Resource Overview Quantile® Measure: 480Q Skill or Concept: Organize, display, and interpret information in bar graphs. (QT‐P‐134) Organize, display, and interpret information in tables and graphs (frequency tables, pictographs, and line plots). (QT‐P‐137) Excerpted from: Gourmet Learning 1937 IH 35 North Suite 105 New Braunfels, TX 78130 www.gourmetlearning.com © Gourmet Learning This resource may be available in other Quantile utilities. For full access to these free utilities, visit www.quantiles.com/tools.aspx.
The Quantile® Framework for Mathematics, developed by educational measurement and research organization MetaMetrics®, comprises more than 500 skills and concepts (called QTaxons) taught from kindergarten through high school. The Quantile Framework depicts the developmental nature of mathematics and the connections between mathematics content across the strands. By matching a student’s Quantile measure with the Quantile measure of a mathematical skill or concept, you can determine if the student is ready to learn that skill, needs to learn supporting concepts first, or has already learned it. For more information and to use free Quantile utilities, visit www.Quantiles.com. 1000 Park Forty Plaza Drive, Suite 120, Durham, North Carolina 27713 METAMETRICS®, the METAMETRICS® logo and tagline, QUANTILE®, QUANTILE FRAMEWORK® and the QUANTILE® logo are trademarks of MetaMetrics, Inc., and are
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3rd Grade
Probability and Statistics
Student Expectation: Students will interpret information from pictographs and bar graphs
Teacher note: In Lesson 1, students collected, organized, recorded and displayed data in
pictographs and bar graphs where each picture or cell might have represented more than
one piece of data. The focus in this lesson is on interpreting the data from pictographs
and bar graphs.
Unit 1 – Lesson 2
The student solves problems by collecting, organizing, displaying, and interpreting sets of
data. The student is expected to interpret information from pictographs and bar graphs.
Study the TEKS . . .
Prior Knowledge
In 2nd grade, students constructed picture graphs
and bar graphs and used those to draw conclusions
and answer questions. However, the pictures or
cells represented only one piece of data.
Next Steps
3rd
4th grade students use concrete objects or pictures
to make generalizations about determining all
possible combinations of a given set of data or
objects in a problem situation. In addition, 4th
graders are expected to interpret bar graphs.
Grade
In third grade . . .
Prior to third grade, the pictures or cells used in graphs represented one piece of data.
Now students create graphs in which the pictures or cells might represent more than one
piece of data. This lesson will take the pictographs and bar graphs the students create
one step further by having them interpret the information. This includes being able
to determine which type of graph best represents the data and to predict a reasonable
answer based on the information on a graph.
Gourmet Curriculum Press, Inc.©
1
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will record and display data in a pictograph in which
each picture represents more than one piece of data
K
Focus Activity
Interpreting Information from Graphs
“Number Cube Toss”
C
Teacher note: The objective for this lesson is two-fold. Students collect data in a number
cube toss activity to create a pictograph, which is a review of a Lesson 1 objective. Students
will then interpret the data from the class pictograph in the Initial Instruction–Part II of
this lesson. Tying the two objectives together allows students to bridge from one concept
(collecting and displaying data) to a more challenging one (interpreting the data).
Group size: Part 1: individual or small groups of up to 5 students (depending on availability
of number cubes); Part 2: whole class
Materials: data chart, page 4; tally table, transparency page 5; one large piece of butcher paper;
number cubes (two per student or small group); crayons or markers; one overhead pen
Teacher note: If there are not enough number cubes available for each student to have two,
then separate students into small groups of up to 5. Students can take turns rolling the
cubes. However, students will roll their own cubes and record on their personal data chart.
Rolling a “one” with two number cubes is impossible. This concept can initiate a discussion
about the term “impossible,” which will be introduced in Objective 5, Unit 1, Lesson 3.
Number of Students
Rolling the Sum
at Least Once
Before class: Copy the data chart, page 4, for each student. Make the following blank
pictograph on the large sheet of butcher paper. Gather remaining materials.
1
2
3
4
5
6
7
8
9
10
11
12
Sum of Two Number Cubes
Each
represents 2 students.
Directions (Part 1):
• Distribute a data chart and number cubes to students.
• Students roll the two number cubes a total of five times each. After each roll, students
will determine the sum of the numbers on the two cubes.
