Virginia Department of Education
Constructions
Pupils learn the steps for basic constructions using a straightedge, a compass, and a pencil. Pairs develop the skills to copy a segment and an angle, bisect a segment and an angle, and construct parallel and perpendicular lines.
101 Questions
Suitcase Circle
Analyze patterns in a circular arrangement. After using a geometric construction to complete a circle, learners use proportional reasoning to make predictions. By determining the length of an arc built from suitcases, they estimate the...
Texas Instruments
Drawing a Line Tangent to a Circle
Explore lines tangent to a circle. In this math lesson, students manipulate circles and lines on a TI calculator. They draw a circle and analyze perpendicular lines intersecting the circle in only one place. This activity works best if...
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...
Corbett Maths
Hexagon Inscribed Within a Circle
Mark off the length of the radius around the circle. Using a compass, the presenter shows how to construct a regular hexagon in a circle. Pupils see how triangles formed in the hexagon are equilateral, allowing for the construction to...
Curated OER
Unit VIII Worksheet 5: Circular Motion
Seven problems send physics stars out of this world! Challenge learners to calculate centripetal force, time to complete revolutions, circular speed, and acceleration. They also are asked to explain scenarios and draw a force diagram for...
Dick Blick Art Materials
Start with a Circle...
The Golden Ratio. The Divine Proportion. Yup. It's math and art blended into one colorful activity. Young artists combine colored tissue paper circles and parts of circles to create geometric patterns. As a bonus, kids get to figure out...
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...
EngageNY
Construct a Square and a Nine-Point Circle
Anyone can draw a square, but can you CONSTRUCT a square? Here is a resource that challenges math scholars to create steps to finish their own construction. They test their ability to read and follow directions to complete a construction...
Mathematics Vision Project
Circles: A Geometric Perspective
Circles are the foundation of many geometric concepts and extensions - a point that is thoroughly driven home in this extensive unit. Fundamental properties of circles are investigated (including sector area, angle measure, and...
EngageNY
Construct an Equilateral Triangle (part 2)
Triangles, triangles, and more triangles! In this second installment of a 36-part series, your young mathematicians explore two increasingly challenging constructions, requiring them to develop a way to construct three triangles that...
Mathematics Assessment Project
Sorting Equations of Circles 1
Round and round we go. Learners first complete a task on writing equations of circles. They then take part in a collaborative activity categorizing a set of equations for circles based on the radius and center.
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...
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...
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...
EngageNY
Tangent Lines and the Tangent Function
Construct tangent lines and make the connection to tangent functions. An informative instructional activity reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a...
Curated OER
Spanish Sentence Construction
After reviewing Spanish articles, nouns, noun gender, subject pronouns, and the verb ser, give your emerging Spanish speakers this practice packet. Several activities are included: an unscrambling exercise, translation practice, an...
Inside Mathematics
Circles in Triangles
Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...
Curated OER
"Circles of Strength: What Do You Stand For?" ~ A Reflection of Us~
Middle schoolers determine how they are included in "Circles of Strength." In this character activity, students reflect on how they are part of "Circles of Strength" in the "Circle of Life." They make an individual circle that includes...
Curated OER
Circle Graphs
In this circle graphs worksheet, students solve and complete 8 different problems that include word problems referring to two different circle graphs shown. First, they follow the directions for each problem and complete the table that...
Curated OER
Deriving the Formula For the Area of a Circle
Students derive the formula for the area of a circle. They form a rectangle by partitioning a circle using construction paper and scissors.
Curated OER
Inscribing a Hexagon in a Circle
This activity is a follow-on activity to inscribing a square in a circle. The overall problem is more complex. It deals with geometric constructions, properties of triangles, and regular hexagons. The final part of the activity finds the...
Curated OER
Inscribing a Square in a Circle
Inscribing a square in a circle brings up a number of interesting geometry topics including triangle congruence and how to prove a quadrilateral is a square. This activity is followed up by finding the area of the square and determining...
Curated OER
Construct, Bisect, Duplicate: Geometry Practice with Compass and Straight Edge
Geometers employ a straight edge and compass to duplicate and bisect segments and angles, construct perpendiculars, parallel lines, figures, and circles with points of concurrency. Ample practice with 65 questions across 8 worksheets. No...