Goal: Think like a mathematician! Identify quantities and relationships in problem situations.
Two thirds of the students in Parkview Elementary School wear something red during the last School Spirit Day. Of the students wearing something red, half of them were wearing red hats. Of the students wearing red hats, two thirds of them are boys. 53 girls were wearing red hats. [How many students are in Parkview Elementary School?]
Source: Noetic Learning LLC
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I did this as my second task for Capturing Quantities, so my students had some experience with the routine at this point. I did edit the task to be our middle school name changed the color to purple, and made it purple shirts (we don’t allow hats!) to make it more relevant. I had the line stating that 53 girls wore red hats which led to many to calculate quantities instead of drawing diagrams, so I removed it after the first two sections. The students in the last two sections did better with diagrams. I could see that students were using the “I can count the number of” language more this time. They also worked to find “hidden relationships”, such as 1/3 of the students of the students wore purple shirts. Hidden relationships had come up in the first problem we did. I also noticed students trying diagrams that looked similar to ones they had seen the first time, especially among among students who had trouble the first time. There are several beginner ELL students in one section. I gave the problem to the teacher ahead of time, and she had previewed it with them. I ended up using the diagram on of them created which helped them feel more a part of the process.
This was third task my students completed, so they were also familiar the routine. My students used the 53 and automatically began solving. I redirected them to draw a diagram to represent/show the important information and to include the rest of the information in the problem as they were only solving for the number of students wearing hats. Since I have such a small group- 6 students- I am able to share all of their diagrams and they have engaged in great conversations about each others work and gain a stronger understanding of the task. I was excited to see that in their reflections students realized that they needed to really breakdown a problem and focus on all of the information, not just the quantities, but also the relationships. One students reflected that, “when looking for quantities and relationships in a word problem, I learned to read a problem over and over again.” This was an easy way to connect back to the Three Reads Routine again and remind students to use these practices in the math classroom.