EngageNY
Writing the Equation for a Circle
Circles aren't functions, so how is it possible to write the equation for a circle? Pupils first develop the equation of a circle through application of the Pythagorean Theorem. The lesson then provides an exercise set for learners to...
Curated OER
Measuring the Area of a Circle
When mathematical errors happen, part of the learning is to figure out how it affects the rest of your calculations. The activity has your mathematicians solving for the area of a circular pipe and taking into consideration any errors...
Illustrative Mathematics
Right Triangles Inscribed in Circles I
One of the basic properties of inscribed angles gets a triangle proof treatment in a short but detailed exercise. Leading directions take the learner through identifying characteristics of a circle and how they relate to angles and...
Illustrative Mathematics
Tangent to a Circle From a Point
Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using information about...
Illustrative Mathematics
The Circle and The Line
Here is a resource where algebra learners show their understanding of a system of equations involving a circle and a line. Once graphed, learners see two points of intersection, one where the ordered pair is read, and a second where...
EngageNY
Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams
First angle measures, now segment lengths. High schoolers first measure segments formed by secants that intersect interior to a circle, secants that intersect exterior to a circle, and a secant and a tangent that intersect exterior to a...
EngageNY
Recognizing Equations of Circles
What does completing the square have to do with circles? Math pupils use completing the square and other algebraic techniques to rewrite equations of circles in center-radius form. They then analyze equations of the form x^2 + y^2 + Ax +...
EngageNY
Secant Lines; Secant Lines That Meet Inside a Circle
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.
EngageNY
Unknown Angle Problems with Inscribed Angles in Circles
We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The lesson then...
EngageNY
Special Triangles and the Unit Circle
Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value of...
EngageNY
From Circle-ometry to Trigonometry
Can you use triangles to create a circle? Learners develop the unit circle using right triangle trigonometry. They then use the unit circle to evaluate common sine and cosine values.
Illustrative Mathematics
Seven Circles III
A basic set-up leads to a surprisingly complex analysis in this variation on the question of surrounding a central circle with a ring of touching circles. Useful for putting trigonometric functions in a physical context, as well as...
Mathematics Assessment Project
Circles and Squares
Squares, and circles ... and squares, and more circles. In this high school assessment task, pupils investigate the ratio of areas of two squares that are circumscribed and inscribed in a circle. They then determine the ratio of the area...
Mr. Williams Maths
Eight Circle Theorems Page
Your learners will find these circle theorems nicely organized with diagrams included that present the geometric relationships between the circle circumference, chords, central and circumference angles and tangents.
Futures Channel
Folding Circles
Students investigate properties of circles. In this geometry lesson, students differentiate between similarity and congruence as they observe polygons. They investigate properties of two and three dimensional shape.
EngageNY
Close Reading of Bullfrog at Magnolia Circle: Main Ideas about the Bullfrog
As your class reaches the end of the book Bullfrog at Magnolia Circle, the seventh lesson in this literary unit helps third graders transition from reading narrative to expository writing. Scholars develop their note-taking skills as...
Curated OER
The Circle's Measure
Listen to the story "Sir Cumference and the Dragon of Pi" and solve the riddle and to save Sir Cumference from the knights. Your students will love mixing an activity with story and will practice their measuring skills while completing...
EngageNY
Close Reading of Bullfrog at Magnolia Circle: Text-Dependent Questions, Main Ideas, and Key Vocabulary about the Bullfrog
As your 3rd grade class finishes reading Bullfrog at Magnolia Circle, the eighth lesson plan of this unit helps readers from an understanding of the very specific information on the final page of the book. As with the entire unit,...
EngageNY
Continued Close Reading of Bullfrog at Magnolia Circle: Text-Dependent Questions and Vivid Words and Phrases
As 3rd graders continue reading Bullfrog at Magnolia Circle, they focus on the concepts of predator and prey in the fifth lesson plan of this unit. Scholars further develop their ability to answer questions using evidence from the text...
Curated OER
Counting Circles
Here is another learning game that will engage your kindergartners and support them with their counting fluency. Forming a circle where everyone faces inward, choose a counting sequence (counting frontward or backward) with no more than...
PBS
Scale City — Scaling up Recipes and Circles in the Real World
What a great big skillet you have. The resource introduces the class to the world's largest stainless steel skillet. The class creates a model of the skillet and a typical 12-inch skillet and compares the relative sizes of their areas....
Curated OER
Great Balls of Fire - I Got Locomotor Skills
Teach and review elementary locomotor skills. Use "Great Balls of Fire" by Jerry Lee Lewis to get youngsters up and grooving to the beat! The dance steps are described in rich detail and you will have the class jumping, skipping,...
Illustrative Mathematics
Representing Half of a Circle
Geometric shapes make great visual models for introducing young mathematicians to the concept of fractions. Looking at a series of four circles, students are asked to determine whether or not one half of each circle is shaded. To support...
EngageNY
Rectangles Inscribed in Circles
Putting a rectangular object into a circular one—didn't the astronauts on Apollo 13 have to do something like this? Learners first construct the center of a circle using perpendiculars. They then discover how to inscribe a rectangle in a...