The circle is an important shape in geometry, with many important terms and relationships to understand. This activity will help your child grasp the concepts of circumference, radius and diameter and better conceptualize how they fit together.
Ask your child to measure the piece of string with the ruler and write down the length.
Help your child make a circle using the piece of string, placing it on a table. Review the term “circumference,” which is the distance around the edge of the circle. Explain that the length of the string is equal to the circumference, because if you were to undo the circle you would have the same length of string and the string is what comprises the distance around the circle. Try to make sure she understands that the length of string and the circumference are equal.
Next, review the term “diameter”. The diameter is the distance from one edge of the circle to the other that goes through the center of the circle. To show what the diameter looks like, get a second piece of string and place it in the middle of the circle from one edge to the other, cutting off any extra string that extends past the circle’s border. This straight piece of string going through the center of the circle is the diameter.
Take the diameter string off of the circle. Take a third piece of string and cut it so that it is half the length of the piece of string representing the diameter. Place this piece of string from the center of the circle to one of the edges of the circle and explain that this piece of string represents the radius. Reiterate the fact that the radius is one half the length of the diameter.
Once your child sees the relationships between these terms, do a practice problem using the pieces of string. Remind your child that the equation for circumference is 2πr, which is 2 times pi times the radius. Take the measurement of the first piece of string and use it to calculate what the radius should be. Another very useful concept in geometry to explain to your child is that if you know one of the relationships of the circle, either diameter, radius, or circumference, you can calculate all of the other values. So when doing math problems, she should focus on finding one of those values in order to be able to find the other values.