Bemidji State University
Summer Math Institute
Summer 2007
Data Investigations and Assessments in the
Math Classroom
Grade 1
Kim Kvam – Red Lake Elementary
[email protected]
Jill Anderson – Red Lake Elementary
[email protected]
Outline to Assess Instructional Changes
1. Lesson Plans – What are you attempting to change or improve?
Our goal is to improve student comprehension of graphing,
estimating, understanding various types of graphs, understanding purpose of
graphs, and realizing the effectiveness of graphs.
2. What actual changes are you making?
We are introducing the concept of graphing along with some
procedures of graphing to enable students to process data in easier manner.
3. What effect should these changes have?
Students should be able to read different types of graphs, enter data
appropriately on a graph, and begin understanding the estimation process.
4. Formulate Hypothesis – Null and Alternative
Null:
Students will not understand the purpose of graphs and feel
confident compiling information in a graph form.
Alternative:
Students will understand the purpose of graphs and feel
confident compiling information in a graph form.
5. Experimental design for collecting data.
Pre-test, post-test, and teacher observation.
Standards Addressed
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines, to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from, and
comparing situations.
Pre-Test
• Show students red, blue, green, yellow, and orange unfix cubes.
Discuss colors aloud to children to ensure color comprehension.
• Instruct students to choose their favorite color unfix cube.
• Ask students who chose the red cube to stand up. Teacher will tally
the number of students standing and mark on a tally chart on the
board.
• We will continue this procedure until all colors have been graphed.
• Questions:
o Which color was chosen most?
o How can you tell?
o What color was chosen the least?
o How can you tell?
o Were any colors chosen the same amount?
o What can learn from this tally graph?
• Explain to students that they will need to transfer the information
from the tally chart onto a bar graph.
• Distribute bar graph and crayons.
• Explain to students that we want to see what they know about
graphing.
• Explain to students that these pre-tests will be placed in their graphing
portfolio so it is important to work independently and do their best.
Pre-Test: Graphing Unit
Name: __________
Match the Tally Marks
1
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two
2
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one
3
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four
4
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three
5
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six
6
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eight
7
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five
8
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seven
9
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ten
10
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nine
Pre-Test: Graphing Unit
Name: __________
10
9
8
7
6
5
4
3
2
1
Red
Blue
Green
Yellow
Checklist for Graphing Assessment
Orange
_____ Student is able to recite the correct amount of columns on a graph.
_____ Student is able to recite the correct amount of rows on a graph.
_____ Student is able to recite the correct amount of circles on a circle
graph.
_____ Student is able to identify the highest and lowest columns on a graph.
_____ Students is able to define what a bar graph, circle graph, and picture
graph are.
_____ Student is able to correctly fill in a bar graph, circle graph, and
picture graph.
Lesson 1 – Tally Marks
http://www.abcteach.com
Minnesota State Standards:
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
Objective:
Students will understand the use of tally marks and be able to use them to
count independently.
Materials:
• Toothpicks
• Pencil
• Tally Worksheets (3)
Activity:
• Teacher will explain tally marks are used to count or keep score.
• Teacher will distribute worksheets.
• “Look at the chart. Each | mark equals one. After there are four |
marks, a \ mark crosses through them which equals five.”
• “After you have made a \ mark through four | marks you start again
with a | mark. When you are done counting everything, you count the
\ tally marks by fives.”
• “We will work on the following worksheet as a class together.”
• We will discuss each number aloud to ensure student comprehension
and answer any questions students may have.
• “Why do you think graphing is useful and important?”
•
•
•
•
Tally marks are used to count or keep score.
Look at the chart.
Each | mark equals 1.
After there are four | marks, a \mark crosses through them,
which equals five.
• After you have made a \ mark through four | marks, you start
again with a | mark.
• When you are done counting everything, you count the \ tally
marks by fives.
Write the tally marks for the number of objects below.
___________________
___________________
___________________
___________________
Write the tally marks for the number of objects below.
___________________
___________________
___________________
Lesson 2 – Favorite Color Crayon
http://www.abcteach.com
Minnesota State Standards:
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
Objective:
Students will understand and be able to read a life sized picture graph posted
on the wall.
