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Grade 2Mathematics Frameworks

Unit 1Venn Diagrams, Charts and Graphs

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Georgia Performance Standards FrameworkSecond Grade Mathematics Unit 1 1st Edition

Unit 1: VENN DIAGRAMS, CHARTS, AND GRAPHS (3 Weeks)

TABLE OF CONTENTS

Overview..............................................................................................................................3

Key Standards and Related Standards.................................................................................5

Enduring Understanding......................................................................................................7

Essential Questions..............................................................................................................7

Concepts and Skills to Maintain..........................................................................................8

Selected Terms and Symbols...............................................................................................8

Classroom Routines.............................................................................................................8

Suggested Routines..............................................................................................................9

Strategies for Teaching and Learning...............................................................................12

Evidence of Learning.........................................................................................................13

Performance Tasks

Performance Task Chart.............................................................................................14Our Favorite Colors....................................................................................................25Graphing People Revisited.........................................................................................25Hula Hoop..................................................................................................................25Pizza! Pizza!...............................................................................................................25Desktop Basketball.....................................................................................................25A Penny and a Quarter...............................................................................................42Field Trip to the Zoo.................................................................................................47

Culminating Task

The Same and Different.............................................................................................49

OVERVIEW

Georgia Department of EducationKathy Cox, State Superintendent of Schools

MATHEMATICS GRADE 2 UNIT 1: Venn Diagrams, Charts and GraphsAugust 2009 of 44

Copyright 2009 © All Rights Reserved


In this unit students will: establish daily mathematics routines to be carried out throughout the year such as

Today’s Number and Daily Graph pose questions that will require the collection of data such as what is your favorite sport organize and record data using tallies, simple tables and charts, pictographs, Venn

diagrams, and bar graphs group objects according to common properties.

Children in second grade are curious about the world around them. This unit is designed to give the student experiences in the processes of data analysis. They will pose questions, decide how to collect data to answer the questions and collect it, keep track of the data in a logical manner, organize the data using a representation that tells the story behind the questions, and possibly make some interpretations and predictions from the data or data similar to it.

Children in the second grade are expected to draw graphs that represent data. These graphs include bar graphs, pictographs, and Venn diagrams. Second graders have worked with graphs in the previous grades; however, this is an important skill to maintain and to build upon. In second grade students should be labeling all parts of the graph (title, horizontal bar, and vertical bar), as well as, representing data in ways other than one to one correspondence. For example, on a pictograph one symbol could represent 5 items instead of just one. A graph key would be required to indicate the value of each symbol. The children are also expected to interpret information from graphs. The activities and tasks in this unit will lead students to these understandings.

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics such as counting, time, money, positional words, patterns, and tallying should be addressed on an ongoing basis through the use of calendars, centers, and games. This first unit should establish these routines allowing students to gradually understand the concept of number and time.

To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the competencies listed under “Evidence of Learning” be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely replace, the textbook. Textbooks not only provide much needed content information but excellent learning activities as well. The tasks in this unit illustrate the types of learning activities that should be utilized from a variety of sources.





KEY STANDARDS AND RELATED STANDARDS

Mathematical standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.

KEY STANDARDS

M2D1. Students will create simple tables and graphs and interpret their meaning.a. Create, organize, and display data using pictographs, Venn diagrams, bar graphs,

picture graphs, simple charts, and tables to record results with scales of 1, 2 and 5.b. Know how to interpret picture graphs, Venn diagrams, and bar graphs.

RELATED STANDARDS

M2P1. Students will solve problems (using appropriate technology).a. Build new mathematical knowledge through problem solving.b. Solve problems that arise in mathematics and in other contexts.c. Apply and adapt a variety of appropriate strategies to solve problems.d. Monitor and reflect on the process of mathematical problem solving.

M2P2. Students will reason and evaluate mathematical arguments.a. Recognize reasoning and proof as fundamental aspects of mathematics.b. Make and investigate mathematical conjectures.c. Develop and evaluate mathematical arguments and proofs.d. Select and use various types of reasoning and methods of proof.

M2P3. Students will communicate mathematically.a. Organize and consolidate their mathematical thinking through communication.b. Communicate their mathematical thinking coherently and clearly to peers, teachers,

and others.c. Analyze and evaluate the mathematical thinking and strategies of others.d. Use the language of mathematics to express mathematical ideas precisely.

M2P4. Students will make connections among mathematical ideas and to other disciplines.a. Recognize and use connections among mathematical ideas.b. Understand how mathematical ideas interconnect and build on one another to produce

a coherent whole.c. Recognize and apply mathematics in contexts outside of mathematics.





M2P5. Students will represent mathematics in multiple ways.a. Create and use representations to organize, record, and communicate mathematical

ideas.b. Select, apply, and translate among mathematical representations to solve problems.c. Use representations to model and interpret physical, social, and mathematical

phenomena.

ENDURING UNDERSTANDINGS

Questions can be answered by the collection of data. Data may be organized to help in its interpretation and to understand its meaning. Data may be organized using pictographs, Venn diagrams, bar graphs, and charts or

tables to answer questions. Organization of information shows relationships.

