# Estimation

Here is everything you need to know about estimation for. You’ll learn the definition of estimation and how to use various estimation strategies to make calculations quicker and easier.

Students will first learn about estimation in 3rd grade math as part of their work with operations and algebraic thinking. They will expand upon that knowledge as they progress through elementary math.

## What is estimation?

Estimation is when you use approximate values in a calculation to give an approximate answer rather than an exact answer.

Estimation helps to make calculations quicker and easier.

Let’s look at some estimation strategies.

Estimation strategy – Rounding

Rounding the decimal numbers to the nearest whole number (or nearest ten,
hundred, thousand) can help to estimate calculation.

Estimate the value of 5.7 \times 6.3

Round 5.7 to the nearest whole number.
● Look at the digit immediately to the right of the rounding digit. If it is equal
to or greater than 5 round up by adding one to the rounding digit.
If it is less than 5, leave the rounding digit alone.
● The digit is 7. \; 7 > 5, round up by adding 1 to the rounding digit. 5 + 1 = 6.
5.7 rounded to the nearest whole number is 6.

You can also check your rounding using a number line. 5.7 is to the right of the
halfway point and closer to 6.

Round 6.3 to the nearest whole number.
● Look at the digit immediately to the right of the rounding digit. If it is
greater than to or greater than 5 round up by adding 1 to the rounding digit.
If it is less than 5, leave the rounding digit alone.
● The digit is 3. \; 3 < 5, round down by leaving the rounding digit alone.
6.3 rounded to the nearest whole number is 6.

You can also check your rounding using a number line. 6.3 is to the left of the
halfway point and closer to 6.

6 \times 6 is an easier calculation to make than 5.7 \times 6.3.

6 \times 6 = 36

So

5.7\times 6.3\approx 36

\approx is the symbol for “approximately”

Estimation strategy – Compatible Numbers

Compatible numbers are pairs of numbers that work well together, they can be
used to estimate calculations.
Compatible numbers can be found by rounding to the nearest number that is
easy to calculate with.

Estimate the value of 2160 \div 29

2160 is close to 2100 and 29 is close to 30.

2100 and 30 are compatible because 2100 \div 30 is an easy calculation to do.

2100 \div 30 = 700

So

2160 \div 29 \approx 700

\approx is the symbol for “approximately”

## Common Core State Standards

How does this relate to 4th grade math and 5th grade math?

• Grade 3 – Operations and Algebraic Thinking (3.OA.D.8)
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

• Grade 4 – Number and Operations – Base Ten (4.NBT.A.3)
Use place value understanding to round multi-digit whole numbers to any place.

• Grade 5 – Number and Operations – Base Ten (5.NBT.A.4)
Use place value understanding to round decimals to any place

## How to estimate calculations

In order to estimate using compatible numbers.

1. Round each number so that they are compatible.
2. Create the new calculation using the compatible numbers.
3. Do the calculation using the compatible numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈}

In order to estimate using rounding.

1. Round each number in the calculation the nearest whole number, nearest ten, nearest hundred, or nearest thousand.
2. Create the calculation using the rounded numbers.
3. Do the calculation using the rounded numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈}

In order to estimate a  real world scenario using rounding or compatible numbers.

1. Read the problem and decide which operation(s) to use.
2. Create an equation.
3. Use rounding or compatible numbers to write a new equation.
4. Do the calculation(s) using the rounded numbers of the compatible numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈}
5. Label the answer.

## Estimation examples

### Example 1: estimate the product using compatible numbers

Estimate the value of 228 \times 19 by using compatible numbers.

1. Round each number so that they are compatible.

228 is close to 220.

19 is close to 20

2Create the new calculation using the compatible numbers.

220 \times 20 =

This calculation is much easier to do than 228\times 19.

3Do the calculation(s) using the rounded numbers of the compatible numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈}

220\times20=4400

228\times19=4,332

228\times19\approx4,400

### Example 2: estimate quotients using compatible numbers

Estimate the value of 2774\div73

Round each number so that they are compatible.

Create the new calculation using the compatible numbers.

Do the calculation using the compatible numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈}

### Example 3: estimate the product of decimal numbers by rounding to the nearest whole number

Estimate the value by rounding to the nearest whole number.

6.9\times 9.6

Round each number in the calculation the nearest whole number, nearest ten, nearest hundred, or nearest thousand.

Create the calculation using the rounded numbers.

Do the calculation using the rounded numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈}

### Example 4: estimate the quotient of decimal numbers using rounding

Estimate the value by rounding to the nearest whole number.

783.12\div2.4

Round each number in the calculation the nearest whole number, nearest ten, nearest hundred, or nearest thousand.

Create the calculation using the rounded numbers.

