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Ways to Help a Student Learn How to Estimate Sums & Differences

In adult life, most people encounter situations where they need to come up with the sums or differences of addition or subtraction problems involving long numbers. But since we do not always have a calculator or a pen and paper handy, it is important to be able to at least come up with estimated solutions for these problems. Techniques exist that can help students develop the habit of rounding numbers up or down depending on the context, which is the key skill needed for estimation.
  1. Basics of Rounding

    • First, teach students the basics of rounding. In our base-10 system of mathematics, the general rule is that the numbers 1, 2, 3 and 4 all round down, whereas 5, 6, 7, 8 and 9 round up. Students may be puzzled by the fact that 5 rounds up instead of down --- if asked, respond that 5 is rounded up by custom, even though it could be rounded either way. Numbers are rounded up or down to a specific digit ending in zero. For example, if we were rounding the number 154 to the tens digit, it would round down to 150.

    Written Practice

    • Have students practice rounding numbers up and down and using the rounded figures to do addition and subtraction problems. At first, introduce the process through written work, wherein students will take problems like 351 - 109 (351 minus 109) and round them to the tens place, giving a difference of 240. Depending on the grade level and degree of comprehension, you can have them go on to rounding to the hundreds or thousands.

    Verbal Practice

    • Because estimation is a process that is meant principally to be used when you cannot write a problem down, the next method you should use is verbal practice. In this, you should give students spoken problems and ask them to come up with estimated answers. Students can also do this exercise with partners if you believe they are able to stay on task. The problems can be presented visually if need be, but it is preferable to have students perform the problems in their heads.

    Contextual Practice

    • Give students similar exercises, but this time frame the question in terms of real-world situations. For example, give them a grocery list with the prices of items and have them come up with an estimate for how much money will be needed. This is also a good way to make sure students understand where and to what extent estimation should be used. For example, if you round up prices to the nearest dollar, you will probably come up with a reasonably close answer to the actual total. But if you round up to ten dollars, your sum will be within a ballpark range of what you need but not nearly close enough -- which is very important when money is involved.

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