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1. Foundations of Geometry
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Geometry

1.01 Introduction to the data cycle and Venn diagrams

Lesson
Practice
Adaptive
Worksheet
What do you remember?
1

Enoch wants to explore the statistical question: "How do the proportions of dog and snake owners compare for students at my school?"

a

Determine whether or not the responses to each survey question could be used to create the given Venn diagram.

i

What kind of pets do you have?

ii

Which type of pets do you have? Select all that apply.

A

Dog

B

Snake

C

None of the above

iii

Firstly, do you own a dog? Secondly, do you not own a dog?

iv

Firstly, do you own a dog? Secondly, do you own a snake?

b

Complete the sentence using the words 'Dog' or 'Snake':

i

The two categories in the diagram are ⬚ owners and ⬚ owners.

ii

2 is the number of people who have a ⬚ AND a ⬚.

A venn diagram with 2 sets: Dog owners and Snake owners. Dog owners consist of number 13, Snake owners consist of numbers 3, The intersection of 2 sets consist of number 2, and outside the sets is number 11.
2

A student creates this diagram of their favorite animals. Is each statement true or false?

a
Zebras have four legs and stripes.
b
Four of their favorite animals have four legs.
c
Three of their favorite animals have stripes.
d
A clown fish has stripes, but does not have four legs.
e
A ring-tailed lemur would have the same classification as a zebra.
f
A lion would have the same classification as a tiger.
A Venn Diagram made up of two overlapping circles showing the relationship between animals with four legs and animals with stripes. Inside the non-overlapping portion of the circle under Four legs are Turtle, Hippo, Lion and Elephant. Under the non-overlapping portion of the circle under Stripes is Clown fish. The overlapping portion contains Zebra and Tiger. Outside the circles and inside the box are Crow and Kangaroo.
3

A gardener creates this diagram of her favorite plants:

a

How many of the plants are flowering plants?

b

How many of the plants are both flowering and succulent?

c

How many of the plants are either flowering or succulent, but not both?

A Venn Diagram made up of two overlapping circles showing the relationship between flowering plants and succulent plants. Inside the non-overlapping portion of the circle under Flowering are Orchid, Daisy, Tulip and Sunflower. Under the non-overlapping portion of the circle under Succulent is Aloe Vera. The overlapping portion contains Christmas Cactus and Crown of Thorns. Outside the circles and inside the box are Bamboo and Ivy.
4

This Venn diagram represents the languages spoken at an international conference.

Shade the region in the Venn diagram for participants who speak only English and French.

A Venn diagram of four languages: English, French, Japanese and Mandarin. All four circles are overlapping
5

The given Venn diagram shows the number of students in a school playing rugby league, rugby union, both or neither:

Find the number of students who:

a

Play rugby league only.

b

Play rugby league.

c

Play rugby union.

d

Play rugby union only.

e

Do not play rugby league.

f

Do not play rugby union.

A Venn Diagram showing two overlapping circles labeled Rugby League and Rugby Union inside a rectangle. The overlapping area has the number 54. The non-overlapping area of the circle labeled Rugby League has the number 169. The non-overlapping part of the circle labeled Rugby Union has the number 138. Outside the circles but inside the rectangle is the number 124.
6

Carl collects data from the local pet shelter and makes a Venn diagram. He is curious about what would happen if he selected a pet at random.

a

Find the probability that his new pet will be a cat that isn't fluffy.

b

Find the probability that his new pet won't be fluffy.

A Venn Diagram showing two overlapping circles labeled Cats and Fluffy inside a rectangle. The overlapping area has the number 12. The non overlapping area of the circle labeled Cats has the number 6. The non overlapping part of the circle labeled Fluffy has number 10. Outside the circles but inside the rectangle is the number 5.
7

The table and Venn diagram show the same information:

GuitarNot GuitarTotal
Piano204060
Not Piano9050140
Total11090200
A Venn Diagram showing two overlapping circles labeled Piano and Guitar inside a rectangle. The overlapping area has the letter B. The non overlapping area of the circle labeled Piano has the letter C. The non overlapping part of the circle labeled Guitar has the letter D. Outside the circles but inside the rectangle is the letter A.

Find the value of:

a

A+B+C+D

b

B

c

B+C

d

B+D

Let's practice
8

Write two statistical questions that could be summarized with the given Venn diagram.