ESSENTIAL QUESTIONS

Why do we need to collect data to answer questions? What can the questions tell us about our data? How can we use data to help us understand answers to questions posed? How can we use a picture graph, pictograph, Venn diagram, bar graph, chart, or table

to organize data and answer questions? How do we use picture graphs, pictographs, Venn diagrams, bar graphs, charts, and

tables, when we compare information? What are ways to gather and record information? How do graphs help us compare and analyze information? How can the elements of a graph help people understand and interpret the data? How does changing the scale affect how the data is communicated or displayed?





CONCEPTS/SKILLS TO MAINTAIN

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

Fluency with single digit addition/subtraction facts to 18 Fair trades with coins or bills Duration and sequence of events Number patterns including skip counting and odd/even Fact families Fractions: halves, fourths Tally marks Picture graphs Estimation: rounding to nearest ten Telling time Measurement – estimating, comparing, and ordering Basic geometric figures and spatial relationships





SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and how their students are able to explain and apply them.The definitions below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers.

Venn Diagram: A picture that illustrates the relationship between two or more sets.

Bar graph: A visual display (graph) of data, used to show data using horizontal or vertical bars.

Data: Information gathered; facts or figures from which conclusions may be drawn.

Pictograph: A visual display (graph) of data shown by using symbols. Also may be referred to as a picture graph.

CLASSROOM ROUTINES

The importance of establishing classroom routines cannot be overstated. Daily routines must include obvious activities such as taking attendance, doing a lunch count, lining up in a variety of ways (by height, age, type of shoe, hair color, eye color, etc.), daily questions, 99’s chart, referring to time and schedules during class, and calendar activities. They should also include classroom routines such as selecting and using materials in a productive manner, returning materials to their appropriate places, treating all materials with respect, remembering where to turn things in, where to record assignments, and remembering classroom expectations. An important routine for teachers is for them to allow plenty of time for children to explore new materials before attempting any directed activity with these new materials. The regular use of the routines is important to establishing successful classroom management that will add to the productiveness of a rich, hands-on, standards based classroom. This will also assist in the development of students’ flexibility and fluency which will support students’ performances on the tasks in this unit.





SUGGESTED ROUTINES

Today’s NumberPut the number for the number of days the students have been in school on the Number of Days in School chart. This chart should be a 99’s chart, so make sure to start with zero. You will actually need two charts so that on the 100th day of school you can start a new chart. This new chart will be the 100’s chart, referred to as a 100’s chart now instead of a 99’s chart because it will start with 100; which is the first three digit number. Obviously you won’t get all the way through this chart (you will stop on 180) but having these two charts together (in a vertical alignment with the 100s chart underneath the 99’s chart; see example below) will provide daily opportunities to engage in discussions about how one, two, and three digit numbers are alike/different. It will also help students “see” the patterns in our number system, (ex. 2, 12, 22, 82, 92, 102, 122, etc.) Additionally this type of daily discussion will help deepen students understanding of our number system. They need to recognize and articulate that we only have/need 10 digits (0-9) to create any number. This is a HUGE stepping stone in building a solid foundation of number sense.

Activities with Today’s Number1. Have the students make up equations that equal the number of days they have been

in school.2. List some of the equations on chart paper or the board and discuss.

Today’s Number is a routine that should be used on a daily basis and continued throughout the year. Routines provide students with regular practice in important mathematical ideas. At the beginning students will generate simple equations such as 1+0=1 or 11-10=1. As the year progresses and the numbers become larger, more complex sentences can and will be created (for example, 1000-897 on the 103rd day).

It is not necessary to do Today’s Number during math time. It can be included at any part of the day. Create a place in the room with a small chart where you record the number of days the students have been in school. Update the chart daily and use the number for the Today’s Number activity.

Variation




0 1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 1920 21 22 23 24 25 26 27 28 2930 31 32 33 34 35 36 37 38 3940 41 42 43 44 45 46 47 48 4950 51 52 53 54 55 56 57 58 5960 61 62 63 64 65 66 67 68 6970 71 72 73 74 75 76 77 78 7980 81 82 83 84 85 86 87 88 8990 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109110 111 112 113 114 115 116 117 118 119120 121 122 123 124 125 126 127 128 129130 131 132 133 134 135 136 137 138 139140 141 142 143 144 145 146 147 148 149150 151 152 153 154 155 156 157 158 159160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177 178 179180 181 182 183 184 185 186 187 188 189190 191 192 193 194 195 196 197 198 199


As students become comfortable with this routine, you can begin to specify how the students make the number. For example, you could have them use only one specified operation, a combination of operations, or any specific instructions that relate to the current unit.

Daily GraphGraphs can be incorporated into the daily routine for taking role, making lunch choices, or answering daily graph questions. Post a daily graph question that students can answer when they come into the classroom each morning as part of a daily routine. Different types of objects can be used to answer the graph question such as clothespins, names on magnetic strips, pictures, photos, etc. Graph questions can correlate with the time of year or a theme or topic the class is studying. Later in the year, have the students help decide the question for the graph. Different types of graphs can be used to display the results of the question, such as tally marks, bar graphs, pictographs, or Venn diagrams. The results can be discussed during calendar time or some other large group time. Ask probing questions about the graph such as:

Which category had the most, greatest, fewest, or least? How many more or less did one choice have versus another? Which was the class favorite? How does our data compare to another class’ data? Would the graph look the same if we completed it again tomorrow?

