6th Grade Math Worksheets: Multi-Digit Division

How to make it

1. Set the dividend and divisorFive-digit dividends and three-digit divisors are preselected. Choose a four-digit dividend for a first week back, or a two-digit divisor to review the fifth grade method.
2. Decide on remaindersWith remainders is ticked and the key writes them as R and a number. Untick it for problems that divide exactly, which suits a class that writes remainders as decimals.
3. Print the sheet and keyNine problems fill a page with space under each bracket for the multiply, subtract and bring down steps. The key is a separate page, ready for self-marking.

Where grade 6 math spends its time

Most of the sixth grade year is new territory: ratios and rates, unit prices, percents, negative numbers on the number line and the coordinate plane, expressions with letters in them, one-step equations, area of triangles and the volume of boxes, and a first look at statistics. Running underneath all of it is arithmetic that students are now expected to do without thinking twice, and the Common Core names it directly: divide multi-digit numbers fluently using the standard algorithm (CCSS 6.NS.B.2), and do the same for decimals.

This site makes the first of those two. It has no generators yet for ratios, decimals, integers, expressions or equations, so the 6th grade math worksheets here are a narrow set: multi-digit division for fluency, plus review pages from earlier grades. If you need a full year of grade 6 practice, use these alongside the class textbook rather than instead of it.

The sheet on this page

Each problem is a five-digit number divided by a three-digit number, set out in the long division bracket the way US classrooms write it, such as 48,615 divided by 237. The quotient is picked first, so answers have two or three digits and never collapse to a trivial 1 or 2. With remainders on, the remainder is always smaller than the divisor, and the key shows the quotient and the remainder above each bracket.

There is a lot of writing under a three-digit divisor: each step multiplies a three-digit number by one digit and subtracts it. That is why the preset prints nine problems rather than twenty. Two or three a day, checked against the key, build more accuracy than a full page done once under time pressure.

Estimating each digit of the quotient

The hard part of dividing by 237 is not the subtraction; it is choosing the next digit. A reliable habit is to round the divisor to the nearest hundred and divide by that: 237 is about 200, so 486 divided by 200 suggests 2. Multiply, check that the result is not larger than 486, and correct up or down by one if needed. Students who write the estimate in the margin make far fewer erasures.

Two other checks catch most wrong answers before the key does. The remainder must be smaller than the divisor, or the last digit of the quotient was too small. And the quotient times the divisor, plus the remainder, must give the dividend; doing that multiplication for one problem on each sheet keeps multi-digit multiplication sharp at the same time.

Review sheets that support grade 6

Several topic pages give useful review in the first weeks of the year. The long division generator covers every size from two-digit dividends up, so a student who struggles with three-digit divisors can step back to two digits for a few days. Multi-digit multiplication sheets practice the step that long division leans on, and fraction worksheets with unlike denominators revisit the fifth grade work that ratios build on.

For the coordinate plane, printable graph paper in quarter-inch or centimeter squares gives students room to draw axes and plot the points from a lesson; the paper is blank, so the teacher sets the task. The fifth grade preset, two-digit divisor long division, is the natural step before this page.

Using the key without giving answers away

Print the key on its own and keep it at the front of the room, or fold it so only one column shows at a time. Students who check each problem as they finish learn more than those who check all nine at the end, because a misplaced digit in problem 2 tends to repeat in problems 3 to 9.

The Sheet number in the footer brings back the exact page with the same settings. That makes retakes simple: a student who missed four problems can do the same sheet again on Friday, then a New variant the next week to show the skill holds on numbers they have not seen.

Year 7 in England and Australia

US sixth graders are eleven to twelve years old, the age of Year 7 in England and Year 6 or Year 7 in Australia, depending on the state. Written division by larger divisors is taught in all of them, though many schools there use short division for one-digit divisors and set out the long form only for bigger ones.

Outside the US the footer leaves out the Common Core code and the problems are unchanged. Sheets print on Letter or A4; print at actual size so the bracket and digits keep their spacing.

Common Core State Standards: © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.