What does a student learn in StateDelaware,GradeGrade 9,SubjectMathematics,Courseany course?

Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work.

Students take a real situation (a phone plan, a savings goal) and turn it into an equation, then work the math. When they get an answer, they check whether it actually makes sense in the original situation.

Students build a math argument by explaining why their answer works, then look at a classmate's reasoning and decide whether it holds up. The goal is to justify steps, not just show them.

Students take a real situation (a road trip, a sale price, a growing population) and write an equation or draw a graph that helps make sense of it. Math becomes a tool for answering questions that actually come up outside of school.

Students choose the right tool for the math in front of them: a calculator when precision matters, estimation when a close answer is enough, or pencil and paper to work through the steps. Picking the right tool is part of solving the problem.

Students use exact math vocabulary and correct units when solving problems and explaining their thinking. A measurement stays in meters, a rate stays in miles per hour, and the words students choose mean exactly what they say.

Students learn to spot patterns and hidden structure in math problems, like recognizing that an expression can be rewritten in a simpler form. That skill lets them solve new problems faster by seeing what they already know.

Students notice when the same steps keep appearing in a problem and use that pattern to find a shortcut or write a general rule. It's the habit of asking, "Why does this keep working?"

Students read a math problem carefully, figure out what it's actually asking, and keep working even when the path isn't obvious. They check whether their answer makes sense before moving on.

Students take a real problem (a triangle, a distance, an angle) and translate it into numbers or equations to solve it, then bring the answer back to explain what it means in the original situation.

Students back up math claims with logical steps and explain why a proof holds. They also listen to a classmate's reasoning and point out where it works or where it breaks down.

Students use math to make sense of real situations, like figuring out how much paint covers a wall or whether a design will fit a space. The math connects to something outside the classroom.

Students choose the right tool for the problem, whether that means a calculator, a sketch on paper, or a quick estimate. The skill is knowing which one to reach for.

Students use exact math vocabulary and label answers with the right units, such as inches or square feet. A precise answer isn't just correct; it's clear enough that someone else can follow the work.

Students spot patterns and hidden structure in shapes, equations, and diagrams, then use what they notice to solve problems faster or explain why something works.

When a solving method keeps working the same way, students stop and ask why. They turn that pattern into a rule or shortcut they can use again.

Students write and solve equations for straight-line relationships, then plot them on a graph. They use those equations to answer real questions, like figuring out total cost over time or when two quantities are equal.

Students write pairs of equations or inequalities and find the values that satisfy both at once. This skill shows up in budgeting, scheduling, and any problem where two conditions have to be true at the same time.

Students read a situation, write an equation where x is squared, and graph the curve it makes. This shows up in problems about thrown objects, areas, and anything that rises then falls.

Students read graphs and write equations for patterns that grow fast (like money earning interest) or shrink over time (like a car losing value). The focus is on recognizing and describing those patterns clearly.

Students add, subtract, and multiply polynomials, then read data from graphs and tables to draw conclusions about patterns and relationships between variables.

Rigid transformations are moves that keep a shape exactly the same size and angles: slides, flips, and turns. Students use those moves to show that two triangles or other figures are identical, then write a formal proof explaining why.

Students use triangle proportions and the sine, cosine, and tangent ratios to find missing side lengths and angles in right triangles. These tools also apply when two triangles have the same shape but different sizes.

Students use rules about angles, arcs, and line segments inside or crossing a circle to solve geometry problems. This includes finding missing angle measures or segment lengths when only partial information is given.

Students use equations and the coordinate grid to prove things about shapes. They might find the slope of two lines to show they're parallel, or calculate a distance to confirm two sides are equal.

Students calculate the area of flat shapes, the surface area and volume of 3-D objects, and apply those skills to real problems like estimating materials or comparing containers.