IE 11 is not supported. For an optimal experience visit our site on another browser.

# 5th grade math skills: Find out what you need to know for your student

Fifth-graders will continue to deepen their understanding of addition, subtraction, multiplication, and division of fractions.

## Addition, subtraction, multiplication, & division

Multi-digit whole numbers

Quickly and accurately, multiply multi-digit whole numbers. Divide whole numbers (up to four digits) by two-digit numbers.

Example:

Solve 4,824 ÷ 12 = ?

Explain or illustrate how you solved this problem.

Tip: Highlight real-world uses of math.

As the math they’re learning becomes more complicated and less obviously connected with their everyday experience, some children start to develop math anxiety. It’s important to keep your child engaged with math and to help her understand the real-life applications of the concepts your child is learning in school. Coming up with a budget for back-to-school supplies or for their monthly allowance is one way for them to practice addition and subtraction. Asking them to help you with cooking or baking shows them how fractions work. Helping you calculate prices when you’re grocery shopping is also good practice.

Understanding place value

Extend understanding of place value: in a multi-digit number, a digit in one place represents 1⁄10 of what it represents in the place to its left, and 10 times as much as it represents in the place to its right.

Comparing decimals

Read, write, and compare decimals to the thousandths place, using the symbols > (greater than), and < (less than). For example:

• Read this decimal number: 23.002.
• Write two and sixty-two thousandths as a decimal number.
• Which sign makes this statement true: 5.389 _?_ 5.420
• The researcher is measuring bacteria that have grown on samples of unrefrigerated food. Your child counts 73.343 million bacteria in Sample A, 73.431 million bacteria in Sample B, and 74.399 million bacteria in Sample C. Put the samples in order, from greatest amount of bacteria to least. Explain or illustrate how you put these samples in order.

Decimals to the hundredths

Add, subtract, multiply, and divide decimals, to the hundredths.

Tip: Practice calculations using decimals.

Connect the work with decimals that your child is doing in class to the real world by encouraging them to shop for bargains. Have them divide the cost of bulk-packaged items by the number of single items to find the cost per item. So how much are you paying per roll of paper towel or per can of soda when you buy in bulk? Or ask your child to calculate how much of a savings you’ll make per item with sale prices offering volume discounts.

Understanding exponents

Understand what an exponent is. For example, the ‘2’ in 10² indicates how many times to multiply the number by itself. 10² can be read as “10 to the second power” or “10 to the power of 2” or “10 squared,” and means 10 x 10, or 100. 10³ (or “10 to the third power” or “10 cubed”) means 10 x 10 x 10, or 1,000.

## How to Master Math: Fractions

June 4, 202000:51

## Fractions

Solving word problems

Solve word problems involving addition and subtraction of fractions.

Example:

The fifth-grade class is assembling a 600-piece jigsaw puzzle. They started yesterday and put together 100 pieces – just one-sixth ( 1⁄6 ) of the puzzle. Today, they put together 400 pieces. What fraction of the puzzle is complete? Draw a picture AND write out the math to show how you solved the problem.

Tip: Highlight real-world uses of math.

As the math they’re learning becomes more complicated and less obviously connected with their everyday experience, some children start to develop math anxiety. It’s important to keep your child engaged with math and to help her understand the real-life applications of the concepts she’s learning in school. Coming up with a budget for back-to-school supplies or for her monthly allowance is one way for her to practice addition and subtraction. Asking her to help you with cooking or baking shows her how fractions work. Helping you calculate prices when you’re grocery shopping is also good practice.

Finding the common denominator

Solve word problems involving the addition and subtraction of fractions with different denominators (bottom numbers), by converting them to fractions that have the same denominator, called a common denominator.

Example:

The tallest girl in the fifth-grade class is 51 7⁄8 inches tall. The tallest boy in the fifth-grade class is 49 1⁄2 inches tall. What is the difference in their heights?

After the party, there are two bowls of lemonade left over. One bowl has 1⁄3 of a gallon of in it. The other contains 1⁄2 of a gallon of lemonade. A friend says you shouldn’t try to combine the two into a 1-gallon container because the lemonade will spill over the top. Do you agree? Why or why not?

Multiplying fractions

Solve word problems involving multiplication of fractions by other fractions, and multiplication of fractions by mixed numbers (a whole number and a fraction, such as 11⁄4 or 21⁄2).

Example:

• In the middle school orchestra, 1⁄3 of the student musicians play a string instrument. Of the students who play a string instrument, 3⁄4 play the violin. What fraction of the orchestra plays the violin?
• In the morning of their field trip to the apple orchard, the fifth-graders picked 4⁄5 of a bushel of apples. After lunch at noon, they picked 21⁄2 times as many apples. Will all of the apples they picked in the afternoon fit into a 2 bushel crate? How do you know?

Tip: Practice using fractions.

Help your child familiarize herself with fractions by asking her to scale recipes for your family. Have them start by halving or doubling a recipe. When they feel comfortable doing this, ask them to convert it by 11⁄2, allowing a recipe that is supposed to feed a family of four to work for a family of six.

Dividing unit fractions

Divide unit fractions (fractions with 1 as the numerator, or top number) by whole numbers. Divide whole numbers by unit fractions.

Example:

If three people share ½ lb. of chocolate equally, how much chocolate will each person get? Explain or illustrate how you solved this problem.

Multiplying by fractions

Understand that multiplying a number by a fraction less than 1 will result in an answer less than the number – for example: 12 x ¾ = 9. Multiplying a number by a fraction greater than 1 will result in an answer greater than the number – for example: 12 x 2 ½ = 30.

## Measurement & data

Converting units and fractions

Convert units and fractions of units within the same system of measurement.

Example:

How many minutes is 1⁄5 of an hour? Explain or illustrate how you solved this problem.

Multi-step unit conversion problems

Solve multi-step word problems using conversions of different-sized standard measurement units.

Example:

I have 75 cm of ribbon. I need seven times as much ribbon to complete a project. How many more meters of ribbon do I need?

Explain or illustrate how you solved this problem.

Using a line plot

Solve problems using information (in fraction units) presented in a line plot.

## Geometry

Understanding volume

Understand volume as the measurement of the space inside a three-dimensional or solid figure. Use the formulas length x width x height or base x height to measure the volume of a three-dimensional or solid object with rectangular sides, like a cube. Measure volume to solve real-world problems.

Example:

A rectangular container of ice cream has a length of 8 inches and a height of 4 inches. What is the volume of the container, expressed in cubic inches?