Earlier this week I wrote a question for my grade two classes to work on. I had decided to try an “equalizing” question with them, where they would have to use addition and subtraction to equalize two groups. The final draft of the question was this:
A farmer has 12 sheep in one pen and 28 sheep in another. He wants to move some sheep so both pens have the same number of sheep in them. How many does he need to move? How many sheep will be in each pen?
I had originally put different numbers into the problem. I thought about using 14 and 36, or 18 and 44. But in the end, I went with 12 and 28 knowing that a) the end number of sheep in each pen would be the “friendly” number 20, and b) that when students represented the number using ten frames or on a 100 dot array, they would see clearly the eight from one pen could be moved over to the eight “open spots” in the other pen.
Even with presenting this easier set of numbers, most of the students in both grade two classes that did the problem found it challenging. Some just wanted to add or subtract the two numbers and use the resulting sum or difference as the answer. Some split the 28 into two groups of 14, but thought they were done. I strongly encouraged the children to draw a representation of the sheep in the original pens and work from there. Though not all students were able to arrive at a solution in the time frame (in my Wednesday primary classes I have only 30 minutes with each class to set up the problem, let them work, and share solutions!) many did find at least one strategy that worked for them. The students also figured out during our discussion that the method of splitting the 28 sheep into the two pens would have worked had they gone on to split the 12 other sheep into the two pens as well. We had 5 good strategies shared/figured out even in our limited time frame.
If you do this problem with grade one students, I would recommend you present fewer sheep (say 8 and 14, or whatever combination you think your students can handle). For grade three students you might also try larger numbers, but make sure the students have some strategies in manipulating and/or representing numbers so they can be successful with the problem. Grade four and five students could be given a problem that has them equalizing with decimal numbers (so obviously sheep are out!).
It was clear to me as my students worked on the problem that more equalizing problems are needed to help them make sense of what is happening in such situations. And next year I will be starting earlier doing “equilizing” questions with my classes.