Below are suggestions for different surveys/graphs that second grade students might enjoy.

Graphing questions Which type of graph do you prefer? Tally marks, bar graph, pictograph, or Venn

diagram? What is your favorite sport? Do you like fantasy, fiction, or non-fiction books best? Would you rather travel in a car, plane, or train? Is your house or apartment number even or odd? Do you prefer a hamburger and fries or pizza? What would you rather do? Cook, draw, read, or write. Which month do you predict will be the coldest: November, December, or January? Which community worker has the most dangerous job: a police officer, a fireman, or a

construction worker? What is your favorite type of fruit: orange, apple, or pear? Which pet would you prefer to have: a dog, a cat, a bird or a gerbil? Which type of shoe would you rather wear: Flip-flops or tennis shoes? Do you predict that more than half of our class will bring their lunch from home today? How do you arrive at school? What is the number of the bus you ride home? How many pockets are you wearing today? Are there more than 100 or less than 100 peanuts in the bag?

Ideas for Venn diagrams I like milk. I like orange juice.





I like riding a bike. I like riding a skateboard. I play soccer. I play baseball. I have a dog. I have a cat. I make my bed at home. I set the table at home. I ride the bus to school. I ride in a car to school. My friends are boys. My friends are girls. There are more than four people living in my house. I have a pet. I like to read chapter books. I like to read picture books. I like to play video games. I like to play outside. I can count to ten in another language. My parents speak another language. I like to ride water slides. I like to ride roller coasters. I like to ride Ferris wheels.

CommentBe sure to include opportunities for both preferential and hard data collection. There should also be a transition from pictographs/picture graphs to Venn diagrams. For example, students should have multiple experiences with pictographs, as well as picture graphs before moving into Venn diagrams. This does NOT mean the other graphs would be phased out.

STRATEGIES FOR TEACHING AND LEARNING

Students should be actively engaged by developing their own understanding. Mathematics should be represented in as many ways as possible by using graphs, tables,

pictures, symbols, and words. Appropriate manipulatives and technology should be used to enhance student learning. Students should be given opportunities to revise their work based on teacher feedback,

peer feedback, and metacognition which includes self-assessment and reflection. Math journals are an excellent way for students to show what they are learning about a

concept. These may be spiral bound notebooks that students can draw or write in to describe the day’s math lesson. First graders love to go back and look at things they have done in the past, so journals could also serve as a tool for a nine week review.

Graphs should be integrated into other content areas (science, social studies, and reading) when possible.





EVIDENCE OF LEARNING

By the conclusion of this unit, students should be able to demonstrate the following competencies:

Pose questions that will result in data that can be shown on a bar graph, pictographs, or Venn diagram.

Use charts, simple tables, and surveys to collect data that can be shown on a bar graph, pictograph, or Venn diagram.

Graph data on a bar graph, pictograph, or Venn diagram and in a simple table. Interpret data shown on a bar graph, pictograph, or Venn diagram.





TASKS

Task Name Task Type/Grouping Strategy Content Addressed

Our Favorite Colors Learning Task/Large Group

Organize and display data in tables and graphsInterpret graphs and tables ( Bar Graphs)

Graphing People Revisited Learning Task/Large Group Organize and display data in tables and graphs

Interpret graphs and tables ( Bar Graphs)

Hula HoopLearning Task/Large Group Organize and display data in tables and graphs

Interpret graphs and tables ( Venn Diagrams)

Pizza! Pizza!Learning Task/Large Group Organize and display data in tables and graphs

Interpret graphs and tables ( Charts and Venn Diagrams)

Desktop BasketballPerformance Task/

Partners Organize and display data in tables and graphs Interpret graphs and tables ( Charts, Graphs and Venn Diagrams)

A Penny and A Quarter Performance Task/Individual

Organize and display data in tables and graphs Interpret graphs and tables ( Venn Diagrams)

Field Trip to the Zoo Learning Task/Small Group

Organize and display data in tables and graphs Interpret graphs and tables ( Pictographs)

Culminating Task: The Same and Different

Performance Task/Individual

Organize and display data in tables and graphsInterpret graphs and tables ( ALL)

The following tasks represent the level of depth, rigor, and complexity expected of all second grade students. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. It is important that all elements of a task be addressed throughout the learning process so that students understand what is expected of them. While some tasks are identified as a performance task, they also may be used for teaching and learning (learning task).




SHooper, 07/27/09,

Can you specify what type of graph is being addressed - otherwise, this column doesn't seen necessary


Learning Task: Our Favorite Colors STANDARDS ADDRESSED

M2D1. Students will create simple tables and graphs and interpret their meaning.a. Create, organize and display data using pictographs, Venn diagrams, bar graphs,

picture graphs, simple charts, and tables to record results with scales of 1, 2 and 5. b. Know how to interpret picture graphs, Venn diagrams, and bar graphs.


ideas. b. Select, apply, and translate among mathematical representations to solve problems.c. Use representations to model and interpret physical, social, and mathematical

phenomena.

