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Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015
Second Grade
Picture and Bar Graphs
Table of Contents
Topic Suggested Number of Days Page No. Part 1: Graphs with a Scale or Key Equal to One
Picture Graphs
Large Picture of Bear
Small Pictures of Bears
Guided Practice Problem #1
Bar Graphs
Warm-up Problem #1
Guided Practice Problem #2
Guided Practice Problem #3
Part 2: Use Data to Write Problems
Warm-up Problem #2
Picture Graph
Bar Graph
Guided Practice Problem #4
Mixed Practice
Part 3: Graphs with a Scale or Key Greater Than One
Picture Graphs
Pictures of Small Bears
Picture Graph Questions
Guided Practice Problem #5
Picture Graph Partner Practice Problem
Bar Graphs
Bar Graph Questions
Guided Practice Problem #6
Guided Practice Problem #7
Part 4: Use Data to Draw Conclusions and Make
Predictions
Interactive Math Notebook (Right Side)
Word Bank
Interactive Math Notebook (Left Side)
Warm-up Problem #3
Guided Practice Problem #8
Mixed Practice
2 days
1 day (2/27)
1 day (3/2)
2 days
1 day (3/3)
1 day (3/4)
2 days
1 day (3/5)
1 day (3/6)
3 days
1 day (3/16)
1 day (3/17)
1 day (3/18)
2
3
7
8
9
10
11
16
17
18
21
22
23
24
25
26
26
30
31
32
33
34
39
40
41
42
45
46
48
51
52
49
Additional Resources:
Large Horizontal and Vertical Bar Graphs for Group Work (These should be printed on legal-size paper.)
MATH_2_A_BAR GRAPHS A 2014_RES)
MATH_2_A_BAR GRAPHS B 2014_RES)
Enrichment Activity
MATH_2_H_GRAPHS 2014_ENR
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 1
Picture Graphs and Bar Graphs
TEKS 2.10A explain that the length of a bar in a bar graph or the number of pictures in
a pictograph represents the number of data points for a given category
TEKS 2.10B organize a collection of data with up to four categories using pictographs
and bar graphs with intervals of one or more
TEKS 2.10C write and solve one-step word problems involving addition or subtraction
using data represented within pictographs and bar graphs with intervals of
one
TEKS 2.10D draw conclusions and make predictions from information in a graph
TEKS 2.4A Recall basic facts add and subtract within 20 with automaticity
TEKS 2.1A apply mathematics to problems arising in everyday life, society, and the
workplace
TEKS 2.1B use a problem-solving model that incorporates analyzing given
information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and the
reasonableness of the solution
TEKS 2.1C select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques, including mental math,
estimation, and number sense as appropriate, to solve problems
TEKS 2.1D communicate mathematical ideas, reasoning, and their implications using
multiple representations, including symbols, diagrams, graphs, and
language as appropriate
TEKS 2.1E create and use representations to organize, record, and communicate
mathematical ideas
TEKS 2.1F analyze mathematical relationships to connect and communicate
mathematical ideas
TEKS 2.1G display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication
Vocabulary: pictograph, picture graph, bar graph, title, heading, label, key,
scale, prefer, favorite, vote, tally, tallies or tally marks, match,
information, data, survey, data chart
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 2
Teacher Background
In these interactive lessons, students collect data, use that data to construct picture graphs
(pictographs) and bar graphs, as well as interpret those graphs to answer questions about the data
presented. Students have previously learned about picture and bar graphs with a key or scale of
1 in first grade. In second grade, students are expected to deepen their understanding of those
graphs by writing and solving one-step word problems they create themselves. Students’
understanding of graphs is also extended to include creating/interpreting picture and bar graphs
with a key or scale greater than 1. Additionally, students are expected to draw conclusions and
make predictions based on information given in pictographs and bar graphs.
Part 1: Graphs with a Scale or Key Equal to One
Materials: red, blue, yellow, and green plastic bears
data chart (pg 2)
large bear signs - one each color bear (pg 7)
blank pictograph
blank bar graph
small bear pictures (pg 8) or bear die cuts in red, blue, yellow, and green
paper
student copies of Guided Practice Problem #1 (pg 9)
student copies of Warm-up Problem #1 (pg 11)
student copies of Guided Practice Problems #2 and #3 (pgs 16, 17)
1. Prior to instruction create a blank data chart on which to record information using tally
marks. An example is provided below:
Our Favorite Bear Colors
Red
Blue
Yellow
Green
Post large pictures of the bears (one of each color---red, blue, yellow and green) in
various locations within the classroom. Students will later “vote with their feet” by
standing near the picture that is their favorite color of bear.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 3
Prepare a blank picture graph and a blank bar graph. On the picture graph, leave room
for a title, headings and a key. On the bar graph, space is needed for a title, headings and
the scale. Examples of the completed graphs are found on page 4 (picture) and page 12
(bar).
