Math

GraphsGraphs

Graphs

Graphs are useful tools for organizing and showing information. People can collect data, or information, by taking surveys. Then they can create tally charts and graphs to help people visualize data, answer questions, and make predictions.

Tally Chart

Tally charts help people count. Each tally mark in a tally chart represents one object. For example, to count three smiley faces, you make three tally marks in the chart. Tally marks are grouped in sets of five, which makes counting easier. Instead of counting marks one-by-one, you can skip-count by fives and add on any remaining marks.

Color of Smiley Faces

Number of Balls

Tally Frequency

red / 1

orange /// 3

green //// 5

blue // 2

black 0

Length of Calls in Minutes

Number of Calls

Tally Frequency

3 / 1

4 /// 3

5 0

6 // 2

7 //// 5

8 //// // 7

9 //// 4

10 / 1

Tally Chart

Look at this tally chart.

How many 7 minute phone calls were made?

5 phone calls

How do you know?

There were 5 tally marks in the 7 minute row so the frequency was 5.

Line Plot

A line plot shows data on a number line with x or other marks to show frequency. This line plot shows the types of balls the children took outside to recess. The count of x marks above each category tells you the number of balls for each category.

X

X X

X X X

X X X X

Balls Taken Out For Recess

X

X

X X

X X X

X X X X

X X X X X

X X X X X X X

3 4 5 6 7 8 9 10

Number of Phone Calls

Length of Calls in Minutes

Look at this line plot. How many 10 minute phone calls took place?

1 phone call

Where does most of the data cluster? What does this tell you?

Most of the date clusters from 7 – 9 minutes. Most of the phone calls were 7 to 9 minutes long.

Where is the gap in the line plot? What does this tell you?

There is a gap at 5. No one made a phone call lasting 5 minutes.

X

X

X X

X X X

X X X X

X X X X X

X X X X X X X

3 4 5 6 7 8 9 10Length of Calls in Minutes

Number of Phone Calls

Pictograph

A pictograph is a graph drawn with pictures. Each piece of information collected is drawn as a picture. This pictograph shows what each child had for lunch today.

How many children ate hamburgers today at lunch?

6 studentsHow do you know?There are 3 hamburgers and each

hamburger represents 2 students.How many students ate pizza for lunch

today?9 studentsHow do you know?There are 4 and half pizzas and each

pizza represents two students.

What the students ate for lunch today

Legend

Each picture represents two students.

Study this pictograph. What is this pictograph showing?

Number of Books Read During Summer

Reader Number of Books

Kendra

Joel

Dan

Mae

Emily

Key: = 4 books

The number of books these kids read during the summer.

Tips on how to draw a pictograph:• A good pictograph shows the information clearly. • A good pictograph has a title. • A good pictograph has pictures showing

information. • A good pictograph has the pictures in a grid. • A good pictograph has pictures which are the

same size. • ALWAYS REMEMBER TO LABEL!

Now you get to make your own pictograph!!!

Draw your own Pictograph

Here is the information for your pictograph.

A 5th grade class was asked what they liked to do best during recess. Here is what they answered:

8 students said they liked to swing, 6 students said they liked to play on the teeter totter, 3 students liked to play on the slide, and 2 students liked to jump rope.

Now draw your pictograph. Remember your title and your legend!

What the 5th Grade Students Like to Play at Recess

Legend

Each picture represents two students.

How did you decide what each picture would represent?

Possible Answer:

I let each picture represent 2 books because 8, 6, and 2 are divisible by 2, and I could show 3 using a whole and half picture.

Bar Graph

Bar graphs are used to display data using a horizontal or vertical rectangular bar that levels off at the appropriate level. This bar graph shows what students in the 6th grade like to do best during the summer.

0

10

20

30

# o

f S

tud

en

ts

Swimming Riding Bikes Sports Vacations

Summer Activity

What the 6th Grade Likes to do in the Summer

Time Spent Riding a Bike

0

10

20

30

40

50

Min

ute

s

Sunday Monday Tuesday Wed Thursday Friday Saturday

Day

KenPat

How much time did Ken spend riding a bike on Sunday and Monday?

