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# 10th grade math skills: Find out what you need to know for your student

In 10th grade, students will continue to deepen their understanding of complex math concepts.

Want to help your 10th-grader master math? Here are some of the skills your child will be learning in the classroom.

## Algebra

Overview

For high school students, math skills and understandings are organized not by grade level but by concept. In algebra, students work with creating and reading expressions, rational numbers and polynomials, and the conventions of algebraic notations. They apply these skills and understandings to solve real-world problems.

Understanding equations

Understand an equation as a mathematical statement that uses letters to represent unknown numbers (such as 2x-6y+z=14) and is a statement of equality between two expressions (“this equals that”). Explain each step in solving a simple equation, and construct a practical argument to justify a solution method. Graph these equations on coordinate axes with labels and scales.

Rewriting expressions

Identify ways to rewrite the structure of an expression.

Equation solutions

Understand that some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of x + 1 = 0 is an integer, not a whole number; the solution of 2x + 1 = 0 is a rational number, not an integer; the solutions of x² – 2 = 0 are real numbers, not rational numbers; and the solutions of x² + 2 = 0 are complex numbers, not real numbers.

Polynomials

Add, subtract, and multiply polynomials (expressions with multiple terms, such as 5xy² + 2xy - 7). Understand the relationship between the zeros and the factors of polynomials.

Polynomial identities

Use polynomial identities to solve real world problems.

A rectangular garden has a length of x + 2 ft. and a width of x + 8 ft. What must x be in order for the garden to have an area of 91 sq. ft.?

One-variable equations

Create equations and inequalities in one variable, and use them to solve problems, including weighted averages, calculation of mortgage and interest rates, and rate of travel.

Example:

A plane takes off from Chicago O’Hare airport, heading east and traveling at 580 miles an hour. Another plane takes off from O’Hare at the same time, heading west and traveling at 530 miles an hour. The two planes will be 1000 miles apart in how many hours?

Graphs

Represent, interpret, and solve equations and inequalities on graphs, plotted in the coordinate plane, and using technology to graph the functions and make tables of values.

## Geometry

Overview

For high school students, math skills and understandings are organized not by grade level but by concept. In geometry, students work primarily with plane, or Euclidean geometry (with and without coordinates). Students build on geometry concepts learned through 8th grade, using more precise definitions and develop careful proofs of theorems (statements that can be proved true).

Transformation

Understand geometric transformation (moving a shape so it is in a different position, but still has same size, area, angles, and lengths) – especially rigid motions: translations, rotations, reflections, and combinations of these – involving angles, circles, perpendicular lines, parallel lines, and line segments.

Geometric theorems

Understand and prove geometric theorems about lines and angles, triangles, parallelograms, and circles. For example, Pythagorean Theorem, Line Intersection Theorem, Exterior Angle Theorem.

Trigonometry

Understand trigonometry as a measurement of triangles (and circles, such as orbits). Apply trigonometry to general triangles. Define the sine, cosine, and tangent trigonometric ratios.

Algebraic reasoning

Understand and use algebraic reasoning to prove geometric theorems.

Volume formulas

Explain volume formulas and use them to solve problems.

Example:

What is the volume of a cylinder that is 10m high, and has a radius of 9m? (Use π = 3.14)

Real-life situations

Apply geometric concepts to model real-life situations.

• Use measures and properties of geometric shapes to describe objects – for example, model a tree trunk or a human torso as a cylinder.
• Apply concepts of density based on area and volume – for example, persons per square mile, BTUs per cubic foot.
• Design objects or structures to satisfy specific physical constraints or minimize cost.

## Numbers

Overview

For high school students, math skills and understandings are organized not by grade level but by concept. In High School Math: Number and Quantity, students extend their understanding of number to imaginary numbers and complex numbers, and work with a variety of measurement units in modeling. Emphasis is on using numbers – in calculations, equations, and measurements – to solve real-world problems, including those that students themselves quantify and define.

Rational and irrational numbers

Understand and explain why:

• the sum of two rational numbers is rational (sum can be written as a fraction or decimal)
• the sum of a rational number and an irrational number is irrational (sum cannot be written as a fraction; written in decimal form, is non-repeating and unending)

Interpreting and converting units

Consistently choose and interpret units in formulas; scale drawings and figures in graphs, data displays and maps. Convert rates and measurements (grams to centigrams, inches to feet, meters to kilometers, miles to kilometers, square inches into square feet, etc.).

Real-world problems

Use measurement units in modeling to solve real-world problems – for example: acceleration, currency conversions, per capita income, safety statistics, disease incidence, batting averages, etc.)

Complex numbers

Understand that complex numbers are formed by real numbers and imaginary numbers – imaginary numbers that, when squared, give a negative result: i&2sup; = -1. Use the relation i&2sup; = -1 to add, subtract and multiply complex numbers.

Understanding vectors

Understand a vector as a quantity that has both magnitude (length) and direction. Add and subtract vectors.

Velocity

Solve problems involving velocity and other quantities represented by vectors.

Example:

• Drew leaves home for a morning walk. He goes 13.5 km south and 5.5 km west. What is his velocity relative to his brother, who is still asleep in bed at home?
• Jack is doing push-ups. Which requires smaller muscular force – if his hands are 0.25m apart, or his hands are 0.5m apart?

For tips to help your 10th-grader in math class, check out our 10th grade math tips page.

Parent Toolkit resources were developed by NBC News Learn with the help of subject-matter experts and align with the Common Core State Standards.