4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
First, students will learn how to divide multiples of powers of ten by other multiples of powers of ten, where the divisor is some one-digit number multiplied by a power of ten. The first method that students should learn is as follows:
$$\begin{align} 240{,}000 \div 300 &= \dfrac{24 \cdot 10{,}000}{3 \cdot 100} \\[1em] &= \dfrac{24}{3} \cdot \dfrac{10{,}000}{100} \\[1em] &= 8 \cdot 100 \\[1em] &= 800 \end{align}$$The second method is to simply cross out zeros. For example, to find \(240{,}000 \div 300,\) I have four zeros on the left and two on the right, so I will finish with two zeros. Now I find the quotient of the numbers, disregarding trailing zeros. I find \(24 \div 3 = 8,\) and tacking on my two zeros gives me \(800.\) This method is less formal, but it's a method I can apply mentally. Here's a video on both methods.
Next, students will learn how to divide up to four-digit dividends by one-digit divisors, using concrete, visual, and abstract methods. For example, divide \(3{,}225\) by \(3.\) Students should also be given such problems with trailing zeros tacked on. For example, divide \(32{,}250{,}000\) by \(300.\) When teaching the abstract methods, start with the box method, as seen here. I think the box method is a bit easier than the usual abstract method, as the box method emphasizes place value. Students should also learn that the dividend is a multiple of the divisor if and only if the remainder is 0. For example, 105 / 7 = 15 R 0, so 105 is a multiple of 7. Next, give your students this challenge. Its only prereq is being able to easily divide small numbers, mentally or otherwise. Finally, give your students this challenge. The only prereq for this challenge is understanding quotients and remainders.