# Estimating sums #### All in One Place

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##### Intros
###### Lessons
1. Introduction to Estimating Sums:
2. Example of estimating the sum of 1617 + 3898
3. How to round mixed fractions
4. Key terms for estimating sums
5. Front-end estimation for sums
6. Estimation by Rounding for sums
7. Underestimating and overestimating sums
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##### Examples
###### Lessons
1. Front-End Estimation of Sums
Estimate the sum using front-end estimation. Then, find the exact sum to check your answer.
1. 6895 + 2413 + 1878 =
2. 0.835 + 0.02 + 0.66 =
3. 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
1. 3128 + 744 + 29 =
2. 3.78 + 0.94 + 5.261 =
3. 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?
1. Write the addition equation that represents this question.
2. Use the front-end estimation method to estimate.
3. Use the rounding estimation method to estimate.
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
1. 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?
1. Write the addition statement that represents the question.
2. Use front-end estimation method to estimate.
3. Use the rounding estimation method to estimate.
###### Topic Notes

In this lesson, we will learn:

• 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)
2. Write zeroes
• All the other digits of the answer become zero; skip this step for mixed fractions