ESSENTIAL QUESTIONS

Why do we need to ask questions and collect data? How can we use data to help us understand the answers to the questions posed? How can we use a pictograph, bar graph, chart, or table to organize data and answer

questions?

MATERIALS

2in x 2in sticky notes or small pieces of paper Blank bar graph, for students to create their own bar graph

GROUPING

Large Group

TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

Part IAsk children if they have a favorite color. Make a list on the board of the colors that children suggest. Have students draw a picture of something with their favorite color. Sort the pictures on the floor then tally the number of pictures in each color on the board, visible for all students to use.





Part IIChildren will create a bar graph that represents the class data for favorite color. Provide students with a blank bar graph to fill in with the information. Remind students to label all parts of their graph (title, horizontal bar, vertical bar, and color names).

Have students share their bar graphs depicting the data for students’ favorite colors. Ask students if the graph they created answers the question, “What is your favorite color?” Also, ask students to explain what their graph tells them about students’ favorite colors. Finally, ask students if the results would be the same in another classroom. Why or why not?

Comment:Please note that the number of categories should be limited to no more than 5. By the end of the academic year students should be proficient in independently creating and labeling their own graphs.

Questions for Teacher Reflection Are students able to explain why they need to ask questions and collect data? Can students explain how they use graphs to organize data and answer questions? Do they understand how to use data to help find answers to the questions posed? Are students able to transfer the data onto their graph? Do they understand that each vote counts as a square on their graph? Do students color more than one block as they record? Do they begin at the bottom and work their way up or just color the block that

corresponds with the number of votes for that color?

DIFFERENTIATION

Extension Students can come up with their own topic to survey and graph. Some ideas might include:

favorite school lunch, color of backpack, number of siblings, types of pets, etc. Students can use blank paper and a ruler to create a color graph. They can graph by attributes other than color of the pictures.

Intervention Allow students to use Unifix cubes if needed to represent each student vote. This will

give them opportunity to see a model of a bar graph before they try recording their answers on paper.





Learning Task : People Revisited STANDARDS ADDRESSED



M2P1. Students will solve problems (using appropriate technology).a. Build new mathematical knowledge through problem solving.b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems.d. Monitor and reflect on the process of mathematical problem solving.


and others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely.

ESSENTIAL QUESTIONS

Why do we need to ask questions and collect data? What can the questions tell us about our data? How can we use data to help us understand the answers to the questions posed? How can we use a pictograph, Venn diagram, bar graph, chart, or table to organize data and

answer questions? How do we use pictographs, bar graphs, charts, and tables, when we compare information?

MATERIALS

Class graph to record shirt color 3 two inch squares of paper per student Crayons

GROUPING

Large Group






Part IIn this activity, the students will gather data from their classmates about shirt color and as well as another class within the school. Have students share what they know about shirts. Allow them to look at the shirt of the person nearest to them. Have them discuss what color they think that person’s shirts is made. As a group, make a list of the different shirt colors. Have students think of some possible questions that could be answered once the shirt color information is collected.

Examples questions include: Which shirt color appears most frequently in our class? Which shirt color appears the least? Which shirt color appears most frequently on the boys in our class? Which shirt color appears most frequently on the girls in our class?

*Special Note: Be sure to record all questions offered because later you will deal with ones that they might not be able to answer based on the information in the graph

Once the shirt color categories have been determined and possible questions recorded, the class will create a graph to record their data. Students will color the two inch square of paper the color of their shirt. Each student will place their square on the class shirt color graph in the appropriate row.

Once the graph is complete, assist the students in determining which questions can and cannot be answered given the collected data. Ask students how they could change the way the data is organized or change the way the question is written in order to answer the questions.Allow more time for them to create other, more “advanced” type questions that can be answered from the information on the graph. You can do this as a whole class or break students into small groups or partners.

Example questions include: If you add the number of people with blue shirts and green shirts will this amount be more

than the number of people with brown shirts? How many total shirts do we have in our class? Based on this information what do you predict will be the most common shirt color in Mrs.

Smith’s 2nd grade class?

Second grade students will continue to need practice with the questions of “how many more” or “how many fewer” there are of an object. Different types of questions encourage the students to look at data as a means to organize information.

Tell students they will be collecting shirt color data from another class the next day. The data gathered from the two classes will be used to compare and answer selected questions.





Part IIStudents will be matched up with a student from another class. They will ask that student for their shirt color from the previous day, using the same data collection procedure from the previous day. Prior to creating the graph the class will decide which of the questions from the day before they want to use for their new graph.

After all of the data is organized, have students discuss the results of the graph from their buddy class. With both graphs completed the class will compare the data and use it to answer the question selected by the class prior to data collection. New questions can also be developed such as:

Which shirt color occurred most often in both classes? Which shirt color occurred the least often in both classes? Which class had more blue shirts? How many more? Which class had the fewest green shirts? How many fewer? What shirt colors appeared less often than blue? Was this true for both classes? Are there any questions about shirt color that can’t be answered using the data collected?

