Illustrative Mathematics
Graphs of Quadratic Functions
The equations look different, but their graphs are the same. How can that be? This activity leads your mathematicians in an exploration of three different forms of the same quadratic function. After comparing the equations, their graphs,...
West Contra Costa Unified School District
Matching Quadratic Functions
Ever sigh when learners ask why they have to know so many different forms of the quadratic equation? Here is a lesson that comes in handy! Using hands-on matching activities, quadratic equations are explored through their graphical...
Mathematics Vision Project
Structures of Expressions
This comprehensive unit investigates transformations of quadratics, having learners follow "Optima" through the development and growth of her quilting business. Deftly weaving the story into the mathematical mechanics, the unit gives...
Curated OER
Transforming Parabolas
In this Algebra II worksheet, 11th graders examine the affects of changing h and k in the vertex form of the parabola. The three page worksheet provides explanation of topic, worked examples, and four practice problems. Answers are not...
Curated OER
Arithmetic Complex Numbers
Students convert quadratic functions from standard form to vertex form. In this algebra instructional activity, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.
Mathematics Vision Project
Module 7: Structure of Expressions
The structure of an expression is a descriptive feature. Learners build a solid understanding of quadratic functions using an analysis of expressions in different forms. The seventh module in a series of nine includes 12 lessons...
Curated OER
Writing Equations of Hyperbolas
In this writing equations activity, students write the equations of a hyperbola. This four-page activity contains 24 problems. Answers are provided on the last two pages.
Curated OER
Central and Inscribed Angles
For this central and inscribed angles worksheet, 10th graders identify and solve 20 different problems that include determining inscribed angles and intercepted arcs. First, they determine the measure of point P if the given angles are...
Curated OER
Concurent Circles I
In this concurrent circles using GeoGebra worksheet, students solve 2 short answer problems. Students construct concurrent circles using the GeoGebra software and determine why their construction of circles are concurrent. Students...
Curated OER
Reflections and Equilateral Triangles II
Given the lines of symmetry in an equilateral triangle, your learners find where the pre-image vertices are mapped onto the new image. They explore the properties of equilateral triangles, the impact of reflections, and the idea that the...
5280 Math
Triangle Area Patterns
Combine algebraic and geometric strategies to find solutions. The task asks learners to find the coordinates of a third vertex of a triangle to create a triangle with a specific area. The project is a set of seven problems that helps...
Illustrative Mathematics
Similar Triangles
Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...
Willow Tree
Three-Dimensional Figures
Time to move into the third dimension! Learn the names of the geometric solids and count faces, edges, and vertices. Then learn to recognize nets that create a given solid.
Curated OER
Building a General Quadratic Function
Learners rewrite a general quadratic function by completing the square to see a new form of the function that more easily identifies the x-coordinate of the vertex and the two roots of the function.
West Contra Costa Unified School District
Arcs and Angles
Noah didn't construct this kind of arc. High school scholars first explore how angles can be formed in circles. They then learn relationships between angles and arcs by conducting an exploratory activity where they position and draw arcs...
West Contra Costa Unified School District
Parallel Lines Cut by a Transversal
Parallel lines seem so right for each other. It's too bad they'll never, ever meet. Learners use tracing paper to discover relationships among angles formed by two parallel lines cut by a transversal. They apply this information to find...
Curated OER
Hyperbolas: Sketching from the Equation
In this algebra worksheet, students sketch graphs of hyperbolas after solving equations to standard form and interpreting the center, vertices, foci, axis, asymptotes, and eccentricity from the equation. There are 58 questions.
Curated OER
Mirror, Mirror
Geometry students use hinged mirrors to discover that the regular polygons are composed of triangles tessellating around a center point. They sketch triangles on paper models of the regular polygons having 3 to 10 sides and compute the...
Illustrative Mathematics
Building a General Quadratic Function
Rewrite a quadratic function to easily see the transformations involved. The instructional task takes a general quadratic function and rewrites it into a form that shows the translations and scaling of the parent quadratic function. The...
Illustrative Mathematics
Building an Explicit Quadratic Function by Composition
Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of composition...
Exploratorium
Rotating String Shapes
Here is a very interesting way of studying triangles and polygons. Pupils work together and use pieces of string to create a variety of shapes. Depending on how many kids are manipulating the string at any one time, the number of...
Exploratorium
String Shapes
You'd never have guessed it, but simple pieces of string make a fabulous manipulative for the study of geometry! In the fine lesson plan here, young mathematicians use string to make a variety of polygons. Pupils sit in various...
EngageNY
Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles
Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...
West Contra Costa Unified School District
Graphing Exponential Functions
Once you know how to graph y = b^x, the sky's the limit. Young mathematicians learn to graph basic exponential functions and identify key features, and then graph functions of the form f(x) = ab^(x – h) + k from the function f(x) = b^x.
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