South East 1 Math

Measuring Using Non-Standard Units

2012-01-27T14:40:00.000-05:00

In our Grade 2 PLC, both groups decided to look at Measurement. We did a three-part lesson as a group looking at how to measure distance using non-standard units.

Our minds - on was brainstorming different tools that we could use to measure distance. Here is what each group came up with:

For our action, we created paper airplanes and then predicted how far they would fly. The unit that we used was index cards. Each teacher wrote their prediction down on the airplane. They then flew the airplane and the recorded how far it went. This was done a total of three times. (We had a great discussion on if we would make a chart for the students to record their information on, or if we would let them decide on their own as to how they wanted to record the data.)

To consolidate the lesson, we had the teachers pair up and then highlight what was the farthest and shortest distance the airplanes flew. The pair then joined another pair and then discuss which one went the farthest and shortest. We then discussed as a class what our finding were. We also used this time to bring in the idea of comparing the distances, and also talking about strategies that could be used to help us compare. Below is our two charts that were created during the consolidation of the lesson.

Happy flying Grade 2!

Three Part Lesson as Bansho

2011-12-09T19:56:00.000-05:00

In Melissa's combined Grade 3/4 class her students are pretty comfortable in being mathematicians. They are very aware of what the learning goals of their lessons are, how to use success criteria to improve their answers, and how to reflect on what their strengths and weakness are (mathematically speaking).

She attended a Grade 3 PD session with the program department the other day and loved the idea of seeing her three-part lesson as a Bansho. So she grabbed some long kraft paper and got to work taking her three-part lesson from paper to wall and got the students thinking.

Her "Minds on" was having the students (in partners) decide what the data could represent. After they had done this, she recorded some of their thoughts along each side of the specific graphs. The students then came up with a prediction: They thought all the data in the pictures was of the same thing, but represented in different ways.

As her "Action" she asked the students to think of something that might be true of most of the students in the class, then conduct a survey to see if they were correct or not.

For her "consolidation" she choose to do a congress where two different students shared their work with the class. She photocopied this work and then put it up on the kraft paper where Melissa recorded the "Stars" (things that the group felt they did well on) and "Wishes" (things that the group felt they needed to improve upon). They also created a highlights sheet to highlight what they learned (as a class) from the lesson.

Seeing their lesson as a Bansho allows the students to not only see the progression of their learning, but also refer to it when they are participating in the consolidation of the lesson. Plus, in doing it on the kraft paper it allows you a chance to leave it up for a bit, then roll it up when you are done. Only to bring it out again to help consolidate previous learning into new learning.

Learning Goals for a Rotary Teacher

2011-12-09T19:40:00.000-05:00

Antonia teaches math on rotary. She has a combined Grade 6/7 math class and also a Grade 8 math class. She was a little unsure of how she was going to be able to display her learning goals for all three grades. She knew that due to lack of space chart paper was not going to work in her classroom. So she decided to use technology to help her. Her school had previously done some planning so that both of her division (junior and intermediate) are doing the same expectations at the same time. This really helps in working within two divisions.

She typed up all of her learning goals for the strand that she is teaching for each grade. She used the specific expectations to help her create these learning goals. She then posted them on the wall in her classroom for the students to see. At the start of the lesson each day she now refers to the learning goals that they will be working on that day. The students are aware of what they are learning, and are able to articulate specific things that they are struggling with. A pro in having them up for the whole unit is that the students are able to see (in a nut shell) where they are going over the next few weeks. (It is up to you how you want to display the learning goals - you can also do them a few at a time if that works better for your teaching style)

Here is what her wall looks like:

At the bottom of her learning goals she also has her success criteria. This helps give the students one place to turn to when they are done their work and want to make sure that they not only understand what the goal of the lesson is, but also what is expected in their work.

Graphing In Kindergarten - YOU BET!

2011-12-09T19:26:00.000-05:00

Casey teaches in a full day kindergarten class. She had been at her daughter's school and saw a great idea for a bulletin board and decided to give it a try with her kindergarten class. (I like to call that "educational shoplifting" :)

She asked her students the question of "How Many People Are in Your Family?" Instead of having them complete the graph on chart paper, she gave each student a small paper plate. On the plate they drew the people in their family. By using the paper plate it allowed her the opportunity to keep the drawings all the same size. This really made it easy for the students to compare the different sizes of their families as they were able to count the plates to help determine how many people are in each type of family. (e.g, More students have 5 people in their family. 9 friends have 4 people in their family) With 29 students it makes for a full bulletin board!

Moving Forward With Success Criteria

2011-12-09T19:17:00.000-05:00

Kristen's combined Grade 5/6 has been working on graphing. They have been looking at graphs and creating graphs on a variety of topics. Kristen found that her students were struggling when physically creating a graph. They are able to read a graph, and make assumptions and interpretations about the graph, but don't always pick the most appropriate graph for the data set they are working with.

To help them overcome this difficulty she created success criteria with all of the things she is looking for in a good graph. On her success criteria you can see how she covers some of the "basics" of graphing (e.g., my graph has a title and labels) but also covers some of the application / communication aspects of graphing (e.g., I can explain why the graph I chose is the most appropriate, My scale is appropriate for the data I'm using because....)

Here is her success criteria for the unit:

It now makes things so much more clearer for the students, because they know what is expected in their work, and it also gives Kristen an anchor to draw some of her descriptive feedback from (e.g., The graph that you chose to represent the data works well as it makes the comparison between the two choices very clear. How could you have used a different title to match your survey question a little bit better?) Both of these things (the success criteria and the descriptive feedback) are going to really have a positive impact on student achievement.

Asking Questions About Graphs

2011-12-07T21:31:00.000-05:00

Haroula's Grade 1 math class is near the end of their unit on graphing. She wanted to give them a culminating task that would not only have them create a graph, but also create questions about the data in front of them.

Each student choose a question to ask their peers. They then went around and surveyed each student in the class and recorded the answer in a tally. She kept things pretty simple by suggesting that there be no more than four options (answers) to choose from. The students then created a graph based on the data they collected.

Haroula then had the students exchange completed graphs. The students then had to ask two questions based on the new graph in front of them. (On the yellow paper) The author of the graph then had to answer the question that was asked of them. (On the orange paper). When the questions were asked and answered, she put the graphs and the questions on display for everyone to see. She included a description of the activity (procedure) as well as the curriculum expectations that were covered in doing the activity. It's great to see not only the completed graphs but also the questions that were asked about each graph.

The Finished Product

Close Up Of The Description Of The Activity.

Marker Students

2011-12-02T21:40:00.000-05:00

We have all had to identify two marker students in our classroom. One of our schools is taking the work of those marker students out of the binder and onto the walls. They have turned a conference room into a living data wall. Each teacher has posted the work of their marker students in all three area of reading, writing and math. They have written down what they notice about the students strengths on the task, their needs and also the "next steps." The "next steps" however are for next steps in the teaching of the topic, not the next steps for the student. At every staff meeting they are going to be spending 10 minutes talking about what they notice about the work of the marker students, and what strategies they can share with each other to help not only the marker students improve, but all of the students in their class improve.

One side of the Room. Each cartoon person represents a student.

The other side of the room. You can see how each teacher has their two students and the 3 subjects.

A sample of a math problem from a student. (The work is taken from The Process Standard Series by Susan O'Connell)

Here are the notes the teacher made about the student's work. They can easily turn the strenghts and needs into effective Descriptive Feedback to the Student.

Learning Goals as a Guide

2011-11-29T21:09:00.000-05:00

The Grade 2 afternoon PLC took a different approach to exploring about math. Together they co-created learning goals for the Geometric Properties and Geometric Relationships expectations in the Geometry and Spatial Sense strand. They then were able to dive into the resources that they had brought with them to find activities and lessons that would be useful to use when teaching those specific expecations.

Starting with the Learning Goals is really helpful before you teach a unit as it really helps you focus on curriculum expectations, but also help you organize all of the wonderful ideas that you have into speficic lessons. Here are some samples of the ideas that they came up with.

Check around in your school for the Dr. Small books and the Van De Walle books. They should be there. If you don't have a copy of the Guide To Effective Instruction, you can download one (for free) at www.eworkshop.on.ca Just click on "Guides To Effective Instruction" and go from there.

Graphic Organizers

2011-11-29T20:55:00.000-05:00

The Grade 2 morning PLC decided to look at graphic organizers as a way to engage their students in the math. They picked Geometry as the strand that they would use to work with the graphic organizers. These organizers came from a series of books by Susan O'Connell called "The Process Standard Series, K-2" There are 5 books in total for each grade band. These come from the communication book.

This one is called an "Idea Pot." You can put the main topic (strand) at the top and then have the students brainstorm all of the different things they know about this topic. If students want to add to this pot as the unit goes on, then use a different colour to add new words to help you (and them) see how much they have grown since the start of the unit.

This Graphic Organizer is called "What I Know" or the Freyer Model. In the centre the students pick (or are given) a word/shape/figure/etc. They then define it, list characteristics of it, give examples of it and give non-examples of it. As our group found out, it is sometimes hard to pick "Exciting" shapes because of the thinking that goes along with explaining it! (Right star group! :)

The last one is called "The Big Three." It's a great way to have students synthesize what they have learned over a period of a few days, or a week. You have them choose 3 things that they think are most important. You can see here how our teachers choose the "Big Three" for 2D shapes, 3D figures and Symmetry.

Super Job Grade 2 teachers! I can't wait to see these in use in your class for Geometry and beyond!

Critically Looking At Questions and Tests

2011-11-23T16:45:00.000-05:00

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

What a Graph Could Mean

2011-11-16T21:16:00.000-05:00

Brian's Grade 6 class has been reviewing the "text features" of a graph. They have also been talking about how graphs can be used to display data that represents a small group of people, or a large group of people.

His Minds On was getting his class to look at a graph (Via the ELMO) that had no "text features" on it. They talked about what was missing and then gave examples of what they might be. Brian recorded these things on an anchor chart to be used as their unit carries on.

For the Action part of the lesson, the students used the same graph, but came up with their own ideas as to what the graph could be about. Some of them choose topics that were important to them (e.g., how much homework students got per grade) and others that were a little more worldly (e.g., the number of people in a union). Once they came up with their topic, they then came up with all of the key elements of the graph (title, lables, key, scale, etc.) and also created 3 questions that could be asked of their graph. One question was a true/false question, a second question was a multiple choice question (with 4 choices) and the final question was a more open question that could fall into a Level 3/level 4 range on a Q-Chart.

To consolidate the lesson Brian had the students look at all of their graphs and talk about what was similar and what was different. They also talked about what questions were easy to make, and about what questions were hard to make. They also talked about why the graph looked the way it did - and that it lent itself to going from smallest to biggest.

The work on display with the expectations covered on the pink piece of paper.

Type of Job and Amount Paid

Number of Ice Cream Scoops Sold Per Day

Recycling Rates by Province

Popular Ice Cream Flavours At The School

Homework Given By Grade

Number of Employees Per Union

Graphing In Grade One

2011-11-16T20:58:00.000-05:00

Ellen's Grade 1 class is starting their unit on Data Management. She choose a lesson from the Guide to Effective Instruction as part of her unit. Using the three-part lesson template she re-worked the lesson to meet the needs of her class.

For her Minds On she had the students complete a graph as a class about what their favourite type of recess snack was. At the top of her graph she included a class list. She used this class list as a way to show her students how to keep track of who had already given their answer. She also drew a picture beside the different choices to help her students use a picture to help them figure out what the word was. Once all of the names were crossed off, the students then started sharing what they noticed about their graph. You can see the nuggets of what they discovered written right on the graph.

For the Action part of the lesson the students brainstormed several questions that they could ask each other about what their favourite things could be. The questions were recorded in one colour and the possible categories (or answers) were recorded in another colour. The students then went to work choosing their question from this list or from their own idea, and then began surveying their friends.

