to help them when they solve a problem.  Even though they choose not to use some of these strategies, they remembered seeing them done by the Grade 6's and wanted to include them for future use.