Summary
The students will be able to describe data represented on charts
and graphs and answer simple questions related to data representations.
Materials
Books:
- Lemonade for Sale, by Stuart J. Murphy, ISBN: 0‐06‐446715‐5
- Tiger Math, by Ann Whitehead Nagda and Cindy Bickel, ISBN: 0‐8050‐6248‐3
- Banana Split and Other Snack Recipes, by Heather E. Schwartz, ISBN: 1‐4296‐1339‐4
- Peanut Butter and Jelly Sushi and Other Party Recipes, by Kristi Johnson, ISBN: 1‐
4296‐1340‐8
- Wormy Apple Croissants and Other Halloween Recipes, by Brekka Hervey Larrew,
ISBN: 1‐4296‐1338‐6
- Oodle Doodles Tuna Noodle and Other Salad Recipes, by Kristi Johnson, ISBN: 1‐4296‐
1341‐6
- Making Graphs, I Can Do Math, by Michelle Wagner Nechaev, ISBN:0‐8368‐4111‐5
- Graphing Activities, by Joy Evans, ISBN: 1‐557‐99124‐3.
- Graph Games, by Susan Holding, ISBN: 0‐690‐34964‐5.
- Get Up and Go!, by Stuart Murphyl, ISBN: 0‐590‐23811‐6
- Graph‐A‐Day, by Michelle Long Windmoeller, ISBN: 0‐7424‐0146‐0
- Graphing Primer, by Laura Duncan Choate & JoAnn King Okey, ISBN: 0‐86651‐486‐4
- Dollars, by Mary Hill, ISBN: 0‐516‐25170‐8
Media:
- Math Concepts for Primary Grades, by 100% PRODUCTIONS 1998‐2001, UIMC (Utah
Instructional Math Consortium), Utah State of Education.
Organizations:
Background for Teachers
Understanding what data and charts/graphs are, collecting data, graphing data, and
making use of the information represented are difficult concepts for second graders to
grasp. Research and common sense tell us a clear vision is a vital aspect of graphing data
and comprehending the information on the charts/graphs. Students must be able to
disentangle the many different items appearing on a graph and easily use the information.
The data must stand out (Elements of Graphing Data, by William S. Cleveland, 1994).
Graphing data on a chart gives us a visual picture so we may see the information from a
different perspective. The quick view of the chart can help us more easily solve a particular
problem.
In Utah, second graders need to collect, organize, display and interpret numerical data in a
variety of ways. Students should be able to describe the data on the charts and graphs and
answer simple questions related to the data representations.
This lesson will help students understand what "data" and charts/graphs are and will use
variety of ways to practice making and reading data charts/graphs. Various games will
engage students in using graphs within the scope of common life activities.
Intended Learning Outcomes
l. Demonstrate a positive learning attitude
5. Understand and use basic concepts and skills
6. Communicate clearly in oral, artistic, written, and nonverbal form.
Instructional Procedures
Content Connections:
Science ‐ Observe, record, and compare how the behaviors and
reactions of living things help them meet their basic needs. Identify behaviors and
reactions of living things in response to changes in the environment, including seasonal
changes in temperature and precipitation.
Invitation to Learn:
Have several crayons of the following colors on a table for students: red, blue, green,
orange. As students are getting ready for math, invite small groups of students to the table
to color in a square on a data chart according to the following preferences. Students who
like the Dallas Cowboys football team use a blue crayon to color in a square in the column
labeled "Dallas Cowboys" (see Football Chart page -- if possible, enlarge the chart to poster
size. After students have marked their choice, display it on a wall). Students who like the
San Francisco 49ers use a red crayon on the column labeled "San Francisco 49ers."
Students who like a team other than the Cowboys or 49ers use a green crayon on the
column labeled "Other Teams." Students who don't know who they like, or who may not
like football, use an orange crayon on the column labeled "Don't Know or Don't Like."
When all students have colored a square on the chart, ask students to think about the data
on the chart. Have students write what they know about the data in their math journals.
The journal entries will help serve as a pre‐assessment to this lesson.
