Recall multiplication facts with factors up to 12 and related division facts with automaticity.

Divide a whole number up to four digits by a one-digit whole number with procedural reliability. Represent remainders as fractional parts of the divisor.

Explore the multiplication and division of multi-digit whole numbers using estimation, rounding, and place value. For example, the produce of 215 and 460 can be estimated as being between 80,000 and 125,000 because it is bigger than 200 x 400, but smaller than 250 x 500.

Students using the standard method will need to remember these steps. Repetition helps, and students can write these steps on the top of their paper or whiteboard before practicing problems!

First, divide. How many groups of 7 can you make from 18? 2 groups. Then, multiply. Multiply 2 by 7, and write the result below 18.

Next, subtract 18 – 14. The answer is 4. Compare 4 to 7. It should be less than 7. If not, that means that you could have found another group of 7 in the “divide” step.

Bring down the 9, and start the steps over again!

Divide: Now, you are seeing how many groups of 7 you can make from 49. You can make 7 groups.

Multiply: Multiply only 7 by 7, not 27 by 7. 7 x 7 = 49.

Subtract 49 – 49 = 0.

Compare: 0 is less than 7.

There is nothing left to bring down! Your answer is 27.

The idea of “partial quotients” is to divide a little bit at a time, using easy numbers like multiples of 10 or 100. This method works better for some students who struggle with their multiplication and division facts, or who have difficulty remembering the steps of standard long division.

It is different from regular long division because students do not have to get “as close as possible without going over.”

In this problem, we are dividing 189 into 7 groups. We want to know how many dots will be in each group.

To start, a student might know that 10 groups of 7 is 70. Since 70 is less than 189, we can record “10” off to the side, knowing that we are making 10 groups, and we can subtract 70 from 189. We are left with 119.

We are left with 119, and we still need to know how many total groups of 7 there are. We know that there are 10 groups so far. We can make another group of 10 to take 70 more away. Then, we will have 119 – 70 = 49.

With the remaining 49, we can make 7 groups of 7.

Our final answer is to add up the numbers of groups we made along the way: 10 + 10 + 7 = 27.