It is always interesting to me to ask children to apply what we've learned in our math books and class lessons. It is like getting a window into the students' minds - concepts that seem clear enough and easily understood when written one way can seem perplexing when they are asked to apply these concepts in a new way. Let me give you an example of today's "thinking problem". This was a lesson in applying place value concepts, logic, trial and error, and perseverance.
First of all, let me back up a bit and say that since the beginning of the year we've been talking about place value - knowing that the "value" of the number is dependent on where a digit is placed in a number. At this point, all of the students in my math group can order numbers from highest to lowest, can make models of numbers using base ten blocks, can draw models of numbers, can take a group of digits and make the highest and lowest numbers possible, etc. We've done countless hands-on activity and games, like the high number game, the guess/digit/place game and on and on.
Today, though, I threw a bit of a wrench into the mix by asking them to take all they knew about place value to do the following:
"Sam picked the numbers 2, 7. 5, 0, 6, 8. How should Sam arrange the numbers to get the largest sum? Write the numbers 2, 7, 5, 9, 6, and 8 in the boxes below and then find the sum. Explain how you know this is the largest sum that Sam can make with these numbers."
I honestly thought that they would find this "SO EASY". WELL. First of all, most children were not sure what the term "sum" meant. A quick review took care of that. Then there was a lot of head scratching, drawing, erasing, and hard work. I kept urging them all to keep trying, to persevere, to work through the problem logically.
You can see by the above example that many numbers were tried before this particular student finally came up with the correct answer. His explanation is getting close: "Well, 8 is more than 7 and so if I add 8 and 7 like 5 and 6 (and?) 0 and 2 so that's = 1612." This child was one of 3 or 4 children that struggled through and came up with the correct answer. Many children wanted to make the largest number (876 plus 520). We will talk more on Thursday about why this leads to the incorrect answer.