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.

Getting Creative With Learning Goals

Raven teaches a combined Grade 5/6 class.  Here is a great way that he got the students to not only understand what the learning goals for the unit on measurement were, but to make it creative and fun.

You can see that some of them are specific to a grade (e.g., Grade 5 or Grade 6) and others are geared towards both grades.  Since most of the measurement unit is about measuring two- and three- dimensional shapes, they used those as the backdrop for the learning goal. 

Its a simple idea, but one that not only engages the students, but will get them thinking about their learning in a positive way.

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.

After the Diagnostic, Starting The Decimal Unit

Kristen began her teaching of decimals with her Grade 5/6 class by using a problem that is based on one from Making Math Meaningful by Dr. Marian Small.  (MMM, p.160, Activity 8.1).  In MMM the problem is about estimating using whole numbers, and in this case Kristen changed the problem to involve decimal numbers to hundredths and thousandths. 

The lesson was set up in Three-Part Lesson format.  Here is the lesson template:

The Minds On focused on having the students order numbers.  She chose to do this to get the students thinking about how decimals can use the same numbers, but mean different things.  We had thought that perhaps some of the students may choose to use ordering as a strategy for solving the problem, but it was not one that we saw.

The action was this problem:  (You can see the minds on at the bottom of the page...It is an Eco-school after all!)

The students also completed a K-W-C as a class to help them flush out the information that was in the problem.

What was great about doing this was that the students got a chance to ask questions that were important to them.  There was some great discussion as to if the animals could only go in 2s or if they could go in groups of 3 or 4 (the answer was yes - but they could NOT go alone).  As well, one student touched upon the fact that the question was asking you to not only solve the problem, but EXPLAIN how you got your answer.  The second step that many students (and teachers) forget to do when solving a problem.

The students quickly got to work in pre-assigned pairs (based on optimal mis-match).  They used markers (no pencil's allowed) and didn't use our "banned" black and yellow (Yellow because you can't see it that well when your work is presented, and no black because that becomes our class editing pen). 

When the students were done their markers were collected.  Kristen really wanted to use the consolidation part of her lesson to help the students make sure that they were giving a really good / Level 3 answer.  So she asked the students the simple question of "What makes a really good answer?"  Using examples from their own work, the students then shared what they thought made a really good answer and why.  These thoughts were recorded on a large piece of chart paper:

The students now have an anchor that they co-created and that makes sense to them.  From it, informal success criteria was created about what makes a good answer.  A follow up lesson to this will be actually putting that success criteria on paper.

The students now were asked to add something that they thought was missing from their work.  They did this in pencil so Kristen could see what the improvement was.  (Hence why the markers were collected earlier on).  This was their independent practice.  They handed in their "updated" work and Kristen went to work providing descriptive feedback to them. 

Since we co-taught this lesson, Kristen was able to record what the students were saying about what made a good lesson as I was putting it down on the chart paper.  The student's focused on 5 different things.  To help her keep track of what the descriptive feedback she was giving to the students she numbered each item in the success criteria from 1-5.  As she gave each pair the descriptive feedback, she then recorded what she had given them feedback on, and what else she noticed that they need to work on.  Here is an example of how she recorded this information:

The first number is what she commented on, and the second or third numbers are what they still need more support in.  Its helpful to keep track of what you are saying to the student because if you notice that you are always writing the same thing, then they are not using the descriptive feedback that you are giving them and putting it into practice.

Here are the student samples showing not only their original answer, but their pencil additions and our black "editing" that matches the descriptive feedback that was given:

Start to finish, this entire lesson (Minds on, Action, Consolidation, Independent Work) took about 65 minutes.  All of the students were engaged, and all were participating in our class discussions. 

Decimal Diagnostic!

Kristen teaches a combined Grade 5/6 class.  They are half way through their first expectation in Number Sense and Numeration.  They have worked through whole numbers and are just about to head into decimals.  Kristen has a wide variety of learners in her classroom and before she started the unit, she wanted to find out what the students already knew about decimals and what were the misconceptions they had about decimals.

Using the newly release Gap Closing materials from the Ministry, (available at www.edugains.ca - Under "gap closing") she turned to the chapter on decimals.  She then used the diagnostic with her whole class to see if there were any struggles or misconceptions.  She recorded how they did on each question and then used the facilitators guide to help determine where to go next.  (You can see how some students have items highlighted - this was what question(s) they struggled with) She went down the list in the facilitators guide that informed her of what to give the students to work on to help clear up their misconceptions.

 She then listed the students that were struggling under the topic they appeared to be struggling with.  For her class she started with the first misconception "tenths" and then went on from there.

As the names were written out, she made sure that the struggles matched the grade group.  For example, both Grade 5 and 6 have been taught tenths, but only the Grade 6s have been taught hundredths (that is the Grade 5 expectation).  Therefore, no Grade 5 students would be expected to work on hundredths.

The next day, Kristen had a computer period with her students.  During this time she had some students work in a small group with her or me on the topic that they were struggling with.  The other students were engaged in playing games involving decimals on the computer.  In the period we were each able to help a group of students clear up the misconceptions that they had.  They rolled their eyes at us when we mentioned that we could see their hamsters working overtime! :)

For the group that we were not able to get to, we made the decision to give them their sheet for homework after explaining what to do. The nice thing with the Gap Closing material is that they have a "Think sheet" which helps to explain the concept that is being taught in simple terms for the student to understand.  This is nice for situations like this when the student has to do work on their own.

Sample Activities From The Gap Closing Materials

What is helpful now is that Kristen can fully start her unit on decimals as she now is aware of not only some of the students who had misconceptions, but also where the strengths of her students are.  This allows her to focus her teaching on the concepts and ideas that they are really struggling with, and hopefully preventing them from getting any more gaps.