A Venn Diagram representing the relationship between teachers who own a pet and teachers who own a car. A portion of the circle labeled owns a pet overlaps with a portion of the circle labeled owns a car.
9

For each given survey question(s), can the results be summarized in a Venn diagram? If so, sketch the Venn diagram. If not, explain why not.

a

What is your favorite sport?

b
Which other languages can you speak? Select all that apply.
A

Spanish

B

French

C

Dutch

D

None of the above

c

Which pets do you have?

A

Cat

B

Dog

C

Other. Fill in the box: ⬚

d
  1. Have you taken public transportation this year?
  2. Do you have your driver's license?
10

The investigative question "Compare and contrast the characteristics of two state animals in Virginia." The following information was collected using a secondary source.

Two of Virginia's state animals are the Red Salamander and Eastern Garter Snake. Organize the given characteristics in a Venn diagram.

Red Salamander

  • Four legs

  • Carnivorous diet

  • Live in moist, forested habitats

  • Cold-blooded

  • No scales

  • Amphibian

  • Brightly colored red or orange

  • State animal in Virginia

Eastern Garter Snake

  • No legs

  • Carnivorous diet

  • Live in moist, forested habitats

  • Cold-blooded

  • Has scales

  • Reptile

  • Greenish, brown, or black

  • State animal in Virginia

11

A survey was conducted and students were asked if they have been out of state before and if they have a passport. The results are recorded in the table.

a

Complete the table to summarize the survey results.

Has a passportDoes not have a passport
Has been out of state
Has not been out of state1
b

Convert the table to a Venn diagram.

Has been out of stateHas a passport
AnayaYesNo
BenNoNo
ConnieYesYes
DaiYesNo
EnzoNoYes
FaridaYesYes
GoldieYesNo
HanYesYes
IsabellaYesYes
JoyYesNo
KhalilYesNo
LizzieYesYes
MasumiYesNo
12

A librarian checks on the status of 30 books one day. The books are categorized based on whether they are fiction and whether they have been borrowed.

a

Using the Venn diagram, complete the table:

BorrowedAvailableTotal
Fiction
Non-fiction
Total
b

What percentage of books are fiction and available?

c

What percentage of books are fiction and have been borrowed?

d

State two more observations or conclusions you can make from the Venn diagram.

A Venn Diagram showing two overlapping circles labeled Fiction and Borrowed inside a rectangle. The overlapping area has the number 15. The non- overlapping area of the circle labeled Fiction has the number 7. The non-overlapping part of the circle labeled Borrowed has the number 6. Outside the circles but inside the rectangle is a question mark.
13

Bree formulated the statistical question "Are there any patterns or trends that can be seen for hobby preferences between building models, crafting, and baking?"

She collected data using this table.

a

Make a Venn diagram to summarize the collected data.

b

How many people like building models?

c

What proportion of people like baking?

d

Which hobby was the most popular?

e

Which two hobbies were most commonly preferred together?

f

What other conclusions or observations can she make?

StudentLikes building modelsLikes craftingLikes baking
NaomiXX
OliverX
PrinceXX
QuienieXXX
ReaganXX
ShielaX
TrinaXX
UlrichXX
ValerieX
WarrenXX
XyzaXX
YvetteXX
ZoeyX
Let's extend our thinking
14

Bradyn is interested in learning more about the relationship between environmental allergies and hobbies. He wants to use the data cycle to investigate.

a

Formulate a question which could be investigated using a Venn diagram.

b

Describe a method which could be used to collect data.

c

Collect data for your formulated question.

d

Organize your data using a Venn diagram.

e

How can we clearly communicate the results? Draw conclusions to answer your formulated question.

f

This Venn diagram shows the data for a sample of students. Are the results similar or different to the results from your sample? Explain.

A Venn Diagram showing two overlapping circles labeled Allergies and Indoor inside a rectangle. The overlapping area has the number 1. The non overlapping area of the circle labeled Allergies has the number 2. The non overlapping part of the circle labeled Indoor has number 3. Outside the circles but inside the rectangle is the number 10.
g

Based on your data analysis, formulate another question that arose. This question does not need to be represented with a Venn diagram.

15

Lois wants to know more about the structure of names. She notices that some students have hyphenated last names and some do not, some have middle names while others do not, and some students wish they could change their name while others are happy with their names.

Go through the whole data cycle at least once using a context that is related to names and where the data can be organized into a Venn diagram.

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Outcomes

G.RLT.1

The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.

G.RLT.1d

Interpret Venn diagrams, including those representing contextual situations.

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