Have you had a chance to try the Sums of Consecutive Numbers problem with your students? If not, you might be wondering how you might launch the problem. I did not give specific ways to launch the problem in the video because of the wide range of learners that might be participating. After further reflection, I thought it might be worthwhile to share how I involved students in the problem.
I started the problem with a grade 3 class late last week. We began by talking about the Global Read Aloud project and what they enjoyed about it. Students said what they enjoyed most was talking with others about the book. After explaining that I wanted to do something similar with a math problem, the class was eager to get started! I shared the title of the problem "Sums of Consecutive Numbers" and asked students to tell me what they knew about "sums". The class quickly agreed that sums were answers to addition problems. Defining "consecutive" was a little more challenging but with the help of a dictionary, students soon agreed that consecutive numbers would be numbers that follow one another in sequence, such as on a number line.
After drawing a number line to use as a reference, we began to brainstorm possible answers. On a large chart, students were able to write their answers once they shared their idea and the class was in agreement that the example fit the rules of the problem.
After we brainstormed a few examples and I felt that students had a strong understanding of the problem, I encouraged students to explore the numbers on their own. Students received a chart for them to record their thinking individually. To begin, students were encouraged to copy the examples from the class chart.
While students were working, I circulated the room and asked questions about their strategies. Some students immediately saw a pattern with the odd numbers - noticing that any odd number could be made as the sum of two consecutive numbers. Other students tried using three or four addends and writing down the sum they discovered.
Students worked for about 15 minutes and then I stopped the class. We discussed our observations about the patterns and wrote them on a chart. I encouraged students to continue working on the problem and told them that they should not be limited to the 50 numbers on the chart. I asked students to continue adding to the chart as they noticed other patterns. I can't wait to check in this week to see what else they have added to the chart!
If you have been waiting for the moment to introduce this problem, I hope this helps you get started! The students were so engaged with this problem that they continued working during their indoor recess! Please ask questions or share how things are going on Twitter at #GETMath! I look forward to hearing from you!
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