5th Grade Math

By the end of fifth grade, students should be able to demonstrate the following math abilities. Many skills are worked on throughout the year and build on each other.

Multiplication and division with larger numbers

• Multiply any two numbers by hand (without a calculator).
• Divide up to four-digit numbers by two-digit numbers by hand (ex. 3450 ÷ 25). The answer can have a remainder (the amount left over) but children in fifth grade are not expected to carry out the division into decimals.

Fractions and decimals

• Read, write and compare decimals to thousandths. For example, which is larger, 0.097 or 0.25?
• Add, subtract, multiply and divide decimals to tenths and hundredths.
• Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. For example, 13 cookies are being shared among 5 children. How many cookies does each child get? 13 ÷ 5 = 13/5 = 2 3/5. So each child gets 2 full cookies plus 3/5 of a cookie. Children often solve these problems in early fifth grade by making drawings to show how they would equally share the 13 cookies.
• Add and subtract fractions that have different denominators, such as 3/4 – 1/8. Solve word problems with addition and subtraction of fractions that have different denominators, using drawings or objects if needed.
• Multiply a fraction or a whole number by another fraction and understand what it means to do this (ex. 4/5 x 1/2 means one-half of 4 fifths, which is 2 fifths.)
• Divide a fraction by a whole number and understand what it means to do this (ex. 4/5 ÷ 2 means 4/5 shared equally among 2 people, each getting 2/5). Divide a whole number by a fraction (ex. 5 ÷ 1/2 means “how many times does 1/2 go into 5?” The answer is 10.)

Measurement and geometry

• Understand how to measure and calculate the volume of a container.
• Draw coordinate graphs to represent pairs of numbers. In this example, the points represent (1,1), (2,2), (3,1), (4,2) and (5,3).