Instructional Procedures:
Lemonade:
- This lesson will build upon information students learned in first grade about
collecting and organizing data. In second grade, students will further expand their
knowledge by learning how to collect a variety of data, make charts and answer
questions related to the charts they make.
- Bring students to the rug area or other area where students can be close to the
teacher and see the pictures from the book.
- With these goals in mind, read the book, Lemonade for Sale. Briefly talk about the
story in general.
- Then ask: "What problem did the children have in the beginning of the
book?" (Clubhouse was falling down and the piggybank is empty.)
- Ask: "How did the children decide to solve the problem?" (Sell cups of
homemade lemonade.)
- Ask: "How many cups of lemonade did the children need to sell to fix the clubhouse?" (30‐40 cups each day for a week.)
- Ask: "How did the children keep track of the cups they sold each day?"
(Sheri made a bar graph.)
- Ask: "How many cups did they sell the first day, Monday?" (30)
- Ask: "How many cups did they sell the second day, Tuesday?" (40)
- Ask: "How many cups did they sell the third day, Wednesday?" (56)
- Ask: "How many cups did they sell the fourth day, Thursday?" (24)
- Ask: "Why didn't the children sell very many cups of lemonade on
Thursday?" (The people were down at the corner watching Jed juggle.)
- Ask: "How did they solve the problem of getting those people who were
watching Jed to come buy cups of lemonade at their lemonade stand?" (Sheri
invited Jed to juggle lemons beside the lemonade stand.)
- Ask: "How many cups of lemonade did they sell on Friday?" (So many that
the sales were over the top.)
- Ask: "What does 'over the top' mean in this story?" (There were so many
cups of lemonade sold that they marked the bar graph to the top and over the
line at the top.)
- Re‐read the pages that show the number of cups of lemonade sold. Show pictures in
the book to the students.
- Make a class chart of the number of cups of lemonade sold by each day (See Cups of
Lemonade Sold page -- enlarge to poster size.)
- Refer to the bar charts/graphs in the book to get the correct number of cups of
lemonade sold each day.
- Make the connection between answers to the questions you've been asking and the
definition of "data." When we collect information about a subject, such as the
information the students have collected from Lemonade for Sale, that information is
called data. Data can come in various forms: numbers, ideas, lists of things, etc.
- Ask the students: "What 'data' is collected in Lemonade for Sale?" (Number
of cups of lemonade sold each day)
- Now have a class discussion about charts/graphs and why they give us good data
information. Include in the discussion where charts are seen in daily life
(newspapers, magazines, grocery stores, etc.). Include the fact that bar graphs can
give us information at a quick glance.
- Write some of the facts about the class on the white board using words and
numbers, for example: Write how many students have black hair -- "Two students
have black hair." Write how many students have blonde hair -- "Seven students have
blonde hair." Write how many students have brown hair -- "Nine students have brown hair." Write how many students have red hair -- "Two students have red
hair."
- Now make a bar chart, labeled "Hair Color Chart," showing the same information
(use the ______ Chart page). An option would be to use a document camera (such as
an ELMO or other brand) hooked up to your computer and a digital projector for
this chart so all students can view the page without having to enlarge it to poster
size. Or you may scan the chart into your computer and use the digital projector to
show this chart on the white board. Color in the squares, using different marker
colors, as you model how to make the chart. Do not write on your canvas roll‐down
screen.
- Through discussion with the students, help them to discover the bar chart is an easy
way to "see" information, and the bar chart is an easy way to get information
quickly.
- Using another ______ Chart page, labeling it "Shirt Colors Chart." Ask students to
decide what the main color of the shirt they are wearing today. An easy way to help
students is to have all the students with blue shirts group together in a corner of the
room; all students with green shirts stand in a different corner of the room, etc.
- Have students work in groups to make a bar chart of the color of the shirts (or some
other similar item) by counting the number of students in their group. Use various
colors of crayons for the different columns.
- In the back of Lemonade for Sale, author Stuart J. Murphy gives some good ideas for
further study of graphs.
- Use some of the ideas Mr. Murphy suggests to help children count various objects
and make bar graphs and paste them in their math journals.
Growing Tigers:
- Review briefly what a bar chart/graph looks like and how it gives us information at
a quick glance.
