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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



Part 2: Use Data to Write Problems

Warm-up Problem #2

Picture Graph

Bar Graph


Mixed Practice

Part 3: Graphs with a Scale or Key Greater Than One

Picture Graphs

Pictures of Small Bears

Picture Graph Questions


Picture Graph Partner Practice Problem

Bar Graphs

Bar Graph Questions



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


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


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.


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.


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.


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:


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.


Red

Blue

Green

Yellow

Each = one student

Each = one student

7

4

4

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.


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.



Use the graph created by the class to solve this question.

How many students in our class chose red or yellow bears?


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


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


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.


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


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.


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


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



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



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



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)


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


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.


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


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?


Markers Sold Last Week

Black

Red

Blue

Purple

Each = one marker


Picture Graph


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


Bar Graph

Picture



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



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.


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 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


Tally the colors of the bears in the bag on the class data chart.

Bears in the Bag

Red

Blue

Yellow

Green


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.


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


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


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?



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


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


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).


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


Red 40

Black 20

Blue 35

Green 15



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. →


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.


Red

Black

Blue

Green


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


bar show number

of llamas

graph

12 llamas

Labeled bars in

answer choices to

find 12 llamas

10

12

6


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


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?



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



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


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 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


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


to day.

The total number of pennies he had on Thursday was more than he

had on Tuesday.

Conclusions


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.


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.


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


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


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.


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:



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.


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


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



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

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