2. Gather and Record Information
Point out the title of the data chart, “Our Favorite Bear Colors.” Allow students to take a
plastic bear which is their favorite color bear.
With bear in hand, students walk to the area where their color bear is displayed. The
teacher then records the class data in the chart using tally marks. Discuss how tally
marks are grouped for easy counting, i.e. four standing straight and then one crossing to
“hold the group together.” This makes a group of five.
An example of a completed data chart is given below using fictitious numbers.
Our Favorite Bear Colors
Red
Blue
Green
Yellow
How many tally marks should we have in our chart? We should have as many
tally marks as we have students in the class.
Why? Each tally mark represents one student.
Have students count the tally marks to make sure the total equals the number of students
in the class. Ask several students to explain their method of counting (i.e. count by 5s
first and then count on the extras by 1s; use 2 of the single tallies to make two more
groups of 5 and then count by 5s, etc.) and briefly discuss.
3. Picture Graphs
After returning to their seats, have students color a small picture of a bear in the color
they chose or give each student a die-cut bear that matches their color.
Explain to students that we can display the information we collected in a picture graph or
pictograph. A picture graph (pictograph) uses pictures to represent the data.
Write in the title on the blank picture graph. Discuss and write the headings.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 4
Go through the data for each color as follows:
Looking at the tally chart, how many students should have red bears? There
should be seven students with red bears. (This should be the actual number
from your class data.)
Have the students with red bears come up and place their bear pictures on the graph.
Explain that the pictures are aligned within the rows and in the columns so it is easier to
compare the data displayed in the graph. Do this with each color separately until all the
bear pictures are on the graph. A sample graph is shown below:
Our Favorite Bear Colors
Red
Blue
Green
Yellow
Add a key to the picture graph and discuss its importance.
Demonstrate the strategy of counting the bears in each row and recording those totals at
the ends of the rows. Verify that all the data has been recorded.
Our Favorite Bear Colors
Red
Blue
Green
Yellow
Each = one student
Each = one student
7
4
4
5
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 5
Discuss and answer several questions related to the class graph. Possible questions are
listed below:
1. Which color of bear was preferred by most of our class?
2. Which color of bear was chosen by the least number of students?
3. How many students picked _____________ as their favorite bear color?
4. How would the graph change if 3 more students chose yellow? Explain.
5. How many fewer students chose ____________ bears than ____________ bears?
6. How many more students preferred ____________ than ____________?
7. What is the sum of the ____________bears and the ____________ bears?
8. What is the difference between the ____________bears and the____________ bears?
9. How would the graph change if 2 fewer students chose blue? Explain.
10. Which colors were chosen by the same number of students?
Use the class graph to complete Guided Practice Problem #1 with students using the
4-step problem-solving process. An example is provided below along with suggested
discussion for Step 3.
Main Idea: students chose red or yellow
Details/Known: graph
Strategy: check each color
Is red “red or yellow?” Yes, red is red. So we count the number of
students who chose red. (Put that number in Step 3.)
Is blue “red or yellow?” No, blue is not red or yellow.
So, do we count the number of blues? No, we don’t count them.
Is green “red or yellow?” No, green is not red or yellow.
So, do we count the number of greens? No, we don’t use that number.
Is yellow “red or yellow?” Yes, yellow is yellow.
So, do we use that number? Yes, we need the yellow number. (Place the yellow
number under the red number in Step 3.)
How many students in our class chose red or yellow bears?
Guide
students in
the checking
of each color
with this
questioning.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 6
Discuss the action which is “put together”. Discuss any fact strategies that could
be used when adding these numbers. For example, if the numbers were 7 + 4…..
I know that 7 + 3 is 10 and 4 is just one more than 3. So 7 + 4 is 11.
How/Why: Added 7 + 4; Found the sum of 7 and 4; etc.
Have students state the answer in a sentence. Ex. Eleven students chose red or yellow.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 7
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 8
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 9
Guided Practice Problem #1
Use the graph created by the class to solve this question.
How many students in our class chose red or yellow bears?
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 10
4. Bar Graphs
Warm-up: (approximately 10 minutes)
Have students complete Warm-up Problem #1 (page 11) to review what they learned
about picture graphs. Remind students to “preview” the graph by looking at the title,
headings and key before they actually begin the 4-step process. This helps them “get to
know” the graph before they start working.
Discuss the solution and briefly review as needed. Have students justify their thinking.
