Data Analysis in the Classroom

Transcription

1 Data Analysis in the Classroom (Developmentally Appropriate Lessons for 3rd Grade Students) What would be better? A bar graph? A histogram? A box plot? There are just too many to decide! Amanda Anderson Title I Teacher Lincoln Elementary aanderson@bemidji.k12.mn.us 1

2 Executive Summary This 10 day unit plan is constructed in a format that best fits my Title I teaching schedule. I have, on average, a total of 14 classes a day. Each class fits in a 25 minute time slot. Within these classes are students who range in age from kindergarten to fifth grade, and developmentally from struggling to advanced. This unit plan teaches the concept of data analysis at a third grade level in 20 minute intervals. The Minnesota state standards that this unit will address, for each grade level, can be found after the Unit Plan Outline and Overview section located below. This unit plan starts with a pre-assessment at the beginning of each week during this two week unit in order to find out the students' prior knowledge of the following concepts: bar graphs, picture graphs, number lines, data, minimum, maximum, mode, and range. Each concept will be addressed over one or two days, and on Fridays the students will be tested through a post-assessment that includes the concepts they learned that week. This assessment will be conducted through activities, formal and informal assessments, and through the use of technology. Standard Based Unit Plan Outline and Overview Day 1 Pre-Assessment (First Part: Questions 1-3) Launch, Explore, Share, Summarize: Looking at Data (Using M&M Data from Last Week: Making a bar graph. Day 2 Continued: Launch, Explore, Share, Summarize: Looking at Data (M&M Bar Graph) Day 3 Launch, Explore, Share, Summarize: Creating Data Bioglyphs Day 4 Launch, Explore, Share, Summarize: Analyzing Data: Bioglyphs (Picture Graph) Day 5 Learning Stations and Post-Assessment: Analyzing Data, Organizing Data, Creating Data Day 6 Pre-Assessment (Second Part: Questions 4-8) Launch, Explore, Share, and Summarize: Creating, Organizing, and Analyzing Data Through a Survey Search (Shoe Sizes-Through a Number Line: Minimum, Maximum, and Range) Day 7 Launch, Explore, Share, and Summarize: Creating, Organizing, and Analyzing Data Through a Dice Roll (Number Line Plot: Putting numbers in orderminimum, Maximum, and Range.) Day 8 Continued Launch, Explore, Share, and Summarize: Creating, Organizing, and Analyzing Data Through Dice and Card Decks (Introducing: mode) Day 9 Launch, Explore, Share, and Summarize: Analyzing Data (finding the mode) My Computer Crashed Day 10 Learning Stations and Post Assessment: Data and Analysis 2

3 Standard Addressed in this Unit Third Grade: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. 3

4 Table of Contents 1. Third Grade Pre-Assessment Day 1: Introduction Day 2: Creating Bar Graphs: M&M's Day 3: Intro. to Bioglyphs Day 4: Bioglyphs Part Day 5: Post-Assessment and Learning Stations Day 6: Intro. to Number Lines..., Day 7: Lines and Dice (Min., Max., Range) Day 8: Dice, Decks, and Mode Day 9: Computer Crash (Mode) Day 10: Post-Assessment and Learning Stations Resource Citations... 4 Page

5 Name Date: What Do You Know? (Grade 3) 1. What is a bar graph? (Make an example.) 2. What does a clear graph need? (Give an example.) 3. Make a graph of your choice. Make sure to label the graph clearly. 4. What is a number line plot? (Give an example.) 5. What is a minimum value? (Give an example.) 5

6 6. What is a maximum value? (Give an example.) 7. Here are a list of numbers: 57, 18, 2, 7, 23, 24, 3, 9, 3, 16, 5 a) Put the numbers in order from smallest to biggest. b) What is the mode? 8. What is a range? (Give an example.) You're Done! Thank you for your hard work! 6

7 Day 1 Pre-Assessment and Introduction Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will complete a written pre-assessment which covers the concepts they will be learning over a period of 5 days. The students will participate in a data analysis activity that shows two different ways to show the same information. (Ice Cream Sundae Surveys) The students, as a class, will develop an understanding of data analysis by looking at and creating a class bar graph of all the different colors of M&M's that were found. (This data will be found from the students collected M&M fraction and percentage activity that they did last week.) Materials (located at the end of each continued lesson): What Do You Know? Pre-Assessment Activity Sheet (page 5) Visualizer to display Class MM' Bar Graph (page 10) M&M Percentage/Fraction Chart Activity Sheet (page 58) Ice Cream Sundae Survey Written Out Activity Sheet (page 11 - For Source See Reference List) Ice Cream Sundae Survey Bar Chart Activity Sheet (page 12 For Source See Reference List) Crayons or Markers of the Following Colors (red, green, blue, brown, yellow, orange) Pencils 7

