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.

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!

Highlights at the end of a Bansho

Jenine's Grade 3 class is getting really good at using different strategies and models to show their thinking.  This was confirmed when doing a highlights sheet after doing a Bansho.  They were given a pattern and were asked to represent it in another way.  Here are some examples of the student work (the yellow slips are the pattern that they had to represent):

Here is the highlights sheet:

Graphing and Estimation - Who Knew!

At the start of September Jay-Ellen had her class create a graph on what month their birthday was in.  Each student put their name and date on a mini-post it note and then lined it up above their birthday month.  They hung this graph up in the classroom for all to see.

A few weeks later she decided to use a jar that she had called "Estimation Station" and have her students estimate how many jelly beans they thought were in the jar.  Here is what the jar looked like:

They collected their estimations on mini post it notes.  When they were done doing their estimates, they then noticed they had a lot of post-it notes and needed a way to organize them.  They thought back to their graph and wondered if they could use a similar strategy to order their estimation from least to greatest.  What became tricky, and involved them using application skills, was when they had multiple estimates of the same number.   Jay-Ellen guided them to look at their graph and then see what they did when more than one person had a birthday in a month.  They knew that they could stack the numbers on top of each other.

A great way to not only compare and order whole numbers, but also to get some estimation and graphing in as well. 

Grade 3 Success Criteria

Here is a picture of the Success Criteria that Arpine created with her Grade 3 class after they solved a problem on their own.

Notice how she used a sign at the bottom of the chart to help the students reflect not only on what to put in an answer, but also on what they can do to improve their answer as well.

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.