9th grade and the beginning of high school marks a decisive phase in your child’s education. The math curriculum for individual grades will vary from school to school, so please consult our subject-specific math benchmarks.
For high school students, math skills and understandings are organized not by grade level but by concept. In High School Math: 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.
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.
Identify ways to rewrite the structure of an expression. For example, recognize that x8 - y8 is the difference between two squares, and can also be written: (x4)2 - (y4)2 or as (x4 – y4)(x4 + y4).
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.
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.
Help support and expand your teen's math skills outside of the classroom.
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.?
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.
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?
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.
For high school students, math skills and understandings are organized not by grade level but by concept. In High School Math: 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).
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.
Understand and prove geometric theorems about lines and angles, triangles, parallelograms, and circles. For example, Pythagorean Theorem, Line Intersection Theorem, Exterior Angle Theorem.
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.
Understand and use algebraic reasoning to prove geometric theorems.
Explain volume formulas and use them to solve problems.
What is the volume of a cylinder that is 10m high, and has a radius of 9m? (Use π = 3.14)
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.
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.
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)
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.).
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.)
Understand that complex numbers are formed by real numbers and imaginary numbers – imaginary numbers that, when squared, give a negative result: i2 = -1. Use the relation i2 = -1 to add, subtract and multiply complex numbers.
Understand a vector as a quantity that has both magnitude (length) and direction. Add and subtract vectors.
Solve problems involving velocity and other quantities represented by vectors.