The students were each given a copy of the graph template and a clipboard. On the back of the sheet, Ellen photocopied a class list so all the students needed to do was to flip over the sheet and cross off the name of their friend who they had just asked. This was an easy way to keep track of who had and who hadn't answered the survey.

For students who struggle with printing, or were not comfortable in writing out their choices (it is early Grade 1) they drew a picture of their choice and then went on their merry way surveying their classmates.

In the final part (consolidation) of the lesson the students shared their graphs and then asked each other questions about what the data they collected said.

Kindergarten Science and Math Connection

2011-11-16T20:44:00.000-05:00

In Adrienne's kindergarten class they have been learning a great deal about seeds and what they do for plants and humans. It is the basis of the classroom inquiry project that her children have been exploring about. As they move through this inquiry, they are also beginning to learn about graphing and sorting as they are covering Data Management right now.

At one of her centres Adrienne created a t-chart with two headings "Seeds" and "No Seeds" Using flyers from local grocery stores the children cut out different objects and place them under the correct heading. Not only were they sorting objects into two groups they were deepening their knowledge about what things have seeds and what don't and also working on their fine motor skills by cutting.

Graph Mats

2011-11-16T20:34:00.000-05:00

In the primary grades, sorting is such an important part of not only Data Management but Patterning as well. How do we help our young learners become better sorters? Why not give them a sorting mat! These sorting mats were finds from the local dollar store. In addition to the plastic that they sit on, I also purchased black electrical tape to make the actual lines on the mat. The mats are hard plastic and are about 11x17. If your dollar store does not have them, then you can use cookie sheets or a large plastic tray. For a large size of any of the mats use coloured duct tape and plastic shower curtains (also from the dollar store) for mats that are big enough for the children to stand on.

For sorting items into two groups.

For sorting or graphing items into 4 groups.

The classic T-chart.

For sorting items into three groups.

Great Glyphs!

2011-11-14T16:43:00.000-05:00

Glyphs are a fun activity that you can do as part of your Data Management strand. A glyph is a set of directions that a student follows which is based on their own answers (or data). At the end of the questions there is a product (a coloured in picture, a piece of artwork) that represents the answers (or data). Below is a Glyph that was done at our recent Kindergarten PLC. (For templates or links to the Glyphs visit the wiki). We created our glyphs using only paper and pencil crayons, but they look MUCH better when you see them done in construction paper.

Our gylph asked us questions which made a pizza.

We displayed our finished work around the glyph.

After the gylphs are completed you can hang them proudly in front of your classroom (along with the instructions on how to make the Glyph) and then pose questions to your school community. These questions could be: How many boys are there in our class? Most of the students in our class are what age? What is the favourite pizza place in our school? You can post chart paper up under the questions for people to answer, and also leave a spot for them to pose questions of their own. A very fun activity to both do and include your school community into. You can also google "Glyphs for Math" to help you get a lot of other good ideas for making Glyphs.

Baggie Games For Fun

2011-11-14T16:29:00.000-05:00

Haroula teaches a combined Grade 1/2. Her and her teaching partner switch off so they are able to teach a straight grade in math. This leaves her with just the Grade 1 students. As we know, Grade 1 students are active little beings who need to move around and need to be able to have some one-on-one time with the teacher to not only express their answers orally, but also to help them gain a better understanding of the concepts that they are being taught.

Haroula made up several different "Baggie Games" for her students to use as part of their math centres, and also for when they were "done" their work. She finds that letting them use the games as part of her math program has helped her to get some of that much needed one-on-one time, while still reinforcing the concepts she is teaching (or has taught) in the large group.

One of the games that she has created is using Dot Cards. She used the pictures of the Dot Cards from the Guide To Effective Instruction in Mathematics: Number Sense and Numeration (GTEI)and then cut the pictures out. She then taped them onto blank playing cards. She has the students play a matching game where they have to match the same numbers together. This helps them work on subatizing and also one-to-one correspondence.

You can see the two different ways to make a dot arrangement to show the number 6.

Here are some of the pictures of the other cards.

A second game that she made was originally in the GTEI but in the Grade 2 section. She modified it to meet the needs of her Grade 1 students. She also included a number line as a tool to help them not only get more comfortable with counting backwards, but also just in using the tool.

Here are the instructions she included. (She has played the game several times in the large group and in small groups)

Here is everything that is in the baggie.

The cards are in a different colour of card stock to help make them stand out.

These games (and others like them) would be a great addition to any math program. You could also use them as part of a family math night, and also as part of a "Math Bag" program where you would send home games for students to play at home.

After the Diagnostic, Starting The Decimal Unit

2011-10-31T14:38:00.000-04:00

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!

2011-10-25T21:33:00.000-04:00

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?

2011-10-24T08:25:00.000-04:00

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

2011-10-06T21:00:00.000-04:00

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!

2011-10-06T20:49:00.000-04:00

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

2011-09-23T12:18:00.000-04:00

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

2011-09-23T12:16:00.000-04:00

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.

Why Minds on Matters

2011-09-23T11:57:00.000-04:00

Part of Sarika's Annual Learning Plan this year is to become more familiar with, and use more regularly, the three part lesson in her math class; and to become more comfortable with (and consistent with) teaching through problem solving. Her Grade 5's are currently learning how to make a table of values and how to recognize patterns.

She has modified problems from her text to use as the "action" part of her lessons for a week. She was able to break down the problem into multiple parts so that the problem is not only extended, but the students can use information they already know from a previous problem and apply it to the problem they are working on.

In this lesson her minds on activity was having the students identify the pattern and extend it on a table of values. The first table was a simple growing pattern that increased by 5 each time. The class talked about what the pattern rule would look like in words and recorded that beside the table.

For the second table of values the students were only given two terms then they were asked to talk to their partner about what thought the next term value would be.

When the students were done they gave us a "thumbs up" sign, and when the majority of the class was showing "thumbs up" the students shared what they thought the next term value would be. One student said it would be "93" and another justified that by saying that "the pattern rule would be start at 31 and add 31 each time". This was recorded on the board. (We used initials and a chart to record their answers and thinking). The students were asked if this could be the only possible number. They were then shown 124 and asked to discuss if they thought it was possible or not to be used as the next term number.

At first there were a few puzzled looks. The majority of the class could not see that multiplication was also a way to extend patterns. A few then began to think of "doubling" and then one student put up his hand and said that it could be the next term because if we "multiplied 31 x 2 we would get 62...62X2 we would get 124..We could then do 124x2 and get 248 for the next term." The light bulbs went on.

Why this Minds on was important for Sarika is that it gave her a lot of information about her class. She knows that they are able to identify and express in words what a pattern rule is, they can extend a numeric pattern, and are working on making predictions about growing patterns. She knows that for her next few lessons, she will have to include problems and activities that involve using multiplication and addition in the patterns, and encourage the students to use these tools to help them solve problems.

But they only have one strategy. Now what?

2011-09-21T16:30:00.000-04:00

Vicky gave her Grade 4 class a question relating to their upcoming Curriculum night BBQ. The students completed a K-W-C chart to help them decode the information from the problem. Her group of students is very comfortable with problem solving, and was not only able to quickly complete the chart, but also infer things that were in the problem (e.g., we need to remember the number of students in our class - 19).

When the students completed the problem, she noticed that almost everyone used the same strategy - Drawing a picture. So she wondered how to get them to do things in a different way, perhaps one that is a little more quicker, and shows a bit more understanding of patterns.

Drawings of Tables

These students started to use numbers and pictures

She got them to talk a little bit about their work in a congress. As the pairs began to talk, probing questions were asked and that helped them pull out ideas, make connections between their thoughts and their work, and have their thinking challenged. As the congress was going on, a chart was created to show the different ways that they could have solved the problem.

Vicky also included the statement "The pattern rule is" because she knew from her ONAP pre-assessment that the students were having difficulty in writing out the pattern rule in full using words. After the chart was made, the students then were posed the question "If you were to do this problem again, what strategy would you use and why?" There responses were very insightful and meaningful. The best one was that the student commented on the fact that they would use the number line because then they would be done their work a lot quicker. :)

Getting Ideas for Problems

2011-09-21T16:16:00.000-04:00

Arpine teaches Grade 3 and wants to incorporate more problem solving into her math program. She found some problems at www.mathwire.com but wanted to open them up a little bit more so that there were more points of entry for her students. She also wanted to introduce the K-W-C to her class to help them get started at solving problems. In creating a few problems all at once it not only helps her with planning, but also helps her to allow her students the time to build on their new learning, and try different strategies out.

Here are a few of the problems that she modified to meet her needs. She used the names of teacher in the building to help make the problems more "real" to the students. As well, she began to incorporate multi answer questions for her students to answer so they become accustom to completing mult-step questions.

One Expectation, Three Ways

2011-09-21T16:07:00.000-04:00

Jenine, Michelle and Janice all teach Grade 3 at three different schools. They are all working on the first overall patterning expectation of describe, extend and create a variety of numeric patterns and geometric patterns. Here are some of the ways that they started their units.

Jenine started her unit with looking at number patterns. The students completed a problem about a classmate. They also did a K-W-C chart to help them comprehend what the problem was asking of them.

The students then got to work solving the problem in similar ability pairs. When they had completed the activity, we did a congress to consolidate their learning.

The students who shared their work were chosen because their work showed strategies that were different. One group re-created a hundreds chart to show what they thought the pattern might be. This opportunity was then used to show the class how you could also use a number line to show the same thinking (and with doing a little less writing!)

At the end of the lesson, a highlights sheet was created to show the students the different strategies that they used to solve the problem. This will then help them complete problems later on in the unit.

Michelle used a different approach to start her unit. She began by having the students orally share what they knew about patterns. She then had them create a pattern of their own. When they were done making their pattern, they talked about the pattern that they had made. Michelle recorded these words on a chart under two headings "Words" and "Attributes"

The students then went back to their desks and used the vocabulary to write about their pattern.

(Click on the picture to see what the student wrote clearer). The students now have a good understanding of what attributes are, and how to use words to describe patterns. From this activity they were able to demonstrate if they can create, extend and describe patterns.

Janice used technology and art to help her class get a grasp of patterns. She gave them a digital camera and they went around their school looking for patterns that they saw in the world around them. Not only did they capture that pattern in a photo, they then wrote about and extended their pattern the next day. Here are a few examples of their real life patterns.

This student noticed two patterns - the colours of the desk tops and also the tiles in the floor.

A very observant student noticed that the Principal's tie and shirt had patterns in them.

Even the heater proved to have patterns in it!

Janice also has her learning goals and success criteria posted for her class to see.

Three different ways, but three great starts to the Patterning unit!

Starting A Unit - What Do They Know: Part Two

2011-09-10T13:24:00.000-04:00

As a follow up to the previous lesson, Brian turned to the ONAP 6 package he has (available through Nelson Canada) to help him get some ideas on where to go next. They have a pattern matching game that he decided to use with the students to get them looking more in depth at what a pattern is, and the different ways you can represent a pattern. Using his ELMO, Brian demonstrated how to play the game, but also had the students talk about what they were seeing on each card and what knowledge they could use to determine if it was a match. (The cards represent patterns in four ways: Table of values, in a model, a pattern rule (in words) and in number pattern form).

After the student's did that, he had each student select a pair that they had successfully found. His question to them was "How do you know your cards match? Justify your answer." He then modeled for them how to write an answer that involves them justifying their answer. He then had the students re-read the answer and point out what key math vocabulary words were that should be in a good answer.

He differentiated the lesson by having students do this for either one or two pairs (so the struggling students could focus more on the quality of their work than the quantity of their work) and also had students who were finished quickly then make another representation of the pattern.