2
• Using a crayon or marker, students color a box in the corresponding column on their
data chart that represents the sum of their roll. For example, if a 5 and a 3 are rolled, the
sum equals eight; therefore, the student would color 1 box above the number 8 on his/
her chart. Be sure to remind students to start with the box at the bottom of the column.
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will record and display data in a pictograph in which
each picture represents more than one piece of data
Focus Activity
Interpreting Information from Graphs
“Number Cube Toss”
• Students continue this process until they have colored five boxes on their chart. If
doing this in small groups, students take turns rolling the number cubes. While a
student rolling the cubes is recording the sum on his/her chart, the next student can
roll the cubes. This will allow the activity to move along and minimize the students’
idle time.
• When charts are completed, collect the number cubes and continue with Part 2.
Directions (Part 2):
• Display the blank pictograph on a wall or board. Explain that the class will create a
pictograph using the data recorded on their data charts.
• Begin by recording information on the tally table, transparency page 5. Call out each
“Sum of Two Number Cubes” beginning with 1. Students raise their hands if they
have any colored boxes for the sum called and tally marks are made for each raised
hand. The number of colored boxes students have for each sum is not important in
this activity. In other words, if a student rolled the sum of 10 a total of five times or
just once, only one tally mark is made on the table.
• When the tally table is complete, keep the transparency on the overhead, but move to
the pictograph. As a class, determine a picture or symbol to use which represents 2
students on the graph such as a happy face, square, or flower. Be sure to discuss how
to represent 1 person.
Number of Students
Rolling the Sum
at Least Once
• Using the tally table as a guide, create the pictograph to represent the data collected
during the activity. Here is an example of a possible pictograph:
1
2
3
4
5
6
7
8
9
10
11
12
Sum of Two Number Cubes
Each
represents 2 students.
• Keep the completed pictograph to use in the Initial Instruction–Part II.
Gourmet Curriculum Press, Inc.©
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will record and display data in a pictograph in which
each picture represents more than one piece of data
Focus Activity—Data Chart
Interpreting Information from Graphs
“Number Cube Toss”
Number Cube
Toss
1 2 3 4 5 6 7 8 9 10 11 12
4
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will record and display data in a pictograph in which
each picture represents more than one piece of data
Focus Activity—Tally Table
Interpreting Information from Graphs
“Number Cube Toss”
Sum of Two Number Cubes
1
2
3
4
5
6
7
8
9
10
11
12
Gourmet Curriculum Press, Inc.©
5(T)
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will learn vocabulary associated with probability and
graphs
Initial Instruction—Part I—Vocabulary
Interpreting Information from Graphs
K
probability: the chance that a particular outcome will occur
outcome: in probability, a result of performing an experiment
such as tossing a coin or rolling a number cube
data: a collection of information usually obtained by observation,
questioning, or measurement
interpret: to decide what data means
pictograph: a graph that shows data by using pictures
bar graph: a graph that shows data by using bars of different lengths
line graph: a graph that shows data using lines that join points
circle graph: a graph that shows data using parts of a circle
range: the difference between the highest and lowest score on a graph
Teaching
in Texas
6(T)
It is important to note that interpreting line and circle
graphs is not a TEKS expectation for students until 5th and
6th grades. If 3rd graders experience difficulties with these
types of graphs, simply eliminate them from the lessons/
activities, and focus only on pictographs and bar graphs.
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information from pictographs and bar
graphs
Initial Instruction—Part II
Interpreting Information from Graphs
K
C
Teacher note: Students will use the pictograph created in the Focus Activity to interpret
data and answer questions. The focus for this part of the Initial Instruction is on basic
interpretation of data and how to determine answers. Higher level thinking skills will be
the focus of the next part of the Initial Instruction. Probability requires many hands-on
experiments, and data will vary; therefore, all answers cannot be given in the Instructional
Strategy. Use the questions to lead the discussion, and base the answers on the class’s
data.
Group size: whole class
Materials: completed pictograph from the Focus Activity (see page 3); Instructional
Strategy, pages 7-9
Before class: Display the pictograph on a wall or board.
Directions:
• Review the data recorded on the pictograph.
• Follow the Instructional Strategy, pages 7-9.
Questioning Technique
Instructional Strategy
Ask: What information does this graph show? (how many times a sum was rolled using
two number cubes at least once)
Ask: Today we are going to interpret the information using this graph. What does that
mean? (to answer questions about the graph and decide what the data means)
Ask: When interpreting this graph, what information is important to remember? (The
picture symbol represents two students.)
