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 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
  • 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)
    36310\frac{3}{10} + 1412\frac{1}{2} + 27 25\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)
    629\frac{2}{9} + 936\frac{3}{6} + 847\frac{4}{7} + 3111\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:

    1258\frac{5}{8} + 1145\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 315\frac{1}{5} miles on the Monday, 734\frac{3}{4} miles on Wednesday, and 538\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.