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This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

Chunk a diagram and connect to what students know about congruent triangles to prove that two lines are perpendicular.

Student worksheet to find the distance of a line.

School mapped out on a grid that applies length and slope.

After this unit, how prepared are your students for the end-of-course Regents examination?  The end of unit assessment is designed to surface how students understand the mathematics in the unit.  It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.  A rich task, that allows for multiple entry points and authentic assessment of student learning, may be available for some units and can be included as part of the end of unit assessment.  All elements of the end of unit assessment are aligned to the NYS Mathematics Learning Standards and PARCC Model Frameworks prioritization. 

Chunk equations of lines to connect them to graphs using what one knows about lines.

This lesson unit is intended to help you assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines and, in particular, to help identify students who find it difficult to:

• Find, from their equations, lines that are parallel and perpendicular.
• Identify and use intercepts.

It also aims to encourage discussion on some common misconceptions about equations of lines.

Use the symmetry of an octagon and a Pythagorean triple to calculate the perimeter of an octagon.

Interactive website to hook student attention about the midpoint betwen two endpoints.

This page contains instructions on how to use the initial task, Squares and Rectangles, to find out what your students already know about using properties of shapes and coordinates.

Connect what students know about the Pythagorean theorem or similarity to justify why an angle in a triangle on a grid is 90 degrees.

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Creativity will be essential here as the only given information is the Cartesian coordinates of the quadrilateral's vertices.