How to make it
- Set the dividend and divisorA 4-digit dividend and a 2-digit divisor are preselected, the fifth grade range. Drop to 3 digits for the first lessons with two-digit divisors.
- Keep or remove remaindersWith remainders is ticked, because real division rarely comes out even. Untick it for a first sheet where every problem divides exactly.
- Print nine problems and the keyNine problems fit a page with space under each bracket. The key gives the quotient and remainder for each; New variant deals new numbers.
Where fifth grade math is heading
Fifth grade closes the arithmetic of whole numbers and opens the door to the middle school years. Children fluently multiply multi-digit whole numbers with the standard algorithm (CCSS 5.NBT.B.5) and find quotients of up to four-digit dividends and two-digit divisors, using place value, the properties of operations and the link between multiplication and division (CCSS 5.NBT.B.6). Fractions move on to adding and subtracting with unlike denominators (CCSS 5.NF.A.1).
The year also brings decimals to hundredths in all four operations, volume of rectangular solids, the coordinate plane and simple expressions with parentheses. This site covers the whole-number and fraction parts with answer keys; it does not yet make decimal or volume sheets, so those 5th grade math worksheets will have to come from the class textbook or another source.
The long division sheet on this page
The preset prints nine problems such as 47 ) 3,856 in the bracket layout used in US classrooms, with the divisor outside the bracket and space under each problem for the steps: divide, multiply, subtract, bring down. Divisors are two-digit numbers, dividends four digits, and many problems leave a remainder. The key shows each quotient and its remainder in pink.
Nine problems sounds like few, but each one with a two-digit divisor takes several minutes and a page of working, so this is a full lesson or a long homework. For a quiz, set How many to five or six in More options; for a short daily review, two problems at the start of math time keep the steps from fading between units.
Teaching two-digit divisors
The new difficulty in fifth grade is the estimate. With a one-digit divisor, the facts give each digit of the quotient directly; with 47, a child has to guess how many 47s fit into 385 and then check. Rounding the divisor helps: 47 is close to 50, and 385 ÷ 50 is about 7, so try 8 and 7 and see which gives a product just below 385. Expect some erasing, and say so in advance.
Some classes begin with partial quotients instead, subtracting easy multiples of the divisor, such as 10 × 47 and 50 × 47, and adding up how many were taken away. The problems on the sheet work for either method because the working is the child's. A table of the first nine multiples of the divisor, written in the margin, is a fair support for the first sheets and can be dropped once estimates get closer.
Other fifth grade math worksheets
For multiplication, the multiplication worksheets at 3 digits by 2 digits, or 4 digits by 2, match the fifth grade standard algorithm goal. For fractions, fraction worksheets with Add, different denominators and Subtract, different denominators give common denominators up to 24, and the key shows answers simplified, with improper fractions also written as mixed numbers.
Long division with one-digit divisors, on the long division generator with a 1-digit divisor, is a useful review in the first weeks of the year. Teachers looking for free 5th grade math worksheets to cover several units can print one sheet from each of these generators, each with its own answer key.
| Fifth grade goal | Generator | Setting |
|---|---|---|
| Divide by two-digit divisors | this page | 4-digit dividend, 2-digit divisor, with remainders |
| Multiply multi-digit numbers | Multiplication | 3 or 4 digits by 2 digits |
| Add unlike fractions | Fractions | add, different denominators |
| Subtract unlike fractions | Fractions | subtract, different denominators |
| Review one-digit divisors | Long division | 3 or 4 digits by 1 digit |
Checking work without the key
Division can be checked by multiplication, and fifth graders should do it as a habit: quotient times divisor plus remainder must give the dividend. If 3,856 ÷ 47 is 82 remainder 2, then 82 × 47 = 3,854 and 3,854 + 2 = 3,856. A remainder as large as the divisor or larger means the quotient digit was too small, which is the most common error on these sheets.
Ask children to check two problems a sheet this way before they look at the key. The habit is worth more than the key itself, because it is available in a test. The other frequent slip is a misaligned digit in the quotient, often a missing zero, as in 3,808 ÷ 38; graph paper keeps the columns straight while the method is new.
Year 6 in England, Year 5 in Australia
US fifth graders are about ten to eleven years old, the age of Year 6 in England and Year 5 in Australia. Long division by a two-digit number with a formal written method is a Year 6 expectation in England, and the sheet fits there on A4, without the US code.
A child who struggles with the steps here is often unsure of the earlier ones, so a few sheets of 4th grade math worksheets with multi-digit multiplication can help before returning. Children who are confident can try 5-digit dividends on the long division maker, which is where sixth grade long division picks up.
Questions
What math do 5th graders learn?
Most US fifth graders learn to multiply multi-digit numbers with the standard algorithm, divide four-digit numbers by two-digit divisors, add and subtract fractions with unlike denominators, work with decimals to hundredths, find the volume of rectangular solids and graph points on a coordinate plane. Schools vary in the order of these units.
Are these 5th grade math worksheets free with an answer key?
Yes. The sheet and its key are free to print or save as a PDF, with no account and no watermark. The key gives the quotient and the remainder of every problem, and New variant makes another set with the same settings whenever you need one.
Can I make long division without remainders?
Yes. Untick With remainders and every problem divides exactly. That suits the first lesson with two-digit divisors, when estimating the quotient is hard enough on its own; bring remainders back once the steps are secure.
Does the site have decimal worksheets for fifth grade?
Not yet. The math generators cover whole numbers, fractions, time, money and place value. For decimal operations, use the class textbook or another source; the multiplication and division sheets here are still useful practice for the steps decimal arithmetic depends on.
How many long division problems should a fifth grader do?
Five to nine problems with two-digit divisors is a full session, since each takes several minutes with careful working. The preset is nine. For homework, four or five carefully checked problems are often better than a full page done in a hurry.
Why does the remainder matter in the key?
The remainder shows whether the quotient is right. If a child's remainder is equal to or bigger than the divisor, the last quotient digit was too small. Comparing the remainder with the key is the quickest way to find where a problem went wrong.
Common Core State Standards: © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.