- Bring students to the rug area or other area where students can be close to the
teacher and see the pictures from the book.
- Instead of having students at the rug, an option would be to use a document camera
hooked up to your digital projector. This set up would make the pictures and
graphs in the book large enough on the screen for all students to see equally well.
- Pre‐read the book, Tiger Math. Keeping in mind the information written on the left
pages, read the story (the right‐side pages) about T.J., a Siberian tiger cub born at
the Denver Zoo. Briefly discuss the story with the children, helping them to know
this is a real story about a real tiger.
- Now go back to the various graphs in the tiger book and discuss how they are
different from the bar graphs students used in the previous activity. Bring out the
following points, as well as any others points students may find:
- Pictures are sometimes used to show "how many" in charts or graphs. This time
it shows how many tigers there are in the wild.
- circle chart is different in shape and uses various colors to show the different
data.
- Small squares can represent individual numbers on a chart.
- Charts can have backgrounds, but that doesn't change the data represented on
the chart -- it gives character or makes the chart fun.
- A chart can have two or more things (this time it's tigers) represented on the
same graph, comparing the two or more things -- see the bar charts and line
charts in the book.
- A line graph is another way to show data.
- Use various questions to compare the charts. Ask what the students can discover
about the tigers' growth, what they ate, and how they compared to each other.
- Look at the chart on page 8. Ask: "How many Sumatran Tigers live in the wild?
Help students to understand that each tiger picture represents 500 tigers in the
wild." (500)
- Ask: "Which kind of tiger has the most living in the wild?" (Bengal Tiger)
- Ask: "Which kind of tiger has 1,500 tigers living in the wild?" (Indo‐Chinese
Tiger)
- Look at the chart on page 10. Ask: "According to this pie chart, which kind of
tiger has the fewest living in the wild?" (South China)
- Ask: "Which kind of tiger has the most living in the wild?" (Bengal)
- Look at the chart on page 16. Ask: "How much more did Matthew weigh at 6
weeks than T.J. weighed at 6 weeks?" (4 pounds) Show students that the
"numbers" on the chart represent pounds.
- Ask the students to give an example of "data" from this book, i.e. the number
of tigers in the wild, T.J.'s weight in pounds, Matthew's weight in pounds.
Ask the students why they think this information is important.
- Have a discussion as to the importance of the data, the information the Denver
zookeepers, and why they wrote the book.
Favorite Food
- Preview the following books: Banana Split and Other Snack Recipes, Peanut Butter
and Jelly Sushi and Other Party Recipes, Wormy Apple Croissants and Other Halloween
Recipes, Oodle Doodles Tuna Noodle and Other Salad Recipes. Let the students know
the goals of this lesson are to (1) collect data from these recipe books (the data will
be in form of their favorite foods); (2) chart that data on large charts; (3) discuss
what information they can "see" from the chart. Also, prepare for this lesson by
making four poster‐size charts of the chart, ______ Chart.
- Looking ahead, a fun follow‐up activity would be for the students to make one of the
class favorite snacks, preferably with the help of a class mom.
- Start the lesson by dividing the class into four groups. Give each group one of the
recipe books and each student a data sheet -- What's My Favorite Food?
- Direct the groups to look through their books, reading the recipes and looking at the
pictures. Each student should choose a recipe he/she likes the most. As students
pick their favorite recipe, they should fill out the corresponding book line on the top
part of the What's My Favorite Food data sheet.
- Rotate the books through all groups using the same process of choosing favorite
foods and having students record their data on the top of the data sheet.
- The next few steps of the lesson can be confusing for students, so proceed
accordingly.
- Ask each group to choose a scribe. You may want to use yarn and make a cardstock
"Scribe" sign for each scribe to wear over his/her neck. Explain the duties of the
scribe -- the person will write what the group chooses. The scribe will use the
bottom part of his/her data sheet, labeled "Group Favorites," to record information.
- Now have the students take turns telling the scribe in their group their favorite food
recipe from Banana Split.
- The scribe will record the data in the appropriate box on the bottom portion of
his/her data sheet. To assess student understanding of charting data, walk around
and monitor groups.