The completed problem is given below:
3
8
7
5
day more
than 3 but
less than 7
graph
between 3 and 7
M 3
T 8
W 7
Th 5
x x x
3 7 5
more less labeled graph
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 11
Warm-up Problem #1
Name______________________
Basketballs Left on the Playground
Each is 1 basketball.
On which day did the students leave more than 3, but less
than 7 balls on the playground? A. Monday
B. Tuesday
C. Wednesday
D. Thursday
Monday
Tuesday
Wednesday
Thursday
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 12
Explain to students that we are now going to display the class information about favorite
bear colors in a different type of graph----a bar graph. A bar graph uses bars to represent
the data instead of pictures.
Write the title on the blank bar graph. Discuss and write the headings. Create a bar
graph using the same bear data collected previously by the class. Point out and discuss
the scale of one. Review how to read a bar graph by following the line at the end of each
bar to the corresponding number in the scale. Also, model how to label the values at the
ends of the bars.
A sample bar graph is shown below-----the class graph will match the data collected
by your students.
Our Favorite Bear Colors
Red
Blue
Green
Yellow
Compare the bar graph to the picture graph. Discuss the similarities and differences
between the two types of graphs. Display the following question. Solve with the teacher guiding the discussion and
recording the 4-step process.
Main Idea: students not choose blue
Details/Known: graph
Strategy: check each color
Is red “blue?” No, red is not blue.
So, do we count the red number? Yes, because we are looking for the students
who did not choose blue. Since red is not blue, we count the red ones. (Write the
number for red in Step 3.)
Is black “blue?” No, black is not blue.
How many students did NOT choose blue as their favorite bear color?
7
4
5
4
0 1 2 3 4 5 6 7 8
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 13
So, do we count the black number? Yes, because the students who chose black
did not choose blue. (Add this number to the number for red.)
Go through examination of each color using this or similar questioning. The students
should have an addition fact with 3 addends in Step 3. Discuss with students the fact
strategies that will help with this addition.
How/Why: Added all the colors not blue.
Added 7 and 4 and 4.
Have students state the answer in a sentence. Ex. 15 students did not choose blue as their
favorite bear color.
Complete Guided Practice Problem #2 with both teacher and students recording the
4-step process. Display the graph and question. Read together and insert speed bumps.
Take a moment to preview the graph by looking at the title, headings and scale. Find the
main idea, label the bars and record the details along with any known information that
might be needed.
Give students time to think about the question and a possible solution. Allow students to
experience a “healthy struggle”. This will help them become more independent problem
solvers and gain confidence in their abilities.
Revisit the main idea and then ask students to share their thoughts on how to solve this
question. If necessary, guide students’ thinking with questioning.
What action is happening in this problem? put together, compare (Emphasize to
students that this problem will require more than one step to solve.)
What exercises are being compared? Jumping jacks are being compared to sit-
ups and pull-ups.
What should we do? put the sit-ups and pull-ups together and then compare that
number to the jumping jacks
What operations should we use? We need to add first and then subtract the sum
from the jumping jacks.
Continue the 4-step process by completing the strategy and how/why sections. An
example of the finished problem is shown on the next page.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 14
Work Guided Practice Problem #3 with students. Display the problem and give
students “think time” to examine and ponder the graph.
What do you see? What do you notice about this graph?
Have students share their thoughts and observations. Discuss in particular the
characteristics of this graph that make it a little different from the others we have been
studying up to now. Especially focus their attention on the 2 different bars of
information. Note the key in the upper right-hand corner which helps us distinguish the
Sports data from the Homework data.
Read the problem together and insert speed bumps.
Find the main idea, label the bars of information for Sports and record the details. Have
students explain why it is not necessary to label the Homework bars.
graph
S 6
P 4
J 7
fewer jumping
jacks than sit-
ups and pull-
ups
Added 6 and 4.
Subtracted 7 from
sum.
6
+ 4
10
10
- 7
3
7 6
4
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 15
Complete the 4-step process by deciding on a strategy, solving for an answer and writing
the how/why.
The finished problem is shown below:
hours Ben
spend sports
two weeks
graph
S w1 3
S w2 4
Added 3 and 4 to
get a sum of 7.
3 + 4 = 7
4
3
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 16
Guided Practice Problem #2
Lee took a test in PE. The graph shows the exercises he did. How many fewer jumping jacks than sit-ups and pull-ups did Lee do?
0
1
2
3
4
5
6
7
8
Sit-ups Pull-ups JumpingJacks
Push-ups
Lee's Exercises
Num
ber
of Exerc
ises
Exercise
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 17
Guided Practice Problem #3
Ben made a graph about the hours he spent on sports and
homework in the past two weeks.
