Measure the Boundary of a Circle
A circle’s circumference is π times its diameter, equivalently 2π times its radius.
About 20 minutes, plus any extended practice
Open lesson 1Circle and Prism Measures
Geometric measures answer different questions: circumference is boundary length, area covers a region, and volume counts space. A formula works only when its input dimensions and output units match the question being asked.
Before you begin
- Multiply decimals; square a whole number; recognize radius and rectangle dimensions.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Measure the Region inside a Circle
Circle area is πr².
About 20 minutes, plus any extended practice
Open lesson 2Build a Volume from a Base and Height
A rectangular prism’s volume equals its base area times its perpendicular height.
About 20 minutes, plus any extended practice
Open lesson 3Count Both Faces in Each Opposite Pair
A closed rectangular box has three pairs of congruent faces.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Circle and Prism Measures
These references informed the topic selection. They do not certify complete standards alignment.