Can I just reiterate how much I love to watch my young students problem solve? Seeing those wheels spin is so fun. So today I posed the following question: "How many dozen eggs do I need to buy for everyone in the class to dye 5 eggs? Will there be any leftover eggs?" Here is a look at what my students started doing. I'm not sure why the 120 Chart was the math tool of choice today, but everyone was using it.

I love the way this student realized that he could draw a line down the middle and have 5 on each side. He is trying to count each set of five in the margins so he knows when he has 5 eggs for all 26 students. 

This student is drawing a line after 26 because he wants to stop his counting after the 26th student. He is drawing 5 dots in each box to represent 5 eggs per student. He is counting up by ones as he draws them. 

Watching his neighbor has given this student an idea on how to solve this problem. I love to see and hear this kind of collaboration between students. 

She is drawing a box around each set of 5 eggs. Notice at the top of her chart she wrote 26 to remind herself that we have 26 students. 

When this student got to the bottom of the 120 Chart she realized she needed more numbers. She looked at how her neighbor had added a second chart and decided to just add her own numbers at the bottom instead. She missed the number 121, but we fixed that together. 

Notice that he added another chart on and renumbered it. He knew we would need 130 eggs, but he's now trying to figure out how many dozen that would be. I loved when he looked up at me and said, "Can I just write on the table?" He didn't want to stop for a paper and pencil and he didn't want to forget 130. Look at the lines he is putting after 24, 36, 48 and 60. He is marking off each dozen. With just a little more time this student would have been the first to solve it. Unfortunately we can't hold up the lunch line by being late. 
Does it matter that no one got the complete answer before lunch? I don't think so. I think the process matters more than the correct answer. Watching them try and then try again, or talk with a friend to figure out a way to solve it is far more rewarding than seeing everyone with an answer. Math is more about process and these students are learning to problem solve. And problem solving is a lifelong skill worth a great deal. To quote one student, "I didn't get the answer, but I really learned something." I'm glad he learned something and if I buy 11 dozen we will have 2 eggs leftover.
(If you are looking for problems such as this to use with your students in grades 1 and 2, you might want to check out my
Math Journaling and Problem Solving product at TpT or
TN.)
The process is so important! Thanks for sharing.
ReplyDeleteTara
The Math Maniac