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Remember the goal of rounding is to be able to calculate the problem easily and quickly. It is different from truncating because with rounding you have a choice to make. Imagine the number 6,834 being on a rope and standing between the number 6,000 and 7,000. Both round numbers are engaged in a number tug of war trying to pull the 6,834 to their side. So how do you know who wins?
Follow these steps.
1. Dizzy Digits. First decide what place you want to round to. How many digits can dance in your head before you get dizzy? 6,834 + 2,378 = is too complicated.
2. Underline what you are going to keep. 6,834 + 2,378
3. Tug of War. Look closely at the digit to the right of the underlined digit 6. How strong is that digit? Remember the tug of war? If both sides pulled the underlined digit which one would win? Will the digit get pulled up or stay the same? The secret is to remember that a number must be 5 or greater to pull the underlined number up, and it must be 4 or less to keep the unlined number the same. The 8 is strong, so the digit increases by one. You add one, and the 6 becomes a 7.
4. Bring on the Donuts. Use your donut machine to make the digits you’ve taken out zeroes. You removed the 834, so 6,834 becomes 7,000. You call it rounding up because the number got bigger. If the number got smaller you would call that rounding down.
After you round the second number follow the next step.
5. Calculate. 7,000 + 2,000 = 9,000.

When you begin estimating calculations, think of your mind as a Mighty Number Transformation Machine or MNTM for short. When you estimate, it can input any number, transform it, and output another number.

How does your mind do this? There are a few different techniques it can use. Today we will focus on the first way which is to shorten numbers to make them easier to work with. In math this is called truncating.

For example, when truncating the number 515 we remember how many groups of 100s there are. We truncate 515 to five.

Dogs like to think of truncating as biting off some digits. The idea behind biting off some digits is to get numbers with fewer digits that are easier to add, subtract, multiply, and divide. Of course even dogs, when they bite the number 45 and leave only a 4, have to remember that the 4 means 4 groups of 10.

So if you were trying to estimate what 432 + 812 = and wanted to use truncating, how would you do it?

You'd say 4 hundred + 8 hundred = 12 hundred = 1,200.

Truncating is a very fast way to estimate.

Comparing is the heart and soul of estimating. In fact, when you estimate you are up to your ears in comparing.

To estimate measurements, you compare length, weight, volume, time, temperature and amounts. To estimate calculations you also compare. Luckily, you are an expert in comparing, whether you realize it or not. You know when your sister's slice of cake is bigger than yours, you know if your friend got more Halloween candy, you even know who has more space in the backseat.

Now you need to apply your expert comparing skills to estimating. It's all about comparing what you don't know to what you do.

For example, you don't know how tall the man on stilts is, but you do know how tall your dad is. You don't know how many hotdogs you can eat today, but you do know how many hotdogs you ate yesterday. You don't know what 24 x 4 equals, but you do know that 25 x 4 = 100 (because you know that four quarters make a dollar). You don't know how many gumballs are in the jar, but you can count how many are in a small section of the jar.

The key words for comparing are greater than, less than, or equal to.

The height of the man on stilts is greater than (>) the height of your dad. Your hunger yesterday is equal to (=) your hunger today. Lastly, 24 x 4 is less than (<) 25 x 4.

Whether you are estimating calculations or measurements, a good place to start is to make sure you are in the right ball park.

When you are measuring this means taking the time to think about whether you should estimate your height in inches, feet, yards, or miles. Of course, a worm would estimate their height in inches and a person would use feet or yards.

When you are estimating calculation it is often helpful to note whether your answer is in the tens, hundreds, thousands, etc. You know that 11 x 15 is going to be more than 100 because 10 x 10 is a hundred. If you have the problem 0.5678 + 0.02342 you know it is less than one.

This is especially helpful when you are checking your answer. If you do a simple quick check to figure out what ball park the answer should be in you can often determine if your decimal point is off or if messed up in another way. A quick ball park check can save your grades!

I like to think of estimating as the pickel in the middle. On the one hand you can guess; estimating is not guessing. If I ask you what 11 x 13 is and you pull a number out of the hat that is guessing.

One the other hand you can do the calculation; estimating is not being precise. If I ask you the same question and you calculate the answer that is not estimating.

Estimating is an educated guess. It is using what you know to get close to the answer. If you say, "11 x 13 is a little more than 10 x 13 = 130, so I estimate the answer is 140," that is estimating.

Place value is a vague concept for many students. Often we think of 10 as ten individual marbles or 10 individual cookies but when we look more at place value it shifts how we think about numbers. Place value has to do with groups. The tens position tells us how many groups of 10 there are, so the number 10 means one group of 10 and zero individual ones.

All of the place values are based on this group concept. When there gets to be too many tens we then group in terms of 100s and that place value is called the hundreds place. So the number 234 is two groups of 100, three groups of 10 and four individual ones. If you understand place value it will help you with many other math topics.

I created this website so that kids and adults alike could learn to calculate like a math superhero. I am the coauthor of a new math series from Barron's titled Adventures in Mathopolis. The first book in the series is called Adventures in Mathopolis: Estimating and Measuring. Math becomes an exercise in fun when kids open this humorous, cartoon-illustrated book. As they enjoy the story, they learn to think, and calculate like a math Superhero!



I have another book coming out in February titled Adventures in Mathopolis: Fractions and Decimals.



For more information go to http://www.cweiskopf.com/