Chapter 3: Estimation and Computation

3.2 Strategies and Procedures for Estimation

3.2.1.1. Description of the Three Main Types of Estimation:

3.2.1.1.1. Estimating a quantity: Finding how many students, days, lunches, classes, and so on

3.2.1.1.2. Estimating a measure: Finding how much length, area, volume, time, and so on

3.2.1.1.3. Estimating an answer (Computational estimation): Finding a sum, difference, product, or quotient

3.2.2. Computational estimation techniques

3.2.2.1. Description of computational estimation: Computational estimation is a process for finding a number reasonably close to the exact answer for a calculation

3.2.2.2. Rounding

3.2.2.2.1. process of replacing a number or numbers in a calculation with the closest multiple of 10, 100, 1000, and so on

3.2.2.2.2. zero, one, two, three, four – round down

3.2.2.2.3. five, six, seven, eight, nine – round up

3.2.2.2.4. There are other rounding schemes – up on odd, down on even, and so on

3.2.2.2.5. Procedure for using the rounding technique

3.2.2.2.5.1. When you might use this technique: Use this technique when rounded numbers produce a calculation that can be done mentally

3.2.2.2.5.2. How to use this technique

3.2.2.2.5.2.1. Find the digit in the place value to which you want to round. This is the key digit.

3.2.2.2.5.2.2. Identify the digit in the place value to the right of the key digit

· If that digit is less than 5 round down – that is, keep the key digit and replace all digits to its right with zeros

· If that digit is 5 or greater, round up – that is, add one to the key digit and replace all digits to its right with zeros

3.2.2.2.6. See example 3.8 p. 134

3.2.2.2.7. Your turn p. 135: Do the practice and the reflect

3.2.2.3. Substitution of compatible numbers

3.2.2.3.1. replacing some or all of the numbers with numbers that are easy to compute mentally

3.2.2.3.2. Procedure for using the substitute compatible numbers technique

3.2.2.3.2.1. When you might use this technique: Use this technique if numbers close to the numbers in the original calculation would make the estimate easy to do mentally

3.2.2.3.2.2. How to use this technique

3.2.2.3.2.2.1. Identify the number or numbers in the original calculation that can be replaced by others to result in an estimate that is easy to do mentally

3.2.2.3.2.2.2. Calculate with the new numbers to obtain the estimate

3.2.2.3.3. See example 3.9 p. 136

3.2.2.3.4. Your turn p. 136: Do the practice and the reflect

3.2.2.3.5. See example 3.10 p. 136

3.2.2.3.6. Your turn p. 136: Do the practice and the reflect

3.2.2.4. Front-end estimation

3.2.2.4.1. calculating with the left most, or front end, digit of each number

3.2.2.4.2. Procedure for using the front end estimation technique

3.2.2.4.2.1. When you might use this technique: Use this technique when an estimate is needed quickly and a rough estimate is acceptable

3.2.2.4.2.2. How to use this technique

3.2.2.4.2.2.1. Assume that all digits except the leading or front end digit(s) in a calculation are zero

3.2.2.4.2.2.2. Do the calculation with the new numbers

3.2.2.4.2.2.3. If you want a closer estimate, adjust the first estimate by using other digits or numbers for those assumed to be zero and estimate again

3.2.2.4.3. See example 3.11 p. 137

3.2.2.4.4. Your turn p. 138: Do the practice and the reflect

3.2.2.5. Clustering

3.2.2.5.1. in some calculations, numbers seem to be about the same or cluster around a common number

3.2.2.5.2. Procedure for using the clustering technique

3.2.2.5.2.1. When you might use this technique: Use this technique to estimate sums when the addends in the calculation cluster around the same number. You can also use it in a similar manner for some products

3.2.2.5.2.2. How to use this technique

3.2.2.5.2.2.1. Identify the number that each of the addends is close to and that is easy to compute with mentally

3.2.2.5.2.2.2. Replace each addend with the same number

3.2.2.5.2.2.3. Use multiplication to estimate the sum for the original addition calculation

3.2.2.5.3. See example 3.12 p. 139

3.2.2.5.4. Your turn p. 139: Do the practice and the reflect

3.2.3. Choosing an estimation technique

3.2.3.1.1. range estimate – estimating that the exact answer is between two estimated numbers

3.2.3.1.2. mental calculations play a large role in estimation techniques

3.2.3.1.3. being able to apply the appropriate technique to a given situation is known as fluency

3.2.3.1.4. Your turn p. 141: Do the practice and the reflect