For students who finished one answer fairly quickly, descriptive feedback was given to them so that they could use it on the next answer. The pictures below show the different responses and the different descriptive feedback that was given: (My apologies for the upside down photo, just click on it and then rotate it on your desktop. A new camera is coming!)

Brian also used the Assessment for Learning Tool (A4L) to help him as he read over the student's work to keep track of the vocabulary words they were using, and to see if anyone was incorrectly using a word or a term. His next lesson will be to administer the ONAP questions to his students to then help give him a more concrete idea of where they have a lot of content knowledge, and where they are still struggling.

Starting A Unit - What Do They Know: Part One

2011-09-10T13:08:00.000-04:00

In Brian's Grade 6 class this week he began to pre-assess his students' knowledge around patterning. The first strand he is doing is Patterning and Algebra and the expectation he is reporting on this term is Overall #1: Describe and represent relationships in growing and shrinking patterns (where the terms are whole numbers), and investigate repeating patterns involving rotations.

He began the lesson by having the students brainstorm all that they knew about patterns. At first they did some thinking on their own and then moved into "think-pair-share" with a partner and then their table groups.

Once they could not think of anything else, he then had them sort their words into three categories: Attributes, Strategies/Tools, and Vocabulary. This is now an anchor chart that they have up in the room for the students to not only refer to, but also to add onto it as new ideas and understandings come up.

Now that their schema had been activated, the students then got a chance to look at a pattern and then figure out what the pattern rule was, and also make predictions as to what the next term number would be if the pattern continued. Here is the pattern they were given: (my apologies as it should show as being a horizontal pattern and not a vertical pattern).

Many of them quickly picked up on that the pattern rule was "Start at 2 and increase by 2 each time." As well, they had a discussion as to if it mattered that the colour chips were turned over or not, and if in addition to the pattern rule, if the model of the pattern was something to consider as well. At this point one student put up her hand and said that she thought the pattern could also be "Term number x 2 = Term Value" The students set off to explore if this theory worked for different term numbers in this pattern.

When they came back they decided that yes, for this pattern that pattern rule worked and they could now be given any term number and find out any term value they needed to. They then added to the anchor chart by adding the number from this pattern to the table of values so they could refer to it at a later time.
From this lesson, Brian decided to continue on to see what else the students knew about different representations about patterns. That will be his next lesson.

Back To School 2011

2011-09-05T12:53:00.000-04:00

To all the Teachers, Principal's, ECE's, EA's, Superintendents, Coaches, IL's, and everyone else involved in educating our students, have a great first day!

Looking forward to making "Math magic" happen with you for your students.

Lesley :)

Math Campp - Day 5

2011-08-25T12:05:00.000-04:00

Our last day of Math Campp was a full morning of eating and last minute networking. After having a brief closing session in our breakout groups, we then formed new groups with a variety of people from each of the five breakout groups.

In these new groups we did a carousel of all the five rooms to see what they had learned and worked on. It was great to see what things looked like (in terms of proportional reasoning and algebra) at all the different levels. Here's just a few snapshots of the great stuff I saw during my carousel time.

In The K-4 session, there was a great poster board of different types of repeating and growing patterns. What is neat is that in the growing patterns, two books were used: "I know and old lady" and "One Duck Stuck" were used to help explore patterns.

Growing Patterns

Repeating Patterns

In the 3-6 room they had posted Learning Goals on a continuum from Grades 3 - 6. I've included the pictures of the learning goals for combined grades. The Learning Goals are for the Patterning and Algebra Strand.

In the 5-8 session (where I was) we had done many activities that could be used not only as "Minds on" type activities, but also as ways to give descriptive feedback, or have students reflect on their learning (Helpful with the learning goals section of the report card). The ideas are on the purple cards and the yellow paper are the learning goals we had for each breakout session.

The 7-10 session was lucky because they used a Mobie for part of their session. The Mobie works in similar ways to a SmartBoard. A key idea from this room was the chart that they had put together on ways to give feedback. Exit passes or exit cards are a great way to get a snapshot of where you students are, and allow them a chance to reflect on their own learning. (Once again, great for using to help give a mark for the Learning Goals and for planning!)

The final room was the 9-12 room. In here there was math for both the academic and applied levels. Two things that really stuck out to me in the room were the group "norms" sheet and also the Learning Goals and consolidation questions for the Grade 9 Academic and Applied classes. I take comfort in this because in Elementary we always wonder if "high school is doing it" and this proves that they are! How great is that consistency for our students! The consolidation question is the question you would ask your students to make sure that you are meeting the Learning Goals set out for the lesson or the unit.

Group Norms - From the GAINS website. Used for group work. One teacher shared how she only needed to touch the sheet to get students back on task.

Grade 9 Academic

Grade 9 Applied

These are just a few of the great ideas that happened over the course of the week. I've got more that I can't wait to share with you as we do our FOS based PLC's during the course of the year! I honestly recommend attending Math Camppp next year if it is offered. Think of it as an "Academic Vacation" it's free, it's fun and it's fabulous!

Math Campp - Day 3 & 4 - Part Two

2011-08-24T12:13:00.000-04:00

As with the reflections from the first two days of Math Campp, I've turned this blog post over to Gwen to get her responses on what was happening in her session during the breakout sessions.

From Gwen @ Dorset Park

On day 3 at “The Fishing Shack,” we got hooked on algebraic thinking. Inspired by the exciting Plenary Sessions lead by Ruth Beatty and Cathy Bruce, our breakout groups tackled problems about linear relations with renewed vigor. We used our own solutions and student work samples, to discuss what learning was evident and to practice giving descriptive feedback. One thing that came to light is that many of us are now feeling that we would like to pursue more professional development with a focus on specific math content. We are taking the bait!

On day 4, we spread the “net,” as in network. We developed learning goals for the Patterning and Algebra strand for our grades and shared ideas for planning for combined grades. We also talked about our understanding of what multiple representations are and what they are not. Before, I would have thought that a demonstration with three different manipulatives would do the trick, but from now on I will be introducing my students to concrete, visual, graphical, and symbolic representations, and encouraging them to make connections between the representations to deepen their thinking. Our new coolest tool in the tackle box is active graphing.

Finally, we shared resources – some tried and true, some brand . We were introduced to the Math GAINS website and were amazed by its sheer breadth and depth. This resource is sure to provide plenty of food for any who swim in its waters. It’s true that good things grow in Ontario!

Thanks Gwen!

For those of you not familiar with the GAINS website, I highly suggest you take a look at it. It's free, and is great for learning all about ways to teach math in the province. You can find it at: www.edugains.ca and click on math gains. There are also valuable links to assessment, literacy, DI and ELL learners.

Math Campp - Day 3 & 4

2011-08-24T12:06:00.000-04:00

For Wednesday and Thursday the focus moved from Proportional Reasoning to Patterning and Algebra. We were treated to the lovely pair of Cathy Bruce and Ruth Beatty. Ruth instructs at Lakehead University and Cathy at Trent University. The main focus of their research is young students and their algebraic thinking.

From the moment they began their plenary session, we were hooked! They showed us a method for teaching patterning and algebra that may of us were unfamiliar with. And yet, it is so simple and so hands on, that the learning for those of us in the room skyrocketed! In fact, many of us can't wait to get back to the classroom to try it out. The underlying concept of additive and multiplicative thinking is what really helps students gain not only more confidence when "doing" the math, but also makes a big difference as it shows us if they really have the conceptual knowledge they need in order to move forward as mathematicians.

Look at this photo below. (It is upside down, so please read it from right to left). Can you tell me what equation this model represents?

1n + 9 (where n=term) or position number x 1 +9

The first position is "Zero" - There are 9 green tiles. If you look at the 9 green tiles they show up in every term. Therefore, the 9 must be the constant. Just by the pure look of it, the students are now more successful in identifying the constant.

The second position is "One" - You can see the 9 green tiles (the constant) but now there is 1 blue cube. Hmm....what times "one" gives me one? students can now begin to make conjectures about what they think the pattern rule is. They can then look to the third position and see if that it is always "position number times 1".

The third position is "Two" - Two times one is two (hence the two little blue cubes). And then once again there are those 9 constant green tiles.

Here is another example:

Can you see it? This one is a little more tricky, but you can probe the students with some questions like "What do you notice is the same about each position?" "Is there any pattens that you notice?" In fact, you can even use different colour tiles to lay on top of the pattern to help the students test their theories and prove and reason their conjectures. What's the answer you ask?

4n + 5 (where n=term number) or position number x 4 +5

Once we started doing these, we then made the jump to graphing the equations and predicting about what the "12th term would be" using graphing and our knowledge of co-ordinate points.

Great stuff to think about!

Math Campp 2011 - Day 1 & 2

2011-08-18T20:43:00.001-04:00

For the week of August 15th - 19th a team of us from SE 1 headed up to Kempenfelt Bay Conference Centre for a week long "Math Campp" sponsored by the Ministry of Education.

The focus of the camp is on Proportional Reasoning and Algebraic Thinking. It was completely free and not only did we receive great PD, but also lodging, food and gas mileage.

Lucky for us, the 5 teachers (and one volunteer from Maryvale) were able to get into three of the 4 sessions that were available. Our teams were as follows: 3-6 session: Gwen (Dorset Park),Maria (Regent Heights), Melissa (Maryvale); 5-8 session: Myself; 7-10 session: Kermin (Regent Heights). So we were all able to learn a lot of different things, and then are all able to bring it back to our schools and our students.

The first two days were focused on Proportional Reasoning. Marian Small and Amy Lin presented the Plenary Sessions for this session. After each plenary session we went into our breakout sessions focused on our grade band. Here are a few of the comments about the first two days of our learning, from those that have attended:

3-6 Breakout Session Thoughts:

Maria @ Regent Heights said:

Just keep swimming…swimming…swimming…(Dorey – (Finding Nemo) was on to something)
That’s what we do in breakout sessions – deep swimming (choosing between a “multiplicative friendly” whale or an old “additive” sea creature.)

During our breakout sessions we:
• attempted and successfully solved mind-boggling math problems;
• discussed how and why we solve a certain problem – what strategies we used and what connections we made;
• asked questions;
• answered questions;
• overcome math fears / uncertainties;
• engaged in deep conversations regarding algebraic thinking and how beautiful mathematical patterns are;
• created learning goals & polished them;
• got amazed at a new multi-faceted resource
and…..networked with lots and lots of other lovely fish!
Melissa @ Maryvale said:

In the Grade 3-6 session, our room theme was “The Fishing Shack”. On the first day, we each received a fishing hat to represent our grade group. From then on, each time we left the class, our “exit ticket”, was a reflection we wrote on “fish note paper.” A fishing quote related to what we had learned that session about proportional reasoning or patterning and algebra guided our written reflection. We also got a trinket to add to our hat, for example, a piece of netting, a reel, hook, etc. The facilitators modelled a 3-part lesson approach each time we met, and we learned a variety of ways to do a minds on, action, and consolidation. For example:

Minds on: Four corners, Game – find your equivalent fraction, & inside and outside circle discussion with teacher guided prompts

Action: Parallel Task, Open Question, & Centres

Consolidation: Exit Card, Gallery Walk, & Bansho

Some “Ah ha” moments we had...

Peer Feedback: We watched a video of TDSB students using MAC books in a classroom to solve a problem. After the problem was solved, students were then told that they had to give their peers feedback on their answer. Each Mac book needed to have at least two pieces of feedback, which the students wrote on a post-it note and posted on the screen of the computer. After feedback was give, the teacher instructed the students to look at the feedback that they were given and see if they found the feedback to be valuable in assisting them to make their answer better. Students were told they could use or not use the feedback that was given to them.

Using a Variety of Materials: When we solved various fraction problems in our groups, it was interesting to see the different types of materials that people selected to use that aren’t the typical fraction strips or circle....such as, geo board and a ruler.