- After the scribes have written groups' choices for all four of the books, prepare for
the next step by bringing students to the rug, asking scribes to bring their data
sheets. No one else need bring their data sheets to the rug.
- Have the poster size ______ Chart taped to a board low enough students may reach it.
Fill in the ______ with "Banana Split." The names, or a shortened version, of the ten
recipes should be written on the bottom of the chart (black marker), each one under
a column.
- Ask the scribes, one at a time, to slowly give the names of the favorite recipes to the
class. A student from that group should go mark a box on the poster‐size chart to
represent the data from Banana Split. Use different colors of markers for each
recipe.
- Make the connection that you are using data from the students' data sheets to make
a chart/graph.
- After the chart is completed with the class data represented, ask probing questions,
like the following. Not all questions will be relevant to each chart.
- Is there a recipe that stands out as having lots more boxes filled in compared
to the other recipes?
- Which recipe has the most? The least?
- How many more or less did one choice have vs. another?
- Are there any recipes that have the same number or very close to the same
number?
- What does that tell you, if they are the same or close to the same?
- Is there a class favorite?
- Is the class favorite an easy recipe to make?
- What else does this data chart tell you about the recipes in Banana Split?
- The questions and discussions centered on the charts are the very basis of
understanding data, charts, and graphs. This understanding will help students
make the connection of data to charts and graphs and further more, to using the
information as students make educated decisions in daily living.
- For more practice, students should make a separate chart/graph for each of the
recipe books.
- IMPORTANT: To make the connection and comprehension of charts and graphs
complete, help students understand different types of charts and graphs by
transferring the Banana Split data to a prepared Excel file. If possible, show the data
on a digital projector so all students can watch you enter the data. Create a chart
from the entered data. Show the chart in the various forms -- bar, pie, line, scatter,
tally, pictograph, etc. Discuss the differences of the charts. Give some examples of
when you would use the different charts. Keep it simple.
- Refer to the Extension Activities for lots of data, charts, and graphs practice.
- Refer to the various websites, including previous years' Core Academy lessons, for
more practice.
- Core Academy 2004, Second Grade, Where Do I Fit on the Graph? This lesson is
especially good for charts and graphs.
Lesson and Activity Time Schedule:
- Each lesson is 55 minutes.
- Each activity is 30 minutes.
- Total lesson and activity time is 90 minutes.
Activity Connected to Lesson:
Land, Air, or Water
- Read the book, Quick as a Cricket, to the students. Have the students decide whether
the animals in this book live on the land, in the air, or in/around water. Have
students collect the data and make a tally chart. Have students discuss the
information from the chart. How does a tally chart differ from a bar chart? Where
else can tallies be used? Give some examples where tally charts work well (counting
people in a room, counting students going to lunch, counting votes in a school
election, etc.). The book, Animal Snackers, is a good one to work with struggling
students.
What's for Lunch?
- Read the book, The Cafeteria Lady from the Black Lagoon. Have a discussion about
favorite school lunch foods. (Remember that some students may never eat school
lunch.) Graph students' favorite foods. Use a bar chart. Now make a different kind
of chart/graph using the same data. Discuss the differences between the two charts.
Now make a third chart using the same data. Again, discuss the differences between
the three charts. Have students write three facts about the charts in their math
journals.
Chart Museum
- Read the book, The Great Graph Contest. There are a variety of data collected and
charts made in this book. Now, re‐read the book and after each kind of chart in the
book, have a discussion about how the characters made their graphs and why they
used that particular chart/graph each time. Have a discussion about the charts and
have students write in their math journals about the various graphs. Make a home
assignment for students to make a creative graph at home with something of their
choosing. Have them bring the chart to school and have a Chart Museum where
students will walk around looking at the various charts. Students should write two
numerical facts about every chart/graph in their math journals.
Group Reporting
- For high ability students, have them do a group read of the book, Graphs. Have
them discuss the creative ways Gary (main character from the book) found to
collect data and make charts. How did he use the information? Was it useful
information? How did he include others in his activities? Have the students figure
out something at school about which they can collect data. Have the group create a
plan to report to the rest of the class the data they collected, the chart(s) they made,
and the valuable information they discovered from their project. Before the
students proceed with their activity, they should make a proposal to the teacher.
