By the end of this unit, students will be expected to:
Typically the long division process doesn't seem to be an issue for most 5th graders. However, using context to decide what difference the remainder makes can be difficult. An example would be, "A class is going on a field trip. There are 198 students and 8 chaperones. Each bus can hold a maximum of 50 students. How many buses are needed for this trip?" Students need to know that you can't answer with "4 R 6" because that does not make sense with the context of this problem. They have to know that they would be able to fill 4 buses, but would have 6 people left, so a 5th bus would be needed.
In terms of the long division process, I allow multiple methods and strategies as long as they work. We have one traditional way that we typically teach, but there are several ways that work well. Some students may need a different method to fully understand the process. Below is an example of the most common method (the "traditional algorithm").
- Divide a number up to 4 digits by a number up to two digits
- Divide larger numbers and multiples of 10s and 100s using patterns
- Use context to determine whether the remainder should be used to round the answer up or down in a word problem
Typically the long division process doesn't seem to be an issue for most 5th graders. However, using context to decide what difference the remainder makes can be difficult. An example would be, "A class is going on a field trip. There are 198 students and 8 chaperones. Each bus can hold a maximum of 50 students. How many buses are needed for this trip?" Students need to know that you can't answer with "4 R 6" because that does not make sense with the context of this problem. They have to know that they would be able to fill 4 buses, but would have 6 people left, so a 5th bus would be needed.
In terms of the long division process, I allow multiple methods and strategies as long as they work. We have one traditional way that we typically teach, but there are several ways that work well. Some students may need a different method to fully understand the process. Below is an example of the most common method (the "traditional algorithm").
Below are two similar methods. On the left is the "traditional" algorithm that many students learn. On the right is an alternative, but similar, method called 'partial quotients'. In this method, the student takes out the largest group they can using their knowledge of multiplication.
Below is another example of partial quotients. This method is not as common, but is reasonable. The two examples are using the same method, but are writing the answers in two different places. In the first, they keep track of the groups along the side, and add them together at the end. In the second, they keep track along the top. This is a great method for students that are building their mental math ability.
Repeated addition can be used when our divisors become large and more difficult to compute mentally. This is a strategy we will use in class. Repeated addition can be used when our divisors become large and more difficult to compute mentally. This is a strategy we will use in class.