8 Procedure: Launch (4 min.): The students will first come to class and complete a short 3 question pre-assessment that contains the concepts they will be learning over the next 5 days. As the pre-assessments are completed and turned in, the students will be divided into two groups. One group will be given the Ice Cream Sundae data in its written out form, the other group will be given the Ice Cream Sundae data in its bar graph form. The teacher will then begin by saying, We are going to have a competition. You have been divided into two teams. Each group has been given the same information, but I am going to ask you questions and the team that can give me the correct answer first gets the point. Ready? Let's begin. The teacher will then ask the two teams the following question: 1. How many students like chocolate and vanilla ice cream? 2. Who likes just plain strawberry? 3. Who likes vanilla and strawberry? 4. How many students like chocolate chip cookie dough and plain vanilla ice cream? 5. Who likes chocolate and strawberry? After the five questions have been answered. The teacher will tally up the points to see who won. She/He will then display the two forms of information on the board using the visualizer. What do you notice about these two pieces of paper? (Possible student responses: One's easier to read, one is made up in lines, one is written like a story, etc.) Excellent. But they both share the same information don't they? Which paper would you choose? (Possible student response: the chart) Why? (Possible student responses: It's easier to read, you can see everything, it doesn't take as long to read.) Wonderful! You're right! This is what we are going to be learning about over the next two weeks. We will be exploring ways to take data, or information that we find and organize it in ways and graphs that make it easier to read. Let's look at some more data. Procedure: Explore and Share (13 min.): The teacher will then display a paragraph on the board through the use of a visualizer and say Here is the information I gathered from our M&M experiment last week. In our Accelerated Math class last week, Miss Anderson took the time to add up everyone's numbers for each M&M color. In Miss Anderson's class there were a total of M&M's. There were quite a few M&M's in each type of color. As a class there were red M&M's, blue M&M's, green M&M's, yellow M&M's, and brown M&M's. Although this paragraph shows us a lot of information, is there a better way we could organize this MM information to make it easier to read? (Possible student responses: Make a 8

9 chart, make a graph, etc.) What a wonderful idea! Let's make a bar graph. The students and teacher will be using graph paper to make a bar graph. They will color each bar to better represent each M&M color. The teacher will also be there to show the proper way to label the bar graph to make it even clearer to the audience of what the bar graph is representing. It is important when we are making a bar graph, to make it clear for our reader. So let's add some labels, and a title to our bar graph to make our data very clear. What are some suggestions? (Possible student responses: The number of M&M's in each color for our class, the color of M&M's, M&M's counting, etc.) The students will turn in their bar graphs once they are completed. These graphs will be turned into a Data Analysis class book. This will not be made until after the end of the two weeks so that all of the different graphs can contribute to this class book. Summarize (3 min.): Towards the end of class, the teacher will get the group's attention and ask, So, what did we learn today about our MM color information? (Student responses: A graph lets you see the numbers better, there are different ways to show the same thing, etc.) Based on the students' responses, the teacher will be able to conclude whether or not the students truly comprehended today's activities. So, what you're telling me, is we learned how the same data can be shown in different ways to make it easier to read. We also learned how to make graphs even clearer with labels, titles, and numbers. Wonderful job, detectives! My M&M Bar Graph Activity Sheet (page 10) Ice Cream Sundae Survey Written Out Activity Sheet (page 11) Ice Cream Sundae Survey Bar Chart Activity Sheet (page 12) M&M Percentage/Fraction Chart Activity Sheet (page 58) 9

10 M&M Bar Graph More than # of M&M's Different M&M Colors 10

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13 Day 2 Creating Individual Bar Charts: M&M's Info. Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will participate in a data analysis activity that compares two different bar graphs. The students, as a class, will develop an understanding of data analysis by using their prior knowledge to create their own bar graph based off of their individual M&M packets from last week. The students will discuss their bar graph comparisons with the other members at their tables. Materials (located at the end of each continued lesson): Visualizer to display Class M&M' Bar Graph as a Guideline for Students (10) Individual M&M Percentage/Fraction Chart Activity Sheets from Last Week My Bar Graph Activity Sheet (page 15) Crayons or Markers of the Following Colors (red, green, blue, brown, yellow, orange Pencils 13