Growing Success: We talked about the value of the 3 types of assessment (of, as, and for) and the triangulation of ways to assess (observation, conversation, product). This was important because sometimes observation and anecdotal notes aren’t always seen as valuable in comparison to other forms of assessment, but with the growing success we can see how important it is.

Bansho: We received the monograph on the Bansho, and tried a Bansho in our group. We discussed the importance of having a guiding question or focus when having students share their work (e.g., why did you use two colours to show when you drew your pattern? What do the two colours represent?). We discussed how this is better than having students come up and say, ”First I did ...., then I...., etc”. We also discussed that not every student needs to share for a bansho. After one student shares, we can ask students with similar answer, ways of solving, etc to put up their work next to the shared question.

For the 5-8 session, You will have to ask me personally what we did :)

For the 7-10 Session

Kermin @ Regent Heights said:

Our group is focused on providing feedback to students. We have brainstormed methods to provide frequent feedback to students with limited investment of time such as exit cards, confidence lines, etc. As well, we are looking at samples of student work and discussing possible responses to advance thinking and understanding.

Along with that we’ve been trying out open-ended problems in an effort to anticipate student responses. For instance, using linking cubes in a ratio of two colours we build animals. My creation, Shelly the turtle was made in a ration of 1:2 (green:yellow).

Our Group From South East 1 and Marian Small

Stay Tuned for Updates from Day 3 & Day 4!!!

Intermediate Learning Goals and Success Criteria

2011-06-28T16:20:00.000-04:00

Sharon decided to put her new learning about Learning Goals and Success Criteria into play with the last strand she was covering in this school year. She made specific goals for each grade, but the Success Criteria remained the same. The strand she was covering is Measurement.

Thank you so much for sharing, Sharon!

Learning Goals and Success Criteria - Lots of Samples

2011-06-28T16:16:00.000-04:00

Over the last few weeks, many schools have been planning their math expectations for September. Once they were in place, the teams then created their Learning Goals and Success Criteria for their first strand. Here are some of the charts they came up with.

Primary Grade

Intermediate Grade

Grade 2

After seeing the Grade 2's Success Criteria, the Grade 3's wanted to add some key pieces to their chart.

Junior Example

Thanks to the teachers at Regent Heights and Wexford for letting me share their work.

Kindergarten Planning

2011-06-28T15:48:00.000-04:00

The Kindergarten Team at Wexford had a planning day where they spent the morning working on Math and the afternoon working on Language. It was the full team - Teachers and ECE's - which was great because everyone had some great ideas and suggestions as to what they wanted to see done in their next school year.

The team decided to follow the long range plans that they received at the last Kindergarten PLC. They also wanted to plan their unit using the template that was shared with them for the Patterning and Algebra expectations. They focused on planning around the Number Sense and Numeration expectations that "go along" with the specific Patterning expectations.

They started by creating their Learning Goals for the unit. In this case they ended up being:

* The number of things I count, is the number of things I say;
* I can choose where I want to start counting;
* When I count I always start at the number 1.

They then created a diagnostic/ending assessment (which will be done orally) for the children to do. But they didn't want it to seem out of context so they pulled in the book "Good Night Gorilla" to help them make the diagnostic a bit more "fun". The discussion they had around it was really rich as it allowed them to predict what answers the children might give, but also discuss about what they would expect to see the children say and do at the end of the unit. They also discussed what the prompt would be for students who need one (you can see it in the picture labelled with a "P").

Now that they had the beginning and the ending figured out, they then planned what they were going to do "in the middle" to help their children be successful at the end. They discussed, debated, and deliberated possible activities - all keeping the expectations in mind to make sure they were not going too far off the rails. They were able to pull in some more literature connections (Ten Black Dots, Chicka, Chicka, Boom, Boom,) and also discuss what they would do in both the large group and the small group settings.

Overall, it was a great morning - and the best part is, they are pretty well planned (math wise) until November! Super work team!

Updating - Blogs I'm Following

2011-06-15T14:19:00.000-04:00

Recently, I've been becoming a little more interested in the role of technology in our classrooms. There is so much out there on the "information highway" that I feel like I don't know where to begin to get on.

A friend of mine shared with me a website that I've added to the "Blog's I'm Following" section of this blog. It's called "Free Technology for Teachers" and has a ton of good websites and different types of technology that you can use with the students in your classroom.

Well worth checking it out :)

Inspiring Post

2011-06-15T14:13:00.000-04:00

A friend of mine shared this blog with me and I thought that the author's words were really inspiring. Take a look at it and see if you feel the same way

http://plpnetwork.com/2011/06/13/this-summer-i-wont-be-learning-how-to-be-a-better-teacher/

Planning For The Next School Year - Primary

2011-06-15T14:08:00.000-04:00

At Wexford they've just begun to do some planning for the 2011 and 2012 school year. They took a very manageable and "do able" approach to planning. Here is what they did:

1. First, they had a discussion on which expectations to cover as a division and when. They made sure to look for similarities between expectations, and also to look for expectations that can be enhanced if there is a specific expectation taught prior to the teaching of that one.

2. Then they created a list of their Learning Goals and their Success Criteria for their first strand - Patterning and Algebra, Overall Expectation #1.

Grade 1 Learning Goals

Grade 1 - Success Criteria

Grade 2 - Learning Goals and Success Criteria

Grade 3 - Learning Goals and Success Criteria

3. Once they had identified their Learning Goals and Success criteria, they turned to the achievement chart and their specific expectations to see what expectations lent themselves to each area of the achievement chart. What was noticed is that some expectations show learning in both areas. For example, "Making a pattern" demonstrates both knowledge of what a pattern is, but also shows application when being asked to make a pattern in a specific context (e.g., Josh looked at sea shells on the beach and noticed they made a repeating pattern. What could the shell pattern have looked like?)

More Learning Goals and Success Criteria

2011-06-13T20:26:00.000-04:00

Here is another way to get creative in how to display success criteria in your classroom.

In Adrienne and Jennifer's Grade 2/3 and Grade 3 classes, they've decided to use a pocket chart to help them add and remove items they are looking for in an answer depending on the strand.

Make And Take With Debbie Diller's New Book!

2011-05-17T09:51:00.000-04:00

Recently a group of 30 teachers, 2 principals, and 1 guidance counsellor, in our FOS got together to learn more about Debbie Diller's new book: Math Work Stations: Independent Learning You Can Count On, K-2 (Stenhouse Publishers - ISBN: 978-1-57110-793-0). The workshop was the idea of Melissa Seco, a Grade 1/2 teacher in our FOS. She was very excited about the activities she found in the book and wanted to share her ideas with others. The cost for the make and take was covered by our SO Nadira Persaud. It was a great chance for teachers to network, share ideas, and create some great new math activities in the process! A big thank you to Mauro (Principal) for letting us use his school library for this workshop.

One busy group making their activities.

Most of the attendees hard at work.

Melissa, our "instigator" for this workshop!

How Do You Mark This?

2011-04-25T14:16:00.000-04:00

In Nancy's Grade 4/5 class they have been working on different strategies to multiply and divide. We gave them the following problem to work on in pairs:

After having them read the problem, we addressed any words that they were unsure about. In this case, smoothie and assuming were new to them. After completing a KWC chart the students set to work solving the problem.

As we walked around the room (and using the A4L tool) we noticed that there was perhaps too much in the problem, but the students were doing a really good job of using different strategies to solve the problem. Then we came to one group. This is what their paper looked like:

At first we both kind of stopped and stared in silence for a few moments. Then the question came into our heads of "How do we mark this?" Clearly, some of the feedback that we would give to the students would be that they need to work on organization! But what about the work? When we started to look at the achievement chart, we noticed that there really were a lot of positives happening in the work. The students have a strong knowledge of adding and are able to apply their knowledge of fractions and reasoning to the problem. They are also able to see that the quickest way to solve the problem is find out the total number of students and divide by two to give the amount of each type of smoothie. We can see their thinking - although this area is a little bit weaker as their organization is not clear, and we can't see how they jump from idea to idea. In terms of communication, they are able to get their ideas across, but it is not that clear to follow.

When we consolidated with the students, we had them come and talk about what they think they did well on, and where they needed to improve. Because we had used a Bansho to organize the work they were then able to clearly see where they needed to improve. To capitalize on this, we then had the class write on a post - it note what they will do differently the next time they solve a problem.

I Understand The Problem - But Now What?

2011-04-25T13:56:00.000-04:00

We know that in getting students to be successful problem solvers that giving them time to problem solve is just the beginning. Comprehending the problem is another obstacle that students (and adults) need to overcome in order to decode the important information from the problem, and then apply skills that they have in their schema to help them solve the problem.

In Sheryl's Grade 1 class they have been doing a lot of work on not only decoding the problem, but also talking about what they can do after they understand the problem. To help them comprehend, they have been using the KWC chart to help pull out the information that they Know, What they need to do, and things that they Can't forget. Sheryl has also began adding onto the bottom of the problem the strategies and tools that the students brainstorm that they can use in order to help get the answer.

You can see that some of the ideas that the students came up with were: Add - using your fingers; with number sentences; using counters. Also Draw a picture. Great strategies for Grade 1's to use, and great strategies to use for this problem!

Descriptive Feedback and Gallery Walk

2011-04-25T13:42:00.000-04:00

When we consolidate our math lesson, a Gallery Walk is a great tool to use to help get students thinking about the math that they see, and the math that they don't always see. A Gallery Walk is also a great way to get students using Descriptive Feedback with their peers to help give specific and clear feedback to each other on ways to improve and "edit" their work prior to handing it in.

A few weeks ago I was at at SIM (Schools in The Middle) Session. During the sharing portion, the Toronto Catholic Board shared with us an example of how one teacher is using Gallery Walk and Descriptive Feedback Effectively with her students.

In this first post it note, you can see how Megan is getting some feedback from her peer that is not really going to help her improve on her math thinking - But more on her presentation skills. Before the teacher hands the work back to the author, she first writes comments down to the student providing the Descriptive Feedback to help them improve on giving feedback.

The teacher is very specific in the feedback that she gives to the student. She tells them exactly how to improve by saying "Comment more on the math than how they talked." Then she gets the student providing the feedback to think more deeply about what they wrote "Why were the titles proper? How do you know?" She then returns the work to the student and allows them to rephrase their original feedback.

You can see now how Megan is able to see exactly what she needs to improve because the peer providing the descriptive feedback to her has done the "good" job on a different colour post it note. Now the feedback to Megan says: "The titles were proper because they are of the polygon properties and the polygons are all sorted properly." The only thing missing in this descriptive feedback is something to improve upon - However, learning how to give effective descriptive feedback is a process, and the students in this class are well on their way to learning how to not only give each other appropriate descriptive feedback, but also how to accept descriptive feedback from their peers.

What Are You Looking For In A Task?

2011-04-25T13:26:00.000-04:00

Recently at the joint Crerar and Workman PLC, the Junior and Intermediate divisions had an open discussion of what they were looking for in a good task. After a list was brainstormed, we then went back and highlighted what part of the achievement chart that key item would address.

What ended up happening was that we came to the conclusion that even though the students are giving us one answer, that answer is rich and covers many different parts of the achievement chart. Look at the picture below and see if some of the criteria that they came up with would be similar to the criteria that you would want in a task you give your students.

Co-teaching With Three

2011-02-28T20:14:00.000-05:00

Richard's co-teaching session was a bit different than his team member's. The reason for that was that Richard has a student teacher with him, Cindy, and we pulled her into our lesson as well. She took a real risk as she was not able to plan the lesson with us, but jumped right in and co-taught with Richard and myself.

