Using The Walls To Improve Students Strategies

Arpine's Grade 3 class was about a week into their unit on Patterning and Algebra.  She was finding that the students were always using pictures as a way to communicate their thinking.  They had been exposed to different strategies (like using a number line) but were always going back to drawing a picture.  Not only is the strategy not varied, it also was taking them a lot of time to complete their work!

As she headed to her class one day she noticed the work of Brian's Grade 6 class posted on the wall.  She stopped and had a look at what they were doing.  They too were doing Patterning but had shown different strategies in their answers.  So she decided to take her class down the hall to look at the wall before she gave them their next problem.  This is what they saw:

The "Wall" of student work.

A brief explanation of what they achieved in the lesson.

One sample of how the students found the pattern.

A second example.

When the students went back to their class something happened.  They wanted to do what the Grade 6 students did.  They now had seen different ways to find patterns, and wanted to demonstrate their thinking in a different way.  Here is a sample of the work Arpine was getting before looking at the "wall"

Here are samples of some of the different strategies that she go after the walk:

These students decided to try a number line.

This student attempted to use tally marks to help show their thinking.

To consolidate this lesson, they then created an anchor chart with the strategies that they could now use to help them when they solve a problem.  Even though they choose not to use some of these strategies, they remembered seeing them done by the Grade 6's and wanted to include them for future use.



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.

Looking Critically At A Rich Assessment Task

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.



Anchor Charts - Problem Solving

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.