Estimation, Exact Numbers, and Mental Math
We are in the middle of an arithmetic unit on adding and subtracting large numbers. There is a lot of review in this unit and we are moving at a fairly good speed. While the unit focuses on addition and subtraction, I am constantly tying some of the strategies, especially for mental math, to multiplication and division. This is a part of a greater effort this year to integrate the four main operations into all of our math curriculum instead of using distinctly separate units of study. (We still focus on one operation at a time but we do a lot of cross-over and spiraling as we do it.)
Today we were discussing mental math strategies to add three-digit numbers. For example, if a fruit stand sold 397 bananas and 412 peaches and you want to figure out how much fruit was sold in all, you can solve this with mental math by subtracting 3 from the 412 and add it to the 397. Then you have 400 and 409, which easily sums to 809. Interestingly enough, though, when I asked my students to share what mental math strategies they used to solve the problem, most just visualised the standard vertical addition algorithm (add the ones, add the tens, and the hundreds).
Then we moved onto a discussion of when we would need to find an exact answer and when an estimate would be appropriate. As an example, I asked my students how many of them had been to Chicago. Everyone raised their hand, which actually surprised me. Then I asked how far away it is. One student said it was about three hours away, another said it was about two and a half hours away, and a third said it was two hours away. I admitted that all three were great examples of estimation, but then I explained that the question was how far, not about how long it would take to travel there. That being said, most people would rather have an approximate travel time over a specific distance. We wrapped up the math lesson with independent practice. We will continue to visit these concepts over the next few weeks, but I feel confident that my class understands when to estimate and when to find an exact number, as well as how to apply these skills when using mental math.