Venn diagrams that organize the data in a story problem makes the information clearer. For instance, a problem explains there are 15 total students in band, 15 total students in choir, 10 students who are in both band and choir. Both the band and choir have the same number of students. A math question for this problem is, "How many total students are in either band or choir?"
Draw two interlocking circles. Label one band and one choir. The section that overlaps represents the students who are in both band and choir. Place the 10 in that section. Find the difference between 15 and 10. The difference is the answer to how many people are in band only and choir only. Now, all of the sections of the circle are filled in with data.
To answer the question presented add all of the sections. The number of students in both band and choir is 20.
Finding common factors of numbers is a skill needed for elementary school students as they begin working with fractions, ratios and more complex math. To find common factors with the Venn diagram, draw two interlocking circles. Label the circles; the labels will be the numbers you are finding the factors of. List the factors of each number. If the factor is common to both numbers, place it in the section where the circles interlock.
Students use the Venn diagram to find common multiples of two or more numbers. This activity works nicely on the interactive whiteboard. Display two interlocking circles on the board. Provide the multiples of the two numbers you are comparing around the circles for the students to manipulate into the proper circle. Ask the students to approach the whiteboard to place a multiple in the proper section. For instance, if the students are finding the multiples of five and four, the circles would be labeled 'five' and 'four'. They come to the board and place all of the common multiples in the interlocking section. The multiples that are exclusive to only five would go in the circle labeled five.
Use a Venn diagram in your class to define the attributes of polygons. In primary grades, the Venn diagram provides a place to sort polygons by shape and color. The circles are labeled 'circles' and 'blue.' Provide the students with a variety of shapes to sort. The blue circles would be properly placed in the interlocking section. Older students sort quadrilaterals. A variety of rhombus, squares and rectangles make this an activity to reinforce the attributes of each.