Materials:
•
•
•
•
Pencil
8 Crayons – Primary Colors
Crayon Worksheets (2)
Student Scissors
Activity:
• Teacher will write each primary color name on the board after
discussing how to spell them with students.
• Teacher will instruct students to write their name and favorite color on
the crayon worksheet.
• Students will then be told to color the crayon box without lines their
favorite of the eight primary colors (the same color they wrote down).
• Students will then cut out their two crayon worksheets.
• Teacher will then have students sit in a circle with their crayon
cutouts.
• “If you chose red as your favorite color and colored your crayon box
red please stick your crayon cutouts to the picture graph under the
word red.” (Continue to name each of the colors aloud and have the
students finish the picture graph accordingly)
• “What can we tell by looking at this graph?
•
•
•
•
•
•
•
•
•
•
•
How many students chose the color red as their favorite?
How many students chose green?
How many students chose blue?
How many students chose yellow?
How many students chose orange?
How many students chose purple?
Which color was chosen the most?
Which color was chosen the least?
Were any chosen the same amount?
What did we learn from our picture graph?
Why is graphing useful and important?”
Lesson 3 – Shoe Attributes Bar Graph
http://www.eduref.org/Virtual/Lessons/Mathematics/Process_Skills/MPS00
07.html
http://www.abcteach.com
Minnesota State Standards:
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines, to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from, and
comparing situations.
Objective:
Students will be able to classify shoes by various attributes such as color,
style, and materials.
Students will collect data and display on a class bar graph.
Students will be able to read and interpret the graph.
Materials:
• 1 Copy of the Story
o The Elves and the Shoemaker
• 2-3 Hula Hoops
• Chart Paper
• Markers
Activity:
• Read the story, The Elves and the Shoemaker.
• “Students we are going to sit in a half circle on the floor. I want you
to take off you shoes and place them in front of you on the floor.”
• “I want you to look at all the shoes in on the floor.”
• “How could we group these shoes?”
• Write the suggestions on the board.
• Chose one kind of grouping. (white/colored, shoes/boots, ties/Velcro)
• Place two Hula Hoops on the floor.
• Make a tag to label each hoop.
• “Please place your shoes in the appropriate hoop.”
• “We are going to count how many shoes are in each hoop. And then
we will record the number of shoes in each hoop on a bar graph.”
• Teacher and students will complete a bar graph for each attribute.
• “What kind of shoes does your class like to wear?
• Do you think other students in the school have the same types of
shoes?
• How could we find out?
• Do more people have tie shoes or Velcro shoes?
• Why is graphing useful and important?”
Shoe Attributes Graph
Lesson 4 – Graphing Rhythms
http://www.eduref.org/Virtual/Lessons/Interdisciplinary/INT0200.html
Minnesota State Standards:
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines, to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from, and
comparing situations.
Objective:
Students will be able to write the rhythm of his/her name.
Students will be able to graph the rhythm and analyze the class circle graph.
Materials:
•
•
•
•
Unlined Index Cards
Pencils or Crayons
Poster Paper
Glue
Activity:
• Before class teacher will group the students by the rhythms (syllables)
of their names.
• When class begins, split the class into these groups and tell them that
everyone in their group has something in common. They must
discover what it is.
• Give them a hint – “It is something about your name!”
• When a group discovers the answer line them up in rows by group.
• Each student receives an index card and a pencil or crayon. Each
students writes hi/her name on the card.
• Working in groups help students write the rhythms of their names on
the cards.
• Next, use the poster paper to create a graph, labeling each rhythm
across the bottom of the paper. Ask each student to glue his/her card
in the column above the corresponding rhythm.
• When all cards are in place, analyze the graph.
• “Which column has the most names?
• Which column has the least names?
• Was it hard to find out how many syllables you have in your name?
• What did you learn from the circle graph?
• Why is graphing useful and important?”
Circle Graph – Student Names
1 Rhythm
8 Rhythms
2 Rhythms
7 Rhythms
3 Rhythms
6 Rhythms
4 Rhythms
5 Rhythms
Lesson 5 – Lucky Charms Line Graph
http://www.lessonplanspage.com/printable/PMathStPatricksDayGraphingLu
ckyCharms35.htm
Minnesota State Standards:
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines, to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from, and
comparing situations.
