# Common Core Standards: Mathematical Concepts Your Child Should Learn in Grade 7

In Grade 7, for Common Core Standards, students use fractions to solve real-world problems involving ratios and unit rates — for example, using a fraction of a cup of seasoning per pound of meat cooked. The rules of operations are applied to negative numbers.

Students incorporate more characteristics and properties of geometric shapes, such as angle measurements and circumference, as a means of describing shapes, while their use of statistics explores the process of making generalizations about a population.

## Ratios and proportional relationships

Fractions are used in ratios, including the unit and rate. Students begin to identify proportional relationships and to describe the relationships that exist, such as percentages used in sales. They use tables and graphs to represent ratios and solve multistep problems involving real-world applications such as calculating tips and interest.

Build on your child’s understanding of ratios by looking at circumstances that involve a fraction. When cooking, encourage your child to predict which recipe will be saltier: a recipe that uses 3/4 tablespoons of salt per three pounds or a second recipe that uses 1/2 tablespoons per two pounds. (These ratios are equivalent and use the same amount of salt per pound.)

## The number system

Students continue to build their understanding of rational numbers and absolute value. They represent addition and subtraction on a number line and understand that subtracting a positive number from another positive number results in the same movement on the number line as when a negative number is added to a positive number. Students also use the rules for multiplying and dividing negative numbers with or by positive numbers and fractions.

Practice adding and subtracting negative numbers so that your child gains a sense of familiarity with the rules for sign change. Using a number line can help your child visualize addition or subtraction as a value moving up or down the number line.

## Expressions and equations

Students rewrite and solve equations and expressions with a *coefficient*, which is the number alongside a variable that’s used for multiplication. For example, in the expression 3*a*, 3 is the coefficient and is used to multiply the value of *a* by 3. Real-world problems that include several steps reinforce students’ previous understanding of equations and inequalities, and students actually use them to solve problems.

Reinforce the meaning of a coefficient by writing several terms that include coefficients, such as 2*a* or 5*a* (but remember that the variable *a* can be any letter). Have your child write out how many *a*’s there would be for each term.

For example, 2*a* = *a* + *a*, and 5*a* = *a* + *a* + *a* + *a* + *a*. After he gets a handle on this, add another term to the problem and make an equation such as 5*a* + 2 = 12 and let him solve to find the value of *a*.

## Geometry

In Grade 7, students begin to use drawings to solve problems, including those that involve the lengths of sides and the size of angles. Students find the circumference (distance around the outside) of a circle and solve multi-step problems using supplementary, complementary, vertical, and adjacent angles.

First use the formula for circumference (3.14 × the diameter of the circle) to complete simple problems on paper. Expand your child’s understanding of circumference by measuring circular objects around the house and calculating the circumference.

## Statistics and probability

Students use the statistical method of sampling (gathering and analyzing data from a small subset of a population) to make generalizations about a larger population. This allows them to compare and contrast groups efficiently while also considering the degree of variability (difference) in certain populations. They also explore probability and ways to express the likelihood of an event occurring.

Find the results of national polls and figure out the number of people actually included in the polls (the sample). Reinforce your child’s understanding of why samples are used in statistics. Ask your child if the population polled truly represents the larger population and discuss any problems that might arise when choosing participants.