Division Strategies, Partial Quotients

Use repeated subtraction first if the idea of division feels new, then move to partial quotients. Check every quotient by multiplying: if 96 divided by 4 is 24, then 24 times 4 should be 96.

Divide with partial quotients, then add the chunks to find the quotient. Partial quotients divide in easy chunks. Subtract a multiple of the divisor, divide what is left, then add the chunks. Problems on the page include 92 ÷ 4, 105 ÷ 3 and 135 ÷ 5. The directions on the page read: Read the example. Then, fill in each step and add the two chunks to write the quotient in the last box. The page opens with a worked example, and the answer key shows every answer.

Yes, both. We made it for 4th Grade long division, and the page works the same whether it lands on a kitchen table or a center rotation. At home, most families go through it together and talk the answers out loud, and that talking is where most of the learning happens with division strategies. In class it runs well as independent work while you pull a small group. Print one copy or thirty, whichever the day needs.

A partial quotient is one chunk of the answer. For 96 ÷ 4, take 4 × 20 = 80 first. Then 96 - 80 = 16 and 16 ÷ 4 = 4. Add the chunks, 20 + 4, to get 24.

Repeated subtraction means taking the divisor away again and again until you reach 0, then counting how many times you subtracted. It shows why division is the same as sharing in equal groups.

Once a student can use partial quotients to divide a 2-digit number by 1 digit, the long division steps are a short step: each partial quotient becomes part of the answer.

The partial quotient sheet supports 4.NBT.B.6, which covers dividing with strategies based on place value, properties and the relationship to multiplication.

2 printable worksheets, all free to preview. Downloads are included with a ClassWeekly free trial, and every page prints on standard 8.5 x 11 paper.

These are written for 4th Grade students, roughly ages 9-10. Many teachers also use them a grade up for review or a grade down as an extension, so use the preview to judge the fit for a particular child.

Yes. Each one shows the Common Core code it covers on its own page, so you can check the alignment yourself rather than taking our word for it.