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Once students are confident in their skills to use place value understanding to round off whole numbers and numbers with decimals, they are ready to dive into estimating decimal products and quotients.
The ability to rely on mental math to perform decimal rounding and estimating is crucial for many practical aspects of life. Yet many children may come across difficulties while learning this topic. To help out, we’ve compiled a few awesome math strategies to teach this.
Apply these strategies in your classroom and see your students’ estimating skills soar!
Strategies to Teach Estimating Decimal Products and Quotients
What Are Decimals?
You may want to start with a definition of decimals. You can define a decimal as a number that contains a decimal point, after which we have digits whose value is smaller than one. So decimals are numbers comprising a whole number and a fractional part, separated by a point.
You can also explain that a decimal is basically a fraction, with a denominator that can be expressed as a power of ten. Provide several examples of what we mean by this. For instance:
6⁄10 = 0.6; 23⁄100 = 0.23; 832⁄1000 = 0.832
You can also point out that a decimal product is the product of two or more decimals that are being multiplied, whereas a decimal quotient is simply the quotient we get when dividing decimals by decimals.
Review Place Value
To be able to round off decimals and estimate decimal products and quotients, students need to have a solid understanding of place value. You can perform a brief bell work activity for this purpose.
For example, write a few whole numbers, as well as a few decimals on the whiteboard, such as 3,234; 46,879, 0.01; 0.587, etc. Underline or highlight a certain digit in each number and ask students to identify their place value.
Are children able to differentiate between digits in the tens and tenths place value? In the hundred and hundredths place? You may also benefit from our article on place value, as well as our articles on tenths and hundredths.
How to Round Off Numbers with Decimals
To perform the estimating of decimal products and quotients, students must first round off the decimals. Students may already remember that they learned how to round off whole numbers in earlier lessons, which you can review using this article.
Remind students that rounding means simplifying numbers so that they’re easier to work with. That is, by rounding a long number, we’re expressing it in terms of the nearest unit (such as the nearest ten, hundred, tenth, etc.).
If the kids are familiar with the rules of rounding off whole numbers, explain that the rules for rounding off numbers with decimals follow a similar logic. You can write these rules in three steps, that is:
- First, we identify the rounding digit and we determine its place value.
- Then, we look at the digit to the right of the rounding digit. If this digit is less than 5, we don’t change the rounding digit. However, if the digit to the right of the rounding digit is 5 or greater than 5, we increase the rounding digit by 1.
- We change the numbers to the right of the rounding digit to zeros, or we drop them if they’re to the right of the decimal point.
- We retain the numbers to the left of the rounding digit, i.e. they remain unchanged.
You can proceed by providing a few examples of how we apply these rules in practice. Write a decimal on the whiteboard, such as 3.6248. For example, let’s say we want to round off this decimal to the nearest hundredths.
Point out that the first thing we need to do is identify the rounding digit, and determine its place value. Feel free to underline or highlight the rounding digit with a marker to help children visualize which digit we need to round.
As we’re asked to round to the nearest hundredths, we start by looking at which digit is in the hundredths place. In the case with 3.6248, the digit in the hundredths place is 2. Now that we’ve identified it, we need to look at the digit to its right.
This digit is 4. Remind students that since we know that the digit to the right of the rounding digit is less than 5, we don’t change the rounding digit. In 3.6248 the rounding digit 2 will remain unchanged.
Finally, explain that we’ll retain the digits to the left of the rounding digit, that is, 3 and 6 remain unchanged. On the other hand, according to our rules above, we need to drop the numbers to the right of the rounding digit, that is, 4 and 8.
This will give us 3.62! So by rounding 3.6248 to the nearest hundredth, we’ll have 3.62.
How to Estimate Decimal Products and Quotients
Now that children are fluent in rounding off decimals, they can proceed with estimating decimal products and quotients. Remind students that estimating means finding an answer that’s close enough to the exact answer.
Highlight that there are plenty of real-life situations where we may want to do a quick estimation relying on our mental math skills and where we don’t need the exact answer. One such case is when we go shopping and we want to check if we have enough money to pay the total bill.
Students are already familiar with the rules for estimating the answer to a certain subtraction, addition, or multiplication problem involving whole numbers. Point out that the rules for estimating a decimal product or quotient follow a similar logic.
Explain that we start by rounding each decimal to the nearest whole number, i.e. the ones place. Then we multiply the two whole numbers to get our estimate (for estimating decimal products) or divide the two whole numbers (for estimating decimal quotients).
