Statistics and Probability 6



Navigating through Statistics

UNIT OBJECTIVES:

1. Students will understand surveys and sampling.

2. Students will be able to analyze data using various forms of visual representation.

3. Students will understand central tendencies of data and be able to reason with these tendencies in abstract situations.

4. Students will be able to draw conclusions about a population from analyzing a set of data.

MONDAY:

Lesson 1: Samples and Surveys

How to appropriately select a sample and knowing the purpose of a sample is to make conclusions about the entire population

Team Project: *Submit proposal

TUESDAY:

Lesson 2: Mean, Median, Mode

Looking at data to determine central tendencies

Team Project: *Collect data and calculate Mean, Median, and Mode

WEDNESDAY:

Lesson 3: Stem and Leaf Plots, Frequency Tables, and Histograms

Compare numerical data grouped into intervals (by frequencies)

Demonstrate how data is distributed, a way to see central tendencies

Team Project: *Create 2 visual representations for data (large posters)

THURSDAY:

Lesson 4: Appropriate Use of Statistical Measures

Organizing data to make it easier to find central tendencies

Team Project: *Draw conclusions from data in writing

FRIDAY:

Lesson 5: Using Statistics to Draw Conclusions

Interpreting data, graphs, and knowledge of central tendencies in order to draw conclusions about a population.

Team Project: * Final Presentation- Portfolio or Poster creation

Routine Things: DO NOW activity allows students to focus their minds for what is to come. It often introduces topics we will be discussing during the lesson or reviews what they have learned from previous lessons.

Final Assessment: The final assessment of this unit will be the Team Project. Throughout the unit, students will be working in teams to develop a survey question, collect data, and analyze the data to draw conclusions about a population. At the end of the unit, they will create a professional presentation in which they present the data they have found via a portfolio or a poster. Each team will orally explain their process and findings to the class keeping in mind to present bias they found, the central tendency that best describes their data, and why they chose to collect the information they did. Students will be expected to have a professional visual and all students will participate in some part of the presentation. Each step of the assessment is worked on throughout the unit as you will find in each lesson. Presentations will be given the following week after the unit where students will analyze other groups’ results to determine if they had accurate arguments and conclusions.

This assessment is broken down by steps and allows students to cement their knowledge of what they learned by applying to their own activity and calculations. It requires students to think critically and abstractly as they participate in each part of this statistical process.

Grade 6 Length: 45 minutes

Statistical Questioning, Samples, and Surveys: This lesson introduces students to statistical questioning, how to determine a good sample for a population, and we will discuss the task that lies ahead for the entire unit. Students will choose a population and a topic question they would like to survey.

Standards:

CCSS:

Statistics and Probability 6.SP

Develop understanding of statistical variability.

1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

CASS: Statistics and Probability

2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:

2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.

2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

Standards for Mathematical Practice:

• Model with mathematics

• Reason Abstractly and quantitatively

• Look for and make use of structure

• Use appropriate tools strategically

Learning Outcomes/Objectives

1. Students will be able to describe the difference between a population and a sample.

2. Students in a group will together create a statistical question that can be tested through a sample.

3. Students will be able to identify a statistical question in a group of questions and provide evidence or reason for this identification.

4. Students will select a sample to answer their question and explain why they have chosen this method of sampling.

Vocabulary:

Sample, population, data, survey, random sampling, representative sample, biased sample

Assessment:

In order to assess learning on this activity, a proposal will be turned in from each group that includes the statistical question they would like to explore, the method in which they will sample the data, and their reasons for choosing both of the above. Each group will turn in one copy.

I will know if they have met the objectives through their reasoning as they describe how their question is statistical and why they chose the method of sampling that they did in order to make conclusions for their question.