VariationGraph it again. Help students make a more abstract version of their graph by asking such questions as: What symbol could you use instead of your drawings or the color block squares?

Questions for Teacher Reflection Were students able to work independently to collect the required data? Are students able to explain how we use charts, tables, and graphs when we compare

information? Do students understand why they need to ask questions and collect data? Do students understand what the questions tell them about the data? Did students come up with a variety of questions about their graphs? Did student questions match their data? Can students use data to help them understand the answers to the questions posed? Are students able to summarize their findings?

DIFFERENTIATION

Extension Ask students to create a graph that will answer one of the alternate questions. Have students develop good questions to use in surveys of their classmates and other

students in the school. They can use the data to prepare charts and graphs to share with the class.

Ask students to write in their Math Journal about their experience.

Intervention





Students may work with a partner who has a better understanding of how to collect data and answer questions about the graph. They could also work with graphs that have already been created by other students. Make sure to have the student who made the graph/questions explain how they made the graph and how they decided on what questions to write to go along with the graph.





Learning Task: Hula Hoop Venn Diagram

STANDARDS ADDRESSED



M2P1. Students will solve problems (using appropriate technology).a. Build new mathematical knowledge through problem solving.b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems.d. Monitor and reflect on the process of mathematical problem solving.


and others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely.

ESSENTIAL QUESTIONS Why do I need to ask questions and collect data? How can I use data to help me understand the answers to the questions posed? How can I use a Venn diagram to organize data and answer questions? How do I use Venn diagrams when I compare information?

MATERIALS

Hula Hoops Yarn

GROUPING

Large Group

TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION *Please note this task follows extensive work in People Revisited task

Using a ring of various attributes, students listen for a rule that describes what each circle represents. Ideas for these attribute cards include: number of buttons on your shirt, earrings, curly hair, laces on shoes, Velcro on shoes, team shirt, jeans etc. Students will then choose





the circle where they fit the rule. Start in the large group setting. Then allow students to work in small groups to determine different rules. Create large circles to represent the Venn diagram using pieces of rope about 10 feet in length. For smaller groups, Hula Hoops may be used to make the circles. For individual Venn diagrams two different colors of yarn can be used. Circles can also be made from tubing used in aquariums. This tubing is inexpensive and can be taped together to make a circle.

This activity can be used across the curriculum. Example: The rule for the first circle could be, “Students Wearing Red.” The rule for the second circle could be, “Students Wearing Blue”. Ask students wearing only red to stand in the red circle and ask students wearing only blue to stand in the blue circle. Ask students wearing other colors to stand outside the circles. Now, change the circles so they overlap. Again, choose students wearing only red to stand in the red circle and students wearing only blue to stand in the blue circle. Ask the students where they should stand if they have on both colors. Students should be able to separate themselves into the two main groups easily. The overlapping group is the most difficult for students to identify. Ask students to explain why they are standing in the overlap of the two circles. Have students who understand the concept explain to classmates their strategy for determining the overlapping category.

Dramatize other comparison situations using the large Venn diagram. You may even want to have pieces of paper that you can write the circle rules on to label each circle. This way, students can see the rule and begin to see that the circles need to be labeled.

Questions for Teacher Reflection Are students able to explain why they need to ask questions and collect data? Can students tell how they use data to help understand and answer questions posed? Do students understand how to use a Venn diagram to organize data and answer

questions? Are students able to use a Venn diagrams to compare information? Can students explain what the overlapping section of the Venn diagram represents?

DIFFERENTIATIONExtension

Ask students to create a Venn diagram using the two overlapping circles on their paper. (It is much easier for them to draw large circles if they have something to trace, i.e. circle patterns, coffee cups, etc.) Have students pick two pattern blocks that are different from one another. Have them label each circle with one of the pattern blocks and then both for the area that overlaps. They may draw a small picture of the pattern block if they want to. Then, they should brainstorm about the attributes of each individual pattern block.

Example of possible questions: How are your shapes unique? What are some attributes that make them different from one another? Are there any attributes that are shared by both?





Encourage students to use math vocabulary such as sides, corners, 2-D shape, weight, and shape names. Question students to assess student understanding of the data posted on the Venn diagram. Use and, or, and is/is not statements to describe the information represented in the diagram.

Students may find it helpful to create a tally table to represent data to then transfer to the Venn diagram.

Intervention Students should have continued practice with Venn diagrams as well as

experiences that involve comparing and contrasting.





Learning Task: Pizza, Pizza!

STANDARDS ADDRESSED





and others. c. Analyze and evaluate the mathematical thinking and strategies of others.d. Use the language of mathematics to express mathematical ideas precisely.



phenomena.

ESSENTIAL QUESTIONS

Why do we need to ask questions and collect data? How can we use data to help us understand the answers to

the questions posed? How can we use a pictograph, bar graph, chart, or table to

organize data and answer questions? What is a survey?

MATERIALS

Surveys 1 & 2 Paper for constructing graphs Crayons Construction paper (optional) The Best Vacation Ever by Stuart Murphy





GROUPING

Large Group


Adapted from AIMS, Solve It!, “Pizza Possibilities” activity

In this task students will conduct two separate surveys. They will use these surveys to create graphs that show favorite pizza choices.

