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.

Where's the PLC Stuff?

If you are looking for our Wiki where all of our information from our PLC's is being kept you just need to visit:  http://southeastone-derful.wikispaces.com.  There you can see the pictures we took, the templates we used, or some Learning Goals already created by teachers in the FOS.

Enjoy!
Lesley :)

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.