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Estimating sums

Topic Notes

In this lesson, we will learn:

  • How to estimate the answer to addition statements
  • The two methods for estimating sums: front-end estimation and estimation by rounding
  • How to check and compare your estimated sums with the exact answer

Notes:

  • An estimation is a rough calculation (or guess) of what the exact answer could be around.
    • We use the symbol ≈\approx when estimating; it means “about equal to”
    • An estimation is less exact, but it’s easier (faster) to calculate

  • When estimating, it is helpful to remember how to round numbers
    • You can round to any place value by:
      • Keeping all the bigger place values (to its left) and fill in all the smaller place values (to its right) with zeroes.
      • Looking at the number in the smaller place value (to its right).
      • If that number is 5 or bigger (≥ \geq 5), round UP.
      • If that number is 4 or smaller (< 5), round DOWN. (keep the same value in that digit)
    • For a mixed fraction, round to the nearest whole number by looking at the fraction portion. If the fraction is ≥12 \geq \frac{1}{2} round UP; if the fraction is < 12\frac{1}{2} round DOWN

  • Two methods to estimate sums: frond-end estimation and estimation by rounding
  • Front-End Estimation:

    • 1. Add the front digits
    • The front digit is the greatest place value out of all your addends (ex. only thousands column; only hundreds column)
    • Adding mixed fractions: add the whole number parts only
    2. Write zeroes
    • All the other digits of the answer become zero; skip this step for mixed fractions
    3. Adjust the estimate
    • If the back digits can be grouped together to make a group of ten (i.e. one front digit), add to the front digit estimate
    • If you are adding mixed fractions, see if the fraction portions can be added to make at least one more whole; if so, add to the estimate
  • Estimation by Rounding:

    • 1. Round
    • Round to the greatest place value of the smallest number out of all your addends
    • If you are adding mixed fractions, round to the nearest whole number
    2. Add the rounded numbers

  • You can compare the exact sum and the estimated sum to see how close they are
    • An underestimate happens when you round DOWN the addends; the estimated sum is LESS than the exact sum
    • An overestimate happens when you round UP the addends; the estimated sum is MORE than the exact sum