Estimating sums

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

• 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 $\geq \frac{1}{2}$ round UP; if the fraction is < $\frac{1}{2}$ 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