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