How many hours did Ben spend on sports in the two weeks?
Week
0 1 2 3 4 5 6 7 8 9 10
Week 1
Week 2
Ben's Activities Homework
Sports
Number of Hours
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 18
Part 2: Use Data to Write Problems
Materials: student copies of Warm-up Problem #2 (pg 21)
question stems (pg 18) written on sentence strips
copy of bar graph (pg 23) glued on anchor chart
student copies of Guided Practice Problem #4 (pg 24) student copies of Graphs Mixed Practice Problems Part 2
(MATH_2_A_2 GRAPHS MIXED PRACTICE 2014_RES)
Warm-up: (approximately 10 minutes)
Have students complete Warm-up Problem #2 (page 21) to review what they have
learned about bar graphs. Remind them to “get to know” the graph by looking at the title,
headings and scale before they actually begin the 4-step process.
Discuss the solution and briefly review as needed. Have students justify their thinking.
1. Picture Graphs
Display the picture graph on page 22 and discuss its features. Point out to students that
this graph is missing a question for us to solve. Explain that the class will be using the
data given in the graph to write our own word problem to solve.
What sentence could we write to begin our word problem?
Have students share their ideas. Guide them, if necessary, to choose the sentence that
summarizes what the graph is about, such as Four colors of markers were sold at the
store last week.
Now, we are going to write a question to finish our word problem.
Place sentence strips containing question stems face down (see below). Have a student
choose one for the class to complete. For example, How many more _________ markers
were sold last week than _________ markers?
Question Stems
1. How many more _________markers were sold last week than _________ markers?
2. How many _________ or _________ markers were sold last week?
3. How many fewer _________ markers were sold than _________ markers?
4. How many markers sold were NOT _________ or _________?
5. How many _________markers and _________ markers were sold last week?
6. How many _________ markers were sold last week?
red
purple
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 19
Let’s create another question about our graph that could have also been used in
our word problem.
Choose another sentence strip and complete that question stem as a class. Continue in
this manner until students seem comfortable with the process.
2. Bar Graphs
Display the bar graph (page 23). Discuss the title, headings and scale. Explain to
students that the class will now write a word problem based on the information in this bar
graph. Afterwards, the class will solve the problem they wrote.
Together with students write a beginning sentence such as The students in Mrs. Gray’s
class chose four favorite pizza toppings.
Proceed to writing a single-step question.
What is a question that could be answered by using the data in the bar graph?
Give students time to formulate a question and then ask a student to share his/her
question with the group. Record the student’s question on an anchor chart which already
has a copy of the Favorite Pizza Toppings graph glued at the top.
Have other students share their questions. Write them on the anchor chart as well.
(Before writing a student’s question on the chart, quickly check that it can indeed be
solved by using the data given in the graph.) Point out to students that any one of these
questions could be used to finish our word problem.
Choose one of the questions from the list to solve. Read the beginning sentence and the
chosen question together. Discuss and complete the 4-step process with the teacher
recording for the class.
Next, work Guided Practice Problem #4 with both teacher and students recording the
4-step process. Read together and take a look at the title, headings and scale. Find the
main idea, label the bars and record the details.
Direct students’ attention to the addition sentence and provide a few minutes for them to
re-examine the graph.
Do you see any of these numbers in the bars of the graph? yes, 9 and 8
Which types of animals have those values? ducks and dogs
How do you think this can help us?
Let’s check each answer choice to find the question that requires us to add ducks
and dogs?
Read each answer choice and decide if it is a question that can be solved with the
addition sentence, 9 + 8 = 17. Label with a Y for yes and an N for no. Ask students to
justify their thinking for each question. Checking the answer choices is a helpful strategy
for this problem.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 20
Complete Step 4 to finish the 4-step process. An example of the completed problem is
shown below.
8 7
4
9
N
N
Y
N
question
9 + 8 = 17
graph
D 8
S 4
Sp 7
Du 9
labeled graph
labeled answer choices
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 21
Warm-up Problem #2
Name ___________________________
Mrs. Clark’s class voted on their favorite ice cream flavor. The
results are shown in the graph.
How many students did NOT choose strawberry?
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 22
Markers Sold Last Week
Black
Red
Blue
Purple
Each = one marker
Part 2: Use Data to Write Problems
Picture Graph
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 23
Look at the graph below. Write a question related to the graph
and solve it.
0 1 2 3 4 5 6 7 8 9
Cheese
Pepperoni
Mushrooms
Sausage
Favorite Pizza Toppings
Number of Students
Part 2: Use Data to Write Problems
Bar Graph
Picture
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 24
Guided Practice Problem #4
Which question about the data in the graph could you use this
addition sentence to solve?