Ask: What do the half-symbols represent on this graph? (one student)
Ask: Why would that be important to remember? (in order to give accurate information)
Ask: If I want to know what sum was rolled most often in this class, how would I
determine the answer? (Look for the sum with the most pictures above it.)
Ask: Why? (The greater number of pictures means the greater number of students rolled
that number at least once)
Ask: What does the data show on this graph for the sum rolled most often? (Answers
will vary.)
Ask: How can we find out how many students rolled this sum? (Count the number of
whole picture symbols, and multiply by two. Then add one for the half-symbols, if any.)
Ask: Is there another way to do it? (Count all the picture symbols by two, and then add
one for any half-symbols.)
Gourmet Curriculum Press, Inc.©
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information from pictographs and bar
graphs
Initial Instruction—Part II
Interpreting Information from Graphs
Questioning Technique
Instructional Strategy
Say: (Point to the sum rolled the most.) Let’s find how many students rolled the sum
of
to make it the most rolled sum. Who can demonstrate how to find the answer?
Volunteer demonstrates how to determine the number of students who rolled the most
common sum and explains the process.
Ask: Now, what if we wanted to know which sum was rolled least? (Find the sum that
has the least number of pictures above it.)
Ask: Why? (The smallest number of pictures means the least number of students rolled
that number.)
Ask: What sum was rolled least? Be careful! (1)
Ask: How do we know that 1 was the least rolled sum? (There are no pictures above it.)
Ask: What does that mean? (No student rolled a sum of 1 when rolling the number
cubes.)
Ask: How would we determine which number was the next least rolled? (Look for the
sum with the next lowest number of picture symbols above it.)
Ask: According to our data, which number was rolled the least number of times after the
sum of 1? (Answers will vary.)
Ask: How many students rolled this sum at least once? (Answers will vary.)
Ask: What about the second most common sum rolled? (Answers will vary.)
Ask: How did you determine that
was the second most common sum rolled? (It
had the second highest number of pictures above it.)
Say: Let’s try some different kinds of questions. How can I determine how many total
students rolled a sum of 4 and a sum of 6? (Count the number of whole pictures for both
the sums of 4 and 6. Multiply by 2, and then add one for each half-symbol.)
Ask: What is a different way to determine the answer? (Count all the whole pictures by
two for the sums of 4 and 6, and then add one for each half-symbol.)
Say: Use one of those methods to determine the total number of students who rolled the
sums of 4 and 6. Raise your hand when you have the answer. (Answers will vary.)
8
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information from pictographs and bar
graphs
Initial Instruction—Part II
Interpreting Information from Graphs
Questioning Technique
Instructional Strategy
Say: Let’s try some more questions like that.
Ask: What is the total number of students that rolled a sum of 7 and a sum of 10? Be
ready to explain how you find the answer. (Answers will vary.)
Allow students time to determine the answer. A student volunteer can share the answer
and explain how it was determined.
Say: I want to know how many more students rolled the sum of
. (Numbers will vary.)
than the sum of
Ask: What steps do I need to take to determine the answer? (Subtract the number of
students that rolled a
from the number of students that rolled a
.)
Ask: What is the answer? (Answers will vary.)
Continue using the graph to ask similar questions.
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will make reasonable predictions using information
from pictographs or bar graphs
Initial Instruction—Part III
Interpreting Information from Graphs
K Ap
C
Teacher note: Having practiced basic interpretation of data, students are now ready to use
their higher level thinking skills to make reasonable predictions based on the information
from a graph. Because answers to this type of questioning may not be clearly determined,
some students may experience difficulty with this skill. Therefore, be sure to explain and
demonstrate to the students the strategies they would use to determine reasonable answers.
Group size: whole group
Materials: Instructional Strategy, pages 10-12; sample graphs, transparency pages 13-14;
overhead marker
Before class: Gather materials.
Directions:
• Place sample graph #1, page 13, on the overhead, and follow the Instructional Strategy
pages 10-12.
Questioning Technique
Instructional Strategy
Ask: What type of graph is this? (a bar graph)
Ask: What information is represented on this graph? (the number of cars sold and car colors)
Ask: Who might have made this chart? (a car dealership or car maker company)
Ask: Why would they have made such a graph? (to know which colors of cars are the
most and the least popular)
Ask: How could this information be used? (to decide which colors of cars to buy or make
and which colors of cars not to buy or make)
Say: Let’s answer some questions using the data shown on this graph.
