Area of the Base...Area of the Base!

Antonia did some creative re-arranging with her teaching partner to allow for our PLC to see her Grade 7s in action for a lesson study.  She used an assessment from ONAP as a way to create a minds on and action for her students to participate in.  Here is a picture of what she gave them for the Minds on activity:

If you notice at the bottom there are two different formula written down for Volume.  The reasoning for this is because we know that in the past students struggle with finding the volume for objects because they forget that they need to find the area of the base first, and then move on from there.  As we took up the minds on, we found that the students also had another misconception:  That you can just divide by two to find out how many candies you need.  While it works in this case, Antonia wanted to make sure that her students understood why it worked - And why it may not work everytime they had to figure out how many of something went into something else.  We also talked about how the formula for finding out the volume of the candies was different than the formula for the box - Because the base was different.  (Once again...area of the base....area of the base...)  Here is what was recorded from the discussion:

For the action, the students were asked to find out what size box they would need to hold 64 candies.  They had to make two boxes (one a rectangular prism and one a triangular prism) and decide which one they thought the candy company should go with and why.  Due to time constraints we did not get to have a consolidation with this group.  However, the teachers that were at the lesson study had some really rich conversations on what we noticed the students were doing well with, and what they were struggling with.  We looked at the student work and talked about what we noticed and what we would do differently in our classrooms with our own classes.

Here are some samples of student work:

This group was very thorough in their answer.

A close up of the math.

You can see they broke their thinking into parts to help them attack the problem.

A close up of some of the writing.

This group started with the notion that they needed to find what half of 64 was.

Trial and Error helped this group decide what the volume of the box needed to be.

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.

Critically Looking At Questions and Tests

The Grade 7 FOS PLC's used their time together today to look at the resources that we use, and then evaluate them on how effective they are.  We know that in our schools we have textbooks, ministry guides and supplemental activities, but there is not one "just right" resource.  So what do we do?

We started our session by looking at an activity sheet from one of the textbooks that are in our schools.

 Each teacher then looked at the questions (individually) and then we shared how we would mark each question.  When sharing, some people shared why they gave a question a specific mark (e.g., There were 4 things, so I gave 4 marks).

After doing this, we then used the achievement chart to decide what type of question each of the printed questions were.  It became very obvious to us that we had a lot of KU type questions and not a lot of communication type questions.  When we converted this into percent, it turned out that at least 40 - 50% of our questions were just KU.  We had some really good discussions which included things like:  If the question did.....or In my class they would..... - But, we were only taking things for face value - If it only shows Knowledge, then it only shows Knowledge.

After noticing what types of questions were on the sheet, we then turned to our curriculum to then have us see what expectations we were covering.  The questions that were not covered by the expectation were then crossed off. 

What we also discovered was that one of the 4 expectations found under Location and Movement in the GSS strand was not covered at all in this activity. 

The teachers then broke off into groups (1 group in the AM, 2 groups in the PM) and then picked one of the questions that was in the curriculum and then "opened it" up more.  This allowed us to have a really good question that focused on more than just one type of question - it was a question that could be used to help assess all four quadrants in the curriculum. 

The four categories at the bottom are what the teachers would be looking for when they mark each question.

Orange - Minds On,  Blue - Action, Green - Home