The strand that Richard's Grade 2's are working on right now is measurement. Richard and Cindy wanted to see what the students knew about time, and if there were any gaps that they needed to fill in prior to teaching the expectation for the grade. The lesson was in the three - part lesson format: Minds on: Compare the times on a digital and analogue clock; Action: answer a problem based on one of the students in his class: M started watching a TV show at 5:30pm (time shown in an analogue clock) when the show was over he looked at the time on the VCR and it said 6:00. M said the show was a half an hour long. Is he correct? Explain your answer. Then to Consolidate, we brought up two students who used two different strategies to share their work.

When the lesson was over Richard, Cindy and myself had the rest of the morning to moderate mark, give each student descriptive feedback on their work, and then do some planning for the remainder of the unit.

What was great about this debrief was not only did Cindy get to see all that is involved in planning and marking, but her and Richard got to have a really focused and professional discussion on strengths and needs of the students in the class. This is especially important because it allows Cindy the chance to make real-time decisions about the students she is teaching, and plan for the remainder of the unit that she is teaching for her teaching block.

After all of the descriptive feedback was done, and the feedback given to the marker students recorded on the template, they then sorted the next steps into areas of need.

These areas were:
a) use information from the question to help them;
b) make sure that all parts of the question are answered; and
c) add more specific details into the answer.

As Cindy plans the remainder of the unit, she's got some things to think about and make sure that she is incorporating into the unit.

Co-teaching, Co-learning, Co-growing

2011-02-28T19:42:00.000-05:00

As part of Dorset Park's pathway, the teachers and admin have decided to take a more focused approach to their math pathway. Since the division is small (3 teachers, 2 with split grades) they have opted to do co-teaching as a way to learn more about math, and to focus in on key ideas and strategies to help students in their classrooms.

Cathy teaches a 2/3 class. Herself and the other 2/3 teacher each "swap" to have a grade in math. Cathy teaches the straight Grade 3 class. For our co-teaching session, we decided to do a pre-assessment task in graphing to see what the students could remember from previous years and help give Cathy some data on what the needs of her students were. The lesson was structured in a three-part lesson format: Minds On: Create a Line plot on eye colour in our classroom;

Action: Compare our data to that from another class (we modified a task in the text to help us accomplish this) and discuss similarities and differences,

and then to Consolidate we made a Venn Diagram with the similarities and differences listed.

Our blackboard after our lesson.

When the lesson was done, Cathy and I had the rest of the morning available to do some moderated marking, and give descriptive feedback to each of the students. Using the A 4 L tool during the lesson was also helpful as it gave us a starting point for discussion. We recorded the feedback we gave her marker students on a specific "Marker Student Feedback" sheet that was shared by George, a current Teaching and Learning Coach who was a SWST teacher last year. This helps us to have specific information about her marker students, and allows her to easily track their progress over the course of the year.

When we were done giving descriptive feedback, we then sorted the steps for improvement into different categories.

What we noticed was that there were four main areas that the students needed help with:
a) Organizing their answer;
b) Answering all parts of the question;
c) Using numbers to help justify their answers; and
d) Incorporating appropriate math vocabulary into their answer.

From these areas, Cathy is now able to begin teaching her unit with the needs of her students in mind. She is able to plan her lessons around these ideas, and help the students become successful in meeting the expectations for this grade.

Success Criteria - Part Two

2011-02-16T21:10:00.000-05:00

This week, Melissa did a follow up lesson with her Grade 1/2 class to help them consolidate their learning on what makes a good answer. She started with the class chart that she co-created with them last week. You can see that they have made some additions to their original chart. She wrote these additions in a different colour.

Her learning goals for this lesson were: To learn about what makes a good answer and to learn how to make an answer even better by ensuring that all four areas of the achievement chart are included (Knowledge and Understanding, Application, Thinking/Problem Solving, Communication). Her "minds on" was to have the children talk about the four areas of the achievement chart and what might go under each area. For the "action" of her lesson, Melissa wrote all of the items from the original anchor chart on "what makes a good answer" and placed them on sentence strips. She then had the students look at the sentence strip that they were given and put it under the category of the achievement chart where it fit the best.

She differentiated this activity by including not only sentences, but also pictures for those students who are struggling readers. The students were given two pieces of work that they did recently. She gave them a

"Star and a Wish" sheet and a highlighter. They then went and highlighted something that they thought they did well, or were a "star" on. They also then filled in their "wish" on what area they need to improve upon or do differently next time. This is not only great for helping them take control of their learning, it also is a great way for them to show self-regulation - a new learning skill on the report card.

When they were done this, she brought them back to the carpet to consolidate their learning. She did this by having them share what their "stars" were and then had them place their work under one of the four categories. After the lesson was done, she then placed the achievement chart, their success criteria and the samples of work and star and wish sheets onto the blackboard. This now acts as an anchor chart for the students to refer to when solving problems.

If you would like to see this lesson, I do have a video of it. Please contact me and I'd be happy to share. As well, Melissa is very welcoming to visitors in her class. Contact me and I can put you in touch with her and you can go in for a visit or a chat.

Cross Strand Problem Solving

2011-02-08T15:21:00.000-05:00

In thinking ahead to Valentines Day, Melissa had her class complete a problem on making valentines. Her lesson was in a three - part lesson format and was the following:
Minds on - Reading a book to them. Action - was the following problem: Sierra made valentine cards for her friends. It took her 5 minutes to make one valentine card. How long did it take her to make 6 cards? (Adapted from The Math Process Standards Series K-2 by Susan O'Connell) Consolidation - To share answers and develop success criteria from it.

Although telling time to the nearest 5 minutes is not in the Grade 1 or 2 curriculum, Melissa has spent a lot of time getting her students to work on composing and decomposing numbers in different ways. Her goal for the lesson was to have the students apply a known strategy to a problem in a different strand. As the students were working, Melissa went around and used the Assessment for Learning tool during her discussions with the students. This allowed her the opportunity to instantly record their strategy, answer and their errors.

Once the students were done, she brought them together to create a list of what made their answer good. This will now be their success criteria for upcoming problems (photos of that to come later). Once the students discussed what made their answer good, they then had the opportunity to go back and "edit" their work to put more detail into their answers. You can see this in the pictures by the different colour that they used.

This pair of students originally had the incorrect answer. They then went back and checked their work and noticed the error.

This pair drew too many tally marks originally, they were able to see their error, but simply didn't go back to change the written portion of their answer.

I have made a video of this lesson as it really shows not only what a good three part lesson looks like, but also how you can create success criteria with your class. If you would like to see the video, or want help in creating success criteria with your class, please let me know.

Combined Grade Planning

2011-02-08T14:59:00.000-05:00

Teaching a combined grade is not always the easiest teaching assignment. Not only do you have two different grades of students, but you also have two different levels of the curriculum to look at. Planning ahead is the key to help you make the most out of your lessons - and to make sure that you are covering all that needs to be covered.

Heather teaches a combined Grade 2/3 class. Her numbers are pretty well split down the middle. Here is a template she used to help her plan her unit for measurement.

She broke down the unit into four main areas: General, Area & Perimeter, Capacity/Mass and Time/Temperature. From there she looked at the specific expectations and then summarized them for each grade. The grades each got their own colour to make it visually easier to read. Once she was done, she then highlighted all that was similar in the two grades, and then circled what was different or new to the grade. This then allowed her to look at the similarities and differences between the two grades, and then helped her zone in on what was different when planning.

The Middle Is What Matters

2011-01-27T09:16:00.000-05:00

For the past several years, many of us have been involved in Literacy or Numeracy pathways. We have spent time creating pre-and post assessments and have tracked our students progress along the way. We moderated marked, and have learned new high yield strategies to help our struggling students improve. From all of this, the most important lesson we have learned is that what you do in the middle (between the pre-and the post) is what makes the difference for your students.

At Wexford the Grade 1 and 1/2 teachers spent their PLC time together looking at Measurement. Measurement is a big strand, and involves many different concepts. Some concepts, such as area and perimeter and volume and capacity are more "meaty" than others such as time. The planning session started by breaking down the strand into chunks based on what was to be taught. Those chunks were: time/temperature, length/height, area and capacity/mass. From there, they then listed what knowledge the students would demonstrate for each heading based on the curriculum. This allowed them to focus in on what "chunk" had more expectations and knowledge needed.

From there they then took out the Q-Chart and created rich tasks for their students to do during the unit. Having the Q-Chart there really helped to open up the questions and allowed them to think of deeper questions to ask their students to really help them show their abilities in all four areas of the achievement chart.

Knowing that communication is an area that their students struggle with, they also created a chart that they will use with their students to help them become better at answering questions. This chart is a great way to get students to reflect on their learning and helps them to ensure that they have a complete answer. Plus, it allows for the teachers to give easy descriptive feedback to the students because they can give the students concrete (and visual) examples of what to do in order to improve their answers.

Success Criteria

2011-01-20T21:41:00.000-05:00

Some of the new "buzzwords" in education are around Learning Goals and Success Criteria. Success Criteria is defined in the Growing Success Document as "Standards or specific descriptions of successful attainment of learning goals developed by teachers on the basis of criteria in the achievement chart, and discussed and agreed upon in collaboration with students, that are used to determine to what degree a learning goal has been achieved. Criteria describe what success “looks like” and allow the teacher and student to gather information about the quality of student learning.” (p.155). That is a great definition but what does it mean?

In Adrienne and Jennifer’s Grade 2/3 and 3 classes they have done a lot of talking with their students about what makes a “good answer.” For their students, they have talked about what items you would find in a “good answer” and what you can do to an answer to make it an even “better” answer. To help their students make sense of all of the discussions that they’ve had around this topic Adrienne and Jennifer co-constructed success criteria for what a good answer looks like in math. To help narrow the focus, they had the students’ zone in on the communication aspect of the achievement chart as that was the area that most of the students struggled with.

For the lesson, they did a three-part lesson where their consolidation was to build the chart on success criteria in communication using the problem from the “action” part of the lesson. Using the student’s own work the class talked about what they thought made a “good answer.” They then started to think of the different levels of achievement and what an answer at that level would look like. As the discussion grew, the students were getting better at clearly articulating what was good about an answer, and what was needed to improve. Now when the students are “done” their problem, they are able to go and check it and then add more detail if they need too. Letting them take more control over their own learning.
There is no one set way to co-construct Success Criteria. Part of the success of the co-creation is being planned in what you are teaching and what you are looking for in the work of your students. As well, having a community of learners where students feel safe to take a risk is also important. Here are the examples from Adrienne and Jennifer’s classes.

Achievement Categories In Simple Terms

2011-01-04T21:00:00.000-05:00

Just before the break I had the opportunity to visit a Grade Six classroom outside of our FOS. In Jessica’s class she co-created an anchor chart on the four categories of math achievement. This chart is hung up in her classroom and allows the students to focus in on what elements are in each area. I appreciated the chart because it is worded in simple language, but is very clear on what is expected in each category. This would be a good activity to do with your class to get them (and their parents) to understand that math is more than just basic rote facts – But rather a combination of different elements that all have real world applications.
Thank you Jessica for allowing myself, and the other coaches into your classroom.

Looking Critically At A Rich Assessment Task

2011-01-04T20:59:00.000-05:00

Sometimes we can come up with a really good question or problem to give our students, but when we go to mark it, we find out that it didn’t turn out like we expected. When we give our students a rich task to work on we need to keep our own success criteria in mind when we create the task. When we start to create the task we have many good ideas, and re-word and re-write the question over and over again. When we are done we need to think about the achievement chart, and if our question A) Does allow the students to demonstrate work at a Level 4 and B) Allows us to have the students perform in all four areas of the achievement chart: Knowledge and Understanding, Application, Thinking/Problem Solving and Communication. Some teachers are Wexford are doing just that.

