In this unit, students will learn that circles share the attributes of perimeter (circumference) and area with other shapes and that the ratio of the circumference to the diameter is a constant. This extends students’ prior knowledge of perimeter and area of twodimensional figures. Students are likely to struggle with understanding the constant \(\pi\) as the ratio of the circle's circumference to it's diameter, and with manipulating the formulas for circumference and area.
Key Concepts:
 A circle is a set of all points that are equidistant points from a given point.
 The ratio of the measures of circumference and diameter is a constant and is denoted by the symbol Pi.
 The meaning of area does not change when figures do not have “sides” and the area of a circle can be related to the area of a parallelogram.
Prior Knowledge Needed:
 Find perimeter and area of 2d figures (squares, rectangles, and triangles); (3.G.A.1, 4.MDA.3, 5.NF.b.4.b, 6.GA.1, 6.GA.2, 6.GA.4, 6.EE.2.A.2.C).
Units on the Horizon:
 3D Figures (Grade 7, Unit 12)
Lessons

Lesson objective: Understand that a circle is the set of points that are all the same distance from another point, called the center. Students bring prior knowledge of circles from grade 3 (3.G.A1) and grade 4 (4.MDA.3). This prior knowledge is extended...

Lesson objective: Understand and apply the definitions of the parts of the circles to answer real life problems. This lesson provides an opportunity for students to apply their knowledge and understanding of radius, diameter, and circumference of a circ...

Lesson objective: Understand that the ratio of the circumference of a circle to its diameter is a constant and it is represented by the symbol π. Students bring prior knowledge of perimeter from fourth grade (4.MDA.3). This prior knowledge is extended t...

Lesson objective: Compute the circumference of a circle when given the radius or the diameter. This lesson helps to build procedural skill by solving the formula for circumference (C = πd). Circle diagrams are used here because they support the conceptu...

Lesson objective: Compute the radius or diameter of a circle given the circumference. This lesson helps to build procedural skill with the formula for the circumference of a circle. Real life examples, such as bicycle tires and tennis balls, are used he...

Lesson objective: Extend understanding of area for rectangles and parallelograms to circles. Students bring prior knowledge of the area of two dimensionsal shapes from grade 4 (4.MDA.3). This prior knowledge is extended to circles as students decompose ...

Lesson objective: Compute the area of a circle when given the radius or diameter of a circle. This lesson helps to build procedural skill with the formulas for the area of a circle. Real world examples are used here because it supports the relationship ...

Lesson objective: Compute the radius and diameter of a circle when given the area. This lesson helps to build procedural skill with exploring the realtionship between area, radius and diameter. Real world problems are used here because they support the ...

Lesson objective: Fluently find the area of a circle when given the circumference or fluently find the circumference when given the area of a circle. This lesson helps to build fluency with solving circle formulas relating circumference and area. Real w...

Lesson objective: Apply the formulas for circumference and area of a circle to creatively solve a problem. This lesson provides an opportunity for students to apply their knowledge and understanding of the area and circumference of a circle to a realli...