 # Math Skills by Grade Level Unless you are a teacher, or you hyper-analyze every math assignment your child gets, it can be hard to know exactly what they should be mastering at each grade level. Is it appropriate to ask your Kindergartener to count the change you got from the supermarket? Can you depend on your 5th grader to accurately convert measurements for a recipe? You probably know the answer because you know your kids! But what should they know and be able to do?

The exact skills expected at each grade level depend on where you live and the kind of school your children attend. But whether their school follows Common Core, Next Gen, or some other framework for learning standards, there are some basic milestones that your child should be meeting based on her developmental age. Here’s what you should expect your child to be able to do as she progresses through the grades. Keep in mind that the skills listed below each grade are what she should be expected to do by the end of the year!

### Kindergarten

This is where students learn basic number sense. Counting, one-to-one correspondence (being able to recognize the specific quantity in a set of objects), and addition and subtraction within 10 are the major skills your kindergartener will be working on. Students will also begin to describe shapes using informal vocabulary like “curve,” “flat,” “corner,” “edge,” etc.

Students now learn various addition and subtraction strategies and can solve addition and subtraction problems within 20. They should be able to count to or above 100 and begin comparing measurements of objects. They should also be able to tell time on an analog clock to the hour and half hour.

By the end of second grade, students should be able to skip count by fives, tens, and hundreds. This forms the basis for next year’s introduction to multiplication. They should be fluent with adding and subtracting within 100 and should be able to apply strategies they’ve learned to problem solve within 1,000. Their measurements become more accurate and they begin to estimate.

In third grade, students begin learning about multiplication, division, and fractions. They explore and should eventually understand the relationship between multiplication and division, and they begin to relate their knowledge of both to fraction concepts. They are also introduced to area and perimeter of rectangles.

Students in Grade 4 become fluent with all four operations and should be able to use a variety of strategies in problem solving with multi-digit numbers. They start exploring division with remainders. They should be able to create and analyze mathematical patterns and will learn the terms ‘factor’ and ‘multiple.’ They are also introduced to decimals as they relate to fractions and begin converting measurements.

Students begin writing their own mathematical expressions to represent situations, both real and imagined. They can solve multi-digit problems in all four operations involving decimals and fractions. They are introduced to volume of objects, the coordinate plane, and properties of angles.

In addition to full mastery of skills in all previous grades, students are introduced to the following new concepts: ratios and proportions, statistics, rational and irrational numbers, inequalities, dependent and independent variables, and pre-algebra concepts.

Students in seventh grade apply the four operations to rational numbers. They can analyze proportional relationships in the real world and can solve problems involving angles, area, surface area and volume. They should also be able to interpret different types of data sets in order to make inferences.

By the end of eighth grade, students should be able to work with linear equations and functions, and they should know how to solve problems with radicals and exponents. This year, students learn the Pythagorean Theorem and should be able to apply it. They should also be able to find the volume and surface area of spheres, cones, and cylinders.

### High School

Math skills in high school are no longer separated by grade level, but by topic. By the end of high school, students should be able to demonstrate the following skills:

Numbers/Quantities

• Fluency with exponents and rational/irrational numbers

• Understanding of imaginary numbers

• Understand and use vectors and matrices

Algebra

• Solve polynomials

• Rewrite rational functions

• Solve systems of equations

• Solve and graph equations and inequalities

Functions

• Understand functions and use function notation

• Build and re-construct functions

• Build and compare linear and exponential models

• Understand basic trigonometry

Geometry

• Understand transformations and congruence

• Prove theorems, including with the use of coordinates

• Explain formulas and use them to solve problems

Statistics and Probability

• Summarize, represent, and interpret data and linear models

• Calculate probability in a variety of situations

• Evaluate experiments, surveys, and studies

• Understand independence and conditional probability

### Conclusion

This year has made it very challenging to keep up with demanding curricula. It’s possible that your students have not yet been introduced to a topic listed above. That’s okay! Trust their current and future teachers to be able to help address the gaps along the way, but you can also reach out to one of our amazing educators for additional tutoring support. Confidence in math can be a delicate thing, and our certified educators and math tutors are pros when it comes to boosting it!