This 5th grade lesson presents the terms radius, diameter, and circumference of a circle, and helps students learn to use a compass to draw circles and simple circle designs.

# Circles

 These figures are round, but they are notcircles.  These are ovals. They are symmetric and round, but they are still not circles. Why not?What makes a circle?  The difference between other round figures and circles is this:In a circle, the distance from the center point to the actual circle line, or circumference of the circle, remains the same. This distance is called the radius of the circle. In other words, all the points on the circumference are AT THE SAME DISTANCE from the center point. This distance from the center point to any point on the circumference is called the radius. A line through the center point is called a diameter. 1. Draw a radius or a diameter from the given point. Use a ruler. Look at the example. Here, a radius is drawnfrom the given point. a. Draw a radius     from the given point. b. Draw a radius from     each of the given points. c. Draw a diameter    from the given point. d. Draw a diameter for     the smaller circle and     a diameter for the bigger     circle from the given points. e. Draw a radius from the     point A and a diameter     from the point B. 2. Learn to use a compass to draw circles. a. Draw many circles with the compass.

b. Now, set the radius on the compass to be 3 cm, and draw a circle.
You can do that by placing the compass next to a ruler, and adjusting
the radius of the compass until it is 3 cm as measured by the ruler.
Some compasses show the radius for you, so you won't need a ruler.

c. Draw a circle with a radius of 5 cm.

d. Draw a circle with a radius of 1 ½ in.

 3. a. Draw two diagonals into this square. Draw a point         where they cross (the center point of the square).         Now, erase the lines you drew, leaving the point.     b. Draw a circle around the square so that it touches         the vertices of the square. Use the point you drew         in (a) as the center point.     c. Fill in:  The _____________________ of the circle         has the same length as the diagonal of the square. 4. a. Draw a circle inside this square so that it touches         the sides of the square but will not cross over them.       b. Fill in:  The _____________________ of the square         has the same length as the diameter of the circle.    You can repeat or practice exercises #3 and #4 in     your notebook. 5. a. Draw a circle with center point (5, 6)         and a radius of 2 units. Use a compass.     b. Draw another circle with the same center         point, but double the radius.  6. Draw these figures using a compass and a ruler only in your notebook. The copies you draw do
not have to be the same exact size as here; they just need to show the same pattern. See hints at
the bottom of this page. Optionally, you can also draw these in drawing software.

a. b. c. d. See https://homeschoolmath.blogspot.com/2013/02/geometric-art-project-seven-circle.html
for one more circle design / art project!

a. Hint: Draw a line. Then, draw the three center points on it, equally spaced.

b. Hint: First, draw the three center points for the three circles, equally spaced.

What is the radius of the big circle compared to the radius of the small ones?

c. Hint: What pattern is there in the radii of these circles? These circles are called concentric circles because they share the same center point.

d. Hint: You need to draw the outer square first. Then measure and divide it into quarters. Measure
to draw the center points of the circles (they are  midpoints of the sides of the smaller squares).

This lesson is taken from Maria Miller's book Math Mammoth Geometry 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### Math Mammoth Geometry 1

A self-teaching worktext for 4th-5th grade that covers angles, triangles, quadrilaterals, cirlce, symmetry, perimeter, area, and volume. Lots of drawing exercises!