Starting A Unit - What Do They Know: Part Two

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

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

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

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

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

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

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!!!