A. Are there more ducks than sparrows in the park?
B. How many dogs and ducks are in the park?
C. What is the total number of animals in the park?
D. Which animal was seen the least?
0
1
2
3
4
5
6
7
8
9
10
Dogs Squirrels Sparrows Ducks
Animals Seen in the Park
Nu
mb
er o
f A
nim
als
Types of Animals
9 + 8 = 17
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 25
Warm-up: (approximately 10 minutes)
Have students complete problem #1 of Graphs Mixed Practice Problems Part 2
(MATH_2_A_2 GRAPHS MIXED PRACTICE 2014_RES) to review what they have
learned about writing questions using data in a graph. Briefly discuss and review as
needed.
3. Independent Practice
Have students work the remaining problems in Graphs Mixed Practice Problems Part 2
(MATH_2_A_2 GRAPHS MIXED PRACTICE 2014_RES). These problems provide a
mixed practice of all the graph material learned so far.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 26
Part 3: Graphs with a Scale or Key Greater than One
Picture Graphs
Materials: 16 red, 14 blue, 8 yellow and 10 green bears put into a paper bag
a data chart for recording information with tally marks
a blank pictograph (see pg 27)
pictures of small bears (pg 30) in red, blue, yellow, green
student copies of Guided Practice Problem #5 (pg 32)
student copies of Picture Graph Partner Practice Problem Part 3 (pg 33)
1. Prior to instruction place 16 red, 14 blue, 8 yellow and 10 green bears into a paper bag.
Also, create a data chart for recording information with tally marks (see below) and a
blank pictograph (see page 27).
Bears in the Bag
Red
Blue
Yellow
Green
2. Gather and Record Information
Tally the colors of the bears in the bag on the class data chart.
Bears in the Bag
Red
Blue
Yellow
Green
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 27
3. Construction of the Picture Graph
Discuss the data contained in the data chart. Write the title and headings on the blank
picture graph. (Note: Do not write a scale on the graph at this time.)
Bears in the Bag
Red
Blue
Yellow
Green
Have students place one plastic bear on the picture graph for each tally mark in the data
chart. When they run out of spaces on the graph itself, have them continue to place the
bears off the edge of the graph. (This activity demonstrates the need for different graph
scales.)
Bears in the Bag
Red
Blue
Yellow
Green
Once all the data has been represented in the graph, ask students to share their
observations. It seems that our data doesn’t fit in our graph.
Discuss what can be done to “fix” our graph. If the suggestion has not been made,
suggest that two bears be placed in each square. Move the bears to show that this is a
practical solution.
Red
Blue
Yellow Etc.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 28
At this point, model making a key where each picture of a bear is equal to 2 bears. Write
out the key and place it beneath the graph.
Use one red bear picture and replace the first two plastic bears with this picture. Have
students continue replacing the groups of two bears with one picture of the corresponding
color.
When pictures are on the entire graph, model for students how skip-counting by 2 is used
to determine the value of each row. For example:
Red
Discuss again with students why a picture in a picture graph may need to stand for more
than one item. (The graph can then hold larger amounts of information – bigger numbers
can be shown.)
Examine several questions from Picture Graph Questions (Key > 1) on page 31 with
students. Choose those that best meet the needs of your students. So they may
concentrate on the new scale and how it impacts interpreting the graph, verbally guide
students through the 4-step process with questioning.
What are we trying to find?
What information in the graph do we need to use?
What do you think we should do to find our answer?
How did we find our answer? Does it make sense? Why or why not?
That way, students are still able to benefit from following our problem-solving plan.
4. Guided Practice
Complete Guided Practice Problem #5 with both students and teacher recording the
4-step process. An example of the completed problem is given on the next page.
Key
Each = 2 bears
2 4 6 8 Etc. to 16
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 29
5. Partner Practice
Have students work with a partner to complete the Picture Graph Partner Practice
Problem Part 3 found on page 33. Encourage students to talk with each other and
cooperatively determine a solution. Allow students to experience a “healthy struggle”.
This fosters independent and confident problem solvers. If needed, support students
experiencing difficulty with guiding questions to stimulate their thinking. Once they are
finished, students may share their solutions and explain their thinking.
red
markers
graph
R 45
Counted by 5s
Labeled graph
5 10 15 20 25 30 35 40 45
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 30
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 31
Picture Graph Questions (Key > 1)
1. How many more red bears are in the bag than yellow bears? 2. How many bears are blue or green?
3. If the blue and green bears were removed from the bag, how many bears remain in the bag?
4. How many total bears were in the bag?
5. Which color of bear is less than red but greater than green?
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 32
Guided Practice Problem #5
Ms. Jones counted the class markers. She put the information in this picture graph.