Ask: What was the color of the cars that sold the most? (silver)
Ask: Is there another way to ask this question? (Which color is the most popular?)
Ask: What was the color of the cars that sold the least? (green)
Ask: How can we ask this question another way? (Which color is the least popular?)
Ask: How many red cars were sold? (20)
Ask: How many blue and silver cars were sold altogether? (40)
Ask: How many more red cars than green cars were sold? (12)
Ask: If someone came into a dealership to buy a car, what color of car are they most likely
to choose according to this graph? (silver)
10
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will make reasonable predictions using information
from pictographs or bar graphs
Initial Instruction—Part III
Interpreting Information from Graphs
Questioning Technique
Instructional Strategy
Ask: What are the chances that someone will buy a purple car according to this graph?
(This information is not on the graph. There’s no chance.)
Ask: How did you determine that? (Purple was not a color listed in the graph of car
colors, so that means 0 purple cars were sold.)
Ask: You are the owner of this car dealership and need to order more cars to sell. Using
the information from this graph, what will you decide as far as colors of cars to order?
(Order more silver cars.)
Ask: Why? (More people bought silver cars than the other colored cars.)
Ask: What other information can you determine from this graph? (Don’t order as many
green cars; order more red than blue cars.)
Ask: If car sales stayed basically the same as indicated on this graph, what reasonable
statement could you make about the sale of silver cars in the following week? (About 24
silver cars will be sold.)
Ask: Knowing this, how many silver cars do you want to order for the next week? (at
least 24)
Ask: What about green cars? Remember sales are about the same as the week represented
on the graph. (Order only 8 green cars.)
Ask: If the sales stayed basically the same, can you predict about how many red cars
would be sold in one month? (about 80) Explain your answer. (20 red cars were sold in
one week, so if sales stayed the same, you could multiply 20 red cars x 4 weeks in a month
and that equals 80.)
Now place sample graph #2, page 14, on the overhead.
Ask: What type of graph is this? (pictograph)
Say: This graph represents the color of marbles students picked out of a bag of marbles.
There was a total of 10 marbles in the bag. Students pulled one marble out at a time,
recorded the color on this graph, and then returned the marble to the bag.
Ask: What do the sack and marble pictures represent? (The sack represents 5 marbles,
and the marble represents 1.)
Say: Let’s use this pictograph to answer some questions and do some predicting.
Ask: What marble color was picked most often? (blue)
Ask: How many blue marbles were picked from the bag? (17)
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will make reasonable predictions using information
from pictographs or bar graphs
Initial Instruction—Part III
Interpreting Information from Graphs
Questioning Technique
Instructional Strategy
Say: Explain how you determined that. (There are 3 sack symbols and 2 marble symbols
for blue; each sack symbol represents 5 marbles, so 5 x 3 = 15 marbles. Each marble
symbol represents 1 marble, so add 15 + 2 to find 17 marbles.)
Ask: Which marble color was picked the least, and how do you know? (White was picked
the least because there are no symbols, which means it was not picked by anyone.)
Ask: How many more green marbles than red marbles were picked? Explain your answer.
(2 more green than red marbles were picked because there were 10 green and 8 red, which
is a difference of 2.)
Ask: Keeping in mind that there was a total of 10 marbles in the bag, which color of
marble do you guess outnumbered the other colors? (blue)
Ask: Why? (The color blue was picked more often, so it makes sense that there would be
more blue marbles in the bag.)
Ask: How many white marbles do you guess were in the bag? (0)
Say: Explain your thinking. (No white marbles were picked.)
Ask: Would it be possible for there to be a white marble in the bag and it never got
picked? (Yes.)
Ask: What can we say about blue and white marbles from the information on this graph?
(There were probably more blue marbles than white.)
Ask: What can we say about red and green marbles? (It is possible that there were more
green than red marbles, but we can’t be sure.)
Ask: Looking at this graph, I wonder how many times a marble was drawn from the bag.
What do you think? (Students should count the total number of marbles represented on
the graph – 35.)
What do I
know from this
information?
Blue
Red
Green
White
Each
Each
represents 5 marbles.
represents 1 marble.
Note: There are a total of 10 marbles in the bag from which students drew.
12
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will make reasonable predictions using information
from pictographs or bar graphs
Initial Instruction—Part III—Sample Graph #1
Interpreting Information from Graphs
Bluemark Motors
Number of Cars Sold in One Week
24
20
16
12
8
4
Blue
Red
Green
Silver
Color of Cars Sold
Gourmet Curriculum Press, Inc.©
13 ( T )
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will make reasonable predictions using information
from pictographs or bar graphs
Initial Instruction—Part III—Sample Graph #2
Interpreting Information from Graphs
Marble Grab
Blue
Red
Green
White
Each
Each
represents 5 marbles.
represents 1 marble.