Challenge the group to use a chart(s) other than a bar chart(s). Or challenge them to
make several different kinds of charts of the same information, explaining the
differences and value of each chart. Give this group a couple days to complete this
task. Make sure they include title, labels, and graphed data. Finally, have the group
report to the whole class, including charts and graphs and other pertinent visual
aids.
Activity Materials:
- Pencils
- Student math journals
- Whiteboard markers
- Various blank charts or paper to make charts
- Colored markers
Books:
- Quick as a Cricket, by Audrey Wood, Illustrated by Don Wood, ISBN: 0‐85953‐151‐1
- Animal Snackers, by Betsy Lewin, ISBN: 0‐8050‐6748‐5
- The Cafeteria Lady from the Black Lagoon, by Mike Thaler, Pictures by Jared Lee,
ISBN: 0‐590‐50493‐2
- The Great Graph Contest, by Loreen Leedy, ISBN: 0‐8234‐2029‐9.
- Graphs, by Bonnie Bader, Illustrated by Mernie Gallagher Cole, ISBN: 0‐448‐42896‐2
Extensions
- For visual and tactile learners, have students bring cutout charts/graphs from
newspapers, magazines, etc. and put up on a bulletin board labeled "Charts and
Graphs."
- For English Language Learners, have students use pictures of items instead of
word headings for charts.
- Use a variety of manipulatives to make charts, i.e. linking cubes, attribute blocks,
counting figures (bears, food items, etc.), double‐sided counters, etc.
- For advanced learners, have students create story problems using their charts and
graphs. Each student should write 2‐3 problems and exchange papers, solving the
problems using the data charts.
- For science, students can plant seeds of various kinds and observe their growth
patterns by charting the amounts of water needed, the length of growth in a week,
the kinds of leaves, etc.
- For science, students can track and chart daily temperature for a week, the
temperatures in a single day, petals on various flowers, etc.
- Movement/P.E. activity: Go to the gym or outside for this activity. Divide the
students into groups of two or three. Each student secretly chooses an animal to
imitate. Students will take turns acting out the animal. Rules can include animal
sounds, or not include sounds. After all students have had a chance to imitate an
animal, have students make a human chart by sorting themselves by birds, water
animals, or land animals. The human chart can be made by making rows of students
designated by the three categories. Now, have student repeat the activity by
choosing a different partner and a different animal according to the three categories.
- The Illuminations website from NCTM (listed under Web Sites) has six really great
lessons on data, charts, and graphs, complete with student activity pages.
Family Connections:
Assignments to do with parents:
- Ask family members to help students find graphs and charts in the newspaper,
magazines, Internet, etc. Bring the cut out or copies of charts/graphs to school and
hang on bulletin board labeled "Charts and Graphs."
- Send home a variety of blank charts with instructions for students to collect data
from a variety of options. They should create charts/graphs from the data and then
write three facts about each chart. Ideas for data: top five most common grocery
list items, foods for dinner, favorite family pizza toppings, kinds of shoes owned by
family members (dress shoes, tennis shoes, slippers, flip‐flops, boots, etc.), the
number different kinds of tools in the tool box, number of buttons on family coats,
number of lights in each room, how many books each family member read in the
last month, kind of trash thrown away, the number of peas or beans or other
vegetables on each family member's dinner plate, number of pieces of mail received
for each day of a week, etc.
Assessment Plan
- Students need a lot of practice using data, graphs, and charts so they will become
familiar with the valuable information.
- Students can complete a chart/graph with title, labels, and collected data. Students
should answer comprehension questions. The U‐TIPS website is a great place to get
sample questions.
- Using graph paper, have students write their whole names and graph the letters;
include title, labels, and graphed data. Have students write three facts about their
graph. Other ideas to graph: number of buttons on each student's clothes that day,
number of pencils in each child's desk, number of baby teeth each student has lost.
Bibliography
The Arithmetic Teacher, Sharon L. Young, April, 1991, pp. 28‐33.
The Arithmetic Teacher, Jean M. Shaw and John Firkins, September, 1993, pp. 27‐40.