Help with Sixth Grade Advanced Math

Advanced Math for Sixth Grade

Rates, Ratios and Proportions

While most sixth grade students learn about ratios and rates in sixth grade, you might move on to study proportions if you're in an advanced math class. A proportion shows the relationship between two ratios, and you can use proportions to solve problems. For instance, if you know that a plane is traveling 800 miles per hour (800:1), you can use a proportion to figure out how many miles it will have traveled after any given number of hours.

This is an advanced math skill because it builds on another important sixth grade math concept: solving equations with one variable. Here's how it works:

1. Set up the proportion. For example, if you want to know how far the plane will have traveled in 3 hours, you can set up the proportion like this: 800/1 = x/3.

2. Multiply the numerator of each fraction by the denominator of the other fraction, and put the 2 answers on either side of an equals sign, like this: 800 * 3 = 1 * x.

3. Last, solve the equation. In this case, you can just simplify both sides to get the value of 'x.' Since 800 * 3 = 2,400 and 1 * x = x, this means x = 2,400. The plane will have traveled 2,400 miles after 3 hours.

Rational Number Operations

Sixth graders typically learn to graph, compare and order positive and negative numbers. If you're in an advanced math class, you might move beyond this to perform operations like addition, subtraction, multiplication and division with negative integers.

Adding and subtracting with negative numbers is simpler if you use a number line. The first number in the addition or subtraction problem is your starting point on the number line, and the sign (positive or negative) in the middle of the problem tells you which direction to go from your starting point. The second number in the problem tells you how many spaces on the number line you should move in that direction.

For instance, imagine you're given the problem -7 - 2. The -7 tells you to start 7 spaces to the left of 0 on the number line, and the '-' sign in the middle of the problem tells you to continue moving to the left. Since the second number is 2, you'll move 2 spaces to the left of -7 to the answer, -9.

For multiplication and division, just keep in mind that 2 negative numbers multiplied together always have a positive answer (-2 x - 3 = 6). When you multiply or divide 2 numbers with opposite signs, the answer is always negative (-2 x 3 = -6).