United States · Common Core State Standards
10th Grade Mathematics
This course bridges the gap between foundational algebra and advanced geometric reasoning. Students explore the intersection of algebraic modeling and spatial relationships while developing rigorous proof-based logic and statistical analysis skills.
01The Language of Proof and Logic
Students move beyond intuitive understanding to formalize geometric relationships using inductive and deductive reasoning.
Students will differentiate between inductive and deductive reasoning and identify their roles in mathematical discovery and proof.
Exploring the structure of mathematical arguments through if-then statements, converses, and contrapositives.
Students will apply algebraic properties of equality and geometric properties of congruence to justify steps in proofs.
Investigating the unique angle relationships formed when parallel lines are intersected by a transversal.
Students will explore properties of perpendicular lines, including perpendicular bisectors and the shortest distance from a point to a line.
Developing the ability to write two-column and flow proofs to justify geometric theorems.
Students will learn to construct proofs by assuming the opposite of what needs to be proven and showing a contradiction.
Students will use a compass and straightedge to perform basic geometric constructions and understand their underlying principles.
Students will apply construction techniques to create parallel and perpendicular lines and justify their validity.
Students will explore the properties of medians, altitudes, angle bisectors, and perpendicular bisectors in triangles and their points of concurrency.
Students will apply the Triangle Inequality Theorem to determine if three given side lengths can form a triangle and to find possible ranges for a third side.
Students will use the Hinge Theorem and its converse to compare side lengths and angle measures in two triangles.
Students will consolidate their understanding of logical reasoning, proof structures, and geometric theorems covered in the unit.
02Transformations and Congruence
Students utilize rigid motions to define congruence and explore the properties of triangles and quadrilaterals.
Defining congruence through the lenses of translations, reflections, and rotations.
Students will explore dilations and other non-rigid transformations, understanding their effect on size and shape.
Students will identify and describe lines of symmetry and rotational symmetry in various two-dimensional figures.
Establishing the minimum requirements for proving two triangles are identical.
Students will apply SSS, SAS, ASA, AAS, and HL congruence postulates to write formal proofs.
Students will explore the properties of isosceles and equilateral triangles and use them in proofs and problem-solving.
Classifying four-sided figures based on their symmetry, side lengths, and angle properties.
Students will use coordinate geometry and formal proofs to establish properties of parallelograms, rectangles, rhombuses, and squares.
Students will calculate the area of various polygons, including triangles, quadrilaterals, and composite figures.
Students will calculate the perimeter of polygons and the circumference of circles, applying appropriate formulas.
Students will identify common three-dimensional figures and calculate their surface areas.
Students will calculate the volume of prisms, cylinders, pyramids, cones, and spheres.
Students will describe and draw the two-dimensional cross-sections of three-dimensional objects.
03Similarity and Trigonometry
Applying dilations to understand similarity and introducing right triangle trigonometry as a tool for indirect measurement.
Exploring how scale factors affect length and area in proportional figures.
Students will apply AA, SSS, and SAS similarity postulates to prove triangles are similar.
Students will apply the Triangle Proportionality Theorem and the Angle Bisector Theorem to solve for unknown lengths in triangles.
Students will use the geometric mean to solve problems involving altitudes and legs in right triangles.
Students will apply the Pythagorean Theorem to find missing side lengths in right triangles and its converse to classify triangles.
Students will discover and apply the side ratios of 45-45-90 and 30-60-90 triangles.
Defining sine, cosine, and tangent as ratios of side lengths in right triangles.
Students will use trigonometric ratios to find missing side lengths and angle measures in right triangles.
Students will apply trigonometry to solve real-world problems involving angles of elevation and depression.
Extending trigonometric principles to solve for missing parts of non-right triangles.
Students will use trigonometric formulas to calculate the area of triangles, including non-right triangles.
Students will introduce vectors as quantities with magnitude and direction, performing basic vector operations.
Students will review and apply concepts of similarity, Pythagorean Theorem, and trigonometry to solve complex problems.
04Quadratic Functions and Modeling
Students master the various forms of quadratic equations and use them to model parabolic motion and optimization.
Students will identify quadratic functions, their graphs (parabolas), and key features like vertex, axis of symmetry, and intercepts.
Comparing standard, vertex, and factored forms of quadratic functions.
Students will graph quadratic functions by identifying key features such as vertex, axis of symmetry, and intercepts.
Students will solve quadratic equations by factoring trinomials and using the Zero Product Property.
Students will solve quadratic equations by completing the square and understand its derivation.
Students will apply the quadratic formula to solve any quadratic equation, including those with complex solutions.
Students will use the discriminant to determine the number and type of real solutions for quadratic equations.
Mastering methods including factoring, completing the square, and the quadratic formula.
Applying quadratic functions to solve problems involving projectile motion and area optimization.
Students will analyze the properties of quadratic graphs, including domain, range, intervals of increase/decrease, and end behavior.
Students will compare and contrast quadratic and linear functions in real-world contexts, identifying when each model is appropriate.