Problem Solving Task

The learning task for this problem is to individually solve the problem to track the path of a boy as he collects his friends on his side of the block. The students have to solve the problem to identify how many houses there are on one side of the street. The students have been working on problem solving in different contexts such as time elapse problems. I think the big idea of this problem would be to be able to track a path backwards and forwards. Instead of just having this problem be add 5, subtract 2, add 13 subtract 1. The problem puts a math concept into a real life situation.

2 effective ways to approach this problem is to draw a picture to help represent the word problem. By drawing a number line with the starting point being the first house on the block and the ending point being the last house on the block, it allows the students to follow the path of the person picking up his friends. Another possible effective way to approach this problem is for the teacher to ask questions like, what house do we start with? What does down the hill mean versus up the hill? Would it be easier if we were able to follow the path in which the person is picking up all his friends? What kind of picture can we draw/use to help us visualize that? One possible student approach (one that majority of my students thought) was to add all the numbers in the problem together. The last sentence in the problem ask how many houses, so the students assumed they  had to add. Another possible student approach would be to draw pictures of houses on their paper. Some of my students drew pictures of houses to represent the houses on the side of the block, but the problem was that the houses are not all in one line. This makes it hard to follow a path because they are in multiple lines.

This student decided to draw a number line for the image and each "notch" he drew on the number line represented a house. He followed the steps in which the word problem asked and labeled each notch with the first letter of the neighbor's name. As he went through the appropriate path he made sure to label on top the number house so he can keep track of how many houses there are. When he got to the last step he was able to count from the 4th house up 13 houses to get to the last house on the block. He then was able to label on top the number of houses and got to the correct answer of 17. Instead of counting to then number 13 he knew to count up 13 houses to 17 instead of stopping at the 13th house. One thing about his mathematical thinking that comes through is how he is able to follow a path by understanding directions step by step. He took time to analyze the direction of what way the person is going on his block. It also shows that he was able demonstrate that there are multiple directions that you can move on the number line block as well as a number line in general. To advance his thinking I would give him other word problems that included the same concept but with a different real world situation. In this context I worked with students in a small group, but I would be interested to see if this student could accomplish this task without any teacher support.