Circles

The radius is the distance from the center of a circle to its edge; the diameter is the distance across the circle through the center, and is always exactly twice the radius; the circumference is the total distance around the outside of the circle, the circle’s equivalent of a perimeter. Identify Parts of a Circle establishes all three before any formula uses them.

π (pi) is the constant ratio between any circle’s circumference and its diameter — no matter how big or small the circle, dividing its circumference by its diameter always gives the same number, approximately 3.14159. That constant relationship is exactly what makes the circumference and area formulas work for every circle.

Use C = πd if you know the diameter, or C = 2πr if you know the radius — both give the same answer, since diameter is always twice the radius. Solve Problems on Circumference of a Circle has kids practice both versions and also work backward, finding the radius or diameter from a known circumference.

Use A = πr², squaring the radius (not the diameter) and multiplying by π. Find the Area of a Circle and Composite Figures is where this formula gets introduced — a common early mistake is squaring the diameter instead, so it’s worth double-checking which measurement was given before plugging into the formula.

Using the diameter in a formula that calls for the radius, or vice versa — since the area formula A = πr² specifically needs the radius, a child given a diameter has to divide it by 2 first, which is easy to skip under time pressure.

A composite figure combines a circle (or a fraction of one, like a semicircle) with other shapes like rectangles or triangles. Find the Area of a Circle and Composite Figures has kids break the figure into its individual pieces, find each piece’s area separately using the right formula, then add (or subtract, for a cut-out shape) those areas together for the total.