At Wexford, the school is continuing on its second math pathway of the year. This time they have chosen to work in grade teams instead of by division. What’s nice about this approach is that it lets the team focus on the strand, or issue, that they really want to. This week, two of the grade teams put together a pre-assessment task to administer to their students. The Grade Six team is looking at Data Management and the Grade 7/8 team is looking at Measurement.

Once each team had created their question, they then stepped back and took a more critical look at their question. They went through each area on the achievement chart and then predicted what their students would demonstrate for each area. They then created their own success criteria of what they expected to see in each of the categories.

For the Grade Six team, they also wrote out a list of possible questions that they could ask the students about the problem. They then went back and also looked at what areas on the achievement chart they question covered (e.g., was it really a higher thinking question, or was it a more basic knowledge and understanding type question). They also discussed what responses might look like at all four level s of achievement.

Grade Six Sample
For the Grade 7/8 team, they too went through each category on the achievement chart, but then found that when they got to communication, the question didn’t allow their students to communicate at a Level 4. So with some quick tweaking, they were then able to fix the question to allow their students to communicate at all four levels.

More information on Success Criteria can be found in the Growing Success document. It’s a great activity to co-teach with either myself or the literacy coach as not only will you provide the students with information on how to improve, but it will help you to clarify what you are looking for in their work.

Blokus Tournament!

2011-01-04T16:30:00.001-05:00

To end of their transformational geometry unit, Paul’s Grade 6 class participated in a Blokus tournament. Blokus is a game that involves using problem solving skills, and strategies, to help you cover as much of the game board as possible. One you select a piece you not only need to decide where you want to put it, but also how you are going to transform that shape into the space you have provided. As the game goes on, students really need to use their knowledge and understanding of transformations to make the pieces fit, or else they’re out!

The class was divided into six teams of four. Three teams were on each side of the classroom. There was a scoreboard posted on the blackboard to help keep track of who was advancing to the semi-finals and what everyone’s score was. For those that didn’t win at their game, the score was still important because the person on each side with the best score (who didn’t win the match at their table) got to be put into a “wild card” spot and advance to the semi’s. After the semi-finals, the same process was repeated with two winners and two “wild cards” advancing onto the finals.

The final round was played on a giant Blokus board. The whole class crowed around it to see the final match. It was interesting to watch the spectators as they were so quiet! Every now and then one of them would whisper to the person beside them and share what piece they would have used, or a move that they would have made if they made it to the finals. What was even better to see was that once the “Blokus Champ” was named, all of the other players shook hands and congratulated each other on a game well played.

As an FOS we have a class set of Blokus games that you can borrow to use with your class. If you are interested in using them, please e-mail me and we can make some arrangements. As well, if you want to learn more about Blokus, or play an electronic version of Blokus on-line or on your mobile phone you can visit www.blokus.com

Problem Solving In Kindergarten

2010-12-22T13:08:00.000-05:00

In Artemis' Full Day kindergarten class, her students were given the opportunity to problem solve - and connect that problem to a larger school wide issue. The school had adopted 6 families for the holiday season. Students and their families were asked to donate clothing, food and personal items to help support the cause.

For the minds on part of her three part lesson, Artemis read the students the book "The Jacket I Wear In The Snow" to get the students thinking about items you need for winter. The problem (action) that Artemis gave her students was this: We've been collecting clothing for families in need. We can put ten things in each box we give them. We are going to make boxes of hats and mittens. What combinations of hats and mittens could you put in a box?

The students did a wonderful job of creating various boxes with different combinations of hats and mittens. As they worked, Artemis was able to record not only the combinations that they made (e.g., 4 hats and 6 mittens) how they counted (was it one-on-one, did they count by 2s?) and probe them to explain their thinking (How do you know you are done? Why do you think you have put ten things in the box?).

To finish off the lesson, (consolidate) the students came back to the carpet and recorded their boxes on a chart. Artemis then continued to ask questions about the boxes that the students made. (Who had more mittens in their box? Alyssa or Shiva? How do you know?)

Bansho For Where To Go Next

2010-12-22T12:53:00.000-05:00

As part of Wexford's Math Pathway, the Junior and Intermediate divisions decided to focus on strategies. To help them gain a better understanding of what strategies their students had for Patterning and Algebra, they had them do a pre-assessment task prior to their PLC. The pre-assessment was done "cold turkey" with no pre-teaching prior to giving it to them. This allowed the teachers to get a real understanding of what strategies their students already had in place.

Where things changed was when they began to look at all of the strategies that their students were using from Grades 4-8. Each teacher looked through their pile of work, and pulled out the different strategies that their students were using. We then assembled those strategies into a Bansho format.

By doing this, it allowed us to look at the strategies that students already had - But also allowed us the opportunity to look at strategies that we may have not been familiar with and see how to use them. As well, it allowed us to make note of strategies that we want to model for our students, and also allowed us the chance to see how to help move out students along in their development of strategies.

40 Teachers and Tarps?!?!

2010-12-03T20:18:00.000-05:00

Recently 40 teachers from South East One got together to create their very own learning carpets. The Learning Carpet is a great tool to use in your classroom as it can cover everything from teaching numbers to graphing. It's also very hands on and a great way for kinestetic learners to complete an activity. Our "carpets" were made from masking tape and tarps. It was a great night had by all. For more information about The Learning Carpet, check out Wendy Hill's website (she's the creator of the carpet) http://www.thelearningcarpet.ca/

Organizing Your Mark Book

2010-11-18T22:24:00.000-05:00

One of the great things about the Growing Success document is that is gives us a strong picture of the types of assessment we need to be doing on our students: Assessing for Learning, Assessing of Learning and Assessing As Learning. Assessment can be recorded in many different ways: anecdotal notes, descriptive feedback and as marks in our mark book.

The Junior Division at Manhattan Park looked at different forms of assessment during their PLC for math. What really "clicked" for them was an idea that they saw in the Damian Cooper book "Talk About Assessment" which all of your schools have a copy of. In thinking of the types of questions they were asking, they also started thinking about how they were assessing the questions. They saw a sample of a mark book where the students were marked in each of the areas of the achievement chart and decided to try it for the unit they were working on.

What Doris and Diana said they liked about this chart (which they modified to meet their needs) was that they could look and see what types of questions they needed to assess to make sure they were getting the true picture of their student's progress. As well, the area at the bottom really allowed them the opportunity to record their observations of each student. This allowed them to have a bank of comments for the report card that was not only student specific, but in parent friendly language.

You can also help parents understand why there is more to a mark in math than just answering questions like 8 x3 = 24, as you can show specific question types their child was successful in, and struggled in.

How To Organize A Unit

2010-11-18T21:55:00.000-05:00

In Ontario, we have a specific Math curriculum that we follow. At times, the expectations seem overwhelming, and knowing where to start can be tricky. Backwards Mapping is one effective strategy that helps us keep track of not only where we want the students to end up, but also where we want to take our students. Creating a unit plan is another strategy.

Maryna used the template below to plan out her unit on Patterning.

She laid out a progression to her lessons, being sure to include tasks that were purposeful, used technology, and allowed her students to demonstrate understanding at all four levels (and categories) of the achievement chart. The plan is not set in stone. As she progressed through the unit, she made changes based on what her observations of the student were - Assessing for Learning, Assessing As Learning - and made sure that she helped close the "gaps" that her students may have had in their learning.

Having a plan not only allowed Maryna to focus more on the students, but it also allowed her the opportunity to make sure that she met the curriculum expectations for her grade, thus preparing them for the future.

Let's Start At The Beginning

2010-11-18T21:35:00.000-05:00

In Heather's Grade 2/3 class she wanted to start problem solving with her students on a more regular basis. In the lesson we co-taught we wanted the students to get comfortable with some of the logistics of problem solving. Things like working in pairs, using a marker to write their answer down, and crossing out wrong answers. These are all huge steps students have to overcome in order to show their thinking. We also hoped to see what different strategies the students used to help her get an idea of where to go in her lessons (Assessment for Learning)

For some students, they took to the challenge like it was nothing new. For some, they needed to be silly with the markers and draw on their hands for a few minutes before they got to work. Getting the students to write an answer down was the hardest part. Many of them were afraid to make a mistake and wanted to make sure that they they put down the right answer - or put down what Heather and I were looking for.

When we congressed, we had the students look at how there were many different strategies that they could have used to solve this problem. We labeled each strategy, and then posted them on the black board in a Bansho so the students could see what their next logical strategy was.

It was a very successful first try at problem solving (and co-teaching). At times we worry about how "messy" the student work is. But we need to remind ourselves that it is okay to be "messy" as it shows us how our students think, and how we can help them become clearer in their though process.

What Makes A "Good Question?"

2010-11-18T21:10:00.000-05:00

What makes a good question? That's a great question!

The primary division at Wexford asked just that question at the start of our pathway. In order to set up our pre-assessment task we needed to create a question. Not just any question, but a question that allowed us to not only meet all four levels of the achievement chart, but one that allowed our students to achieve at one of the four levels.

We looked at the above question (please ignore the writing below the purple pattern - it was our scratch pad for our thinking on another task). We asked ourselves if it was a "good question." Looking at the achievement chart, we noticed that it did cover knowledge and understanding - It shows us if the student can make a pattern and knows what attributes are. Our next question became "Can a student achieve a Level 4 on this question?" After some debate and discussion we concluded that no, they couldn't. Quite simply because we didn't give them the chance to demonstrate they had thorough knowledge of patterns.

The second problem we looked at was very different. As we went through the achievement chart, we were able to identify how the solution would allow the students to demonstrate their knowledge in each area, and at different levels. It also allowed us to anticipate student solutions, and discuss ways that the student could improve in their answer.

For the pre-assessment, the teachers came up with a very open, very appealing question for the students. It also was able to be used from Grade One to Grade Three. It was along the lines of:

Our school council wants to design a new school t-shirt. They want it to have a pattern that has different attributes on it. What could the shirt look like? Explain the pattern.

Beginning Our Pathway

2010-11-18T20:37:00.000-05:00

Participating in a math pathway is something that will be new to many of us. Clairlea has been involved in a great deal of professional development surrounding math for the past three years. In that time they have done a lot of work on creating rich tasks for their students, and also have co-taught with myself, Susan (our IL) and now each other.

When they started looking at the route that they wanted to take this year, they started by thinking of the different types of assessment that we use in our classrooms. To help organize their brainstorming, an "Idea Pot" was used. An idea pot is a great tool to use in our classrooms as a way to keep track of our ideas on a particular topic.

Once we discussed the ways in which we assess, we turned to the achievement chart to look further into the areas of knowledge and understanding, application and thinking/problem solving. These three areas come up a lot when we talk about EQAO results, but what do they really mean?

The group was divided into three smaller groups. Each group became an "expert" on a specific type of question. The groups sorted through various EQAO questions and picked out the questions that applied to their type of question. They then organized their data using a Freyer model using the following headings: Definition of type of question (in parent friendly language); examples of that type of question; non-examples and answered one of the questions.

In defining the term in parent friendly language, it then helped us have some dialogue around the idea of Learning Goals and Success Criteria. As well, it helped give us some ideas for writing the new Provincial Progress Report.

After doing this activity it helped us shed light on the types of questions we ask our students, and gave us some insight into being aware of covering the four levels of the achievement chart.

One Question, Multiple Strategies

2010-09-19T21:12:00.000-04:00

I've spoken before on the importance of teaching through problem solving, and how it truly benefits the students as it allows them to make meaning from the math, rather than us telling them what to do. In Paul's Grade 6 class we co-taught a lesson on number patterns. This three part lesson gave us a great understanding of where the kids were at, and where we could take them next.

We began by completing a KWC -P chart with the class. The "P" stands for plan. We chose to add this to our regular KWC because he was finding that his students were very reluctant to get started on any type of activity, and thought that if they had some pre-discussion on what to do, they may be more independent and more successful.

