The Middle of Volume

Shannon invited a team of teachers into her Grade 7 class to participate in a lesson study around volume.  Her class had been learning about how to estimate, measure and record the volume of different objects.  To get an idea of how well they have synthesized everything, Shannon decided to use one of the sample problems from the curriculum document as a way to not only see how well her students were doing, but also to see if there was anything else she needed to do to help them meet the overall curriculum expectation.

Here is a summary of the lesson:

Minds on:  The students were asked to use 3 of the following numbers (3, 4, 5, 6, 7) and substitute it for the length, width, and height of a package, and find the volume of that package.  They then had to sketch what they thought the package looked like.  After they were done, they shared how they found the volume, and some important information was recorded on chart paper to help them with the action (e.g., what the formula of a rectangular prism is, to remember that you are multiplying to get volume so your answer needs to end in xx3)

Action:  They did the problem from the curriculum document for Grade 7 about "The Neumann Company." They did the problem on chart paper in mixed ability groupings.

Consolidation:  As the groups presented, a highlights sheet was created with some of the important things that they needed to include when they were trying to find the dimensions of a shape when they were given the volume, but were un-aware of the length, the width and the height.  Here is a chart of what they came up with:

Afterwards, the teachers  debriefed in another room where the group helped Shannon give some written descriptive feedback to her students.  Here are some examples of the work, and what feedback Shannon gave them:

The whole experience was a great way for teachers to see a lesson in action, debrief the lesson, talk about possible changes that could be made to improve the lesson, and then give great descriptive feedback to the students that will help them improve.  Thank you so much for opening your doors to us Shannon.

I remember something...But I forget what I'm missing!

Sheila's Grade 7 class was used as our demonstration class for our PLC recently.  Sheila had been working in the Geometry strand in math and was going to be switching into Measurement.  Her lesson the day before had been on investigating right prisms and wanted to make the switch to surface area.  She wanted to see what they remembered about surface area before moving on. 

For the "minds on" the students were asked "What are some things that you have seen covered?"  After wait time, and time to turn and talk, the class shared things that they had seen covered.  Some of the answers were:  clothes (as they cover our bodies and come in different sizes), tarps for cars, wrapping paper (for presents), vehicles as they can be wrapped with advertising and (the group's favourite) chocolate covered strawberries.  The class then had a discussion on what they would have to do if they wanted to paint the top of their desk.  They decided that they would need to find out the area of the top of the desk in order to paint it.  (Especially if they didn't want to waste paint).  They then had a discussion about what they would need to do in order to find our how much paint they would need for the entire desk.  After some discussion, the class decided they would need to find the surface area of the desk to help tell them how much paint they would need to buy.

For the "action" the student used their polydron structures from the previous lesson to find out "how much" they would need to cover the polydron.  To provide some differentiation between the students half of the class was given a rectangular prism and the other half was given a triangular prism.  They then quickly went to work finding out the surface area of the polydron structure.  For a few of the groups, they knew that they had to do something "different" for the triangle, but couldn't remember what it was.  As a group they tried to come up with solutions and ideas on what it was they were "missing."  It was suggested that they turn to their text to help them "remember."  (One group announced quite loudly "Isn't that cheating?" to which the response was "No, it's using a tool to help you.")

To consolidate, each group presented their work during a congress.  The class gave descriptive feedback to them on what elements were done very well, and what they could do or add next time to improve upon their answer.  The pictures below are of their final work, after the congress:

This group had a cube and quickly used a formula to solve for the surface area.

A net was drawn to help them remember the area of all of the surfaces.

You can see that this group applied a lot of what they had learned previously in Geometry to help them solve their problem.

Organization was a strength for this group.

An organized chart was created to help add up the area of each of the faces of the triangular prism.

  A lot of learning happened this morning for both students and teachers alike.  A thank you for this great experience goes to Sheila and her students.

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!

Just For Problem Solving

Alla wanted to make the Learning Goals and Success Criteria she used in her class be specific to when they are problem solving.  Her goal for narrowing her focus was to really zone in on where her students are struggling in math - Problem Solving.

These are the Learning Goals she has shared with them around problem solving:

She chose to underline the key words of knowledge and understanding, apply, communicate and thinking to help the students gain greater understanding of everything that is involved in making your answer complete.  It helps the students see that there are many parts to an answer, and not just writing down a number.  This is especially critical given the fact that half of her class will be heading off to high school next year, and they need to be aware of not only the different areas on the achievement chart but also the different types of questions (or components of a question) which show different aspects of their learning.

Here is a picture of the success criteria that was co-created with the students during the course of the year :

Nothing that is on the success criteria is "new" to the students.  These have been her expectations all year long - The students can use this chart as a reference point, and Alla can use this chart to provide specific descriptive feedback to the students on how they can improve.

Descriptive Feedback In Intermediate

Courtney has also been using descriptive feedback in her combined Grade 7/8 classroom.  She is using it as a way to not only support struggling students, but to also stretch the thinking of students who are quite successful as well.  Here is some of the feedback she gave to her students recently when they completed a task on angles.

Notice how she starts with a positive statement, then gives her feedback in the form of a question.  This will allow the students the opportunity to reflect on not only what is being asked, but put it into contexts of the entire problem. 

Students Responding To Descriptive Feedback

Michelle teaches a combined 3/4 class.  There are a few times a week where she gets to work solely with her Grade 3s.  They were just finishing up the Location and Movement aspect of Geometry and Spatial Sense.  She decided to give them an EQAO type problem to work on.  When they were done, she then offered each of them some descriptive feedback as to what they could do to improve.

What was even more important was that she gave them some time to respond both orally (and in writing) to the feedback that was given.  We know that students tend to improve quicker and develop better understanding of concepts when they get the chance to apply the descriptive feedback that was given to them.  Here are some examples of what she wrote, and how the students responded.

This was the work with the feedback on it.

You can now see how the student used the feedback to improve their answer.

This student responded by writing under the descriptive feedback.

 Thank you so much for sharing Michelle!