EngageNY
How Do Dilations Map Lines, Rays, and Circles?
Applying a learned technique to a new type of problem is an important skill in mathematics. The lesson asks scholars to apply their understanding to analyze dilations of different figures. They make conjectures and conclusions to...
EngageNY
Analytic Proofs of Theorems Previously Proved by Synthetic Means
Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....
EngageNY
How Do Dilations Map Segments?
Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions.
EngageNY
What Are Similarity Transformations, and Why Do We Need Them?
It's time for your young artists to shine! Learners examine images to determine possible similarity transformations. They then provide a sequence of transformations that map one image to the next, or give an explanation why it is not...
EngageNY
Equations for Lines Using Normal Segments
Describing a line using an algebraic equation is an essential skill in mathematics. The previous activity in the series challenged learners to determine if segments are perpendicular with a formula. Now they use the formula to determine...
Curated OER
Transformations and Matrices
There are four activities in this extensive lesson covering the identity matrix and scaling, the linear representation of translations, the linear representation of rotations, and reflections. In small groups, they use the Cabri II...
Curated OER
Inquiry Unit: Modeling Maximums and Minimums
Young mathematicians explore the maximun area for patio with the added complexity of finding the mimimum cost for construction. First, they maximize the area of a yard given a limited amount of fence and plot width v. area on a scatter...
EngageNY
Are All Parabolas Similar?
Congruence and similarity apply to functions as well as polygons. Learners examine the effects of transformations on the shape of parabolas. They determine the transformation(s) that produce similar and congruent functions.
West Contra Costa Unified School District
Derivative – Standard Definition
Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson begins with looking at limits of simple linear and rational functions, and leads to the definition of the derivative....
Curated OER
One Good Turn Deserves Another
Students make observations about shapes and 1-, 2-, and 3-dimensional objects. They conduct observations and make predictions regarding transformations of simple geometric shapes. They identify shapes that occur in household items.
Curated OER
Pick's Theorem
Students investigate polygons and their lattice. In this calculus lesson, students record data using different methods. They analyze their data and draw conclusions based on the relationship between the area and the interior lattice.
Curated OER
Quadratic Equations and Parabolas
Students graph and solve quadratic equations. For this functions lesson, students analyze a quadratic equation using three points on a curve to define the graph of a quadratic function. They find the vertex and intercepts of the graph.
Curated OER
Investigating Equations of Lines
High schoolers investigate linear equations as they use technology (Cabri, Jr.) to explore the equations of lines in slope-intercept form. The technology allows learners to manipulate the line and observe the changes in the parameters of...
Curated OER
Investigating the Slopes of Parallel and Perpendicular Lines
High schoolers investigate parallel and perpendicular lines. They use Cabri Jr. to construct and explore the relationships between the slopes of parallel and perpendicular lines. The drawing and measurement tools available with Cabri Jr....
Curated OER
Sled Kite Proportions
Students build sled kites. in this kite building lesson, students must read directions for kite building and enlarge the proportions of the given kite pattern. Students focus on the angles and line of symmetry in their kite.
Curated OER
Surveying our First President
Students act as surveyors. In this George Washington lesson, students read transcriptions from Washington's surveying journal and then try surveying skills on their own.
Curated OER
Visualizing Multiplication
Upper graders represent multiplication of a two-digit number by a two-digit number as the area of a rectangle with dimensions of the two factors. They find patterns for the number of different base ten blocks in a rectangle representing...
Alabama Learning Exchange
What You Know About the Bermuda Triangle?
Get lost in the classifications. Using the backdrop of the Bermuda Triangle, pupils classify it by angle and side measures. They also learn information about the triangle and its history.
Shodor Education Foundation
Pythagorean Theorem
Most adults remember learning about the Pythagorean theorem, but they don't all remember how to use it. The emphasis here is on developing an intuitive understanding of how and when to use the theorem. Young mathematicians explore...
Shodor Education Foundation
Visual Patterns in Tessellations
Geometers explore the concept of tessellations. They use a tessellation applet to manipulate shapes and design their own tessellation using the applet.
Virginia Department of Education
Lines and Angles
Explore angle relationships associated with transversals. Pupils construct parallel lines with a transversal and find the measures of the angles formed. They figure out how the different angles are related before constructing...
EngageNY
An Area Formula for Triangles
Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....
Alabama Learning Exchange
Triangle Congruence with Rigid Motion
Combine transformations and triangle congruence in a single lesson. Scholars learn to view congruent triangles as a rigid transformation. Using triangle congruence criteria, learners identify congruent triangles and the rigid...
Curated OER
Exploring Quadratic Data : Transformation Graphing
High schoolers analyze the vertex form of a parabola and find an approximate fit of a model. They explain the quadratic parabola function and its properties by developing quadratic models. They use translation and dilation to change the...
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