14 Procedure: Launch (4 min.): The students will first come to class and find their individual M&M fractions/percents charts from last week on their desks. As the students enter the classroom, they will find that their desks have been arranged into four groups (with approximately 4-5 students at each group). Remember yesterday when we looked at our who class's M&M information and we organized it into a bar graph? What do we need to put on our bar graphs to make sure it as clear as possible for our reader? (Possible student responses: A title, different labels, clear writing, etc.) Perfect! All wonderful answers! I can tell you have your detective hats on. Explore and Share (13 min.): Today you will be using those wonderful detective skills and looking at the activity sheet you mastered last week that has all the information you wanted to know about your M&M packet. Now, seeing your data, try exploring ways that you could take this information and make it easier for your reader to look at through some type of bar graph. Make sure to take your time because you will be showing your graph to another person at your table. That person will have to try and explain what you were wanting to show in your graph so it needs to be clear. Have fun exploring! The students will then be given the My Bar Graph activity sheet and they will begin exploring ways to make bar graphs using their own M&M packet information from last week. The teacher will then be walking around for guidance, modeling, and assistance while students are working on their graphs and sharing their graphs with a partner. You can either have the students chose who they want to present their bar graph to, or partners can be drawn through the use of Popsicle sticks that have the students' names written on them. Share and Summarize (3 min.): Towards the end of class, the teacher will get the group's attention and ask, So, what did we learn today about our own M&M bar graphs and our neighbor's M&M bar graph? (Student responses: My graph was different than my partner's, I decided to add a title to my graph to make it more clear, I drew M&M's instead of coloring in the boxes to show the different numbers of M&M's in each color, etc.) Based on the students' responses, the teacher will be able to conclude whether or not the students truly comprehended today's activities. Why is this a better way to learn about bar graphs, than just having me stand up here and talk about them? (Possible student responses: It's more fun this way, we learn more, we get to try making our own bar graphs, etc.) Well, from what we shared I can see that we are all not professional bar graph detectives. I'm proud to work with such a hard working group. 14

15 My Bar Graph 15

16 Day 3 Data Analysis: Bioglyphs Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will be introduced to the concept of bioglyphs. The students will participate in a data analysis activity that compares different characteristics between a variety of bioglyph drawings. The students, as a class, will develop an understanding of data analysis by using their bioglyphs as a way to represent themselves and comparing these characteristics with other students in their class. The students will analyze data through symbols by creating two different bioglyph characters. Materials (located at the end of each continued lesson): Bioglyph Guide Packet (pages, For Source See Reference List) Bioglyph Face Activity Sheet #1 (pages 18, 19, 20) Bioglyph Face Activity #2 (pages 19, 20, 22) Bioglyph Guess Recording Sheet (page 21) Visualizer to Display Bioglyph Directions as Needed Crayons, or Markers Pencils Tape 16

17 Procedure: Launch (4 min.): The students will first come to class and find a question displayed on the board through the use of a visualizer. The question reads, What is a bioglyph? (Possible student responses: A picture? A graph? I don't know, etc.) Great responses. A glyph is a way to collect, show, and think about data in other ways, such as pictures, rather than using numbers. Today you are going to draw two different types of bioglyphs that represent you. This means that what you choose best describes who you are as a person. Take your time. Don't share your bioglyphs with anyone because we will all be detectives and try to guess who is who. You will get a sheet to write down your guesses. Now, let's explore! Procedure: Explore (11 min.): The teacher will then pass out the two different bioglyph face activity sheets as well as the recording sheet they will use to make their guesses. While the students are working, the teacher will be walking around for guidance and answer any questions the students may have. As the students complete their bioglyphs, the teacher will collect them and start to display the glyphs on the board using tape. Remember, put your name on the back or your bioglyph in pencil so that we can't see your name on the paper. If a student finishes both of his or her bioglyphs early, they can start to guess who represents the already displayed bioglyphs. Once the students have made their guesses, the teacher will instructs the students to stand by one of their bioglyphs. Then, one by one the students will start to see how accurate their guesses were. Share and Summarize (3 min.): Towards the end of class, the teacher will get the group's attention and ask, So, what did we learn today about bioglyphs, or about our classmates? (Student responses: Bioglyphs are still a way to show data, I know someone else who has blue eyes, etc.) Exactly. This is still looking at sets of data, and it is still a way to analyze information, but this is a type of picture graph. It shows information in picture form rather than number form. So, even though we did not add, subtract, multiply, or divide we still learned about how to read a chart, what that chart means, and what it shows the reader. Very good detectives! Bioglyph Bioglyph Bioglyph Bioglyph Guide Packet (pages, 18-22) Face Activity Sheet #1 (pages 18, 19, 20) Face Activity #2 (pages 19, 20, 22) Guess Recording Sheet (page 21) 17

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23 Day 4 Data Analysis: Bioglyphs Part 2 Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will use their prior knowledge of bioglyphs, to analyze different bioglyphs by looking for similar characteristics. The students will be creating picture graphs in their groups to represent the different bioglyphs at their tables. The students will use their prior knowledge of graphs, to create a clear picture graph that represents the bioglyph information they receive. The students will also help the teacher create a bar graph representing the students' correct answers when they guessed on the different bioglyphs in yesterday's activity. Materials (located at the end of each continued lesson): Bioglyph Guess Recording Sheets (page 21): Should be completed. Visualizer to Display Bar Graphs as Needed Crayons, or Markers Pencils Picture Bioglyph Graph Paper (page 26) Bioglyph Correct Answer Class Chart (page 28) Bioglyph Activity #1: Should be completed. Bioglyph Activity #2: Should be completed. Picture Graph Example to Display on the Visualizer (page 27) Tape 23