Part IRead The Best Vacation Ever by Stuart Murphy, a story about a family that cannot decide where to go on vacation until they take a survey. If this book is not available, discuss with students ways they could determine where their family would like to go on vacation. Another option would be to discuss where the class would like to go on a field trip. The purpose of this activity is to make the process of surveying, data collection, and graphing relevant to the students as they use this information to make informed decisions.

Ask students to survey five family members and/or classmates about their favorite pizza crust. Brainstorm with the students to determine which two crusts they think would be the most common. Responses to the survey will be recorded on the survey form with a check mark. Point out to the students that a survey form is different from a graph. Allow students to take the survey home to gather the information needed for the first graph.

When students’ pizza crust surveys are returned, discuss the results. Based on their survey, have students estimate which crust was the most popular. Have them justify their estimates making sure they are reasonable and based on their own survey results. Estimates can be double-checked with a quick show of hands.

Part IIFor survey two, the students will write a question that will generate the information needed to determine what their families like on their pizzas. Brainstorm a list of possibilities and have the students make the decision for their survey choices based on this discussion. Remind students that most surveys will use information that is common to all people. This could lead to a discussion about how survey items are chosen and their purpose.

Allow the students to decide what kind of form they will use for the survey. Discuss possible ways their answers could be recorded. Some students may choose to use the same format as Survey One; others may prefer tally marks or a method of their own design. If students use the Survey Two form they will need to label the topping columns or draw a picture.

Once the items for survey two have been decided, have students determine what kind of graph will be needed to record the information. Discuss how many columns and rows would be needed





as well as the type of graph the class will be using. Have students create a blank graph they will use for their survey data.

After students have created a survey and graph have them use this to ask their question to the same people they surveyed the first time. Allow students to take this survey home if necessary.

When the surveys come back the next day, discuss the results with the class. Have students use their results for a quick show of hands to determine the most popular pizza choice.

Students will then use the results from both surveys to create a paper model of the pizza that most of their families and/or classmates liked. This will be done on the second half of the two- part survey form.

Once the pizzas are created the students will share their pizzas in an open area where they can be sorted different ways. As a class, determine how the pizzas should be sorted in order to make a graph of their survey results. Discuss the findings.

Part IIISurvey the students about their favorite pizza toppings. Allow them to make a paper model from construction paper.

The students will sort their completed pizzas to determine what kind of graph needs to be made. Students will create their own graph, pictograph, or chart to compare the pizzas. Display pizzas, graphs, and student written commentary about the experience.

Possible questions to pose to students What can we learn from surveys? Why would we survey people? What did we learn about our class when we compared pizzas? How do you think the graph results would change if we asked more adults than children? What might be some good survey questions to ask for another graph or chart?

Questions for teacher reflection Can students create their own graphs? Are they able to take the information from two graphs and come up with a single answer? Can they create survey questions that can be used to collect data?

Variation Limit the pizza topping choices to two and create a Venn diagram of the results. Create a pizza station using the toppings from the surveys. Allow students to recreate

their favorite pizza.





DIFFERENTIATION

Extension Have students develop a list of survey questions on a topic of their choice. Allow them to

survey additional classrooms or grade levels to compare results. Create a three-circle Venn diagram labeled cheese, mushrooms, and pepperoni. Choose

one model pizza and record the information on the diagram. Continue with other pizzas.

Intervention Provide the student with the questions and the survey so that all they have to do is collect

the information and record the results.





Pizza! Pizza!Survey One

What kind of crust is your favorite?

Thick Crust Thin Crust

1

2

3

4

5

TOTAL





Pizza! Pizza!Survey Two

Survey Question

_________________________________________________?

Topping #1 Topping #2 Topping #3

1

2

3

4

5

TOTAL

Performance Task: Desktop Basketball

STANDARDS ADDRESSED

M2D1. Students will create simple tables and graphs and interpret their meaning.




http://school.discoveryeducation.com/clipart/clip/pizza2.html%00%E5%A1%B9%EF%92%81%E1%B4%BB%E4%A1%BF%E2%B2%AF%E5%B6%82%E8%97%84%E6%8C%A7%00%00%EA%AE%A5

http://school.discoveryeducation.com/clipart/clip/pizza2.html%00%E5%A1%B9%EF%92%81%E1%B4%BB%E4%A1%BF%E2%B2%AF%E5%B6%82%E8%97%84%E6%8C%A7%00%00%EA%AE%A5


a. Create, organize and display data using pictographs, Venn diagrams, bar graphs, picture graphs, simple charts, and tables to record results with scales of 1, 2 and 5.

b. Know how to interpret picture graphs, Venn diagrams, and bar graphs.M2P1. Students will solve problems (using appropriate technology).

a. Build new mathematical knowledge through problem solving.b. Solve problems that arise in mathematics and in other contexts.c. Apply and adapt a variety of appropriate strategies to solve problems.d. Monitor and reflect on the process of mathematical problem solving.





phenomena. ESSENTIAL QUESTIONS

Why do I need to ask questions and collect data? How can I use data to help me understand the answers to the questions posed? What type of graph should I use to display the data?

