Last week, I wrote about the importance of estimation skills and I promised details on how to practice estimating in different ways. The simple answer is simply to practice whenever you get the chance! Here are some ideas and resources for when and how to do that.
Any time you are working on a math problem with children, ask them to estimate the answer before you calculate a precise answer. A good way to do this is to use the "Goldilocks method". Come up with one answer you know is too high, one answer you know is too low, and then an answer that you think is about right. Then, after you have done your calculations go back and compare the answer to the estimate. This is where you will learn to ground your calculations in mathematical and physical reality. If there is a big discrepancy, then you challenge is to figure out why. Is there an error in your calculation? Was your estimate unrealistic? What should you change in order to get a more precise and accurate result?
When you’re out for a walk or drive, take a photo or two of large groups of objects. A meadow full of flowers, a flock of birds, or a stand of trees will all work. At home, look at the photo and try to estimate how many of your object there are. Wikimedia Commons or Google Image search can also provide you with great photos. Here’s one to get you started.
How many trees?
Here is a great video about ways to estimate objects that you can't easily measure.
Estimation180 is a brilliant source of estimation problems. Each day's problem includes a photo with something to estimate and then a reveal that shows the answer. There are some resources and handouts available on the website which I encourage you to check out, but you don't need to overcomplicate this activity.
Would You Rather is another wonderful website full of easily accessible math problems. For each problem, the goal is to choose which of two options you'd prefer and then justify it with math. Not all the problems encourage estimation, but many require it. For example, here's a great problem: Would you rather have 500 grams of quarters or 1 kilogram of nickels?.
As you start paying attention to estimation, you'll begin seeing estimation questions everywhere. For example, as I write this, I am sitting on my rooftop deck. I see three airplanes on final approach to the airport, and I'm wondering if I can estimate how far apart they are. There are also three very tall radio towers in my view. How tall are they? I don't know how far away they are, so I'd have to make some pretty big guesses. I might have more luck estimating the height of the church across the street. I can also hear occasional traffic. How many cars go by in an hour? How does that change at different times?
If you read any form of news or non-fiction with your children, stop and consider any numerical claims. Estimate the implications of these claims for yourself. Are they realistic? What do you need to know in order to make a reasonable estimate?
You may notice that answering these types of problems well requires more than just guessing. In fact, in many cases, it requires some sophisticated number sense: frequently you need to multiply or divide to go from a reference measure to an estimate. You may end up with fractional units, and then you need to decide whether those fractions are relevant. This is part of the power of estimation!
PARENT COACHING
Need help supporting your child’s estimation skills? I can help! I now offer coaching for parents. During these Zoom sessions, we will explore your particular situation exclusively, and come up with a plan for your next steps. Sign up today!