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In the fourth grade, students learn how to perform division with remainders. This includes learning how to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.
To do so, they rely on their knowledge of place value, the properties of operations, and/or the relationship between multiplication and division. Although this may sometimes come across as challenging to students, there are a number of ways in which math teachers can provide support. Read on to find out more.
What Are Whole Number Quotients and Remainders?
For starters, explain to students what we mean by finding whole-number quotients and remainders. Fourth graders are already familiar with the terms quotient and divisor, so place emphasis on remainders. Point out that when we have a division problem, we sometimes end up with a ‘leftover’. This is called a remainder.
For example, if there are 7 bones and only 2 dogs, we can’t share them evenly (unless of course, we break one bone in half but then we won’t be talking about a whole number, but rather, a fraction). So we can give 3 bones to each dog and we’ll have one bone as a remainder.
Point out that the whole number quotient of 7 divided by 2 is 3 with 1 as a remainder. However, when we’re dealing with dividends that are two, three, four, or multi-digit numbers, things can get a bit trickier and we can’t always rely on mental math. One way to go about it is ‘friendly multiples’, which we’ll discuss in the next paragraph.
How to Teach Finding Whole Number Quotients and Remainders
Explain to students that they will be learning how to find whole number quotient and remainders. Point out that you will be using multiplication to solve division problems, i.e. ‘friendly multiples’ of the divisor. Explain that friendly multiples are numbers that are easy to work with, for instance, 10.
Then provide an example of how this works in practice by solving a division problem, such as 79 ÷ 3. Point out that you will recompose the dividend into friendly multiples of the divisor, that is 3. Since we already know that 3 x 10 = 30, the friendly multiple that we’ll use here is 10.
Then we subtract 30 from 78, which will leave us with a new dividend, 49. Explain that you can recompose this dividend again by using 3 x 10 = 30 and subtracting this from the dividend. This will then leave us with 19, for which we can’t apply 3 x 10 again.
Touch on how at this point, we will look for a new friendly multiple of the divisor 3. By relying on our previously acquired knowledge of multiplication, we know that 3 x 6 = 18. We can then subtract 18 from 19 and we’ll be left with 1! So the remainder is 1. Highlight that we should always keep recomposing the dividend until we can’t anymore!
So, we recomposed 79 into friendly multiples of 3. Now we know that 30 + 30 + 18 + 1 = 79. We also know that we used 10 twice as a friendly multiple and 6 once. By adding the friendly multiples, that is, 10 + 10 + 6, we’ll get the quotient, i.e. 26!
In other words: 79 ÷ 3 = 26 remainder 1
Helpful Multimedia Resources
You can also use this video in class to show how to find whole number quotient and remainders by using friendly multiples of the divisor, or this one to illustrate another handy division method that relies on using place value disks.
Activities to Practice How to Find Whole Number Quotients and Remainders
Online Division Game
This is an online game that students can play individually, which also makes it suitable for homeschooling parents. Just make sure there are enough technical devices for each student in the class.
The students can start with dividing two-digit by one-digit numbers with remainders, and slowly progress to three-digit by one-digit numbers with remainders and finally, four digits by one-digit numbers with remainders.
Divide and Color
This activity is a fun twist to the popular saying ‘divide and conquer’. To implement this simple activity in your class, you’ll need to print out a sufficient number of copies of the Divide and Color Worksheet, depending on the number of students you have, as well as coloring crayons.
The worksheet contains several division problems, all of which focus on dividing a two-digit number by a one-digit number. In all division problems, students must find the quotient and the remainder. As they do so, they also color the images on the worksheet with crayons.
Students can do this activity on their own or together with another student. If you decide to pair students, make sure that students who are struggling with math don’t end up with other struggling students. But rather, make sure pairs have students with diverse math levels.
Before You Leave…
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This article is based on:
Unit 4 – Multi-Digit Whole Number Division