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Estimating products

Topic Notes

In this lesson, we will learn:

  • How to estimate the answer to multiplication statements
  • The three methods for estimating products: estimation by rounding, estimation by clustering, and estimation with compatible numbers
  • How to check and compare your estimated products 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 for rounding numbers:
    • If the number to the right of the digit you are rounding to is ≥\geq 5, round UP; if the number is < 5, round DOWN
    • For mixed fractions, round to the nearest whole number: if the fraction part is ≥\geq 12\frac{1}{2}, round UP. If the fraction part is < 12\frac{1}{2}, round DOWN.

  • Three methods to estimate products are: estimation by rounding, estimation by clustering, and estimation with compatible numbers.

  • Estimation by Rounding:
    • 1. Round
    • Round each factor to its greatest place value
    • For mixed fractions, round to the nearest whole number
    2. Multiply the rounded factors
    • Multiplying mixed fractions requires converting back to improper fractions first

  • Estimation by Clustering:
    • 1. Round all the addends to the same place value
    2. Do all the estimates cluster around the same number?
    3. Multiply: [cluster number] × [number of addends]

  • Estimation with Compatible Numbers:
    • 1. Look at the denominator of the proper fraction (fraction that is <1)
    2. Look at the whole number in the mixed fraction
    3. Change the whole number to a “compatible” number
    • A compatible number is something that is close to your original number (i.e. 1-2 more or less), but it’s a multiple of the denominator
    4. Multiply, using cross cancellation!

  • You can compare the exact product and the estimated product to see how close they are
    • An underestimate happens when you round DOWN a factor; the estimated product is LESS than the exact product
    • An overestimate happens when you round UP a factor; the estimated product is MORE than the exact product