# Estimating sums

### Estimating sums

#### Lessons

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 $\geq \frac{1}{2}$ 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
• Introduction
Introduction to Estimating Sums:
a)
Example of estimating the sum of 1617 + 3898

b)
How to round mixed fractions

c)
Key terms for estimating sums

d)
Front-end estimation for sums

e)
Estimation by Rounding for sums

f)
Underestimating and overestimating sums

• 1.
Front-End Estimation of Sums
Estimate the sum using front-end estimation. Then, find the exact sum to check your answer.
a)
6895 + 2413 + 1878 =

b)
0.835 + 0.02 + 0.66 =

c)
36$\frac{3}{10}$ + 14$\frac{1}{2}$ + 27 $\frac{2}{5}$ =

• 2.
Estimating Sums by Rounding
Estimate the sum using estimation by rounding. Then, find the exact sum to check your answer
a)
3128 + 744 + 29 =

b)
3.78 + 0.94 + 5.261 =

c)
6$\frac{2}{9}$ + 9$\frac{3}{6}$ + 8$\frac{4}{7}$ + 3$\frac{1}{11}$ =

• 3.
Estimating Sums Word Problem - 1
A pirate finds a map that shows the route to some treasure. The instructions tell the pirate to go: 25.42 km North, then 61.3 km West, and finally 79.018 km North-East.

• About how many kilometers is the entire route to the treasure?
a)
Write the addition equation that represents this question.

b)
Use the front-end estimation method to estimate.

c)
Use the rounding estimation method to estimate.

d)
Calculate the exact answer.

• 4.
Estimating Sums Multiple Choice
Estimate the sum using multiple estimation methods. Then choose the best answer:

12$\frac{5}{8}$ + 11$\frac{4}{5}$ =

A. Less than 23
B. Between 23 and 24
C. Greater than 24

• 5.
Estimating Sums Word Problem - 2
This week, Elizabeth ran 3$\frac{1}{5}$ miles on the Monday, 7$\frac{3}{4}$ miles on Wednesday, and 5$\frac{3}{8}$ miles on Friday. About how many miles did she run in total for the week?
a)
Write the addition statement that represents the question.

b)
Use front-end estimation method to estimate.

c)
Use the rounding estimation method to estimate.

d)
Calculate the exact answer.