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.
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