50 minutes

On what day did Pat ride his bike the longest?

Wednesday

Did Ken or Pat ride their bike less on Wednesday?

Ken

Draw your own Bar Graph

Here is the information for your bar graph.

Tony and Sherry both worked at Pizza Hut. Here are the hours they each worked last week.

Tony worked Sunday for 8 hours, Tuesday for 3 hours, Wednesday for 4 hours, and Friday for 6 hours. Sherry worked Monday for 4 hours, Tuesday for 4 hours, Wednesday for 3 hours, Friday for 5 hours, and Saturday for 6 hours.

Don’t forget a title for your graph. Remember to label!

Time Spent Working at Pizza Hut

0

1

2

3

4

5

6

7

8H

ou

rs

Sunday Monday Tuesday Wed Thursday Friday Saturday

Day

TonySherry

Histogram

Histograms are used to display data using a horizontal or vertical rectangular bar that levels off at the appropriate level. Histograms are very similar to bar graphs except that the bars are connected and show a block of time or measurement. This bar graph shows how long children stayed in the swimming pool on a hot afternoon.

How Long Children Staying in the Swimming Pool

02468

10121416

0-30 31-60 61-90 91-120 121-150

Time (in minutes)

# Of C

hildre

n

Distances Ridden on Trail

02468

101214161820222426

0-4 5-8 9-12 13-16 17-20

Distances (in miles)

Num

ber

Of C

yclis

ts

During which time period was the trail the most crowded? The least crowded?

7 P.M. – 10 P.M.; 1 P.M. – 4 P.M.

Can you tell how many cyclists were on the trail at 5:00 P.M.? Explain.

No; the histogram shows data for intervals of time, not individual times.

On another day, 3 more cyclists were on the trail at 8 A.M., 5 fewer were on at 2:00 P.M., and 10 more were on at 5:30 P.M. How would the histogram for this day be different?

The 7 A.M. – 10 A.M. bar would go up to 58;The 1 P.M. – 4 P.M. bar would go down to

20 and the 4 P.M. – 7 P.M. bar would go up to 70.

Draw your own Histogram

Here is the information for your histogram.

The local amusement park had visitors all day long on Saturday. From 10:00 – 12:00 100 visitors were at the park, from 12:00 – 2:00, 300 visitors were at the park, from 2:00 – 4:00 450 visitors were at the park, from 4:00 – 6:00, 350 visitors were at the park, and from 6:00 – 8:00, 200 visitors were at the park.

Don’t forget a title for your graph. Remember to label!

Visitors at the Amusement Park

0

100

200

300

400

500

10:00-12:00

12:00 -2:00

2:00 -4:00

4:00 -6:00

6:00 -8:00

Time (in hours)

Num

ber

Of V

isito

rs

Plotting Ordered Pairs

An 'ordered pair' is simply two numbers in a certain order. For example, the numbers '2' and '3' can form two ordered pairs:

2, 3       and      3, 2 When an ordered pair is used to locate a

point on a grid, the two numbers are called the 'coordinates' of the point. In this diagram, the point (2, 3) has been marked with a red dot. The coordinates of this point are '2' and '3'. 

On a graph grid, the point (0,0) is called the 'origin' The first coordinate of a plotted point is called the 'x' coordinate (move over). The second coordinate of a plotted point is called the 'y' coordinate (move up). So, to locate the point: (2, 3) on our graph grid above, we start at the origin, move 2 units horizontally (over) and 3 units vertically (up).

F

B

D

0123456789

10

0 1 2 3 4 5

Coordinate Graphs & Ordered Pairs

What are the coordinates for these points?

B (1, 3)

D (4, 9)

F (2, 8)

FB

E

AC

D0123456789

10

0 1 2 3 4 5 6 7 8 9 1011

Use the coordinate grid to name each ordered pair.

1. A (7, 3)

2. B (1, 8)

3. C (4, 4)

4. D (3, 0)

5. E (6, 5)

6. F (2, 9)

Line Graph

Line Graphs can be used when you're plotting data that has peaks (ups) and valleys (downs), or that was collected in a short time period. This line graph shows how many children were in the 6th grade over the past 5 years.