As the students were working on their problem (in pairs) Paul went around and visited each pair and probed them on their thinking and ideas. I worked with one pair a little more closely to help make sure that they were on task, and focused. We used the assessment for learning tool (A4L) to keep track of what strategies the students were using. Originally, we thought that they would use one of five strategies. However, we added a sixth strategy as one group used a strategy we hadn't thought of.

We chose three different groups to share their solutions with the class as part of our whole class consolidation. One group had the right answer, but didn't have a complete solution as I don't think they picked 13x8 = 104 on their first try! As the group was telling us what they did, I filled in the blanks for them by using a different colour marker. We called this "editing." You can see samples of it below in some of the pictures.

The second group was the pair that I was working with. We chose to have them share for multiple reasons. One of the reasons was to build their confidence. Both students are currently on an IEP and need a chance to participate and show their strategy. A second reason was that they had put a lot of depth and thought into their answer and gave not only the answer, but a suggestion as to what the leftover money could be saved for.

The third group really blew our minds. They got an answer of 7.7 At first, I thought they were way off base, but when I began to ask some questions about how the 7.7 came into play, a lot of knowledge and understanding came into play. The 0.7 of the lawn was because the student has a dog. Her mom doesn't cut all of the grass each time she mows because the dog likes to have longer grass to play in. Therefore, if the student mowed her mom's lawn she wouldn't charge the full price for the lawn mowing. She would only charge 0.7 of what her regular cost is.

We then had the rest of the groups come and put their work up on the board in a Bansho format. In total, we ended up with 6 different strategies that were used to solve this problem. So much richer and more meaningful than us showing the students 1 strategy and making them use it.

Welcome Back!!!!

2010-09-19T20:38:00.000-04:00

Welcome Back to the 2010 - 2011 School Year!

During the second last week of August I was lucky enough to be a part of Math E Motion - A week long camp for teachers and students (in Grades 6-9) which focused on teaching and learning through problem solving. The culminating activity for the students was a hands on project that was based on a math problem they had chosen earlier on in the week. The students picked "Under The Sea" as the theme for all of their projects. They showed these problems to their peers, parents and friends at an afternoon long "Math Fair."

Over the course of the 5 days, they worked together in partners to take the problem off the paper and make it come to life. In total there were 18 different projects. Each pair had different strengths and weaknesses, and each pair was also working at different academic levels. The end results were nothing short of spectacular! The students really worked hard, and put forth some excellent work. Should the program run again next summer, I highly recommend participating in it. You will be glad that you did. If you want to run a "Math Fair" in your school, or have questions about it, please let me know. I'd love to work with you to make one happen!

This problem was finding out the minimum number of moves you needed to make to cut off the dragon's heads and tails - For if you made one cut, one or two more things could grow.

Probability and logical reasoning are at the heart of this activity where you had to guess which box had 2 blue balloons, 2 pink balloons and 1 blue and 1 pink balloon.

For this game you have to place the numbers 1-8 in a row to find out what the greatest possible sum could be for each row.

Welcome To Kindergarten Night

2010-05-24T22:32:00.000-04:00

This past week I was invited to be a part of General Crerar's Welcome to Kindergarten night. The principal (Heather) and the kindergarten teacher (Chris) had set up several stations for parents to visit. These stations were: Math, Public Health, Toronto Public Library, and a Teacher station where Chris had some activities set up for them to do with her.

The math station consisted of two games for parents to play with their children: Part, part whole bingo and a shake and spill game using the 10 frame mat.

Each child also got a "math goodie bag" which had the two games in it, plus a few other math items for them to use at home. The bags cost under $1 per child, and were made up of items that were purchased at a local dollar store. The items in the bag were: A deck of cards, 10 two sided counters, a large die, stickers, part-part-whole bingo game, a ten frame, a piece of sewing elastic (to make shapes with) tangram puzzles, and a piece of foam to make the tangrams with.

It was great watching the parents and their children do math together. As well, it gave me the chance to share some fun cooperative learning games with them, so they can help their child grow as mathematicians. Great job Chris and Heather. The night was a great success!

Congress and Assessment

2010-05-24T22:17:00.000-04:00

In Lisa's Grade 4/5 class I was invited in to co-teach a lesson with her. Her school is doing a math pathway this term and her pre-assessment task is "The Checkerboard Problem." The question asks students how many squares are on an 8 x 8 checkerboard. We posed the question to the students, handed them checkerboard templates, and then set to work making notes on our Assessment for Learning (A for L) tool.

All of the students quickly got the answer of 64 - none of them got the correct answer of over 200. But what amazed us was how many different strategies the students were able to use in order to come up with the correct answer. Lisa had told them she wanted them to try to solve it in at least two ways. Many of them were able to solve it in more ways than just that.

Many of the students shared their strategies with us. We were able to see that the students had a lot of different strategies to call upon when solving a problem. After they described what they did, we used a different colour marker to give that strategy a name that they could remember it by. One key strategy was missing, so at the end of our congress I shared with them how to make a table to help them find an answer.

When our congress was over, we then let them know that although they had really good strategies, none of them got the answer correct. We told them that there are more than 200 squares on the checkerboard. At first they looked at us with an "Are you kidding" face - But then one student piped up that she could see some of them that she hadn't before.

The congress allowed us a chance to see what strategies the students already had in their schema, and then the A for L tool helped us see which ones were most commonly used. At the end of the pathway, it will then be interesting to see if the students are still using the same strategies, or if new ones have become a part of their problem solving tool kit.

Student Success in an HSP Class

2010-04-30T17:34:00.000-04:00

Karen's HSP class is composed of a variety of students, all at different levels of ability. She has been trying out problem solving in her class and has been surprised at the results. She has been encouraging the students to use a graphic organizer (seen above) to help her students comprehend what is being asked of them.

Karen is finding that the level of engagement her students have has increased since they started doing problems. As well, she admits that the first few times made her want to pull her hair out - But - now that the students have more schema to draw upon, they are achieving success and doing so independently.

The second picture shows some student samples from a problem that the class had done around fractions.

What is a Bansho?

2010-04-22T21:16:00.001-04:00

Bansho is a High Yield strategy that you can use in your class with your students. It is used in Japan as a way to help students learn different processes in which they can solve a problem. Bansho literally comes from the Japanese word meaning "blackboard." In math, we use it as a way to display student solutions from the least to most mathematically rich. It is not about assessing the students work - It is about looking at solutions, annotating work and discussing solutions.

The above Bansho was done at the FOS Transitions session. The teachers completed a problem in pairs and then we (the facilitators) organized their solutions. The organization of the solutions also involves some thought and discussion. As more samples came up, some were moved to different places along our Bansho. Once the solutions were organized, as a group we discussed them and put a label at the bottom of each one. On the far left we had identified the work as logical reasoning, to the far right we had graphing.

Bansho allows students the opportunity to see many different ways of solving a problem. It works best when your students are in an environment where the consolidation (or congress) is happening in your class. In fact, once your students are comfortable in consolidating their work you can then move onto doing a Bansho as consolidation.

You can learn more about a Bansho by visiting these websites:

www.lkdsb.net/Program/elementary/junior/OAME2007%20JapaneseBanshoHdt.pdf

(This one is a PowerPoint from the LNS - Lots of colour pictures)

http://www.eworkshop.on.ca/ - Grade 5 - Growing Weave Designs

www.criced.tsukuba.ac,jp/math/sympo_2006/takahashi.pdf

www.curriculum.org/secretariat/may2.shtml

(This is a video with not only a Bansho clip - but other High Yield strategies in Literacy and Numeracy as well)

Visual Data

2010-04-20T17:32:00.001-04:00

We have all become aware at how important data has become in education. As part of our PLC time at Dorset Park we took a traditional data wall to a whole new level - We made it visual, and practical.

Our session began by doing moderated marking on our Pre-assessment activity. As the marking was underway, we began to select examples of student work that was from the four levels. The students names were removed, and then placed under the grade that they were in (and under the appropriate level). Once the moderated marking was done, we then added the percentage of students who were at each level for each grade.

As we were posting the work there were some great conversations happening. One of the benefits to doing this kind of data wall is that since all of the teachers are doing the same concept (fractions) they are able to talk about strategies and teaching points that they have found successful. In addition, you can see similarities and differences between the levels, and gain a better understanding of what the students can do to improve.

Having it up allows for the conversations to continue, and then grow. Our plan is to put the culminating task activities (in the four levels) beside the Pre-assessment so we can see the changes in how the students respond.

(Thank you to Ed for being in our picture.)

Problem Solving in Kindergarten

2010-04-08T20:48:00.001-04:00

In Gwen's kindergarten class they have been talking a lot about the weather - And the topic of rain clouds and rain drops came up. Gwen used this discussion to have her kindergarten children participate in a Parallel Task.

The children were given a drawing of a rain cloud. They could choose between one rain cloud or two (this is what makes the task parallel). Once they had made their choice the students then rolled the number cube to determine how many raindrops the cloud would have. They wrote the number, and drew the rain drops.

From this activity, Gwen met many different Kindergarten math expectations:

Process Expectations:

* Problem Solving, Connecting, Representing and communicating;

Overall Expectations:

* Demonstrtate an understanding of number, using concrete materials to explore and investigate counting, quantity, and number relationships; and

Specific Expectations:

* Investigate some concepts of quantity through identifying and comparing sets with more, fewer, or the same number of objects;

* Recognize some quantities without having to count, using a variety of tools or strategies;

* Use, read, and represent whole numbers to 10 in a variety of meaningful contexts; and

* Begin to make use of one-to-one correspondence in counting objects and matching groups of objects.

In addition to this, Gwen was given a great assessment opportunity as she could then make observations about her students knowledge of number. For example, she could see who was able to print numbers correctly, who could demonstrate one-to-one correspondence, who could show synchrony (assigning one word for every object), and who can use the 1-9 sequence when counting (stable order principle) and cardinality. As well, she was able to see who can self correct when they make a mistake.

Problem solving can be done in kindergarten - And when it is, the results are amazing!

Thanks for sharing Gwen!

Assessing For Learning and Consolidation

2010-04-05T21:32:00.000-04:00

Nancy and I have been doing a lot of co-teaching in her Grade 5/6 class. All of our co-teaching sessions have been focused around teaching through problem solving in a three part lesson. This past week we had the students work on a problem around conversion of fractions, decimals and percents. (Picture #3)

We used the Assessing for Learning tool(A for L) as a way to document not only what strategies the students used to solve the problem, but also what errors they make. What came to our attention was a rather large error which became the topic of our consolidation or the third part of our lesson. (Pictures # 1 & 2) Nancy has also modified the A for L tool to meet her needs by making the squares a bit bigger, and also including a box for her to level the students work as well. (Not every time that we use the A for L sheet do we give the students a level - it is mainly used to simply assess for learning)

The students were quite easily able to figure out 1/4 of an amount and then find out what 50% of the remaining amount was. We saw several strategies and heard several different explanations as to how they got through steps one and two. However, where the misconception occurred was when the students got to the part of the question where they had to solve for 0.3.

The students were well aware of how to convert the decimal into a fraction - Except that they were trying to convert this particular decimal into 1/3 which then would give them the wrong answer. Many of the students said that they didn't know what to do when it came time to "deal" with the 0.30. For some that were stuck, we prompted them with open ended questions to them to help make sense of what they should do next.

During our consolidation piece we had one pair come up and share their work with the group. We had pre-selected this pair because we knew they had used the same strategy as most of their peers, and had made the same mistake. As they explained their answer I annotated what was missing from their words and their sheet by using a different coloured marker. When we came to the part about the 0.3 we had them share their answer and asked the class if this looked right. Almost everyone agreed. We then led the students into looking back on the first two questions they solved using the fraction and the percent. We put each one of those into a decimal, percent and fraction form on the board beside of us. We then did the same with 0.3, 30% and then 1/3. It was at this point that a few of the students got the "light bulb" look and put up their hands. They said that 1/3 was not equal to 0.3 but it was 0.33 instead. We then used number lines to help us show the difference between 0.3 and 0.33.