24 Procedure: Launch (4 min.): The students will first come to class and find a question displayed on the board through the use of a visualizer. The question reads, How could we make a bar graph out of our bioglyph guesses from yesterday? The teacher will begin by saying, Good morning, detectives! I have a question up on the board, after you read it think of some ways we could make a bar graph. Once you have a few ideas please raise your hand and share your findings. (Possible student responses: One part of the graph could be the number of guesses we made, we could label the number of guesses that we each got right, etc.) Wonderful, let's follow those ideas! The teacher should provide guidance if students are still a little unsure of how answer the question. The teacher will then construct a bar graph where the number of students total are on one axis, and the number of correct guesses are on another axis. Make sure to include labels and a title to reinforce the idea of making a clear, precise graph that makes it easy for the viewer to read. This could be reinforced with teacher talk. Example: Now what should we add to our bar graph to make it even clearer? (Possible student responses: labels, a title, etc.) Procedure: Explore (11 min.): Wonderful! Now that we have our class bar graph, you are going to work with the other members at your table and make a picture graph comparing all of your bioglyphs together. You will make one picture graph for each bioglyph type. Since there are two bioglyph activities each group will come up with two different picture graphs. Now, what is a picture graph? A picture graph is a way to include symbols or pictures in an organized way to show information. Each group can make their picture graph in a way that works best for their group. I will place an example of a picture graph up on the visualizer to help guide you, but know that your graph should look different than mine because your group has different information. The teacher will be walking around for guidance and assistance as the students work in their teams while making two different picture graphs. Share(3 min.): Towards the end of class, the teacher will get the group's attention and ask each group (a total of 4 groups) to share their different picture graphs with the class. They should present on how they set up their picture graphs, what they found that was the same in their group, and what they found that was different about their bioglyphs in the group. The teacher will provide guiding questions as the groups present. Example questions are as followed: How did you organize your picture charts? What did you do to make it easier for your audience to read? What's another way you could have organized your picture chart? What symbols did you use? What did your group have in common, or what was the same in your group? 24

25 6. What was different in your group? 7. If they added colors: Why did you chose those colors? Why did you chose to add color to your picture graph? Summarize (2 min.): So, what did we learn today about our picture graphs? (Student responses: You can organize graphs in different ways, you don't always have to use numbers, it's another way to look at things, etc.) Precisely. We are still looking at data and information, we are just organizing this information in a different way. Not only did we create a bar graph together, but you worked with your team and created two different picture graphs. Fabulous graph making, detectives! You sure know how to organize your information in a way that makes it easier for your audience to read. 1. Picture Chart Graph Paper (page 26) 2. Bar Graph Paper to Display Students' Bioglyph Guesses (pages 27) 3. Picture Graph Example (page 28) 25

26 My Group's Bioglyph Picture Chart 26

27 's Class Total of Correct Bioglyph Guesses The Number of Students Who Guessed Correctly The Number of Correct Guesses 27 18

28 My Picture Graph Example Means Eye Color: Means Hair Color: Out of 9 students: Blue Eyes: 4 (2 had blond hair, 2 had brown hair) Green Eyes: 2 (1 had red hair, 1 had brown hair) Brown Eyes: 3 (2 had brown hair, 1 had black hair) Brown Hair: 5 Blond Hair: 2 Black Hair: 1 28 Out of 9 students:

29 Day 5 Post-Assessment and Learning Stations with Data Analysis Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will be using their prior knowledge of data, data analysis, bar graphs and picture graphs to re-explore the games and activities learned this week through the use of learning stations and manipulatives. The students will be using their prior knowledge of data, bar graphs, picture graphs, and data analysis to complete a post-assessment focused on the mathematical concepts learned this week. Materials: Post-Assessment: Same as pre-assessment found on page 5 (Questions 1-3). Post-Assessment Chart (page 35) Bioglyph Activity Sheet: Scarecrow Glyph (page 31 For Source see Reference List) Construction Paper to Draw the Bioglyphs on Directions for Today's Learning Stations (page 32) Markers or Crayons Fruit Snack Bar Graph Activity Sheet (page 33) Fruit Snack Picture Graph Activity Sheet (page 34) Fruit Snacks (One for each student.) Computers (for Everyday Math Games) 29

30 Procedure: 1. The students will be working at two learning stations. (One station will be focusing on the students creating their own bar graph and picture graph based on their own package of fruit snacks, the other station allows the students to create another bioglyph through the theme of making a scarecrow. Any time left over, can be spent on playing Everyday Math games on the computer. The students will be rotating among these two stations approximately every 7-8 minutes. This way every group has a chance to explore every station. With there being students at a time, these two projects will be spread out over four tables so that approximately 4-5 students can sit at each table. 2. While the students are working at the different learning stations, the teacher will be walking around with a checklist to informally and formally assess the students on their comprehension of graphs, bar graphs, picture graphs, and data. This form of assessment takes about 5 minutes to complete for each student. 30