MATERIALS

Plastic cup Paper wad for a “basketball” Paper and pencil for recording information and drawing a graph

GROUPING

Partner or individual


Prior to the activity, each pair of students should have a plastic cup taped to one edge of a desk/table, a ¼ - sheet of paper to wad up for a “basketball”, and paper/pencil for recording and drawing a graph of the data.





Tape the cup to the edge of the desk. Students will take turns gently tossing the crumpled paper into the cup taped to the desk. Allow each student ten tosses before switching players. The student who is not tossing the basketball will be the scorekeeper and will use tally marks to record baskets made. After each child has had a chance to make ten tosses, the students will use their table of basketball toss tally marks to create a graph. Since they have had many experiences with graphs by second grade, students can choose the type of graph they want to make. Upon completion of their individual graphs, have students compare their results. If a student is working independently, then the activity could be repeated twice. The student would then have two different sets of tally marks to graph and compare.

Ask students to pose a question that the data from the graph would answer.Question examples: What type of game data is represented in this graph? How many baskets did you make? How many baskets did you miss? How many throws in all did you shoot?

VariationYou can have the students attribute a value to each crumbled up piece of paper. For instance perhaps they have ten pieces to throw. Make each one worth 10 cents. You could call the game “Shoot for a Dollar”.

Question examples: How much money did you make? How would the amount change if you earned a quarter for each shot? How about

50 cents for each shot? A dollar for each shot? How many baskets do you need to make to earn $5.00? What if you earned a dollar for each shot made, but lost 50 cents for each shot

missed, what would your total be? Let’s say you are at the carnival playing this game. It costs $1.00 to get eight

shots. For each shot you make you will get back 25 cents. Think about how you did in the game in class. Based on this, would you play the game at the carnival? Why or why not?





Questions for Teacher Reflection Were students confident about the information they reported? Were they able to explain their results, and how the data was shown on the graph? Are students able to explain why they need to ask questions and collect data? Do they understand how to use data to help find answers to the questions posed?

DIFFERENTIATION

ExtensionIncrease the number of tosses to twenty and have the student create their own graph of tosses made and tosses missed. Have students compare this to their first graph of ten tosses. Do they notice any significant differences? Ask students what they think would happen if they made thirty tosses? Forty tosses? How would their graph change?

InterventionGive students a pre-made bar graph or pictograph that would require them to color in the appropriate number of blocks or pictures for each successful basket.





Performance Task : A Penny and a Quarter STANDARDS ADDRESSED:








phenomena.

ESSENTIAL QUESTIONS

Why do we need to ask questions and collect data? How can we use data to help us understand the answers to the questions posed? How can we use a Venn diagram to organize data and answer questions? How do we use Venn diagrams when we compare information?

MATERIALS

Penny Quarter Yarn or circle templates to make Venn diagram Blank Venn diagram

GROUPING





Individual


Provide each student a penny and a quarter to compare. Brainstorm with the children what they know about these coins.

For example:Both buy thingsBoth are roundBoth have symbolsQuarter is biggerPenny is brown Quarter is silverPenny is worth less than quarter

Children will work alone to make a Venn diagram about the two coins. Ask students to share some of their ideas about the coins.

Students may have difficulty drawing a Venn diagram. You may wish to have patterns available for the children to trace or provide a worksheet with the pattern on it.

Questions for Teacher Reflection Can students explain why they need to ask questions and collect data? Are students able to explain how they use the data to answer questions? Are students able to use a Venn diagram to organize the information? Were students able to construct a Venn diagram correctly?

DIFFERENTIATION

Extension Ask students to compare concrete items that they are familiar with (such as dogs and

cats). Ask children when they might use a Venn diagram and what kind of data it shows. Ask students to write in their Math Journal about this experience.

Intervention Students should have continued practice with Venn diagrams as well as experiences that

involve comparing and contrasting. Allowing students to work with a partner may help with this particular task.





Examples of Georgia student work are shown below.





Learning Task: Field Trip to the Zoo STANDARDS ADDRESSED

M2D1. Students will create simple tables and graphs and interpret their meaning.

a. Create, organize and display data using pictographs, Venn diagrams, bar graphs, picture graphs, simple charts, and tables to record results with scales of 1, 2 and 5.

b. Know how to interpret picture graphs, Venn diagrams, and bar graphs.






phenomena.

ESSENTIAL QUESTIONS

Why do we need to ask questions and collect data? What can the questions tell us about our data? How can we use data to help us understand the

answers to the questions posed? How can we use a pictograph, bar graph, chart, or

table to organize data and answer questions?

MATERIALS

Book about zoo animals Index cards or 3 x 3 blank cards Pictograph cards





GROUPING

Small Group


Students will be creating a pictograph in this task.

Background InformationStudents have worked with graphs in the previous grades, however second grade is the first opportunity students have to work with scale increments of 1, 2 and 5. Using graph keys with values other than one to one correspondence can be difficult for second graders. Students will need to have had experience reading graphs with different picture to number correspondence before completing this task. This task is the first task in which students transition from picture graphs to pictographs.