Objective:
Students will be to count, sort, make predictions and interpret a line graph.
Materials:
•
•
•
•
•
•
Small Bags of Lucky Charms
Tally Sheet
Graph Sheet
Large graph Paper
Crayons
Pencils
Activity:
• Distribute individual bags of Lucky Charms cereal to each student.
• Distribute one tally sheet and one graph sheet to each student.
• Have students predict how many marshmallows and pieces of cereal
are in their bag.
• Have students individually count and sort the marshmallows in his/her
bag and then complete the tally sheet.
• Using the tally sheet the students will complete the bar graph on the
next sheet and answer these questions aloud.
• “Which Lucky Charm did you have the most?
• How many did you have?
• Which Lucky Charm did you have the least?
• How many did you have?
• How many total Lucky Charms did you have in your bag?”
• On a pre-made large graph, go around the room and ask each student
for their totals of each individual marshmallow and color in the graph.
• After the large graph is completed teacher will ask the following
questions.
• “Of which Lucky Charm did the whole class have the least?
• How many did you have?
• What was the total number of Lucky Charms for the entire class?
• Were your predictions close?
• Teachers may guide the students in answering the questions.
• Discuss the predictions. Find out who made accurate predictions.
• Once the activity is complete, the students may eat the cereal.
• Why is graphing useful and important?”
Lucky Charms Tally Sheet
1. Red Balloon =
__________
Total =
__________
2. Purple Horseshoe =
Total =
3. Green Clover Hat =
Total =
4. Pink Heart =
Total =
5. Blue Moon =
Total =
6. Pot of Gold =
__________
__________
__________
__________
__________
__________
__________
__________
__________
Total =
__________
7. Shooting Star =
__________
Total =
__________
8. Rainbow =
Total =
__________
__________
Lucky Charms Graph
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10
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7
6
5
4
3
2
1
Red
Balloon
Purple
Horseshoe
Green
Clover
Hat
Pink
Heart
Blue
Moon
Pot Of
Gold
Shooting
Star
Rainbow
Lesson 6 – Gingerbread Graphing
http://eduref.org/Virtual/Lessons/Mathematics/Progess_Skills
Minnesota State Standards:
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines, to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from, and
comparing situations.
Objective:
Students will be able to use tally marks to count items.
Students will be able to transfer tally marks to a bar graph.
Students will be able to successfully read and understand a bar graph.
Materials:
•
•
•
•
•
•
•
•
The Gingerbread Man by Madge Tovey
Blank tally chart (teacher- created)
Blank bar graph (teacher-created)
Markers
Chalkboard
Gingerbread man cookies
Plastic baggies
Napkins
Pencils
Activity:
• Ask students “What kind of cookies do you eat at Christmas time?
How many of you have ever eaten a gingerbread man cookie?
• Read the story, The Gingerbread Man to students to motivate them for
lesson.
• After discussing story, ask students “Who remembers how to make a
bar graph?”
• “Who can tell us what tally marks are used for?
• What is the definition of a tally mark?”
• Teacher will then write the definition of a tally mark on the board.
• Teacher will ask “Who can come to the board and show how the
numbers 1-5 are represented with tally marks?
• Inform students they will be using their skills with tally marks in
today’s lesson.
• Distribute a baggie containing a gingerbread man cookie and a napkin
to each student.
• Remind them they are not allowed to take a bite from the cookie yet.
• Once all cookies are handed out ask students to think about which
body part they would like to take a bite from.
• Instruct students to take one bite from their cookie.
• Once students have taken a bite from their cookie and placed them on
the napkins, place the gingerbread man cookie tally chart on the board
(containing each body part of the gingerbread man cookie - - head,
right arm, right leg, body, etc).
• Start at the top and ask students to raise their hand if they took a bite
out of a specific body part.
• Count the number of students with their hands up and place the
appropriate amount of tally marks after the corresponding body part.
Once each body part has been tallied up, flip over the pre-made blank
bar graph for students to see.
• Explain that there are six columns that represent the body parts of the
gingerbread man cookie and 20 rows that represent each person in the
class. Then name off each body part and amount and fill in the tally
mark results on the graph with the body part that matches up.
• When the bar graph is complete, ask students “Are any columns the
same height?”
