Grade 6 math introduces students to new skills for Common Core Standards involving the use of ratios and unit rate, absolute value, and variables and exponents to extend students’ abilities to use math to solve a variety of problems. Geometry expands to include the calculation of area and volume, while statistics is introduced as a means of learning about a population.

## Ratios and proportional relationships

Students encounter new concepts in this domain as they take a look at ratios and unit rate for the first time. A ratio is a comparison between two numbers; for example, if you have 7 dogs and 12 cats, the ratio of dogs to cats is 7 to 12 or 7:12.

A unit rate is a ratio that compares a number to a singular quantity, such as miles per gallon (mpg) or dollars per pound. They describe ratios in terms of their relationship with the singular quantity to express amounts using unit rate. Students use both concepts to solve real-world problems.

Take advantage of meal preparation as a teachable moment. This is a great opportunity to show your child what ratios look like and how they are used in real-life situations. Look at the sticker on a package of meat purchased at the store (hide the price per pound) and have your child explain how much it costs per pound based on the number of pounds and the total price.

For example, if a package of ground beef costs \$7 and weighs four pounds, your child can divide 7 by 4 to determine how much the meat costs per pound (\$1.75).

## The number system

The number system domain overlaps considerably with operations. Grade 6 students find out how to divide fractions by fractions and use addition, subtraction, multiplication, and division to fluently solve problems with multi-digit numbers. Students encounter negative numbers and describe the relationship between positive and negative numbers on a number line.

They also encounter the concept of absolute value — a number’s distance from zero on a number line regardless of whether the number is to the right or the left of zero. The distance from zero is always a positive measurement. This number system includes the use of rational numbers — whole numbers and fractions.

Reinforce absolute value with positive and negative numbers using a number line and a small object. Draw a number line starting at negative 10 on the left, zero in the middle, and positive 10 on the right with intervals of 1. Place an object on a positive or negative number and ask your child to tell how far away the object is from zero.

Ask your child to describe the number in terms of absolute value, or the distance from zero. Repeat with different numbers of objects placed on positive and negative numbers. Remember that no matter how far the number is from zero on the number line, the absolute value of the number is always positive.

Avoid confusion with fractions by continually reminding your child that a fraction is only a part of a whole. This especially helps when dividing fractions. For example, if your child needs to divide 6 by 2, ask her how many groups of 2 are in 6, with the answer being 3.

If your child needs to divide 3/4 by 1/2, use the same logic. How many groups of 1/2 are in 3/4? She’ll find one whole group of 1/2 and half of another group of 1/2 in 3/4.

## Expressions and equations

Students use symbols (such as x and y) to represent and solve for unknown quantities in equations. They’re also introduced to the use of exponents in equations.

An exponent is a number that appears above and to the right of a number to indicate how many times it must be multiplied by itself; for example, 23 = 2 × 2 × 2 = 8. The symbols representing inequalities (> and <) are used in problems and for the purpose of representing values on a number line.

Get familiar with the use of exponents by practicing problems that use them on a frequent basis. Ask your child to explain what an exponent indicates and support him in explaining that the exponent tells you how many times a number should be multiplied by itself.

## Geometry

Students find the area and volume of shapes and are also asked to draw shapes in the coordinate plane for the purpose of finding the length of sides.

Continue to practice finding the area and volume of shapes on paper or by measuring objects around your home environment and applying the formulas for area and volume.

## Statistics and probability

Students explore the purpose and use of statistics and identify situations that involve the need for data collection because the characteristics of a population will vary. When looking at collected data, they must be able to display data in various ways (such as on graphs and charts) and make determinations about the distribution of data as it relates to the similarities and differences in the population.

Reinforce your child’s grasp of statistics by collecting some data of your own. Create a list of choices, such as colors or ice-cream flavors, and let your child poll friends and/or family members. Then she can make a visual representation on paper or in a computer spreadsheet and draw conclusions about the preferences of the people (or population) represented in the poll.