** This lesson and activity will be the basis for the following lessons in this unit as the students go through the process of taking a sample, analyzing the data, and using the sample to make conclusions about the population. They will learn as they experience the process.**

Materials: Whiteboard, paper, pencils, students

Room Environment:

Students will sit in individual desks for the beginning of the lesson as they learn about statistical questions, samples, and surveys. This will be the discussion portion of the lesson.

*This lesson is mostly a lecture-type lesson in order to explain the process the students will be going through and the project they will be doing for the unit. It will be important for students to clearly understand the goals and directions for this group project.

For the activity, students will move their desks into the group set-up (they know this routine) as they work with their groups to come up with a question.

Modifications for diverse learners:

EL: The modifications in this lesson to benefit EL students are the visuals presented for the vocabulary terms. EL students may also use visuals and oral explanation to explain their writing journal entry for the DO NOW.

Special Needs: Special needs students will have a modified assignment to work with an aid in creating a visual if they cannot do group work. Otherwise, they will be placed in a group that can support them in their needs.

GATE: GATE or advanced students will be encouraged to give an example of a way in which a sample might be biased along with their visual.

Procedure:

Anticipatory Set:

1. DO NOW ACTIVITY: The question on the board that the students will come in and answer will be the routine activity that prepares students minds for learning. Today’s activity will be to have students write in their math journals everything they know about statistics. If they have no knowledge of what statistics are, they may write predictions and use educated guesses to consider what statistics might include. These directions will be written on the white board as students enter the classroom.

2. Today we are beginning our next unit and the best part is you all will get to choose what you want to learn about!

3. In this unit we are going to discover information about people. What are some things you’d like to know about people? What are you interested in?

4. Students will brainstorm ideas about what they’d like to learn about- People’s families, pets, favorite foods, etc. We will write these ideas up on the board for reference throughout the class period.

Teaching/Instructional Process:

5. After coming up with ideas on the board, I will point out two examples of questions in order to highlight what a statistical question is. I will ask students which one they could test on their own and how they would go about that test. We will do this several times.

6. We will have a 5 minute discussion on what a statistical question (or survey) is and what a population and a sample are. We will have these words written on the board.

7. Students will then be split up into groups of 3-5, each group asked to develop a visual representation of one of the new vocabulary words in 5 minutes (the word will be assigned by me). They will have large construction paper or poster board in order to display the vocabulary word (assigned to them by me), the definition, and a visual. Then each group will have 2 minutes to present their poster to the class.

8. This brief activity will introduce the topic to the class and require that the students become the teachers so that they can all better understand the difference between a survey, population, and sample. Students may use their textbooks to guide them if they need to know the definition of their words.

9. After each team presents one or two minutes, students will return to their seats facing the front for further explanation of the unit project.

Guided Practice and Monitoring:

10. With their new knowledge of a survey and a sample, students will be asked to split into groups of 2-4 students. The students will have the freedom to choose their groups BASED ON what their topic of interest might be. They will need to know that these people will be the people they will work with for the entire unit and project and to chose their groups wisely. In order to group quickly and not waste time I will tell students they have exactly one minute to quietly find a group and sit at a table with their group. They may absolutely not have more than 4 people to a group.

11. Students will come up with a statistical question that they will be able to draw conclusions from a sample about a population.

12. They will form a proposal that includes the following:

a. Statistical Question they will use to survey a

b. Sample that will represent a

c. Population

Following these three items will be an explanation of why they chose their topic and how they will go about taking the sample. This proposal will be their exit ticket out of the classroom.

Monitoring/Check for Understanding:

13. In order to monitor and check for understanding, I will have different methods of assessment throughout the lesson.

14. Firstly, I will take a diagnostic assessment of the students for the unit as I look at their journal entries from the DO NOW in order to assess where students are at in their knowledge and understanding of Statistics.

15. Next, I can formally assess if students have met the objective of understanding the difference between a sample and a population through the posters they have created of these vocabulary words.