Class Markers
Black
Red
Blue
Purple
How many red markers did Ms. Jones count?
A. 9
B. 45
C. 40
D. 8
Each = five markers
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 33
Picture Graph Partner Practice Problem Part 3
Dee counted the starfish she saw on the beach each day during
Spring Break.
Starfish Counted on the Beach
Monday
Tuesday
Friday
Saturday
Each = 2 starfish
How many fewer starfish were counted on Friday and Saturday
than on Monday and Tuesday?
A. 6
B. 14
C. 12
D. 26
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 34
Bar Graphs
Materials: 40 red, 20 black, 35 blue, and 15 green unifix or other cubes put into a paper bag
a blank bar graph (see pg 35)
student copies of Guided Practice Problems #6 and #7 (pgs 40, 41)
1. Prior to instruction place 40 red, 20 black, 35 blue, 15 green unifix cubes in a paper bag.
Also, create a data chart for recording information (see below) and a blank bar graph (see
page 35).
2. Gather and Record Information
Remove the unifix cubes from the bag and have students sort them into piles according to
their color. Count the red unifix cubes as a class and record the number in the data chart.
Following the same procedure, count the cubes in each of the other colors and record in
the data chart.
3. Construction of the Bar Graph
Discuss the data displayed in the data chart. Write the title and headings on the blank bar
graph. (Note: Do not write a scale on the graph at this time.) An example is shown on
the following page:
Unifix Cubes in the Bag
Red
Black
Blue
Green
Unifix Cubes in the Bag
Red 40
Black 20
Blue 35
Green 15
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 35
Unifix Cubes in the Bag
Red
Black
Blue
Green
Call each color one at a time and have students place those unifix cubes onto the blank
bar graph. When the cubes are placed on the graph, they will run off the edge.
We seem to have a problem with our graph. What do you think we should do?
Discuss with students what can be done to present all the data within the graph. Each
cell can stand for more than one cube.
Review what happened with the picture graph about the bears in the bag – we put 2 in
each space. Have students help put the unifix cubes into stacks of two. Point out the
large number of stacks.
Take suggestions from the class on how many unifix cubes should be put in each stack if
we want to have fewer stacks. Point out they are determining the scale. The scale is the
value (or number of cubes) that each space is going to represent.
Eventually get to the point where the class stacks the unifix cubes into groups of 5. Place
the groups of 5 within the spaces on the graph as shown below for each color.
Remove each stack one at a time and color the corresponding space to create a bar.
When all bars have been created, model how to label the x-axis with the scale. This
graph has a scale of 5. Explain to students that we can count by 5s when writing the
numbers in the scale.
Red
Etc. →
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 36
Read the graph by following the line at the end of each bar down to the number at the
bottom and label these values at the end of the bars.
As a class, discuss and solve several of the Bar Graph Questions (Scale > 1) on page 39.
Once again, guide students through the 4-step problem-solving process verbally as done
previously in the picture graph section.
Complete Guided Practice Problem #6 on page 40 and Guided Practice Problem #7
on page 41 with both students and teacher recording the 4-step process. Examples of the
completed problems are provided on the following pages.
Unifix Cubes in the Bag
Red
Black
Blue
Green
Unifix Cubes in the Bag
Red
Black
Blue
Green
0 5 10 15 20 25 30 35 40
40
20
35
0 5 10 15 20 25 30 35 40
15
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 37
bar show number
of llamas
graph
12 llamas
Labeled bars in
answer choices to
find 12 llamas
10
12
6
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 38
Note to Teacher:
This problem contains bars that fall between two numbers in the scale. Two
recommended strategies are given below:
Students use their knowledge of place value and making groups of 10 to help
them determine the missing number (15) between 10 and 20 for pizza. It is then
labeled on the scale and on the pizza bar. The nacho bar falls between numbers
as well; however, that information is not needed to solve the problem so it is not
labeled. This strategy is illustrated in the example above.
Students rely on their knowledge of counting by 5s to label all of the missing
numbers in the scale.
15
15
20
40
graph
CN 40
P 15
T 20
more 2nd graders
preferred chicken
nuggets than
pizza and tacos
Labeled graph
Added 15 and 20
Subtracted the sum from 40
1 5
+ 2 0
3 5
4 0
- 3 5
5
3 1
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 39
Bar Graph Questions (Scale > 1)
1. How many fewer blue than red cubes are in the bag?
2. How many red or green cubes are in the bag? 3. Which color has between 10 and 20 cubes in the bag?
4. Which two colors have the same number as blue?
5. How many cubes are in the bag altogether?
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 40
Guided Practice Problem #6
Mrs. Ray’s class saw the following animals during their trip to the zoo.
