I often give my math homework in a "problem of the day" format. I draw a lot of the problems from Think About It! Primary Math Problems of the Day by Marcy Cook, published by Creative Publications. There are different kinds of problems. Some involve estimation. Last week students were asked to estimate how many of our math binders it would take to make a stack 1 meter high. On Fridays we review the homework as a group, sharing answers and strategies. It's a great time for the "math talk" that both helps individual students learn to put math thinking into words and gives students a chance to hear other students' ideas to broaden their perspectives.
The math binder estimation problem sparked a lot of discussion. First I asked, as I often do, what information can help us make a smart guess? Answers included how long a meter is and how thick a math binder is. Then we pulled out a meter stick and tackled the problem of how to find the actual amount. As we stacked the binders we could see that even if we got all the other math groups' binders, we wouldn't have enough binders to get to a meter. Several students showed us their ideas of what we could do. One pointed out that five binders reached the 10 centimeter mark. He explained that there are 100 centimeters in a meter, so 10 groups of 5 would be 50. Another pointed out that 10 binders were 17 cm. and she said we could add by 17's until we got to 100 (though we got to 102 rather than 100 even.) We used both ways and discovered we came up with 2 different answers. What was going on? Several students then recognized that the binders were thicker on one side, so how we stacked them effected the outcome. It was a lively math investigation.
The other problem from this week that sparked a lot of interest was the one that asked how many legs were on 4 octopi. Students were asked to write an equation to represent the problem and answer. Several students volunteered to write their equations on the board, and we talked about the different equations. Two people added up 4 eights, but one got 31 and the other got 32, so we all checked the math. Several had used multiplication equations, and we agreed that 4 X 8= 32 and 8 X 4= 32 were both correct and could both represent the problem. One person had 16 + 16= 32 and a classmate suggested an additional equation of 8 + 8= 16 would make the connection between that equation and the problem clearer.