Number of Students in the 6th Grade

0

5

10

15

20

25

30

2004 2005 2006 2007 2008 2009

Year

Num

ber

of S

tude

nts

Beth's Airplane Trips

012345678

1995 1996 1997 1998 1999 2000

Year

Nu

mb

er o

f T

rip

s

During how many years did Beth travel more than 4 times?

4 years

In which years did the number of trips increase?

1997 – 1998

In what year did Beth travel the least?

1995

Draw your own Line Graph

Here is the information for your line graph.

Last week, Brian’s school had snow days all week long. Here is how much snow fell each school day last week. On Monday 4 inches of snow fell, on Tuesday, 2 inches of snow fell, on Wednesday 4 inches of snow fell, on Thursday 6 more inches of snow fell, and on Friday 1 inch of snow fell.

Don’t forget a title for your graph. Remember to label!

Inches of Snow That Fell Last Week

01234567

Monday

Tuesday

Wed

nesday

Thursday

Friday

Day

Inch

es

Stem and Leaf Plot

A Stem and Leaf Plot is a method of organizing intervals or groups of data.

Here is an example:

Key: 3 | 6 = 36

A stem and leaf plot allows you to see easily the greatest, least, and median values in a set of data. It gives you a quick way of checking how many pieces of data fall in various ranges. It also lets you see the value of every piece of data.

 

How many students’ heights were measured?

19 students

How many students are taller than 56 inches?

10 students

What is the height of the tallest student?

63 inches

What is the mode of the students’ heights?

57 inches

What is the range of the students’ heights?

16 inches

What is the median student height?

57 inches

4 7 8 8 9 9

5 2 4 4 5 7 7 7 8 9 9

6 0 0 1 3

Key: 4 l 7 means 47 inches

Look at this Stem and Leaf Plot and

answer the questions.

Draw your own Stem and Leaf Plot

Here is the information for your Stem and Leaf Plot.

Yesterday, Tina’s teacher kept track of how many ounces of milk each student drank in one day. Here is the data she collected: 12, 20, 8, 32, 24, 32, 36, 21, 28, 32.

Don’t forget a title for your graph. Remember to label!

Milk Drunk in One Day

0 8

1 2

2 0 1 4 8

3 2 2 2 6

Key: 1 l 2 means 12 ounces

SURVEYS Population – group you want

information about Sample – a part of the population Representative – if the sample you

survey represents all the students Not representative – only a certain

group of the population is represented Random – every student has an equal

chance of being surveyed Not random – only certain students

have a chance of being surveyed.

At a band concert, survey 100 people to find out whether people in your town prefer vocal or instrumental music.

Population

A. People in your town

B. 100 concert-goers

C. Band members

Sample

A. 100 band members

B. People in your town

C. 100 concert-goers

Survey 10 band members to find out how long band members practice each day.

Population

A. 10 band members

B. All students in school

C. All band members

Sample

A. All band members

B. 10 band members

C. All students in school

Survey every 10th person in a phone directory to find out if adults in one city prefer concerts, plays, or movies.

Population

A. All adults with phones

B. All adults in one city

C. Every 10th person in phone directory

Sample

A. Every 10th adult in phone directory

B. All adults with phones

C. All adults in one city

During band practice, survey all drummers to find out if fifth graders prefer playing brass, woodwind, string, or percussion instruments.

Population

A. Drummers

B. Band members

C. Fifth graders

Sample

A. Band members

B. Fifth graders

C. drummers

In a school of 600 students, survey every 5th student entering the cafeteria to find out how many students have attended a concert.

Population

A. 600 students

B. 5 students

C. Every 5th student entering the cafeteria

Sample

A. 5 students

B. Every 5th student entering the cafeteria

C. 600 students

Good Graphing Websites

http://nces.ed.gov/nceskids/createagraph/ http://math-and-reading-help-for-kids.org/math

_games_for_kids_on_graphing.html http://www.lethsd.ab.ca/mmh/graphing/graph.

htm