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32 Directions For Today's Learning Stations Station 1 and 2: 1. Open your pack of fruit snacks. 2. Count how many there are of each type of fruit snacks. 3. Create a bar graph showing your fruit snack information. 4. (You can make your bar graph however you would like.) 5. Create a picture graph showing your fruit snack information. 6. (You can make your picture graph however you would like.) 7. Now you can enjoy eating your fruit snacks. Station 3 and 4: 1. Read the clues on the bioglyph scarecrow activity sheet. 2. Make your own scarcrow based on the clues the sheet gives you. 3. You can create it on any of the colored pieces of paper available. 4. Have fun creating! 32

33 My Fruit Snack Bar Graph 33

34 My Fruit Snack Picture Graph 34

35 Name of Student Date: Classroom Teacher Data Analysis: Bar Graphs Picture Graphs Bioglyphs Grade Level: 3 Mastery Level Yes, fully mastered! Understands the Needs Additional majority of this Help and Guidance concept. Provide Example: 1. Is the student able to use the clues in the bioglyph activity to properly create a scarecrow? 2. Is the student able to create a bar graph based on the information he/she receives from his/her package of fruit snacks? 3. Is the student able to help others figure out the day's activities? 4. Is the student able to create a picture graph based on the information he/she receives from his/her package of fruit snacks? 5. Are the two graphs clear to the reader? (Are there labels or numbers?) 6. How does the student organize the bar graph? 7. How does the student organize the picture graph? 8. Does the child use different strategies to plot their data on any of the activity tables and charts? 9. Would the student be able to explain the concept of bar graphs, picture graphs, and data to another person? 35 Additional Comments

36 Day 6 Introduction to Number Lines: Minimum, Maximum, and Range Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will be introduced to the idea of a number line by doing a number line together as a group using shoe sizes. The students will be introduced to the concepts of minimum, maximum, and range through a shoe size number line activity. The students will be using subtraction skills when finding the range on the number line. Materials: White Board or Visualizer Data Analysis: Pre-Assessment (page 5: questions 4-8) Shoe Survey Number Line Activity Sheet (page 38) Shoe Survey Recording Sheet for the Visualizer (page 39) Pencils 36

37 Procedure: Launch (4 min.): The students will first come to class and be asked to take off their right shoe and place their shoe in order with the other students in their class from the smallest shoe size to the largest shoe size. These shoes will be lined up in an area where everyone can see the different shoe sizes. Once the shoes are lined up the teacher will say What are we learning by organizing our shoes this way? (Possible student responses: To see that the shoes are different sizes, to see the smallest and biggest shoe, to make a graph, etc.) Excellent, we have shown another way to organize data in clearly for our audience. We have placed our shoes in a line to see our smallest value (or shoe) and our largest value (our shoe). This is what we will be exploring today. Not only will we be organizing data in a new way called a number line, but we are going to be looking for specific information as well. Go ahead and grab your shoe and then grab a seat. Explore and Share(13 min.) The teacher will then ask the students to raise their hands and say their shoe size. As the students are saying their different shoe sizes, the teacher will write the different sizes on the Shoe Survey Recording Sheet that is displayed through the use of the visualizer. Great! Now that we have this information what would be an easier way to show this data to our audience? What did we do with our shoes? (Possible student responses: We put them in order from smallest to biggest, we organized our shoes to make them neat, we lined them up, etc.) That's right. When we have a bunch of numbers, it's easier to find what we're looking for when we put the numbers in order from smallest to biggest, or least to greatest. Let's try that. The teacher will then place the shoe size numbers in order from least to greatest. So what is our smallest value in this list? (Depending on the class, answers will vary.) Wonderful! The smallest value is also called the minimum value. What's the largest value in this list? (Student responses may vary.) Excellent, the biggest value is also called the maximum value. I am now going to point to either the minimum or smallest value and the maximum, or largest value and I want you to call out to tell me which one I am pointing at. Summarize (2 min.): After about seven or eight repetitions, it will be time for the teacher to wrap up today's lesson. So, what did we learn about or try today? Based on the students' responses, the teacher will be able to conclude whether or not the students truly comprehended today's activities. So, not only did we learn more about number lines, but we were able to put numbers in order from smallest to biggest, and we were able to find the maximum (biggest) and minimum (smallest) values. Bravo, detectives! 1. Pre-Assessment (page 5: questions 4-8) 2. Shoe Survey Number Line Activity Sheet (page 39) 3. Shoe Survey Recording Sheet for the Visualizer (page 38) 37

