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
- 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 5, round UP; if the number is < 5, round DOWN
- For mixed fractions, round to the nearest whole number: if the fraction part is , round UP. If the fraction part is < , round DOWN.
- Three methods to estimate products are: estimation by rounding, estimation by clustering, and estimation with compatible numbers.
- Estimation by Rounding:
2. Multiply the rounded factors
- Round each factor to its greatest place value
- For mixed fractions, round to the nearest whole number
- 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
4. Multiply, using cross cancellation!
- 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
- 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