Estimating Differences

Estimating Differences

Lessons

In this lesson, we will learn:

  • How to estimate the answer to subtraction statements
  • The two methods for estimating differences: front-end estimation and estimation by rounding
  • What to do if you get an estimated difference of zeros
  • How to check and compare your estimated differences with the exact answer

Notes:

  • An estimation is a rough calculation of what the exact answer could be around. It is less exact but easier (faster) to calculate!

  • When estimating, it is helpful to remember the rules on how to round numbers. If the number to the right (of what you are rounding to) is:
    • Greater than 5 ( \geq 5), round UP
    • Less than 5 (< 5), round DOWN
    • For mixed fractions, look at the fraction portion to round to the nearest whole number. If the fraction is \geq 12\frac{1}{2}, round UP. If the fraction is < 12\frac{1}{2} , round DOWN.

  • Two methods to estimate differences: front-end estimation and estimation by rounding
  • Front-End Estimation:
  • 1. Subtract the front digits
    • The front digit is the greatest place value out of all your addends
    • Subtracting mixed fractions: subtract the whole number parts only
    2. Write zeroes
    • All the other digits of the answer become zero; skip this step for mixed fractions
    • *Note: you do NOT need to adjust the back digits for estimating differences; you only need to adjust when estimating sums

  • Estimation by Rounding:
  • 1. Round 
    • Round to the greatest place value of the smallest number out of all your addends
    • If you are subtracting mixed fractions, round to the nearest whole number
    2. Subtract the rounded numbers
    • If you get an estimated difference of zero, you must start over by rounding to the next place value smaller (to the right)
  • Introduction
    Introduction to Estimating Differences:
    a)
    Example of estimating the difference of 2314 - 1598

    b)
    Key concepts for estimating differences and rounding review

    c)
    Front-end estimation for differences

    d)
    Estimation by rounding for differences


  • 1.
    Front-End Estimation of Differences
    Estimate the difference using front-end estimation. Then, find the exact difference to check your answer.
    a)
    7853 - 794 =

    b)
    0.665 - 0.018 =

    c)
    2838\frac{3}{8} - 5510\frac{5}{10} =


  • 2.
    Estimating Differences by Rounding
    Estimate the difference using estimation by rounding. Then, find the exact difference to check your answer.
    a)
    9876 - 714 =

    b)
    5329 - 5276 =

    c)
    4.41 - 0.589 =

    d)
    69.372 - 67.981 =

    e)
    1723\frac{2}{3} - 959\frac{5}{9} =

    f)
    5316\frac{1}{6} - 3224\frac{2}{4} =


  • 3.
    Estimating Differences Word Problem - 1
    Rachel has 152.6 cm (length) of wrapping paper, but she only needs 18.934 cm to wrap a small gift box. About how much wrapping paper will she have left over?

  • 4.
    Estimating Differences Word Problem - 2
    Stevie bought a new activity tracker. His goal is to walk 21,000 steps each week. His activity tracker shows his steps from Monday to Thursday so far:

    • Monday: 4,152 steps
    • Tuesday: 3,607 steps
    • Wednesday: 2,892 steps
    • Thursday: 4,368 steps

    About how many more steps does he have to walk for the rest of the week to reach his goal?
    a)
    Using front-end estimation, about how many steps has he walked already? Then, how many more steps does he need to walk to reach his goal?

    b)
    Using estimation by rounding, about how many steps has he walked already? Then, how many more steps does he need to walk to reach his goal?

    c)
    Calculate the exact number of steps Stevie still has to walk to reach his goal.

    d)
    Using only subtraction, estimate how many more steps Stevie needs to walk with both front-end and rounding estimation methods.


  • 5.
    Estimating Differences Multiple Choice
    Estimate the difference using multiple estimation methods. Then choose the best answer:

    21111\frac{1}{11} - 1378\frac{7}{8} =

    A. Less than 7
    B. Between 7 and 8
    C. Greater than 8

  • 6.
    Estimating Differences Word Problem - 2
    Use different estimation methods to estimate the difference. Which method gave a more accurate estimate and why?

    829\frac{2}{9} - 712\frac{1}{2} =