38 Recording Sheet Class List of Different Shoe Sizes List #1 List #2 (Organized) 38

39 39 Class Shoe Sizes

40 Day 7 Number Lines and Dice: Minimum, Maximum, and Range Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will be introduced to the idea of a number line by doing a number line together as a group using dice rolls. The students will be introduced to the concepts of minimum, maximum, and range through a dice rolling number line activity. The students will be using subtraction skills when finding the range of the number line. The students will be using addition skills when finding the sum of their different dice rolls. Materials: White Board or Visualizer Dice Rolling Number Line Activity Sheet (page 43) Dice Rolling Recording Sheet for the Visualizer (page 42) Pencils Dice (3 dice for each student) Procedure: Launch (4 min.): The students will first come to class and be asked to roll three dice. They will be asked to do five different rolls using the three dice and write down their answers each time they roll. They need to add the numbers of their three dice together to get the sum or total of each roll. 40

41 Explore and Share(13 min.) The teacher will then ask the students to raise their hands and share their five different totals. As the students are saying their different sums, the teacher will write the different answers on the Dice Rolling Survey Recording Sheet that is displayed through the use of the visualizer. Great! Now that we have this information what would be an easier way to show this data to our audience? Remember what we did yesterday and how we organized our shoes? (Possible student responses: We put them in order from smallest to biggest, we need to organize our numbers, etc.) That's right. When we have a bunch of numbers, it's easier to find what we're looking for when we put the numbers in order from smallest to biggest, or least to greatest. Let's try that. The teacher will then place the dice totals in order from least to greatest. So what is our smallest value in this list? (Depending on the class, answers will vary.) Wonderful! What is another name we can use that means the same thing as the smallest value? (Minimum) What's the largest value in this list? (Student responses may vary.) Excellent, and who remembers another word that means the same thing as the biggest value? (Maximum) Fabulous! Today, you are not only going to find the maximum and minimum value on your own but you are also going to find your range. A range is where you take the biggest number and subtract the smallest number from it. Another way to say this is: maximum value minus your minimum value. Let's find the range with the data we have with our class's dice rolls. The teacher will then demonstrate how to find the range and will leave this information displayed on the board for the students to use as a guide when they move on to the next activity. Now you are going to do 20 rolls with your dice, record your total each time, and then organize your numbers so that they are in order from smallest to biggest. Then, I want you to circle your minimum value and your maximum value and find the range. You will turn this into me when you are done. Happy exploring, detectives! The teacher will walk around the classroom for guidance, assistance, and will check for comprehension. Summarize (2 min.): So, what did we learn about or try today? Based on the students' responses, the teacher will be able to conclude whether or not the students truly comprehended today's activities. So, not only did we learn more about number lines, but we were able to put numbers in order from smallest to biggest. You were also able to find your own minimum values, maximum values, and your range with your dice rolling data. Your are all becoming such strong data detectives! 1. Dice Rolling Number Line Activity Sheet (page 43) 2. Dice Rolling Recording Sheet for the Visualizer (page 42) 41

42 Recording Sheet Class List of Different Dice Rolls List #1 List #2 (Organized) 42

43 43 Class Dice Roll Data

44 Day 8 Dice and Decks: Introducing Mode Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will be introduced to the idea of mode by looking at their individual dice rolling data from yesterday. The students will be introduced to the concept of mode by keeping track of a deck of cards. The students will be looking at data to identify the mode out of a list of numbers. Materials: White Board or Visualizer Class Dice Rolling Data from Yesterday The Student's Individual Dice Rolling Data from Yesterday (page 43) Deck of Cards Recording Sheet for Students (page 47) Pencils Decks of Cards (1 deck for each student) 44

45 Procedure: Launch (3 min.): The students will first come to class and they will see the class's dice rolling data from yesterday displayed on the board using the visualizer. Once everyone is seated, the teacher will ask the students, Who knows what is the mode in this dice data? (It will be quite possible that none of the students will know the answer to this question.) The teacher will then quietly circle the mode based numbers with a colorful marker. After the teacher does this he/she will ask the question again. There should be a few raised hands at this point to answer the question. Correct! Now, who can tell me why this number is the mode? There may be some theories, but if no one responds, the teacher will go through and ask the students to count the circled numbers. Are there more of this number than any other number? (Yes!) Very good. That is what the mode is. The mode is the most frequent number listed. Or, the number that is listed the most. If there were the same exact amount of each number then we could say that there are many modes. Some books might say that there are no modes. Explore (12 min.) The teacher will then say, Your job detectives, is to now try to find the mode in your dice rolling data that you did yesterday. If you find that there is more than one mode, circle them both. The students will then go through their dice rolling data and search for the mode in their data. The teacher will be walking around to provide guidance and to check for comprehension. The example used at the visualizer, will remain displayed so that the students can look back at it for guidance. After the majority of students have found the mode, the teacher will then pass out a deck of cards for each student. Now you are going to shuffle the cards in your deck. You are then going to draw 25 different times. Each time you will be putting the card that you drew back in the deck randomly and shuffle. Each card will be worth a specific number of points. Once you are done writing down your answers, find your mode and circle it. Since you are all great data detectives, explore your data and find your minimum value, maximum value, and range as well. You can rearrange your numbers after you are done drawing your cards. Happy exploring! Share (2 min.): After the students have finished recording their card drawing data the teacher will ask each student to share their maximum values, minimum values, ranges, and modes. The teacher will be recording the students' information on the white board as they present their findings. The teacher will then guide the students to see if there were any common values among the information they've shared in order to deepen their comprehension on these concepts. 45