Note: There are a total of 10 marbles in the bag from which students drew.
14 ( T )
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information using line and circle graphs
Initial Instruction—Part IV
K
Interpreting Information from Graphs
C
Teacher note: The focus of Part IV is on line and circle graphs. Interpretation of data
displayed on these graphs may be more challenging to students than the bar or pictographs.
Line graphs were introduced in the first unit of this objective. However, this is the students’
first exposure to circle graphs. The purpose for introducing circle graphs here, however, is
only for interpretation purposes; the students will not be creating any circle graphs.
Group size: whole class
Materials: Instructional Strategy, pages 15-17; sample graphs, transparency pages 18-19
Before class: Gather materials.
Directions:
• Place the line graph, transparency page 18, on the overhead. Follow the Instructional
Strategy provided.
Questioning Technique
Instructional Strategy
Ask: What type of graph is this? (a line graph)
Ask: What information is displayed in this line graph? (the number of students absent
from Preston Elementary from January through May)
Ask: Let’s answer some questions using this graph. How many students were absent in
January? (50)
Ask: How did you determine your answer? (Possible response: Find January across the
bottom or horizontal line of the graph, and follow it up vertically to the point on the line,
which is 50. You or a student volunteer may want to demonstrate this procedure.)
Ask: Using the same procedure, how many students were absent in May? (30)
Ask: How many students were absent in April? (5)
Say: Explain your answer. (The point for April is halfway between the 0 and 10 on the
vertical line, so that would be 5.)
Ask: How many students were absent for both January and February? (95)
Ask: How did you arrive at that answer? (There were 50 students absent in January and
45 in February, so add 50 + 45 = 95.)
Ask: Since there is not a number 45 on the vertical line, how did you know there were
45 students absent in February? (The point for February is halfway between 40 and 50,
which is 45.)
Ask: What month had the second fewest absences? (March with 25)
Ask: How many more students were absent in May than in April? (25)
Gourmet Curriculum Press, Inc.©
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information using line and circle graphs
Initial Instruction—Part IV
Interpreting Information from Graphs
Questioning Technique
Instructional Strategy
Ask: How did you determine your answer? (There were 30 students absent in May and
5 in April, so subtract 30 - 5 = 25.)
Ask: If there were 20 more students absent in May, how many total students would have
been absent in that month? (50)
Ask: How did you get that answer? (There were 30 students absent in May, and if 20
more are absent, you add 30 + 20 = 50.)
Ask: What if 20 more students were absent in April? How many total students would be
absent? (25)
Say: Explain your thinking. (There were 5 students already absent in April, so if 20 more
were absent, add 5 + 20 = 25.)
Ask: Where would the point be to indicate 25 students? (halfway between the 20 and 30
points)
Ask: Why? (There is not a point for 25, since the horizontal lines are in increments of 10.
25 would be halfway between 20 and 30.)
Ask: If you were a teacher planning an important math test, which month would NOT
be a good choice and why? (January would not be a good month for an important test
because more students are absent during that month than the others.)
Ask: Why do you think that more students are present at school during the month of
April than all the others? (Possible answer: The weather in April is warmer, and it’s the
end of flu season.)
Now place transparency page 19 on the overhead.
Say: Now let’s look at a different type of graph called a circle graph.
Ask: Why do you think it is called a circle graph? (The data is represented in a circle.)
Say: To interpret data from a circle graph, you need to focus on the information in each
of the circle sections. Each section represents data just like a bar does on a bar graph, or
the picture symbols on a pictograph, or the points on a line graph.
Ask: What information is displayed in this graph? (the favorite flavors of jelly beans)
Ask: Which section of the circle graph is the largest? (the one labeled “red”)
Ask: Using information that you learned about pictographs and bar graphs, what do you
think this could mean? (Most people selected red as their favorite jelly bean flavor.)
Ask: How would that be represented on a bar graph? (the tallest bar) On a pictograph?
(the one with the most picture symbols) On a line graph? (the highest point)
16
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information using line and circle graphs
Initial Instruction—Part IV
Interpreting Information from Graphs
Questioning Technique
Instructional Strategy
Ask: What was the least favorite flavor of jelly beans? (black)
Ask: How did you know this? (It is represented by the smallest portion of the circle
graph.)
