| Adults use rounding and estimation in their | | | | following the rounding rules can be |
| everyday lives. They approximate the | | | | problematic in estimation, consider the |
| temperature, the cost of items, the time, and | | | | question 7359 divided by 82. The first |
| even their age. Consider this | | | | difficulty is deciding what place to round |
| conversation:"How much did it cost to fix | | | | to. Let's say that the student decides to |
| your car?""Six hundred bucks!"Without any | | | | round to the nearest hundred in the first |
| words such as: about, approximately, around, | | | | number and the nearest ten in the second |
| roughly, or nearly, it can be assumed that | | | | number, thus the question is now 7400 divided |
| the second person rounded the actual cost. | | | | by 80. At this point some students might |
| Before they had their car fixed, they | | | | resort to a calculator, others to long |
| probably received an estimated cost of the | | | | division, and others might stare confusedly |
| repair from the shop. Adults experience | | | | at their paper. An adult with more intuitive |
| rounding and estimation skills in their daily | | | | sense might look at the numbers and recognize |
| lives. Children need to learn these important | | | | that if she rounded 7359 to 7200, it would be |
| skills partly because they often hear | | | | fairly simple to divide by 80 (because 72 |
| estimation and use estimation, but more | | | | divided by 8 is easy).Many people develop an |
| importantly, it helps to solidify math | | | | ability to estimate both by following the |
| learning by teaching them the idea of | | | | rules and by breaking the rules of rounding. |
| reasonableness.Even though rounding and | | | | Many children need to be taught these skills, |
| estimating are related, there is a | | | | so there is a genuine purpose to their |
| significant difference. Rounding involves | | | | estimation rather than just another question |
| converting a known number into a number that | | | | to answer. Estimation should be thought of as |
| is easier to use. Estimation is an educated | | | | a tool to quickly determine whether an answer |
| guess of what a number should be without | | | | is reasonable or not. One way of teaching |
| knowing the actual number. In the | | | | estimation for this purpose is by allowing |
| conversation above, it is unlikely that the | | | | students to break the rounding rules and find |
| second person remembered the actual price of | | | | an easy question that they can do in their |
| the bill; they likely rounded the number at | | | | head. In the question 3564 - 2801, rounding |
| the time, so they could better remember | | | | to the nearest hundred results in 3600 - |
| it.Children usually learn rounding as an | | | | 2800, but 3700 - 2700 is much easier to |
| explicit skill, often with the purpose of | | | | handle, and it is not so far off the real |
| estimating the answers to math questions. | | | | answer. If the purpose of estimating was to |
| They commonly use estimation to check the | | | | get as close to the real answer as possible, |
| reasonableness of an answer by either | | | | you might as well use a calculator to check |
| estimating ahead of time or after they have | | | | your answer instead.Parents can help develop |
| completed the question. Students run into | | | | students' estimation skills by regularly |
| difficulty when estimating because they don't | | | | asking real questions. For instance, ask them |
| have the intuitive sense that adults do to | | | | how long they think it will take to get to |
| break the rules.For the uninitiated, the idea | | | | hockey practice (time), have them add up the |
| of rounding is fairly simple - decide where | | | | cost of the groceries as you are shopping |
| to round the number (e.g. the hundreds | | | | (money), get them to count the number of |
| place), either keep the digit at the rounding | | | | people in one area of the mall and have them |
| place the same or round it up, and replace | | | | estimate how many people are in the whole |
| the digits to the right with zeros. The | | | | mall (multiplication or addition). Educators |
| decision to keep the digit the same or to | | | | should make estimation a regular part of the |
| round it up is based on everything that comes | | | | problem solving process. In a science |
| after the digit. If it is less than half, the | | | | investigation, students make hypotheses and |
| digit remains the same; if it is greater than | | | | predictions, so why not make an estimate in a |
| half, the digit is increased by one; if it is | | | | math problem? Students can develop their |
| exactly half, the digit remains the same if | | | | estimation skills by answering questions on |
| it is even and increases by one if it is odd. | | | | worksheets and comparing their estimated |
| For example, to round 638 to the nearest | | | | answers to the actual answers. has thousands |
| hundred, you would base your decision on the | | | | of worksheets with answer keys that you could |
| "38" portion of the number. Since it is less | | | | use for this purpose.Remember these rules for |
| than half (50), the digit in the hundreds | | | | estimation: (i) KISS - keep it simple silly, |
| place remains the same, and the 38 is changed | | | | (ii) break the rounding rules if necessary, |
| to zeros, so the rounded number is 600. If | | | | (iii) ensure students see a purpose for |
| the question is to round 7500 to the nearest | | | | estimation, (iv) give students a lot of |
| thousand, you would round up to 8000. 8500 | | | | practice and experience with estimation and |
| also rounds to 8000, but 8501 rounds to 9000. | | | | rounding, (v) include estimation in problem |
| Hopefully, this illustrates that rounding | | | | solving and other daily math work. The main |
| follows a strict set of rules that often | | | | rule for parents and teachers: support your |
| cause difficulties for children in | | | | students and be flexible! |
| estimation.To give you an idea of how | | | | |