Do the calculation using the rounded numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈}

Benny has saved \$127.54. Sandy has saved 2.5 times as much money as Benny. Estimate how much money Sandy has saved. Read the problem and decide which operation(s) to use. Create an equation. Use rounding or compatible numbers to write a new equation. Do the calculation(s) using the rounded numbers of the compatible numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈} Label the answer. ### Example 6: word problem using estimation Janna has \$21.16. She wants to buy the large candy bars for her party. The large candy bars cost \$1.84. Estimate how many large candy bars she can buy. Read the problem and decide which operation(s) to use. Create an equation. Use rounding or compatible numbers to write a new equation. Do the calculation(s) using the rounded numbers of the compatible numbers to give an approximate answer, using the ‘approximately equal to’ symbol \textbf{≈} Label the answer. ### Teaching tips for Estimation • Reinforcing number sense is essential to estimation strategies. Use number lines and manipulatives to help students build a deep understanding of numbers and how they relate to one another. • Have students check their answers for reasonableness by estimating products, estimating quotients, estimating sums and estimating differences. • Estimating strategies are used in real-life constantly. Use real-life learning activities in class so that students can see the importance of estimating skills. • When teaching the strategy of compatible numbers, emphasize to students that they estimated pair of numbers must work well together. Rounding strategies such as rounding to the nearest whole number might not give a pair of compatible numbers. • Demonstrate to students that the closer the rounded numbers are to the actual number the better estimate they’ll get. • Although worksheets with estimation math problems help students practice the strategies, having students do real-life problems is more meaningful. ### Our favorite mistakes • It is common to find the actual calculation rather than use estimation Estimation strategies are used to make the calculation quick and easily done mentally. 5.8\times2.3 is not easy to do quickly. So using the estimation strategy of rounding 5.8 to 6 and 2.3 to 2 will make the calculation quick and easy. 6\times 2 = 12. The actual answer is 13.34. • Students have difficulty understanding estimation or applying an estimation strategy. Students have trouble estimating “how many” because they have weak number sense. Number sense helps you to understand how numbers relate to one another. Reinforcing number lines and visual models helps students to make sense of the numbers. • Students think they have to use one particular estimation strategy. Estimation strategies exist to help students make calculations quick and easy. There is NOT one right strategy to estimate. Students should use the strategy they are most comfortable with. ### Practice Estimation questions 1. Use compatible numbers to estimate the value of 22\times 19? 418 400 419 190 22 is close to 20 19 is close to 20 20\times20 = 400 22\times 19\approx 400 The actual answer is 418 which is close to 400. 2. What are the appropriate compatible numbers to estimate the value of 219\div74 220 and 70 200 and 70 210 and 70 220 and 75 Compatible numbers are a pair of numbers that work well together. In this case, estimating 219 to be 210 and estimating 74 to be 70 will make a pair of compatible numbers. 210\div30 is easy and quick to calculate. The compatible numbers are 210 and 70. 3. Estimate the value of 7.2 \times 98 using rounding. 720 700 705.6 706 7.2 rounded to the nearest whole number is 7. \;\; 2 < 5 , so round down by leaving the rounding digit alone. 98 rounded to the nearest hundred is 100. \;\; 8 > 5, so round up by adding 1 to the rounded digit. 7\times100=700 7.2\times98\approx700 4. Estimate the value of 389\div81 using rounding. \approx{4} \approx{6} \approx{3} \approx{5} 389 round to the nearest hundred. 8 > 5, so round up by adding one to the rounded digit. 3 + 1 = 4, so 400. 81 round to the nearest ten. 1 < 5, so round down by leaving the rounding digit alone. 400 \div 80 = 5 389 \div 81 \approx{5} 5. Jenny has saved \$114.65 in her savings account. Brandon has saved 1.5 times the amount of money. Estimate the amount of money Brandon has saved.

\approx{\$171.98} \approx{\$220}

\approx{\$229.30} \approx{\$245}

You will estimate the value of 114.65\times 1.5.

Round \$114.65 to the nearest ten. 4 < 5 so leave the rounded digit alone, so it will round to be \$110. \; 1.5 round to the nearest whole number. 5 = 5, so round up by adding one to the rounded digit. 1 + 1 = 2.

\$110\times2=\$220

\$114.65\times1.5\approx \$220

6. There are 678 boxes in 11 storage spaces. Estimate how many boxes there are in 1 storage space by rounding the values to the nearest ten.

\approx{57} boxes

\approx{68} boxes

\approx{64} boxes

\approx{58} boxes

You will estimate the value of 678\div11.

Round 678 to the nearest ten. 8 > 5, round up by adding 1 to the rounded digit. 7 + 1 = 8, so the rounded number is 680.

Round 11 to the nearest ten. 1 < 5, leave the rounded digit alone, so the rounded number is 10.

680\div10=68

678\div11\approx68

## Estimation FAQs

What is the difference between rounding and compatible numbers?

Rounding is taking a number and rounding it to a specific place, for example rounding to the nearest tens place, nearest hundreds place, nearest hundredths place, etc.. Compatible numbers are numbers that work well with each other.

What is better to use when estimating, rounding or compatible numbers?

There is no right or wrong way to estimate. In many cases it depends on the actual problem.

Do you always have to round to the nearest ten, nearest hundred, or nearest thousand when estimating numbers?

Round to the place that will make the calculations the easiest to do.

Does the estimated answer have to be close to the exact answer?

The closer your estimated answer is to the exact answer, the better the estimate.

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