Ask: How would this information be represented on a bar graph? (the shortest bar) On a
pictograph? (the one with the least picture symbols) On a line graph? (the lowest point)
Ask: What is the second favorite flavor of jelly beans according to this graph? (white)
Ask: How were you able to determine this? (White is the second largest section of the
circle graph.)
Ask: If more people liked orange jelly beans, how would the circle graph change? (The
orange section of the circle graph would get larger and the other sections would get
smaller.)
Ask: You have learned to interpret data from four different kinds of graphs. Which
one do you find the easiest to interpret? (Answers will vary.) Tell me why. (Answers
will vary.)
Black
Number of People in the Pool
Orange
Noon
Red
1:00 p.m.
White
2:00 p.m.
3:00 p.m.
Each
represents 10 people.
Gourmet Curriculum Press, Inc.©
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information using line and circle graphs
Initial Instruction—Part IV—Sample Line Graph
Interpreting Information from Graphs
Preston Elementary:
Student Absences for January through May
Number of Students Absent
50
40
30
20
10
0
Jan.
Feb.
Mar.
Month
18 ( T )
Gourmet Curriculum Press, Inc.©
Apr.
May
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information using line and circle graphs
Initial Instruction—Part IV—Sample Circle Graph
Interpreting Information from Graphs
Favorite Jelly Bean Flavors
Black
Orange
Red
White
Gourmet Curriculum Press, Inc.©
19 ( T )
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will gather data and use that data to create and
interpret bar graphs, pictographs, and line graphs
Initial Instruction—Part V
Interpreting Information from Graphs
Optional Reading Activity
Ap S
An
Teacher note: This activity requires students to bring in their favorite hats to be used
to create a graph for interpretation. Plan to send home the parent letter, page 22, a few
days before scheduling the lesson. Students will use their hats to create different kinds of
graphs to be used for interpretation.
Teaching in Texas note: One of the graphs the students will create in this activity is a
line graph. If you have opted not to teach this type of graph at this time, simply skip this
section of this lesson.
Group size: whole class
Materials: parent letter, page 22; blank graphs, transparency pages 23-25; copy of book
Caps for Sale by Esphyr Slobodkina; overhead markers in various colors; large floor area to
sort and group hats; extra hats for students unable to bring one from home
4-5 days before lesson: Make 1 copy of the parent letter, page 22. Fill in the date for hats
to be brought to school. Sign and date it, and then make one copy for every 2 students.
Cut the pages in half.
Before class: Gather materials.
Directions:
• Gather students around as you read the book. Students should leave hats at their desks
to avoid becoming distracted during the story.
• Read and discuss the story with the class.
• Have students bring their hats to a large floor area. If time permits, allow students to
tell about their hats.
• Explain how they will be sorting their hats to gather information that will be used to
create a graph.
• Students sort (categorize) their hats by style. For example, all baseball caps, cowboy
hats, winter hats, etc., might be grouped together.
• Once hats are sorted by style, place the blank bar graph, transparency page 23, on the
overhead. First, as a class, label the horizontal line of the bar graph to identify the
different styles of hats. Next, determine a system to number the vertical line (i.e., by
1’s, 2’s, 5’s, 10’s, etc.).
• Select one student to be the Graph Maker. His/Her job is to make the bars on the bar
graph as instructed by the rest of the class. Based on the information provided by
classmates, the Graph Maker draws appropriate bars on the graph.
20
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will gather data and use that data to create and
interpret bar graphs, pictographs, and line graphs
Initial Instruction—Part V
Interpreting Information from Graphs
Optional Reading Activity
Directions, continued:
• After completing the bar graph, students sort the hats by color. When sorted, place the
blank pictograph, page 24, on the overhead. Write the different colors of hats in the first
column of the pictograph. Students decide on a picture symbol to represent the hats and
the number of hats to be represented by that symbol. (Be sure the symbol is a simple
drawing!) Then draw the picture symbol in the box at the bottom of the graph.
• Choose a different student to be the Graph Maker for this graph. The other students
will provide the information based on the sorted hats, and the Graph Maker draws the
appropriate number of symbols for each color.
• Finally sort the hats by materials such as straw, felt, wool, or canvas. Place the blank
line graph, page 25, on the overhead, and fill in the missing labels on the horizontal
and vertical lines.
