Elementary school students are required to learn how to estimate math problems mentally and will probably use this skill throughout their middle school and high school careers. There are different methods for estimation that are useful for different types of problems. The three most useful methods are the rounding, front-end and clustering methods.
Rounding is one common method used for estimating. Determine the place value to use for the particular problem you want to estimate. For example, if you wanted to estimate the total cost of several different grocery items, you would want to round to the nearest tens place because it is money. If working with extremely large numbers, you might want to round to the nearest one million. Round up by one if the digit to the left of the digit you're rounding to is five or larger. Round down by one if it is four or less. For example, if you are rounding to the nearest 10 and your number is 33, you would round to 30. Now that your numbers end in zero, you can easily do mental math to solve the problem, whether that requires adding, subtracting, multiplying or dividing.
If all the numbers in the problem contain the same number of digits, you can use the front-end method of estimation. Add up the first digit of each number in the problem, without rounding them. For example, if you need to estimate the value of 3,293 + 4,432 + 6,191 you would add 3 + 4 + 6 = 13. Modify your answer by adding zeroes to have the same number of digits in the numbers. In this example, there are four digits, so you would add two zeroes and end up with an estimation of 1,300.
To use the clustering method of estimation, find the best common number that ends in zero that the numbers in your problem cluster around. For example, you might have to add the numbers 29 plus 33 plus 27 plus 28 plus 35. All the numbers seem to cluster around 30. Substitute the cluster number, in this case 30, for each number. You can now use mental math to determine that 30 + 30 + 30 + 30 + 30 gives you an estimation of 150.
Uses of Estimation in Mathematics
Estimation is used in mathematics before you do a problem to help you solve it faster and easier, and after you solve a problem to help you determine whether your answer is reasonable. Estimation is also useful when you only need an approximate amount instead of a precise value.
- "Harcourt Math"; Evan Maletsky et al.; 2002
- Manitoma: Mental Math and Estimation
- Basic Mathematics: Cluster Estimation
- Math: Estimating and Rounding Decimals
About the Author
Lindsay Haskell began writing fiction and nonfiction in 2008. Her debut novel, "Grace," is to be published in January 2011. Having lived in five different countries and traveled across five continents, Haskell specializes in Third World social and political issues, with a concentration in the Darfur conflict. She is currently a first-year student at Wellesley College studying history, Africana studies and English.