When I work with elementary students, they are often confused when they reach the estimation unit, and so are their parents. They get hung up on the skill rather than understanding why the concept is even relevant. Students prefer to find the exact answer because estimating seems like extra work and, developmentally, estimating is a challenging task for young children. According to John A. Van de Walle, a math education researcher, estimation is a higher-level skill that requires students to be able to conceptualize and mentally manipulate numbers. Instead of just adding or subtracting columns, they actually have to analyze each number in the problem and make a determination as to round up or down depending on that “magic number” [which is 5]. Then the extra challenge is whether to round to the nearest one, ten, hundred or thousand. Or maybe it’s supposed to be front end estimation. What’s the difference? Who cares? Why would anyone other than a math teacher need to understand this anyway?
The Common Core Standards include estimation skills for every grade level. We’re interested in using language with children that includes such words and phrases as about, close, just about, a little more (or less) than, and between. From a 10,000 foot view, we want our students to be able to do the following mathematically:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
In real life, estimation is part of our everyday experience. When you’re shopping in the grocery store and trying to stay with in a budget, for example, you estimate the cost of the items you put in your cart to keep a running total in your head. When you’re purchasing tickets for a group of people or splitting the cost of dinner between 8 friends, we estimate for ease. Contractors or consultants often work in a world of estimates. Rarely do we know all the facts up front and there could be many variables at play. Therefore, a ballpark number is perfectly sufficient. Annie Murphy Paul addresses this particular issue in her recent TIME magazine article called “Why Guessing is Undervalued”.
For students, estimating is an important skill. First and foremost, we want students to be able to determine the reasonableness of their answer. Without estimation skills, students aren’t able to determine if their answer is within a reasonable range. This inability to reason causes them to make computational errors without it even being on their radar. For example, if a student is asked to multiply 523 x 34 and they arrive at a product of 177,820, we want students to independently recognize that 177,820 couldn’t possibly be a reasonable answer. If they use the estimation of 500 x 30 to arrive at 15,000, they quickly realize that their place value is way off and that their work needs to be redone.
Second, we want students to be able to use mental math to more quickly arrive at a reasonable ballpark solution. When I worked as a talent development and learning specialist at Time Warner, I remember sitting in meetings with marketers and finance executives as they kicked around cost estimates for various projects. The leaders in the room could compute estimates quickly and mentally. They didn’t need calculators to find reasonable percentages or cost ranges. They could look at the data and mentally compute estimates that were sufficient for moving the agenda forward. It was only afterwards that they would build their Excel models and determine exact costs and time lines. If we want to teach our children to be successful in business, we need to promote strong estimation skills.
Third, we want students to use estimation beyond adding, subtracting, multiplying and dividing. We also want students to be able to reasonably estimate time and distances. About how long does it take for us to get from Point A to Point B? Approximately what time will it be when you finish all of your homework? About how many miles is a walk from The Guggenheim Museum to the Sony Technology Lab if 20 blocks is about a mile. Time estimation skills are an important part of executive functioning, and we want students to develop a sense of estimating reasonable time for both short and long range planning.
When teaching computational estimation to elementary and middle school students, there are at least five different strategies to consider depending on the context. It’s important to teach all five so that students develop a repertoire of strategies for various situations. But most importantly, we want students to understand why estimating is valuable before getting caught up in the minutiae of the skill, and we certainly want students to understand that estimation does not replace the need to come up with accurate answers. What we’re really talking about is teaching students to be critical thinkers and to understand what’s being asked of them.
- Rounding whole numbers
- Estimating a sum
- Front end estimation
- Compatible numbers
- Cluster estimation