How does Grade 10 Math differ from Grade 9 in NY?

Grade 10 Math in NY focuses on Geometry, building on algebraic concepts from Grade 9. It introduces new spatial reasoning skills and proof-based thinking essential for advanced mathematics.

What support is available for struggling Grade 10 Math students?

Support includes after-school tutoring, online resources, peer study groups, and individualized help from teachers. Many schools also offer math labs for extra practice and one-on-one assistance.

What are the key learning expectations for Grade 10 Math in NY?

Students are expected to master geometric transformations, understand congruence and similarity, apply trigonometric ratios, and develop skills in constructing viable arguments and critiquing others' reasoning.

How challenging is the Geometry course in Grade 10?

Geometry can be challenging as it introduces new ways of thinking about math. It requires strong spatial reasoning and logical thinking skills. However, with consistent practice and support, most students can succeed.

How is Geometry assessed in Grade 10 NY curriculum?

Assessment includes regular quizzes, unit tests, projects, and a comprehensive final exam. Some schools may also incorporate standardized test preparation for state assessments or college readiness exams.

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Grade 10 Math Courses - NY Curriculum

Discover Grade 10 Geometry in NY's curriculum. Explore transformations, congruence, and trigonometry. Prepare for advanced math with our comprehensive course overview and learning pathways.

NY Grade 10 Math Curriculum - Geometry

ID	Math Standard Description	StudyPug Topic
NY.GEO-G.CO.1	Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.	Parallel and perpendicular line segments Line symmetry Angles in a circle Chord properties Circles and circumference Arcs of a circle Areas and sectors of circles

NY.GEO-G.CO.2

Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.

Introduction to transformations

Rotational symmetry and transformations

NY.GEO-G.CO.3

Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that carry the polygon onto itself.

Horizontal and vertical distances

NY.GEO-G.CO.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Congruence and congruent triangles

NY.GEO-G.CO.7

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Triangles congruent by SSS proofs

NY.GEO-G.CO.8

Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

NY.GEO-G.CO.9

Prove and apply theorems about lines and angles.

Parallel lines and transversals

Pairs of lines and angles

Parallel line proofs

Perpendicular line proofs

NY.GEO-G.CO.10

Prove and apply theorems about triangles.

Isosceles and equilateral triangles

Classifying triangles

NY.GEO-G.CO.11

Prove and apply theorems about parallelograms.

Area and perimeter of parallelograms

NY.GEO-G.CO.12

Make, justify, and apply formal geometric constructions.

Perpendicular bisectors

NY.GEO-G.CO.13

Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.

Inscribed angles and proofs

NY.GEO-G.SRT.1

Verify experimentally the properties of dilations given by a center and a scale factor.

Enlargements and reductions with scale factors

NY.GEO-G.SRT.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Similar triangles

NY.GEO-G.SRT.4

Prove and apply similarity theorems about triangles.

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

NY.GEO-G.SRT.5

Use congruence and similarity criteria for triangles to: a. Solve problems algebraically and geometrically. b. Prove relationships in geometric figures.

Similar polygons

NY.GEO-G.SRT.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of sine, cosine and tangent ratios for acute angles.

Use sine ratio to calculate angles and sides (Sin = o / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

NY.GEO-G.SRT.7

Explain and use the relationship between the sine and cosine of complementary angles.

Use cosine ratio to calculate angles and sides (Cos = a / h)

Cofunction identities

NY.GEO-G.SRT.8

Use sine, cosine, tangent, the Pythagorean Theorem and properties of special right triangles to solve right triangles in applied problems.

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

NY.GEO-G.SRT.9

Justify and apply the formula A= 1/2 ab sin (C) to find the area of any triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Area of triangles: 1/2 a*b sin(C)

NY.GEO-G.C.1

Prove that all circles are similar.

Central angles and proofs

NY.GEO-G.C.2a

Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.

Central and inscribed angles in circles

NY.GEO-G.C.2b

Identify, describe and apply relationships among radii, chords, tangents, and secants of a circle.

Central and inscribed angles in circles

NY.GEO-G.C.5

Using proportionality, find one of the following given two others; the central angle, arc length, radius or area of sector.

Radian measure and arc length

Converting between degrees and radians

Trigonometric ratios of angles in radians

NY.GEO-G.GPE.1a

Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Find the center and radius of a circle, given the equation of the circle.

Conics - Circle

NY.GEO-G.GPE.1b

Graph circles given their equation.

Conics - Circle

NY.GEO-G.GPE.4

On the coordinate plane, algebraically prove geometric theorems and properties.

Introduction to vectors

Slope equation:

m = \frac{y_2-y_1}{x_2- x_1}

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

NY.GEO-G.GPE.5

On the coordinate plane: a. Explore the proof for the relationship between slopes of parallel and perpendicular lines; b. Determine if lines are parallel, perpendicular, or neither, based on their slopes; and c. Apply properties of parallel and perpendicular lines to solve geometric problems.

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NY.GEO-G.GPE.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

NY.GEO-G.GPE.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

NY.GEO-G.GMD.1

Provide informal arguments for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of prisms

NY.GEO-G.GMD.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Surface area and volume of pyramids

NY.GEO-G.GMD.4

Identify the shapes of plane sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

NY.GEO-G.MG.1

Use geometric shapes, their measures, and their properties to describe objects.

Scale diagrams

NY.GEO-G.MG.2

Apply concepts of density based on area and volume of geometric figures in modeling situations.

Word problems of polynomials

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