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.

Using A K-W-C Chart

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

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

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!

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