STEM Innovation Academy of the Oranges
445 Scotland Road South Orange, NJ 07079
 STEM Innovation Academy of the Oranges
 Integrated Mathematics II

In this unit students will use inductive reasoning and forming conjectures to perform rigid transformations for coordinate geometry. By the end of this unit, students will be able to write conjectures, use rigid transformations to justify conjectures, and use coordinate representations of figures and transformations in the coordinate plane to investigate and solve application problems. Students will also be able to specify a sequence of transformations, given a geometric figure and rigid transformations, that carry one figure onto another and describe transformations as functions and ordered pairs.

Unit 2: Dilations & Similarity
In this unit, students will start to explore nonrigid transformations, such as dilation, scale factor, and similarity, to identify unique relations within similar figures. Students will be able to understand dilation is not a rigid transformation and creates a similar figure, perform dilation on both a noncoordinate and coordinate plane with the scale factor given, and generalize a function rule for dilation with the origin as the center. Students will also be able to find the scale factor, given coordinates and graphs, dilate a line segment, and find the point on a line segment between two points that partitions the segment in a given ratio. By the end of this unit, students will be able to understand and utilize the Triangle Angle Theorem to solve problems. Students will also be able to define similarity, and apply the similarity postulates as a means to identify if two triangles are similar.

Unit 3: Triangles & Trigonometry
In this unit, students will dive deeper into the world of triangles with a focus on unlocking new problem solving techniques. Students will be exploring special right triangles, and the Pythagorean Theorem to understand how concepts, such as the distance and midpoint formulas, can be derived, and utilized on the coordinate plane. By the end of this unit, students will be able to apply the concept of similarity to explore trigonometric ratios for acute angles, and use trigonometric ratios to solve problems. Students will also explore inverse trigonometric functions, and be able to use them to find angle measures and solve complex problems.

In this unit, students will investigate the concept of intersecting and nonintersecting lines, and the angles created via their conjunction. Students will be exploring angle relationships to find unknown angle measures, and defining parallel and perpendicular lines. Students will also investigate the converse of corresponding angle relationships, prove the slope criteria for parallel and perpendicular lines, and write equations of lines that are parallel and perpendicular to given lines. By the end of this unit, students will be able to create formulas for the sum of the interior and exterior angles of a regular polygon. Students will also be able to utilize the criteria for special quadrilaterals to identify different types of quadrilaterals, recall math properties, formulas of lines/ line segments to prove given figures are quadrilaterals.

In this unit, students analyze relationships between segments and angles in circles, which leads to the construction of inscribed and circumscribed circles of triangles. Students solve problems involving arc length and sector area, and they use the similarity of all circles and ideas of arc length to develop the concept of radian measure for angles.

In this unit, students will investigate the area and perimeter of 2D geometric shapes, as well as the volume and surface area of 3D shapes. Students will be discovering the area and perimeter of shapes created by line segments on a coordinate plane, and investigating the volume and surface area of real world structures. By the end of this unit, students will be able to solve the area, perimeter, volume, and surface area of a variety of shapes based on various diagrams, contexts, situations, and descriptions given.