Estimating sums

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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. 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
    1. 3128 + 744 + 29 =
    2. 3.78 + 0.94 + 5.261 =
    3. 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?
    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. 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
    1. 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?
      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.
      4. Calculate the exact answer.
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    Topic Notes
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    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 β‰ˆ\approx when estimating; it means β€œabout 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 (β‰₯ \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 β‰₯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