In fourth grade, students focus most on using all four operations - addition, subtraction, multiplication, and division - to solve multi-step word problems involving multi-digit numbers. They extend their understanding of fractions, including equal (equivalent) fractions and ordering fractions. They add and subtract fractions with the same denominator (bottom number), multiply fractions by whole numbers and understand relationships between fractions and decimals.

## Addition, subtraction, multiplication & division

**Multi-digit whole numbers**

Quickly and accurately, add and subtract multi-digit whole numbers up to 1 million (1,000,000).

**Factors**

Understand factors – whole numbers (numbers without fractions) that can be multiplied together to get another number. Understand that one number can have several factor pairs – for example, 3 and 4 are factors of 12 (3 x 4 = 12), and so are 2 and 6 (2 x 6 = 12), and 1 and 12 (1 x 12 = 12).

Understand a prime number as having only one factor pair: one and itself.

**Relationship to place value**

Read, write, and compare multi-digit whole numbers, understanding that the value of a digit is ten times what it would be in the place to its right – for example, seven is 10 times greater than 0.7. Use understanding of place value to round multi-digit whole numbers to any place.

**Remainders**

Multiply a number of up to four digits by any one-digit number and multiply two two-digit numbers. Divide a number of up to four digits by any one-digit number, including problems with remainders. Explain and illustrate using equations and visual rectangular models.

Example:

Two hundred fifty doughnuts are divided evenly among six classrooms, How many doughnuts will each classroom receive, and how many doughnuts are left over for the principal?

**Word problems**

Solve multi-step word problems with whole numbers, using addition, subtraction, multiplication, and division problems with remainders. Use mental math and estimation strategies (such as rounding) to check how reasonable an answer is. Write equations for these problems with a letter standing for the unknown quantity.

Example:

A rectangular field has a perimeter of 400 yards. The field has a length of 125 yards and a width of w yards. Find w. 400 = 125 + 125 + w + w.

## Fractions

**Breaking down fractions**

Break fractions down into smaller fractions that have the same denominator (bottom number) in various ways.

Example:

3/4 = 1/4 + 1/4 + 1/4

3/4 = 1/4 + 2/4

**Adding and subtracting**

Add and subtract fractions with the same denominator (bottom number).

Example:

5/8 + 2/8 = 7/8

7/8 - 5/8 = 2/8

**Working With mixed numbers**

Add and subtract mixed numbers with the same denominators.

Example:

1 1/6 + 2 4/6 = 3 5/6

**Equivalent fractions**

Using visual fraction models – number lines, fraction bars (see example below), understand how fractions can be equal (equivalent) even when the number and size of the parts (the numerators and denominators) are different. Recognize and create equal (equivalent) fractions – for example: 2⁄4 = 1⁄2 (or 2⁄4 = 1⁄4 + 1⁄4).

**Numerators and denominators**

Compare two fractions with different numerators (top numbers) and different denominators (bottom numbers) by changing one or both fractions so that they both have the same denominator. For example, in comparing 3⁄8 and 4⁄16, use visual fraction models to understand that 4⁄16 is the same as 2⁄8.

Example:

3/8 > 2/8 so 3/8 > 4/16

**Comparing numerators**

Understand that in comparing two fractions with the same denominator, the larger fraction is the one with the larger numerator.

**Multiply fraction by whole number**

Solve word problems involving multiplication of fractions by a whole number.

Example:

Mary wants to make bows for six friends. Each bow requires 5⁄8 of a yard of ribbon. How many yards of ribbon does Mary need?

**Fractions as decimals**

Write fractions with denominators of 10 or 100 as decimals.

Example:

Write 4/10 as 0.4

Write 0.83 as 83/100

**Comparing fractions and decimals**

Compare numbers written as fractions and numbers written as decimals, using the symbols > (greater than), = (equal to), and < (less than). Use visual models such as fraction bars or number lines to explain and justify the answer.

## Measurement & data

**Word problems**

Solve word problems involving addition, subtraction, multiplication, and division of:

- units or intervals of time (seconds, minutes, hours)
- units of money (using decimal notation – for example: .25, .05, $2.35)
- units of mass (grams, kilograms)
- units of weight (ounces, pound)
- units of volume (milliliters, liters)
- units of distance/length (inches, feet, yards, miles, centimeters, meters, kilometers)

Example:

Practice converting larger units to smaller units by multiplying. For example, three hours = 3×60 = 180 minutes.

Emma studied for one hour. Ethan studied for 15 minutes. What is the difference in the number of minutes they studied? Emma's study session was how many times longer than Ethan's?

## Geometry

**Perimeter**

Understand perimeter as the measurement around something, and area as the measurement of the flat surface inside the perimeter of something. Find perimeter and area to solve real-world cost problems.

Example:

Juan wants to carpet his bedroom. His bedroom is two yards wide and five yards long. The carpeting costs $7 per square yard. How much will Juan’s new carpet cost? Explain or illustrate how you solved this problem.

Juan decides to put a decorative border high all the way around his room near the top of the walls. The border costs $3 per yard. How much will the border cost? Explain or illustrate how you solved this problem.

Tip: Use math in house projects

Encourage your child to use his math skills for projects around the house. If you’re wallpapering or carpeting, for example, have him calculate wall or floor areas and figure out the total cost of various materials.

**Lines and angles**

Draw and identify different types of lines and angles, including line segments, rays, parallel lines, perpendicular lines, and right angles. Use the presence or absence of these lines or angles to categorize or group (classify) two-dimensional shapes or figures such as rectangles, parallelograms, trapezoids, and triangles.

Tip: Keep an eye out for math concepts

Encourage your child to spot examples of some of the math concepts he is learning about. See how many right angles or right triangles he can spot. Or have him look for parallel lines, such as train tracks or pillars in a building.

**Lines of symmetry**

Understand line of symmetry: a line across a two-dimensional figure such that the figure can be folded along the line into identical matching parts. Identify the most common symmetrical shapes: circles, squares, rectangles, ovals, equilateral triangles (three equal sides), isosceles triangles (two equal sides), hexagons, and octagons.

For tips to help your fourth-grader in math class, check out our fourth grade math tips page.

*Parent Toolkit resources were developed by NBC News Learn with the help of subject-matter experts, and align with the Common Core State Standards.*