Children in sixth grade are typically taught basic use of exponents. They learn that 2^2 is equal to 2x2, and that 4^4 means 4x4x4x4.
Children work with exponents in relation to larger math problems. For example 2^2 + 4^4 = (2x2) + (4x4x4x4). This is simplified to 4+256= 260.
Students learn about integers and negative numbers. Students may learn to add, subtract, multiply and divide negative numbers. Many teachers will use a number line to illustrate addition and subtraction of integers. In addition, students are taught that when you multiply or divide like signs, you get a positive answer, and when you multiply or divide unlike signs, the answer is always negative.
Factoring is introduced in sixth grade. Children learn how to break apart numbers and factor them into their prime factors. For example:
24
6x4
(3x2)x(2x2)
In sixth grade, students will review previously learned material regarding fractions, decimals and percents. During the fraction unit, students will be taught to multiply and divide fractions involving mixed numbers. For example. 2 1/5 + 4 3/5 is solved by first adding the fractional portion and then adding the whole portion, for a total of 5 4/5.
Students will explore the relationship between fractions and decimals and will learn to convert between the two notation methods.
Sixth-grade students also will learn how to solve basic problems involving percents. They will begin to understand how to use percents to figure price discounts. For example: The shirt is priced 30 percent off of its regular price. The regular price is $13. Find the discounted price.
To solve the above problem, first you much find out the amount of the discount. 13x0.30 = 3.90, so the shirt costs 13-3.90 or, $9.10
Sixth-graders review properties of geometric shapes and learn to use compass, protractor and straight-edges to construct specific geometric shapes. They use a protractor and compass to measure and identify angles. Students in this grade learn that a 90-degree angle is called a right angle, angles larger than 90 degrees are called obtuse and angles smaller than 90 degrees are called acute angles. Some sixth-graders may learn or review how to find the area, perimeter and volume of a geometric shape.
Sixth-graders study symmetry, congruence and similarity, and they use these concepts to draw geometric shapes to scale.
Metric and English systems of measurement are expanded upon from previous years.
Problem-solving skills are reviewed and practiced. Students learn to interpret and use more complex graphs, analyze and solve word problems. The concept of average, mean and mode are introduced, and students learn how to take a simple statistical sample.
Current calculator and computer skills are expanded by using calculators and computers to solve some mathematical and real-life problems. Computers may be used to help analyze graphs or find averages. Students in sixth grade often learn about professions that use computers to help analyze data or solve problems.