• “Which column has the highest amount?
• Which column has the lowest amount?”
Gingerbread Man Graphing
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7
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5
4
3
2
1
Head
Right
Arm
Left Arm
Right
Leg
Left Leg
Body
Lesson 7 – Number Sentences, Estimation, and Graphing
http://www.eduref.org/Virtual/Lessons/Mathematics/Arithmetic/ATH0045.h
tml
Minnesota State Standards:
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines, to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from, and
comparing situations.
Objective:
Students will be able to demonstrate the various factors of ten.
Students will be able to design various number sentences.
Students will be able to select and estimate the number of beans in a jar.
Students will be able to demonstrate proper vocabulary after the completion
of the lesson.
Students will be able to produce a chart of the various examples they get
from the experiment.
Materials:
• Cup
• Plates
• Colored Beans
Activity:
• The beans will be placed in a jar and the students will be asked to
guess the number of beans in the jar. After the students have guessed,
the teacher will count what appears to be half of the beans in the jar.
After half of the beans have been counted the students will be given a
chance to change their estimation.
• The students will be asked to retrieve their plates, chart, beans, and
cup for this lesson. Then they will be given time to freely experiment
with the materials. Their attention will then be brought back to the
teacher.
• The teacher will model the activity and have the students follow the
model and complete the following process.
• Place a set of beans into a cup and shake them loose onto a plate.
• Count the total number of green beans and the total number of white
beans.
• Write an addition problem making the number of green beans the first
number in the number sentence and the number of white beans the
second number in the sentence.
• Chart their equation on the give chart.
• Count the total number of beans.
• Repeat steps 1-5 six times.
• Color the “X” blocks in different colors. The teacher will ask for
results and differences of their data by comparing graphs of the
children.
• “What patterns do you see on the chart?
• How did you feel about writing the addition sentences?
• What did you notice about the chart?
• Why is graphing useful and important?”
Beans
Guess # Beans Actual # Beans
White Beans
Green Beans
Write two addition sentences using the colored beans.
__________ + __________ = __________
Green Beans
White Beans
__________ + __________ = __________
White Beans
Green Beans
Lesson 8 – Skittles Graphing
Minnesota State Standards:
1.1.1.6. Use words to describe the relative size of numbers.
1.1.1.7. Use counting and comparison skills to create and analyze bar graphs
and tally charts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines, to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from, and
comparing situations.
Objectives:
Students will be able to:
•
•
•
•
•
•
Count, sort and classify skittles by color.
Record data on a chart.
Use data from a chart to create a pictograph.
Use data from a chart to create a bar graph.
Use data from a chart to create a circle graph.
Analyze and interpret data.
Materials:
•
•
•
•
•
Small Baggies filled with Skittles
Pencils
Paper
Rulers
Crayons or Markers
Activity:
• Teacher will give each student (or pair of students) one baggie filled
with Skittles.
• Ask students to open the bag, sort, and classify the Skittles according
to color.
• Ask students to record the information on a chart.
• After illustrating various pictographs, ask students to use their data to
create their own pictograph.
• Compare graphs. Have students discuss the differences and the
similarities of the graphs.
• Put class into small groups of 4-6. Ask the groups to combine their
data and make a new chart showing the results.
• After discussing bar graphs, ask the groups to create and color a bar
graph using the new figures. Have students compare the group graph
to their individual pictographs.
• Ask students to combine all the date to include on a class chart.
Round the numbers to the nearest tens for ease in creating a circle
graph and do as a class on the board or overhead projector.
Skittles Tally Sheet
Green
Red
Purple
Yellow
Pink
BLUE
Skittles Graphing Sheet
Green
Yellow
Red
Pink
Purple
Blue
1
12
2
3
4
5
6
7 8
9 10 11
Post-Test: Graphing Unit
Name: __________
Match the Tally Marks
1
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two
2
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one
3
|
four
4
|||| |
three
5
||||
six
6
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eight
7
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five
8
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seven
9
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ten
10
10
Post-Test: Graphing Unit
|||| ||||
nine
Post-Test: Graphing Unit
9
8
7
6
5
4
3
2
1
Red
Blue
1. What are graphs used for?
Green
Yellow
Orange
2. What does your bar graph show?