One other group - who were the only ones to correctly get the answer in the first place - put up their hands to share (and show us) how they solved for 0.3 and what it would look like in the context of the problem.

Had we not been doing this problem, this issue might never have come up. The three part lesson is a really powerful tool to help us teach our students better - It allows us the chance to take a simple, and easily corrected, mistake and fix it on the spot. Because of the consolidation piece (or congress) we were able to not only show our students different ways to show a number as a decimal, a fraction and a percent, but also stop them from making the same mistake later on.

Student Centered Assessment

2010-03-25T17:49:00.001-04:00

Adrienne's Grade 2/3 class is starting to work towards self assessment. We were co-teaching a lesson together in a three part lesson format (M.A.T.C.H.) and things took a different turn when we were about to consolidate:

Here is how the lesson went -

Minds on - We had the students discuss things they don't do everyday, but perhaps every other day.

Action - The problem we decided to do was about Jake and his sisters and how many times in a month Jake walked the family dog. Before we sent them on their way to solve the problem, we had them complete a KWC chart to help clarify their knowledge. They wrote the items in the "K" column, but for the sake of Time, we scribed their answers for the other two columns.

Consolidation - As we were about to start the consolidation piece. Adrienne brought forth the idea of turning their work into an anchor chart to help the students assess themselves on their own work. This is what her school is focusing on for their pathway for this term (Note: the pathway is rooted in Literacy, but Adrienne wanted to try it out in Math as well).

We brought the students back to the carpet and asked someone to share the answer with us. The answer was written down verbatim. It was "He walked 8 times." We asked the students what kind of answer this was and why. At first, the students thought that it was a Level 1 answer. But then quickly decided that it was not a Level 1, but a Level 2 answer. (The bright pink paper is because of this change). They then provided justification for their levelling: It doesn't explain how or why we got the answer; the answer is a little confusing; not sure how they got the answer. We then began to work ahead and had someone share why they thought that their work was a Level 3. Once again, they went through the same criteria and came up with justification: there is an explanation that is clear; only 1 small mistake; fully answered the question; showed the work - the pattern rule.

At this point we had to stop for recess and then prep. However, later in the day Adrienne went back to the carpet with the students and had them do the same for Level 1 and Level 4 work. Once all of the Levels and justifications were up, students then got the chance to Level themselves according to the criteria that they had come up with. But - They didn't stop here.

The students then went back and, (using a coloured pencil crayon) made additions to their work to help the quality of their work improve. This was called the "editing process."

For Home, the students were then asked to complete a journal question relating to the work that was done in class today.

The picture shows the work displayed on her wall. How it is set up shows both the problem and the graphic organizer (In this case the KWC chart) and it also has the samples of the student work (with the names cut off) of where it would have fallen BEFORE "editing." If you notice, there are a lot of samples in between Level 2 and Level 3 - This is because those students are at a Level 2+ (based on their original work).

This activity was very powerful for both Adrienne and her students. She now will plan further lessons with those Level 2 students in mind and have a visual reference to help guide her in her planning.

Including the inital part of the lesson, she spent about 50 minutes in total on this lesson - Not a great amount of time, but a powerful use of time. Which goes to show, that a three part lesson can be accomplished in one day.

Ch-Ch-Changes

2010-03-21T21:59:00.000-04:00

For us in education, the next few months are a time of change: Some may hear that they are surplus from their school and will begin to put together a new resume; Some may find themselves in a new grade, and begin to gather resources and ideas to use in September; Some may apply for jobs at other schools, or for other positions; and for some, they may find themselves moving up into a more visible leadership position as a coach, instructional leader, vice principal, principal, or even a superintendent.

Regardless of where we find ourselves in June, we need to remind ourselves that we are all leaders, not only in our classrooms but in our schools, and our FOS. A friend of mine recently forwarded me these thoughts on leadership: May they help inspire you in whatever you wish to achieve in the next few months.

When leaders make a mistake,they say, "I was wrong."
When followers make mistakes,they say, "It wasn't my fault."

A leader works harder than a follower and has more time;
a follower is always "too busy"to do what is necessary.

A leader goes through a problem;
a follower goes around it and never gets past it.

A leader makes and keeps commitments;
a follower makes and forgets promises.

A leader says, "I'm good, but not as good as I ought to be;"
a follower says, "I'm not as bad as a lot of other people."

Leaders listen;
followers just wait until it's their turn to talk.

Leaders respect those who are superior to them and tries to learn something from them;
followers resent those who are superior to them and try to find chinks in their armor.

Leaders feel responsible for more than their job;
followers say, "I only work here."

A leader says, "There ought to be a better way to do this;"
followers say, "That's the way it's always been done here."

~~ Author Unknown ~~

Anchor Charts - Problem Solving

2010-02-17T13:34:00.000-05:00

In Ellen's Grade 2/3 class they have been creating math anchor charts to help them when they get stuck. One of the charts that the class made was on what to do when they come to a problem. They laid out their problem solving process into four steps: Read, Think, Talk, Write. Each part was detailed on the main anchor chart and the students can refer to it at anytime.

To help her students remember where to look in the class for help, she puts the "Read, Think, Talk, Write" phrase at the end of the problem. (See the first picture for an example of this). As the students solve their problem, they are encouraged to write down their thinking onto their work. In the second picture, you can see how the students used circles around their work in order to keep their ideas separate. They listed things that they knew and didn't know, and then worked together to come up with an answer.

Getting your students to communicate their thinking is a road block that we face year after year. It is not something that comes easy. We need to allow students time to not only comprehend the problem, but also talk about their ideas and strategies (congress) and make corrections when their thinking changes. Problem solving is a skill that takes years to improve upon. This is why the curriculum insists that children start at Kindergarten and continue on for their entire educational career. It's not easy to teach, in fact at times you'll want to pull your hair out - but - you really help students not only make sense of the math they are working on, but see how it applies to the world around them.

Using A K-W-C Chart

2010-02-17T13:13:00.000-05:00

In Michelle's Junior HSP class they've begun to tackle problem solving in a way that makes a math / literacy connection: A K-W-C chart.

A K-W-C chart uses three different headings to help students make sense of the information in the problem that they are working on. Each heading has a specific purpose:

K - stands for "What do I know from the question?" This could be specific items such as "There were 4 cats and 3 birds" or "Each scarf was 100 cm long."

W - stands for "What is the question asking?" Basically, you have the students restate the question in their own words. Sometimes this is really a short sentence, sometimes it is a bit longer.

C - stands for "Are there any special considerations or conditions?" This section can be a little tricky to fill out because sometimes the conditions are also things that we know. When doing the chart with your students, feel free to go back and forth between the K and the C when you first start. Eventually, you can move onto the discussion of is that a K or is it a C? A condition would be something that must be remembered in order to complete the problem. For example, a condition could be "there were 20 pairs of shoes in total" or "You can not create the same shape more than once."

In using this tool when problem solving, it helps students to comprehend the problem better, and then solve it better. The first few times you complete a K-W-C chart with your students may be difficult, but in time they will really adapt to it and find it a useful tool in problem solving.

This idea was taken from Arthur Hyde's book called "Comprehending Math: Adapting Reading Strategies to Teach Mathematics, K-6" it is filled with other good teaching strategies and problems to use in your classroom. He has a second book called "Understanding Middle School Math" which focus' on Grades 6 and above.

The Power of Congress

2010-01-29T10:10:00.000-05:00

For the past two weeks I've been working with Savita who teaches a split Grade 3 /4 class. We have been focusing on measurement. Our lessons have been done through problem solving and have been very hands on for the students. In addition to using geoboards, we have also had the students use the computer and the Smart Board to help share their strategies.

Earlier this week her and I both had a huge "Ahh" moment when one of her students described (during the math congress) how she was sure we had found all of the possible rectangles. It was a real eye opener. Both Savita and I realized that had we not congressed, then this great insight would never have been shown to us or the rest of the class.

We had chosen a problem from the Math Makes Sense textbook and had done a KWC (Know, What the question is asking, and special Conditions) Chart to help students comprehend what the problem was asking. (See first picture)The problem that the students were working on was the following:

You want to make a rectangular garden with a perimeter of 24m. The garden must have the greatest possible area. What should the dimensions of the garden be?

The students had all worked on the possible perimeters and areas and several had choosen to share what their gardens would look like and what the dimensions would be. After we had a few responses the students were asked "Do we know which one has the greatest possible area?" and "Do we agree with it?" The children all agreed that they thought the 7m x 5m garden had the greatest area. When they were asked a third question of "How do you know" is where the conversation got intersting. (See second picture)

Some students said that they knew which one it was because it had the biggest area of all the gardens we had drawn. We then probed them with "Are you sure?" and in the crowd of nodds, one girl put up her hand and said:

I'm sure, because if you go to 6m x 6m then all you get is a square. And the conditions said that we had to have a rectangular garden. If you look at the numbers we have 11m x 1m, then 10m x 2 m.

At this point I prompted her more by asking her if there was a way we could write this out to prove that her answer was correct. The class came up with the idea of a chart and then we got to work making our chart and putting in the dimensions and the area. We also drew a 6m x 6m shape and got a square - just as predicted. The students then began to see a pattern between the dimensions. They also said that we didn't need to keep going because it didnt' matter which number came first because when we multiplied the two together we always got the same area.

Had we not taken the time to have the congress, we never would have known the deep level of understanding that this student had, or the connections to other mathematical concepts that the rest of the class was able to make. A huge lightbulb moment for all in the room.

Differentiated Instruction In Math

2010-01-14T09:03:00.000-05:00

In the math classroom, Differentiating Instruction is a key component of ensuring student success. We know that teaching through problem solving and using a three part lesson are ways to incorporate DI into our classroom, but what else can we use?

One of our FOS books clubs is studying the book "Good Questions: Great Ways to Differentiate Mathematics Instruction" by Marian Small (It is available from Nelson Education). The book breaks down the math into specific areas of: Number and Operation; Geometry; Measurement; Algebra; and Data Analysis and Probability. At the start of each chapter, there is a discussion on the "Big Ideas" for the strand, and then divides up the strand into the Grade Bands of K-Grade 2; Grades 3-5; and Grades 6-8.

At our last session, Melissa shared with us the problem that she did in her Grade 1/2 class, and the samples of student work. The question she gave them was "Here is one Tangram animal. Make your own tangram animal." How is this question differentiated? For weaker students, they could simply copy the animal that was provided. For students who needed more of a challenge, they now could create their own animals.

Some other good open questions from the book are:

K-2: Choose a type of shape. Tell as many things about it as you can.

3-5: Make a square on a geoboard. Move the elastic so that one corner is no longer a corner. What different shapes can you make?

6-8: A shape has a triangle for a cross-section. What could the shape be?

Welcome To Our Blog!

2009-12-16T11:32:00.000-05:00

Welcome to 2010!

It is hard to believe that just 10 short years ago we were all storing cases of water and canned goods "just in case" the power didn't work at the stroke of twelve.

This year, I am hoping to make math more accessible to you and your students. The purpose of this blog is to keep track of the weekly e-mail that I send to your schools, and to use it as a way to bring more to your teaching practice. I'm hoping to incorporate more pictures and videos into this blog which will give a more visual look to the math.

As always, i'm available to come into your classrooms and co-teach with you, help you work on teaching through problem solving, look at different ways of assessing student work, or any other area that you want support in. You can contact me via TEL or outlook.

I hope that 2010 will be the year you "Pick math. Choose math. Love math!"

Lesley