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Math

	Federal Way Public Schools

Number Sense
Lesson 5

Estimation

Objectives/Vocab/Tips > Examples 1 | 2 | 3 > Practice: 1 | 2 | 3 | 4 > Reflection

Objective:

Estimation

In this lesson you will demonstrate your understanding of situations where estimation can be used and computation isn't required. You will use estimation to predict computation outcomes and then use your estimations to determine if an actual computation result is reasonable.

Vocabulary:

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Estimate

Estimation

Approximate

Rounding

Compatible numbers

Front-end estimation

Mental math

Tips to Remember:

Rounding

Rounding is one of the most common estimation strategies. Rounding is done because we want to work with numbers that are easy to work in our head without using pencil and paper. When you round to estimate, you can either follow the directions to the place value given to you in the problem or if you are not told, round it to the highest place value. For example, 578 would be rounded up to 600. We round up because 578 is closer to 600 than to 500 on a number line. We are able to work with 600 using mental math much easier than using 578. If our number were 534, we would round down to 500 since 534 is closer to 500.

When rounding to a particular place value, you need to find the place value you are rounding to and then look at the digit in the place value right behind it. If that digit is between 0 and 4 you keep the digit in the place value you are rounding to the same and place 0's in the rest of the place values. If the digit is between 5 and 9 you want to add 1 to the digit in the place value you are rounding to. For example:

Round 2853 to the nearest thousand.

Begin by finding the thousand place value. The digit 2 is in the thousands place value.

Next, go to the first place value just behind the thousands place value which is the hundreds place. In this case it is the digit 8.

Since the digit is an 8, we need to add 1 to the digit in the thousands place value and then place 0's in the rest of the place values.

3000 is answer rounding 2853 to the nearest thousand.
3000 is much easier to work with than 2853 using mental math.

Front-end Estimation

Front-end estimation is another strategy that can be used to arrive at estimated solutions. This means we add the digits with the greatest place value (the front end digits) to help give us an estimate. Then with the rest of the digits we use those to do any adjusting to the our estimate. For example if we have to estimate the following:

	6	3	5
	2	9	3
+	4	5	5

We begin by taking the front-end digits only, and adding them together. We need to remember that we are adding digits that are in the hundreds place.

600 + 200 + 400 = 1200

Now we look at the rest of the digits and adjust our estimate depending upon what is left.

35 and 55 equal about 100
93 is about 100

So let's add 200 more to our estimate. Our new front-end estimate for the original problem is now 1400.

Compatible Numbers

Compatible numbers is an estimation strategy that may be used. This strategy is where you replace some or all of the numbers with numbers that are much easier to work with using mental math. Let's look an example.

$429 + $128 + $564 + $459 + $79 + $298

Let's look for numbers that work well together and are easy to add. Usually adding 25 is pretty easy so we have 50 and 75 as well. Of course there is 100 which we really like! Let's adjust our numbers using compatible numbers.

$425 + $125 + $550 + $450 + $75 + $300

Now we can add these by doing a little rearranging.

$425 + $75 + $550 + $450 + $125 + $300

$500 + $1000 + $425

$1925 would be our estimate using numbers that fit easily with other numbers and are easy to work with using mental math. Other compatible numbers would include 2 and 8, 5 and 5, 3 and 7, 4 and 6, 1 and 9, and any 10's. Look for numbers that go together and help you.

Estimate, Don't Compute!

When you are asked to estimate, be sure to use an estimation strategy from the beginning of your solution to the problem. Do not find the exact answer to the problem and then round for your answer. Estimating means you want to "quickly" arrive at an approximate answer for the problem.

Example 1 >>