Special Note:Prior to doing this task the teacher will need to have pictures or books with pictures of animals found at the zoo available for the students to look at and read. Show pictures of animals that might be found at a zoo in an animal book or with pictures printed from the internet or a magazine.

Part IRead the Field Trip number story problem below to the class (you will do this twice). As students listen to the story the first time, encourage them to make a mental picture in their minds of the story.

Field trip number story Mr. Mack’s class went on a field trip to the zoo. There they saw four elephants, two tigers, six monkeys, and eight snakes. They wanted to create a graph to show the different number of animals they saw. Imagine what their graph might look like and create a pictograph that represents this information.

Part IIDiscuss as a class how the information from the story problem could be recorded so that students will have it in a form from which they can create a graph. Hopefully, students will suggest making a chart and using tally marks. If not, help students create a chart to record the tally marks for each animal.

Read the story a second time, allowing the students to make tally marks to represent the zoo animals from the story.





Students should use pictograph cards to create a graph where each card stands for one animal. Allow students to recognize there are not enough cards to use one card for each animal. This will lead them to the understanding that if we use two as our scale interval for this task we will have enough cards.

On your key, each picture will represent two animals so there will not be as many pictures as there are animals. For example, since they saw four elephants you would only need to have two pictures because you count the pictures by twos to represent the number of elephants.

Have students count the zoo animal picture symbols by twos to reinforce the concept of each block on the graph representing two objects. They can use the pictograph symbols from the next page.

Student directions may be given as follows: Refer to the tally chart made earlier in task. Working on your own, draw a pictograph that shows all the animals they saw at the zoo. Give your graph a title. Remember each picture represents two animals. Label all parts of your graph. In your math journal, or on the back of your paper, write three questions for a friend to

answer about your graph.

Part IIIHave children exchange their graphs and questions written about their graphs with a partner. Graphs and questions may be shared with the class or put up in a classroom display. Each time the students discuss the results of a graph, be sure to include questions focusing on subtraction by comparison.

Sample questions:How many more elephants than tigers were there? How did you figure this out? How many fewer monkeys than snakes were there? What did you do to determine this?How is this graph like/different from others we have discussed?What question could we write that this graph would help us solve?What question could we write that this graph would NOT help us solve?

Questions for Teacher Reflection Do students mention graphing experiences they have had in the past? Are students able to think of graphs they have seen before, or relate the activity with the

zoo story to other graphs they have seen or created? Are students exhibiting an understanding of how this information is relevant? Do students understand why they need to ask questions and collect data? Are students able to use data to help them understand the answers to the questions posed?





DIFFERENTIATION

Extension Have children come up with other animals that were seen and include those animals on their graph.

InterventionThe teacher may allow those children to work in partners or small groups. They could also use manipulatives while making the graph.





Culminating Task: The Same and Different

This culminating task represents the level of depth, rigor, and complexity expected of all second grade students to demonstrate evidence of learning.

STANDARDS ADDRESSED








phenomena.

ESSENTIAL QUESTIONS

Why do we need to collect data to answer questions? What can the questions tell us about our data? How can we use data to help us understand answers to questions posed? How can we use a pictograph, Venn diagram, bar graph, chart, or table to organize data

and answer questions? How do we use pictographs, Venn diagrams, bar graphs, charts, and tables, when we

compare information?





MATERIALS

None

GROUPING

Individual


Students will create a question they could pose to classmates to collect data. The question should have at least two answers. Questions should be verified by teacher for appropriateness.Using a table or chart students will record their data using tally marks and then make a Venn diagram with correct labels. Students will explain their interpretation of their Venn diagram by writing at least three statements.

This task will require circulating around the room in order to monitor the questions students pose to ensure that a Venn diagram applies.

Students will work independently and should be given an opportunity to gather data, make the Venn diagram, and complete their writing in the classroom.

Questions for Teacher Reflection Can students explain why they need to ask questions and collect data? Are students able to explain how they use the data to answer questions? Did students come up with a variety of questions about their graphs? Did student questions match their data? Are students able to use a Venn diagram to organize the information? Were students able to construct a Venn diagram correctly? Can students use the Venn diagrams to compare information? Are students able to pose their own questions based on a Venn diagram? Were students able to work independently to collect the required data? Are students able to explain how we use charts, tables, and graphs when we compare

information? Are students able to summarize their findings?

Please NoteGraphs need to be incorporated into the daily routines, not just taught for a few weeks in the school year. Suggestions can be found at the beginning of this document in the Classroom Routines section. Examples of how to use graphs on a daily basis include: taking role, making lunch choices, or answering daily questions. Teachers should be posting a daily graph question that students can answer when they come into the classroom each morning as part of a daily routine . Different types of objects can be used to answer the graph question such as clothespins, names on magnetic strips, pictures, or photos. Graph questions can correlate with the time of





year or a theme or topic the class is studying. As students become more comfortable formulating their own questions then have them help decide the question for the graph. Different types of graphs should be used to display the results of the question such as tally marks, bar graphs, pictographs, or Venn diagrams.




unit 1 organizer: - wordpress.com › 2009 › 08 … · web viewfor individual venn diagrams two...

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