• Select a third student to be the Graph Maker for the line graph. He/She plots the points
for each type of hat material as instructed by the rest of the class using the sorted hat
and connects the points with lines to create a line graph.
• When all three graphs are complete, students put away their hats and gather around
the overhead to interpret the graphs.
• Place one graph on the overhead, and use the following questions as a guide for the
class discussion:
• What (color, style, material) was most/least common?
• How many hats are
(insert a color, style or material)?
• How many total hats are
and
(insert 2 colors, styles or
materials)?
• How many more hats are
than
(insert 2 colors, styles or
materials)?
• If 5 more hats were
(insert color, style or material), then how
many would there be now?
• If you sold hats at a store in our neighborhood, what information from this graph
would be helpful? Why?
• Follow the same procedure for the remaining two graphs.
Extension 1: Students brainstorm different ways to sort hats and select the best type of
graph to represent the new sort. Use a blank graph for the students to create graphs based
on the new sort.
Extension 2: Choose one way to sort the hats, and divide the students into three groups.
Each group creates a different type graph to represent the same data. Then compare the
three graphs.
Gourmet Curriculum Press, Inc.©
21
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will gather data and use that data to create and
interpret bar graphs, pictographs, and line graphs
Initial Instruction—Part V—Parent Letter
Interpreting Information from Graphs
Optional Reading Activity
Dear Parents/Guardians:
We are studying graphs and interpreting information from graphs in math. On
, our class will read together the book Caps for Sale by Esphyr Slobodkina.
Afterwards, students will use hats brought from home to sort, graph, and interpret
information. If possible, please send one hat to school with your child on the above date
to be used in this fun learning activity. His/Her favorite hat or one in any style or color
will do. If you would like to send in an extra hat for those students unable to bring one, it
would be greatly appreciated. All hats will be returned home the same day.
Thank you for your help with this lesson.
Sincerely,
Dear Parents/Guardians:
We are studying graphs and interpreting information from graphs in math. On
, our class will read together the book Caps for Sale by Esphyr Slobodkina.
Afterwards, students will use hats brought from home to sort, graph, and interpret
information. If possible, please send one hat to school with your child on the above date
to be used in this fun learning activity. His/Her favorite hat or one in any style or color
will do. If you would like to send in an extra hat for those students unable to bring one, it
would be greatly appreciated. All hats will be returned home the same day.
Thank you for your help with this lesson.
Sincerely,
22
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will gather data and use that data to create and
interpret bar graphs, pictographs, and line graphs
Initial Instruction—Part V—Blank Bar Graph
Interpreting Information from Graphs
Optional Reading Activity
Title
Gourmet Curriculum Press, Inc.©
23 ( T )
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will gather data and use that data to create and
interpret bar graphs, pictographs, and line graphs
Initial Instruction—Part V—Blank Pictograph
Interpreting Information from Graphs
Optional Reading Activity
Each
24 ( T )
represents
Gourmet Curriculum Press, Inc.©
hats.
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will gather data and use that data to create and
interpret bar graphs, pictographs, and line graphs
Initial Instruction—Part V—Blank Line Graph
Interpreting Information from Graphs
Optional Reading Activity
Title
Gourmet Curriculum Press, Inc.©
25 ( T )
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information from bar graphs, pictographs,
line graphs and circle graphs
Initial Instruction—Guided Practice
Interpreting Information from Graphs
K Ap
C
Teacher note: This Guided Practice gives students another opportunity to review as a whole
class the skills taught in the Initial Instruction.
Group size: whole group
Materials: “Pool Population” graphs, transparency page 28; “What’s in a Name?” graphs,
transparency page 29
Teaching in Texas note: Part II, page 27, the “What’s in a Name?” graphs is optional, since line
and circle graphs are not a part of the TEKS.
Before class: Gather transparencies.
Part I Directions:
• Place the “Pool Population” graphs, transparency page 28, on the overhead. Have the
students identify the two different types of graphs shown. (pictograph and bar graph)
• Discuss how the two graphs show the same information – the number of people in the pool
from noon until 3:00 p.m. Students can use either graph when answering the following
questions. You can use them as a starting point and guideline for a class discussion:
1. What is the most popular time to go swimming? (3:00 p.m.)
2. What time of day would you find the least number of people in the pool? (noon)
3. How many people went swimming at noon? (25) At 1 p.m.? (30) At 2 p.m.? (50) At 3 p.m.? (60)
4. How many more people went swimming at 2:00 than at noon? (25 more people) Explain
how you got the answer. (50 people went swimming at 2:00, and 25 went swimming at
noon. 50-25=25) What is another way to say that? (There were twice as many people
swimming at 2:00 as there were at noon, or there were half as many people swimming
at noon as there were at 2:00.)