6 camels 12 llamas 4 tigers 18 monkeys
0 2 4 6 8 10 12 14 16 18
Which bar should we use to show the number of llamas the class saw?
A. 0 2 4 6 8 10 12 14 16 18
B. 0 2 4 6 8 10 12 14 16 18 C.
0 2 4 6 8 10 12 14 16 18
Animals Seen at the Zoo
camel
llama
tiger
monkey
llama
llama
llama
Anim
als
Number of Animals
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 41
Guided Practice Problem #7
How many more 2nd graders preferred chicken nuggets than pizza
and tacos combined?
0 10 20 30 40
ChickenNuggets
Nachos
Tacos
Pizza
Favorite Lunch
Number of Students
Foo
d T
yp
e
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 42
Part 4: Use Data to Draw Conclusions and Make Predictions
Materials: student copies of Focus bar graph for IMN (pg 45)
Word Bank written on a chart tablet (pg 46)
partner copies of Word Bank
student copies of Baseball Practice picture graph for IMN (pg 48)
student copies of Warm-up Problem #3 (pg 51)
student copies of Guided Practice Problem #8 (pg 52)
student copies of Graphs Independent Practice Problems Part 4
(MATH_2_A_3 GRAPHS CONCLUSIONS PREDICTIONS IP 2014_RES) student copies of Graphs Mixed Practice Problems Part 4
(MATH_2_A_4 GRAPHS MIXED PRACTICE 2014_RES)
Focus: Display the penny bar graph (pg 45) and give each student a copy. Remind them
to “get to know” the graph by looking at the title, headings and scale. Instruct
students to find the values of the bars and label these values at the ends of the
bars. Provide sufficient time for them to complete the task and then briefly
discuss the graph and the correct values for the bars. Emphasize that this graph
shows how the total amount of pennies Kyle collected changes from day to day.
1. Explain to students that we can draw some conclusions from the data in this graph.
Display the chart tablet with the Word Bank and read the words aloud together.
We can often use words from the Word Bank when developing our conclusions.
Let me give you an example:
50
40
30
20
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 43
When I look at the information in the graph, I see that the bars are getting higher.
From that I can make the conclusion that the total amount of pennies Kyle
collected is increasing from day to day.
Record the conclusion on the board for all to see.
What conclusion could we make if the bars were getting lower? His total amount
of pennies would be decreasing from day to day.
Let’s form another conclusion about the data using the words “more than.”
Allow students to study the graph for a moment and formulate a conclusion using “more
than.” Have them share their thinking. If necessary, guide students to form a conclusion
such as The total number of pennies he had on Thursday was more than he had on
Tuesday. Record this conclusion in the list.
Have students work with an “elbow partner” to formulate a different conclusion using a
word or words from the Word Bank that has not yet been used. Have several students
share their conclusions, and explain how they came to those conclusions. The teacher
then adds them to the list. Some possible conclusions have been added below:
Conclusions
The total amount of pennies Kyle collected is increasing from day
to day.
Conclusions
The total amount of pennies Kyle collected is increasing from day
to day.
The total number of pennies he had on Thursday was more than he
had on Tuesday.
Conclusions
The total amount of pennies Kyle collected is increasing from day
to day.
The total number of pennies he had on Thursday was more than the
total he had on Tuesday.
Kyle had the least total pennies on Monday.
Kyle had fewer total pennies on Wednesday than he did on
Thursday.
The total number of pennies he had on Tuesday was less than the
total he had on Wednesday.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 44
2. Direct students’ attention back to the graph. Explain that we can also use the information
presented in a graph to make a statement about what will happen in the future. A
statement about the future is called a prediction. We can search the data in a graph for a
pattern that will help us make a prediction that is reasonable.
Let’s look carefully at the data in our graph. On Monday, Kyle had a total of 20
pennies. On Tuesday, he had a total of 30 pennies. On Wednesday, he had a total
of 40 pennies and on Thursday, he had a total of 50 pennies.
Do you see any kind of pattern? After Monday, the total amount of pennies
increased by 10 each day; On most days, Kyle collected 10 pennies.
How many pennies do you think Kyle will save on Friday? 10
What prediction can we make about his total number of pennies on Friday? On
Friday, Kyle will have collected a total of about 60 pennies for his class project.
Is this prediction reasonable? Why?
Record the prediction on another part of the board.
Have students glue their copy of the penny graph on the right side of their Interactive
Math Notebook (IMN). Then, have them choose 1 conclusion from the list on the board
and write it below the graph. Students also record the prediction in their IMN below the
chosen conclusion. See picture below.