46 Summarize (2 min.): So, what did we learn about or try today? Based on the students' responses, the teacher will be able to conclude whether or not the students truly comprehended today's activities. So, not only did we learn more about maximum and minimum values, but we also were able to use our math skills to find the range of your numbers and we learned about mode. Wow! We learned a lot today! 1. Card Drawing Recording Sheet (page 47) 46

47 Recording Sheet Card Drawing Point System Card Drawing List Organized Card Drawing List = 2 points = 3 points = 4 points = 5 points = 6 points = 7 points = 8 points = 9 points = 10 points Jacks = 11 points Queens = 12 points Kings = 13 points Aces = 14 points Minimum Value: Maximum Value: Range: Mode: 47

48 Day 9 Finding the Mode: Computer Crash Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will be use their prior knowledge of mode, to locate mode in a variety of number lists. The students will be introduced to the idea of more than one mode through an activity called Computer Crash. Materials: White Board or Visualizer Computer Crash Activity Sheet (page 50) Pencils, or Markers Ice Cream Cups (1 cup for each student) Spoons (1 cup for each student) Rootbeer Computer supporting Everyday Math Games 48

49 Procedure: Launch (5 min.): The students will first come to class and find a seat. The teacher will then begin by saying, So, my fabulous detectives, I need to ask you a favor today. I was typing in different scores into my computer. All of a sudden my computer crashed when I was trying to find the mode of my different grade score lists. My computer kept saying there was no mode on some of my grade lists. Let me show you an example. One grade list had the following numbers: 7, 14, 2, 6, 11, 10, 20. Can you tell me where the mode is in this list? The students will be slightly confused because they learned yesterday that a mode is the most frequently used number in a series of data, and here there is one of each. They might agree with the computer and say there is no mode. I can understand why you might think that because you are trying to look for the number that is listed the most and a lot of teachers and computers will think that there is no mode. But, actually there is a mode. In fact, there are many modes in this list. Each number, because it is listed the same amount of times equally...is a mode. So here, I would say that they are all modes. Explore (10 min.) Now, what is the mode in this list? The next numbers to be listed are the following: 23, 15, 17, 3, 8, 15, 7. (Mode: 15) Very good, you saw that the number 15 was listed more than any other number so 15 is the mode. Would you please help me find the modes for the rest of my grade lists. I need your help while I fight with my computer. The students will then work on finding the mode in a variety of grade lists. While the students are working, the teacher will pretend to be frustrated with the computer. The teacher will also walk around the room to provide guidance, assistance, and to check for comprehension. When most of the students seem to understand today's activity, the teacher will then secretly serve up root beer floats. If the students finish this activity early, they can play Everyday Math games on the computer. Share and Summarize (5 min.): When the teacher sees the students are done with the activity she/he will gather the class's attention. The teacher and students will then go over each list and discuss the different modes. After the review is complete, the teacher will ask the students What should I say if I see that every number in my data list shows up the same amount of times? (Possible student responses: that there are no modes, that they are all modes, etc.) Exactly! Some may say there are no modes, but now you know that there is a different way at looking at these types of problems. To show my appreciation of your help on finding the modes in my grade lists, I have made you root beer treats al a mode, meaning root beer floats and ice cream. Enjoy! The students can enjoy their floats and socialize for the last few minutes of class. 1. Computer Crash Activity Sheet (page 50) 49

50 Name: Computer Crash Grades Mode 7, 11, 6, 15, 9, 45, 2, 6 1, 15, 16, 1, 8, 5, 6, 9, 3 2, 2, 3, 3, 5, 5, 5, 5, 6, 7 77, 78, 80, 83, 85, 78, 86 65, 54, 58, 53, 52, 33, 27 55, 58, 62, 58, 65, 62, 62 88, 89, 90, 91, 89, 90, 89 76, 75, 72, 70, 89, 77, 78 24, 22, 26, 28, 84, 84, 36 36, 35, 33, 36, 65, 36, 32 77, 78, 76, 77, 77, 77, 77 82, 83, 82, 83, 85, 82, 83 65, 27, 68, 53, 65, 61, 60 68, 67, 58, 87, 57, 32, 33 25, 24, 26, 21, 17, 26, 20 24, 62, 13, 13, 24, 62, 24 28, 29, 52, 53, 27, 26, 51 50

