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Long Division (Standard Algorithm for Division)
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What you will learn from this videoWhat you will learn
- We will learn how to divide using the standard algorithm.
- We’ll see that we can use the standard algorithm to divide 2, 3 and 4 digit numbers.
- And we'll see how this knowledge can help us do experiments, bake cookies, and pollinate trees!
- Discussion Questions
Before Video
What is place value? How does the place value of a digit compare to the place value of the digit on its right?ANSWERPlace value is the value of a digit based on its place in a number. The place value of a digit is 10 times the place value of the digit to its right.
Thousands place.
6 × 100 + 7 × 10 + 2 × 1, or 6 one hundreds, 7 tens, and 2 ones.
When I break a number up to divide using an area model, I break it apart by place value. When I divide a number using partial quotients I try to find the largest multiple of the divisor so that there is none of the greatest place value left after I subtract.
Students may use partial quotients or an area model. Some may think of the problem as 48 ÷ 12 = 4, and then multiply by 10 to get 40.
After Video
What are the four repeated steps of the standard algorithm for long division?ANSWERDivide, Multiply, Subtract, Bring down
When I divide, I can look at multiples of the divisor to help me find the dividend.
When there are no more digits to bring down and I have a remainder of 0, or when there are no more digits to bring down and the remainder is smaller than the divisor.
The standard algorithm is a very efficient way to divide.
I can start by making a list of multiples of 7. 4 is less than 7, so consider multiples of 7 close to 45. Multiply: 7 × 6 = 42. Subtract: 45 – 42 = 3. Bring down the 6 to make 36. Find multiples of 7 close to 36. Multiply: 7 × 5 = 35. Subtract: 36 – 35 = 1. Bring down the 4 to make 14. Find multiples of 7 close to 14. Multiply: 7 × 2 = 14. Subtract: 14 – 14 = 0. No numbers remain to bring down, and the remainder is 0. 4,564 ÷ 7 = 652.
- Vocabulary
- Area model DEFINE
A rectangular diagram or model used for multiplication and division problems, in which the factors or the quotient and divisor define the length and width of the rectangle. Also called the box method.
- Partial quotients DEFINE
A strategy for division where we subtract multiples of the divisor from the dividend until we get to 0, or as close to 0 as possible.
- Algorithm DEFINE
A procedure in mathematics or a description of a set of steps that we can use to solve a mathematical computation.
- Long division DEFINE
A process of dividing a number that has at least three digits by one that is two digits or more, sometimes leaving a remainder.
- Standard algorithm for division DEFINE
A series of repeated steps for performing division problems. The steps in order are: divide, multiply, subtract, bring down.
- Partitioning DEFINE
Division into equal parts.
- Dividend DEFINE
In division, the amount or number to be divided.
- Divisor DEFINE
In division, a number that divides another number, either completely or with a remainder.
- Area model DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide