# 9.22: Venn Diagrams

**At Grade**Created by: CK-12

**Practice**Venn Diagrams

Have you ever tried to adjust measurements? Take a look at this dilemma.

Isabelle, Isaac and Marc are very excited that their plans were accepted! The skate park builders are about to begin construction. The local lumber store has agreed to donate all of the wood that the team needs. To figure out what to ask for, the trio has collected a list of materials needed for the half pipe and the quarter pipe. Here is the list.

**Half Pipe**

42 8’ 2 \begin{align*}\times\end{align*}

5 8’ 2 \begin{align*}\times\end{align*}

4 8’ 2 \begin{align*}\times\end{align*}

12 8’ 1 \begin{align*}\times\end{align*}

4 8’ 4 \begin{align*}\times\end{align*}

2 \begin{align*}\frac{3}{4}''\end{align*}

12 \begin{align*}\frac{3}{8}''\end{align*}

**Quarter Pipe**

13 8’ 2 \begin{align*}\times\end{align*}

4 8’ 2 \begin{align*}\times\end{align*}

1 8’ 4 \begin{align*}\times\end{align*}

2 \begin{align*}\frac{3}{4}''\end{align*}

4 \begin{align*}\frac{3}{8}''\end{align*}

The team needs to organize the materials to figure out what materials both ramps have in common, and then which materials are unique to each ramp. By doing this, they can provide the lumber company with a list of materials needed for both ramps.

Isabelle thinks that it would be a good idea to design a Venn diagram, but Marc and Isaac aren’t sure how to do it. Isabelle thinks that she knows, but she isn’t sure.

**In this Concept, you will learn how to draw a Venn diagram to organize these materials. Pay close attention and you will have a chance to complete this diagram at the end of the Concept.**

### Guidance

We just used patterns to solve a word problem where common elements are featured.

**What about Venn Diagrams? What is a Venn Diagram?**

**A Venn Diagram shows the common numbers in two sets of objects or numbers by using overlapping circles.**

There are 280 girls and 260 boys playing on soccer teams this fall. If each team has the same number of girls and the same number of boys, what is the greatest number of teams that can be formed?

Now a Venn Diagram is used to show things that are common and things that are different. For this example, we can write the prime factors of 280 in one circle, the prime factors of 260 in the other circle and the common factors in the part of the circle that overlaps.

**By looking at this diagram, you can see that the common factors between 280 and 260 are 5, 2, and 2. If we multiply these together, we will have the total number of groups possible.**

**5 \begin{align*}\times\end{align*} × 2 \begin{align*}\times\end{align*}× 2 \begin{align*}=\end{align*}= 20**

**There are 20 possible groups.**

*A Venn Diagram helps you to organize data in a visual way to notice patterns and solve for the answer.*

Now it's time for you to try a few on your own.

#### Example A

True or false. A Venn Diagram is used when comparing two topics.

**Solution: True**

#### Example B

True or false. A Venn Diagram is best used for a survey.

**Solution: False**

#### Example C

True or False. A Venn Diagram will show you what two or three different topics have in common.

**Solution: True**

Here is the original problem once again. Reread it and then draw a Venn diagram to organize the materials for the two ramps.

Isabelle, Isaac and Marc are very excited that their plans were accepted! The skate park builders are about to begin construction. The local lumber store has agreed to donate all of the wood that the team needs. To figure out what to ask for, the trio has collected a list of materials needed for the half pipe and the quarter pipe. Here is the list.

**Half Pipe**

42 8’ 2 \begin{align*}\times\end{align*}

5 8’ 2 \begin{align*}\times\end{align*}

4 8’ 2 \begin{align*}\times\end{align*}

12 8’ 1 \begin{align*}\times\end{align*}

4 8’ 4 \begin{align*}\times\end{align*}

2 \begin{align*}\frac{3}{4}''\end{align*}

12 \begin{align*}\frac{3}{8}''\end{align*}

**Quarter Pipe**

13 8’ 2 \begin{align*}\times\end{align*}

4 8’ 2 \begin{align*}\times\end{align*}

1 8’ 4 \begin{align*}\times\end{align*}

2 \begin{align*}\frac{3}{4}''\end{align*}

4 \begin{align*}\frac{3}{8}''\end{align*}

**The team needs to organize the materials to figure out what materials both ramps have in common, and then which materials are unique to each ramp. By doing this, they can provide the lumber company with a list of materials needed for both ramps.**

**Isabelle thinks that it would be a good idea to design a Venn diagram, but Marc and Isaac aren’t sure how to do it. Isabelle thinks that she knows, but she isn’t sure.**

**If Isabelle draws a Venn diagram, what would it look like?** A Venn diagram shows the common elements of two different things. In this case, the Venn diagram would have two circles. One circle would be for the half pipe and one for the quarter pipe. We can begin by listing all of the needed materials in each circle.

**By organizing the date in this way, the students will be able to keep track of the lumber that has been donated. They can also be sure to request an accurate amount so that none is wasted. Using the Venn diagram has simplified the work for our skateboarding trio!!**

** Information in this problem is courtesy of** http://www.xtremeskater.com/

*and their free skateboard ramp plans!!*### Vocabulary

Here are the vocabulary words in this Concept.

- Venn Diagram
- shows the common numbers in two sets of objects or numbers by using overlapping circles

### Guided Practice

Here is one for you to try on your own.

What are the common factors of 12 and 80?

**Answer**

You can draw a Venn Diagram in your notebook to show these two values and their factors.

Here is a list of factors.

12

1 12

2 6

3 4

80

1 80

2 40

4 20

**The common factors are 1, 2, and 4.**

### Video Review

Here are videos for review.

James Sousa, Set Operations and Venn Diagrams Part 1

James Sousa, Set Operations and Venn Diagrams Part 2

James Sousa, Solving Problems with Venn Diagrams

### Practice

Directions: Create a Venn diagram for the following data.

1. The factors of 20 and 30.

2. The factors of 45 and 55

3. The factors of 67 and 17

4. The factors of 54 and 18

5. The factors of 27 and 81

6. The factors of 9 and 18

7. The factors of 100 and 200

8. The factors of 8 and 80

9. The factors of 120 and 144

10. The factors of 120 and 140

11. The factors of 80 and 100

12. The factors of 10 and 60

13. The factors of 70 and 140

14. The factors of 6 and 60

15. The factors of 330 and 900

Euler diagram

An Euler diagram is similar to a Venn diagram and is a visual representation of the relationship between sets, subsets, and members.Outcomes

The possible results of 1 trial of a probability experiment.probability

The chance that something will happen.Sample Space

In a probability experiment, the sample space is the set of all the possible outcomes of the experiment.Venn Diagram

A Venn diagram shows the common numbers in two sets of objects or numbers by using overlapping circles.### Image Attributions

Here you'll learn to develop and use the strategy: use a Venn Diagram.