51 Day 10 Post-Assessment and Learning Stations with: Data Anlalysis Standard: Data Analysis: Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays Collect, display, and interpret data using frequency tables, bar graphs, picture graphs, and number line plots having a variety of scales. Use appropriate titles, labels, and units. Objectives: The students will be using their prior knowledge of data, data analysis, mode, minimum, maximum, number lines, and range to re-explore the games and activities learned this week through the use of learning stations and manipulatives. The students will be using their prior knowledge of maximum, minimum, range, mode, and number lines to complete a post-assessment focused on the mathematical concepts learned this week. Materials: Post-Assessment: Same as pre-assessment found on page 5 (Questions 4-8). Post-Assessment Chart (page 57) Card Deck Mode Activity: They can work in pairs and draw a card every other time. 1. Card Decks (One per student) 2. Card Deck Recording Sheet (page 56) Dice Roll Mode Activity (page 53) 1. Dice (1 for each student) 2. Dice Recording Sheet (to find mode) Minimum and Maximum Height Activity (page 54) 1. Height Activity Sheet 2. Meter Sticks or Tape Measures Directions for Today's Learning Stations (page 55) Makers or Crayons 51

52 Procedure: 1. The students will be working at three learning stations. (One station will be focusing on finding the mode in a deck of cards with a partner, another station will focus on finding the mode through this week's dice rolling activity, the third station allows the students to measure the height of the other members at their learning stations and find the minimum value, maximum value, and range of numbers. The students will be rotating among these three stations approximately every 6 minutes. This way every group has a chance to explore every station. With there being students at a time, these two projects will be spread out over four tables so that approximately 5 to 6 students can sit at each table. 2. While the students are working at the different learning stations, the teacher will be walking around with a checklist to informally and formally assess the students on their comprehension of number lines, maximum values, minimum values, mode, and range. This form of assessment takes about 5 minutes to complete for each student. 52

53 Recording Sheet Different Dice Rolls List #1 (Find the Mode) List #2 (Find the Mode) 53

54 Recording Sheet Group's Different Heights Measure each person in centimeters. Person's Name Person's Height Question: Answer: 1. Who is the tallest person at your table? 2. What is their height? 3. Who is the shortest person at your table? 4. What is their height? 5. What is your group's range? 54

55 Directions For Today's Learning Stations Station 1: 1. Find the mode by randomly picking a card out of a deck. 2. Make sure to shuffle the deck each time after you put that one card back in the deck. 3. You may play this with a partner if you want. Station 2: 1. Finding the heights of the other people at your table. 2. Everyone at your table needs to have their height measured. 3. You can use meter sticks or measuring tapes, whatever is easier for you. 4. After everyone writes down their height, you are going to find the minimum value, the maximum value, and the range from your group's information. Station 3: 1. Roll one dice over and over and write down the number that shows after the dice lands. 2. You will fill up one list 1 and then find the mode. 3. You will do the same thing again and complete list two. 4. You can play this with a partner if you would like. 55

56 Card Drawing Point System List 2 = 2 points 2 3 = 3 points 3 4 = 4 points 4 5 = 5 points 5 6 = 6 points 6 7 = 7 points 7 8 = 8 points 8 9 = 9 points 9 10 = 10 points 10 Jacks = 11 points 11 Queens = 12 points 12 Kings = 13 points 13 Aces = 14 points Minimum Value: 17 Maximum Value: 18 Range: Mode:

57 Name of Student Date: Classroom Teacher Data Analysis: Number Lines, Mode, Maximum Value, Minimum Value Grade Level: 3 Mastery Level Yes, fully mastered! Understands the Needs Additional majority of this Help and Guidance concept. Provide Example: 1. Is the student able to find a mode quite often while trying the different learning stations? 2. Is the student able to find a maximum value? 3. Is the student able to help others figure out the day's activities? 4. Is the student able to create a number line on the postassessment? 5. Is the student able to find a minimum value? 6. Is the student able to find a range? 7. Is the student able to organize numbers to find the information asked? 8. Would the student be able to explain the concept of bar graphs, picture graphs, maximum, minimum, mode, and range to another person? 57 Additional Comments

58 M&M Fractions and Percents First, write down your guess of how many M&M's there are of each color. Next, write down how many M&M's you think there are in all. Then, explore your M&M's to see how close you were. After that, come up with your M&M fractions and percents. M&M Colors Red Yellow Brown Orange Green Blue Your In the Your In the Your In the Your In the Your In the Your In the Guess Bag Guess Bag Guess Bag Guess Bag Guess Bag Guess Bag Your Fraction Your Fraction Your Fraction Your Fraction Your Fraction Your Fraction Fraction in Bag Fraction in Bag Fraction in Bag Fraction in Bag Fraction in Bag Fraction in Bag Your Percent Your Percent Your Percent Your Percent Your Percent Your Percent Percent in Bag Percent in Bag Percent in Bag Percent in Bag Percent in Bag Percent in Bag 58