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!

Co-Planning, Co-Producing

Carm and Jan invited me in to co-teach with them a lesson on area using non-standard units.  Carm teaches Grade 1 and Jan teaches a combined Grade 1/2 class.  Jan and I met to plan first and decided to use an idea from the curriculum document as the action part of our lesson.  We made it a parallel task so that there was a slight difference between what the Grade 1 and Grade 2 students did.  This was done to meet the needs of the two different curriculum expectations.  When Carm and I met to plan she had already seen the lesson from Jan and we decided to use the same lesson for her Grade 1s.

Here are the learning goals that the two of them had created for area:

Minds On:  The students used large sheets of construction paper to help measure the area of the learning carpet.  Before they began, they were reminded of what estimate meant and several students took turns sharing their estimates:

When they were done estimating, they found the area and shared how they came up with their answer.  This was recorded on the bottom of our chart.  You can see that the students shared 4 different ways of counting the sheets of paper to find the area.  Great examples of how they applied what they already knew to this task.

Action: 

The students quickly went to work using square of paper to help them measure the area of the op of their desk (The paper was super cheap:  550 sheets for $1.25 at Dollarama)

The students then had a picture of their desks taken, and then they used this picture to help them complete their answer.  We saw that the students used the strategies that we talked about to help them show how they counted up to 48 to get their final answer. 

Consolidate:  The students talked about how they got their answers with a partner.

We had two great lessons in two great classes!  The students were engaged and really able to demonstrate a lot of prior knowledge when solving this task.

Using a resource for a different concept

Demitra's school has a copy of the resource "Puddle Questions:  Assessing Mathematical Thinking."  In it there is a question about how you would measure a puddle.  Demitra decided to modify the question to meet her needs for assessing what the students know about area.  She also wanted them to self-reflect on their work and she wanted to be able to give them some descriptive feedback on what they could do better.  Sounds like a tall order, but when it fit together nicely and the students really got a lot out of the lesson.

Minds-On:  Each group was given a large triangle made out of construction paper.  They were asked how they could find out the area of it.  They then set to work discussing and trying different ways.  What was great was that each group came up with a different way, and they all knew that the units that they used must all be the same.

Action:  After being given the task, Demitra reviewed the success criteria that had been co-created together.  The students gave examples of what the criteria might look like in terms of the task.  For the actual task, the students were asked to draw a puddle and find the area of it.  They could use any way they wanted to.  Some students drew lines, others used cubes, pentominoes, finger spaces, and some even drew shapes that they thought would be "easy" to count.

Consolidation:  Demitra had one-on-one conferences with each of the students to not only assign them a mark (based on the four categories in the achievement chart) but also to give them some feedback on what they had done well on, and what they could improve upon

When this student brought his work up, he came up ready to chat about why he thought he needed to make a smaller puddle.  He said it was because a smaller puddle would have a smaller area and that would be faster to count than the puddle he had drawn.  He also said that he would have used a bigger unit to measure the area with and this would also cut down on the number of units he had to use.  This is why his feedback was to think about how he could have shared his oral knowledge in a written way.

This student used a K-W-C chart to help them make sense of what they had done.  You can see there was a bit of a thinking error in their work as they used pentominoes to answer the question, but when they couldn't successfully draw them onto their puddle, they jumped to just drawing lines on the shape they had traced.  When probed, this student was unable to share why it was important that all tools they used to find the area needed to be the same size.

This lesson left Demitra feeling pretty confident in her student's abilities to find the area of a shape.  The one-on-one conferences also helped her ask some deeper questions to help determine the students knowledge and understanding of area and how well they were able to apply that knowledge and understanding to the problem at hand.

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.

Modified, But Marvelous!

Mary attended the FOS PLC's for Grade 2.  She is currently teaching a SERT program with students who are at different grade levels and different learning styles.  She took one of the measurement lessons that we did together and modified it to meet the needs of her classroom.

She had done some previous lessons with her students on what distance is.  They co-created an anchor chart that is hung up in the classroom.  You can see how the chart is written in simple language, uses colours and also uses pictures to help students.  It is a really good example of how you can use the students in the chart (and to help you make the chart) to make them more engaged in the learning.