5. What was the total number of people in the pool at 1:00 and 3:00? (90 people) Explain your
answer. (There were 30 people in the pool at 1:00 and 60 people at 3:00. 30+60=90)
6. Why do you think there are less people swimming at noon? (Possible answer: It is
lunchtime, so many people might be eating at that time.)
7. How many more people got in the pool in the hour between 1:00 and 2:00? (20 more people)
8. If you were a lifeguard on duty at this pool, what hour of the day would it be most
important to pay attention to what is happening in the pool? (3:00) Why? (Possible
answer: There are more people in the pool at this hour than at any other, so a lifeguard
would have to watch over more people.)
9
If the law says that there has to be one lifeguard for every 35 people in the pool, when
would you need to add a second guard? (2:00 p.m.)
10. Ask students to create a title for this graph. (Reasonable answer: Number of people in the Pool)
26
Gourmet Curriculum Press, Inc.©
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information from bar graphs, pictographs,
line graphs and circle graphs
Initial Instruction—Guided Practice
Interpreting Information from Graphs
11. If you were selling cookies to raise money for the Pool Association, what hour of the day
would you probably not sell as many cookies? (noon) Why not? (There are not as many
people there to buy the cookies.)
12. Predict if the pool population would increase or decrease at 4:00, and explain your thinking.
(It would probably increase because the population increased each hour since noon.)
13. Which graph was easier to use to answer the questions? (Answers will vary.) Why?
(Answers will vary.)
Part II Directions:
• Now place the “What’s in a Name?” graphs, page 29, on the overhead. Have the students
identify the types of graphs shown. (line and circle graphs)
• Discuss how these two graphs show the same information – the number of letters in third
graders’ first names. Students can use either graph when answering questions.
• Use the following questions as a guideline for these graphs:
1. How many letters did most third graders have in their name? (4)
2. How many letters did the least number of third graders have in their name? (2 and 6+)
3. How many people had 2 letters in their name? (4) 3 letters? (28) 4 letters? (32) 5 letters?
(28) 6+ letters? (4)
4. How many more students had 4 letters than 6+ letters in their name? (28) Explain how
you got your answer. (There are 32 students with 4 letters in their name and 4 students
with 6+ letters, so subtract 32 - 4 = 28.)
5. What is the total number of students with 3 and 5 letters in their name? (56) Explain
your answer. (There are 28 students with both 3 and 5 letters, so multiply 28 x 2 = 56.
Or, add 28 + 28 = 56.)
6. If your name is added, how would the graphs change? (Answers will vary.)
7. Predict the number of third graders with 7 letters in their name, and explain your
reasoning. (Answers will vary. Possible response: There would be a low number because
their aren’t many names with 6+ letters in them.)
8. How would the graphs change if last names were used? Then explain your thinking.
(Answers will vary. Possible answer: There would be more people with 6+ letters in
their last name because last names are usually longer than first names.)
9. Which of these two graphs was easier to use to answer the questions? (Answers will
vary.) Why? (Answers will vary.)
10. What are some possible titles for this graph? (Reasonable answers: Names and Numbers
of Letters or How Many Letters in Your Name)
Gourmet Curriculum Press, Inc.©
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Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information from bar graphs, pictographs,
line graphs and circle graphs
Initial Instruction—Guided Practice—”Pool Population” Graphs
Interpreting Information from Graphs
Title:
Noon
1:00 p.m.
2:00 p.m.
3:00 p.m.
Each
represents 10 people.
Number of People in the Pool
60
50
40
30
20
10
Noon
1 p.m.
2 p.m.
Time
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Gourmet Curriculum Press, Inc.©
3 p.m.
Unit 1 – Lesson 2
Probability and Statistics
Student Expectation: Students will interpret information from bar graphs, pictographs,
line graphs and circle graphs
Initial Instruction—Guided Practice—”What’s in a Name?” Graphs
Interpreting Information from Graphs
Title:
32
28
24
20
16
12
3
4
Title
rs
te
et
l
2
rs
4 letters
te
2
let
8
4
0
5
6+
5 letters
3 letters
6+
Number of 3rd Graders
40
36
Gourmet Curriculum Press, Inc.©
29 ( T )