Estimation

There are 3 types of estimation that are asked of students: 

• Measurement estimation: finding an approximate measure without making an exact measurement.
• Quantity estimation: finding an approximate number of items in a collection. 
• Computational estimation: finding a number that is an approximation of a computation that we cannot or do not wish to determine exactly.

Measurement estimation: 

When students don’t yet have a strong sense of a measure, such as the duration of a second, a minute, or an hour, the length of an inch or a meter, or the heft of a pound, their estimates will be more like guesses. As they practice estimating and then reflect on their estimate, they will develop this sense and their estimates will become more reasonable. When teaching estimation, it's good to avoid using the term “guess”; instead, use the words “about” or “approximately” when asking students to estimate.

Quantity estimation 

is similar to measurement estimation. The size of the item in a collection and the size of the collection both contribute to making a good estimate of the number of items in the collection. As with measurement estimation, students benefit from repeated opportunities to estimate and then reflect on the accuracy of their estimate. 

Computational estimation

 is an important math strategy and should be an integral part of instruction and class work. Its importance grows in upper elementary and beyond as students work with rational numbers and complex topics. When we do not need an exact answer we can use an estimate. We also estimate to give ourselves a ballpark answer as a double check that our exact answer is reasonable. How good of an estimate we need – how close it should be to the actual computation – depends on context. 

The goal of computational estimation is to be able to flexibly and quickly produce an approximate result that will work for the situation and give a sense of reasonableness.

Good estimators tend to employ a variety of computational strategies that have developed over time. When teaching estimation, it is important to:

• Use real examples of estimation: comparative shopping, adding up distances in planning a trip, etc.
• Use the language of estimation: such as about, close, just about, a little, etc.
• Accept a range of estimates and offer a range as an option: ask students for an estimate that is way too high and one that is way too low.
• Emphasize that there is no one correct or "winning" estimate: There is a trade-off between how easily an estimate is made and how close it is to the actual computation.
• Focus on flexible methods, not answers: the primary goal is to help students develop strategies for making estimates quickly.

Estimation 180 is a website hosted by Andrew Stadel that has great resources for building number sense in middle school using estimation problems.