For the minds-on of the lesson the students created paper airplanes.  For the action, the students predicted how far they thought their airplane would fly.  Mary used the tiles in the hallway as the non-standard unit of measure as there were many of them, and the students could count them easily. After each flight, the students then wrote down the actual distance that their airplane went.  They then repeated this two more times.  As each student was having a turn, they came up with different ways that they could count the tiles.  Some counted by 1s, some by 2s, and some by 5s.  Regardless of how they chose to count, they all came up with the same answer.  Here is the recording sheet that they used to record their information:

For the consolidation the students came together on the carpet to share their results and answer questions about the data that they had in front of them. What is great about this lesson is that although the students were measuring using non-standard units, they also got the chance to use skills from other strands like Number Sense and Numeration (for skip counting) and also a bit of Data Management as they talked about the data they had collected, and made inferences about what they saw.  Their learning was recorded on a chart:

The students also talked more about the unit that they used to measure with by justifying why they thought the tiles were a good unit to measure with and also listed other things they could use to measure distance.

It was a great lesson that Mary modified to meet the needs of her students, but could easily be done in any given classroom.

Linking It To Other Things

Raven's Grade 5/6 class recently went to see the movie The Lorax.  He decided to use some of the schema the students had about the movie and tie it into a measurement problem for his students to do.  Here is the problem he gave them:

The question brought up a lot of good discussion points with his class.  They each worked in groups to complete the work.  When they were done, the work was placed on the blackboard and the students engaged in a congress to talk about what they had done, and what they noticed.  The students engaged in some rich talk about where exactly the trees would be located, and if there was an easier way to help them find out how many they would plant.  There was talk about how the model that is drawn may not actually represent the math that was happening on the page.  This is a great discussion to have as many students get confused when it comes to area and perimeter.  I've found that sometimes when using the geoboards to help find area and perimeter students don't always count the pegs correctly, and therefore come up with an incorrect answer because of the strategy that they used.

When they were done their discussion, Raven created a highlights chart with some of their thinking.  The students can use this chart to help them as they progress through the unit:

This is a great example of how a topic that the students are interested in, or learning about in other subject areas can be used to create problems to solve with your students.

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.

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.

Measuring Length

How do Grade 1/2 students learn about non-standard units?  The answer to that is easy:  They just do it!  To help our Grade 1 PLC get some ideas and have some discussion around measurement Ranald offered up his classroom to the 9 teachers for us to use to get some ideas and brainstorm some solutions on how to tackle our measurement hurdles.

Ranald wanted to try something a little different with his class, so he decided to do his lesson as a Bansho.  When you do that, you have everything from your learning goals and success criteria right through to your highlights/summary sheet all in one spot.  Usually this is done on brown craft paper or mural paper.  Here is what his finished one looked like:

He began with putting his learning goals up for his students to see. 

Then was his Minds on activity.  In this lesson they were deciding what non-standard unit would be the best to use when measuring various classroom objects.  You can see they had to estimate first (a skill that many students struggle with) and then they did the actual measurement based on what unit they chose.

 For the action, the students were given a piece of paper and rolled a number cube to see how many cubes they would be using to measuring.  Ranald chose to do this as a way to help speed the process along to get the students measuring objects around the room.  The students then got to work moving around the classroom finding things that were about as long as their "ruler."

As a consolidation, the students then shared how long their ruler was, and then what they measured in the room that were about that long.  You can see some of the things that they measured from the classroom:



 The class also created a highlights sheet of things that they need to remember when they measure objects. 

What the group found interesting was that the highlights that were created had more to do with the minds on than the action part of the lesson.  That lead the group to a great discussion as to what we could have done different to pull more highlights from the action than the minds on.


Seeing the lesson, and another person's classroom, is just part of the experience.  Talking about the lesson and what changes we would make is a greater part of the experience.  When we talk as a group we are able to flush out other lessons, and talk about where we think the unit can go and how to move the students along. 

Thank you for a great morning Ranald!