Prediction
On Friday, Kyle will have collected a total of about 60 pennies for his
class project.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 45
Kyle made a graph to show the total number of pennies he
collected for a class project.
70
60
50
40
30
20
10
0
Conclusion:
Prediction:
Monday Tuesday Wednesday Thursday
Pennies Collected Tota
l Pennie
s C
ollecte
d
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 46
Word Bank
increases increasing increased
decreases decreasing decreased
more than less than least
fewer most equal
Word Bank
increases increasing increased
decreases decreasing decreased
more than less than least
fewer most equal
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 47
3. Display the baseball picture graph (pg 48) and give each student a copy. Give students
time to take a quick look at the title, headings and key. Briefly discuss the graph and its
characteristics. Have students compare this graph to the penny graph we just studied.
How is this graph the same as the penny graph?
How is it different from the penny graph?
Guide students to see that this graph shows how many hours Jon practiced baseball each
week.
Instruct students to show their skip counting on the pictures and then label the total
values at the ends of the rows.
Remind students that we can formulate a conclusion from the information given in a
graph.
What conclusion can we make from the information in this graph?
Have a student choose a word from the Word Bank and generate a conclusion as a class
using the chosen word.
Instruct students to now form a conclusion of their own that is different from the one
done by the class and write it on the lines beneath the graph.
A few possible conclusions are listed below:
Jon practiced the least number of hours in Week 1.
Jon practiced more hours in Week 3 than he did in Week 2.
Jon practiced as many hours in Week 4 as he did in Weeks 1 and 2 together.
Jon practiced fewer hours in Week 2 than he did in Week 4.
The number of hours Jon practiced increased each week.
4. Direct students’ attention back to the graph, and briefly talk about making a prediction.
What prediction would you make about the number of hours Jon will practice
baseball in Week 5?
Have them write their prediction on the lines provided on their paper. Once they have
finished, they may glue their paper on the left side of their IMN. If desired, allow
students to “Pair-Share” their conclusion and prediction with other students.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 48
Jon made a graph to show the hours he practiced baseball each
week the past 4 weeks.
Jon’s Baseball Practice
Week 1
Week 2
Week 3
Week 4
= 1 hour of practice
Conclusion:
Prediction:
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 49
Warm-up: (approximately 10 minutes)
Have students complete Warm-up Problem #3 (page 51) in which they construct a bar
graph with a scale of 2 and draw a conclusion from the information presented in the
graph. Remind students they may use the Word Bank if needed.
Once students have finished, briefly discuss the graph to check for accuracy. Also, have
students justify and explain how they formulated their particular conclusion.
5. Guided Practice
Work through Guided Practice Problem #8 with students. Read the problem together,
insert speed bumps, and begin the 4-step process by finding the main idea and recording
the details/known information. Examine the graph with students. Read the title,
headings and scale.
Look at the data from Week 1 to Week 4. What do you notice?
Guide students, if necessary, to see that the last three weeks decrease by 1 minute. This
is a trend in the data, and it will help us make a reasonable prediction for Week 5. Check
each answer choice. Have students justify their thinking to the group and then label.
Finally complete the how/why part of the process. An example of the completed problem
is provided on the following page.
6. Independent Practice
Students complete Graphs Independent Practice Problems Part 4
(MATH_2_A_3 GRAPHS CONCLUSIONS PREDICTIONS IP 2014_RES)
independently.
7. Mixed Practice
Have students complete Graphs Mixed Practice Problems Part 4
(MATH_2_A_4 GRAPHS MIXED PRACTICE 2014_RES) independently. This
exercise provides a variety of graph problems for students to solve.
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 50
reasonable prediction
time one mile Week 5
graph
Wk 1 10
Wk 2 8
Wk 3 7
Wk 4 6
labeled graph
found pattern in data
checked answer choices
10
8 7
6
too much
too much
yes
too little
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 51
Warm-up Problem #3
Name ____________________________
Create a bar graph using the data below. Label the scale by
2s. Remember to include a title and headings.
10 students like summer
6 students like spring
2 students like winter
4 students like fall
Title: ________________________________
Number of Students
Conclusion:
Season
Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 52
Guided Practice Problem #8
Mrs. Messer was training for a race. She made a graph to show how much time it took her to run one mile.
What is a reasonable prediction for how much time it will take Mrs. Messer to run one mile in Week 5? A. In Week 5, Mrs. Messer will run one mile in 12 minutes. B. In Week 5, Mrs. Messer will run one mile in 8 minutes.
C. In Week 5, Mrs. Messer will run one mile in 5 minutes. D In Week 5, Mrs. Messer will run one mile in 1 minute.
Num
ber
of
Min
ute
s