Example on Estimating Decimal Products:
You can now proceed with a few examples of how we apply this in practice. Write two decimals on the whiteboard that we’ll be trying to multiply, such as 6.94 × 3.8. The first thing we need to do is round each decimal on its own to the nearest whole number.
Explain that to find the nearest whole number for 6.94, we’ll first identify the digit in the ones place, as this is our rounding digit. In 6.94, the digit in the ones place is 6. We then look at the digit to its right, which is 9. Since 9 is bigger than 5, we’ll increase 6 by 1, and get 7.
We drop the numbers to the right of the rounding digit and we get 7. So the nearest whole number for 6.94 is 7. Now perform the same procedure to round off 3.8 to the nearest whole number, which is 4.
Finally, point out that the only thing left to do is multiply 7 and 4 in order to estimate the decimal product of 6.94 and 3.8. In other words, 7 × 4 = 28. We can also calculate on a calculator to check the exact answer, which is 26.372. So the estimate was pretty close!
Example on Estimating Decimal Quotients:
You can now proceed with a few examples of how we estimate decimal quotients. Write two decimals on the whiteboard that we’re trying to divide, such as 23.8 ÷ 4.75. Again, the first thing we need to do is round each decimal on its own to the nearest whole number.
However, make sure to point out that we must start with rounding off the divisor, which will become obvious later on. Since the divisor is 4.75, we’ll try to find the nearest whole number for it. We’ll first identify the digit in the ones place, as this is our rounding digit.
In 4.75, the digit in the ones place is 4. We then look at the digit to its right, which is 7. Since 7 is bigger than 5, we’ll increase the rounding digit by 1. We drop the numbers to the right of the rounding digit and we get 5.
So the nearest whole number for 4.75 is 5. Now we need to look at the dividend and try to round it off to the nearest whole number that can be divided by 5 without a remainder, in other words, a compatible number. This is the number 25.
Finally, point out that we transformed 23.8 ÷ 4.75 into 25 5 and perform the division. 25 ÷ 5 = 5. Then we can check on a calculator what the exact answer is, i.e. 5.01. So our estimation was actually pretty close!
Activities to Practice Estimating Decimal Products and Quotients
Estimate Products Game
This is a simple online game that students can play as a warm-up for more difficult activities. The game can help students reinforce acquired knowledge on how to estimate the product of decimal numbers. The only thing needed is a sufficient number of devices in your class.
Provide instructions for the game. Explain that students play the game individually, which makes it ideal for homeschooling parents, as well. They are asked with estimating the decimal product of numbers by using their skills of rounding decimal numbers to the nearest whole number.
Pass the Ball Game
This fun game will help students practice their skills at estimating decimal products and quotients, as well as reinforce their ability to perform quick mental math. The game is a group activity. To play the game, prepare cards with math problems, an answer sheet, and bring a ball.
Each card contains one math problem related to estimating decimal products and quotients. For example, 403.9 ÷ 7.22, 80.12 ÷ 9.4, 7.199 × 5.72, etc. The answer sheet contains the exact answers, as well as the best estimation answers to all math problems.
Arrange students in a circle. Place the cards face down in the middle of the circle. Assign one student as a checker who sits in the middle of the circle and holds the answer sheet. Provide instructions for the game.
The students pass the ball to one another. You can select a random person to start this. Once the ball is passed to a student, the checker selects a random card and reads the problem out loud. The student at this point passes the ball to the next student and tries to solve the problem.
The student has to think fast and solve the problem before the ball comes back to them, only relying on their mental math skills. In the meantime, each student keeps passing the ball to the one standing next to them.
When the ball reaches them again, they have to be able to provide an answer. If the answer is correct, they remain in the circle and keep playing. If it’s incorrect, they have to exit the circle and stop playing.
The student with the ball then re-starts the process by choosing a random person to give the ball to. The checker selects a card anew and the whole thing is repeated. The last person to remain in the circle is the winner. Keep playing as long as time allows it.
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This article is based on:
Unit 3 – Decimals and Equations
- 3-1 Rounding and Estimating
- 3-2 Estimating Decimal Products and Quotients
- 3-3 Mean, Median, and Mode
- 3-4 Using Formulas
- 3-5 Solving Equations by Adding or Subtracting Decimals
- 3-6 Solving Equations by Multiplying or Dividing Decimals
- 3-7 Using the Metric System