16. After this vocabulary activity, I will Cold Call students to assess whether they understand the difference between a sample and a population. After this brief discussion, I will ask students to switch their stoplights to green, yellow, or red to see which students need further guidance.

17. Another method of checking understanding will be taking a look at their final proposals. I will have a summative assessment of the lesson objectives by analyzing the students’ proposals and reasoning. This will also be a formative assessment as I can take interventions strategies to reinforce the concept if need be the next day.

Closure:

18. After teams have had 15 minutes to construct their proposals, students will make their way back to their seats for a quick review game.

19. To review the material we have just gone over, students will participate in board races. The room will be split into for and one student from each section will come up to the board. (Students are familiar with this type of review game). I will ask students a question based on one of the following topics:

a. Is the following a statistical question? Yes or no?

b. Is the following a sample or a population?

c. Which group in this study is the sample? Or which is the population?

d. Write an example of a statistical question.

e. Write a study you could conduct for the following question- write the population and sample.

20. Students score points for their team when they write the answer first.

Independent Practice:

21. Students are challenged to go home and find a statistical study similar to the ones we have just proposed in class. They may find these studies online, in magazines, or newspapers. They will be asked to bring in their example to share with the class the next day.

Sources: Envision Text

Grade 6 Length: 45 minutes

The M’s of Central Tendencies

Standards:

CCSS:

Statistics and Probability 6.SP

2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

CASS:

1.1 Compute the range, mean, median, and mode of data sets.

2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

Standards for Mathematical Practice:

• Make sense of problems and persevere in solving them

• Reason abstractly and quantitatively

• Look for and express regularity in repeated reasoning

Learning Outcomes/Objectives:

1. Students will be able to define mean, median and mode.

2. Students will be able to calculate the mean, median and mode in multiple sets of data.

3. Students will create a song/rap with lyrics that demonstrate their knowledge of the mean, median and mode in a set of data.

To make process on their unit project:

4. Students will design a plan to carry out their survey and collect data.

5. Students will calculate the mean, median, and mode of this data by the next class period.

Vocabulary:

Mean, median, mode, range, central tendencies

Assessment: Student’s progress will be assessed through the completion of their music video with lyrics provided.

Materials: Computer and projector for YouTube videos, camera’s or iPads/iPhones to record videos, set of data for example on how to calculate mean, median, and mode.

Room Environment: Students will begin class at their individual seats, move into project groups for the DO NOW activity, and then return to their individual seats for the YouTube video and instruction portion of the lesson.

Students will be numbered off to form groups for the creation of their M’s song/rap.

Modifications for diverse learners:

EL- EL students have the video as a way of catering to their needs as well as working with a team to discuss their survey question. EL students will be encouraged to participate in discussion and may do so in writing if they are afraid to speak.

Special Needs- Group work will allow students with special need to have support in the classroom.

GATE- Gate students will be able to add motions to their lyrics and make a music video with extra time they may have. They may also be encouraged to rhyme or create their own tune.

Procedure:

Anticipatory Set:

1. DO NOW: Students will follow directions on the board that direct them to join with their groups and discuss how they will collect data for their survey question. (Their proposals will be returned on their desks when they walk in with a ** SEE ME if their question was not accepted.) Students will have 3 minutes to decide how and when to collect the data for their experiment.

2. Next we will watch the YouTube video on Mean, Median and Mode

3. Students will be asked to jot down ideas of what the mean, median, and mode are by what they hear in the YouTube video.

Teaching/Instructional Process:

4. As a class we will discuss what we heard and learned from the YouTube video.

5. We will then, from the notes students had, create our own definitions for these three new vocabulary words.

6. Using the attached set of data, I will demonstrate how to calculate the mean, median, and mode. This will be done on the whiteboard in front of the class.

7. We will do two more examples together as a class to work through finding the mean, median, and mode of a set of data.

Guided Practice and Monitoring:

8. Students will work through Practice Sheet 19-5 from EnVision.

9. Once they finish this individual practice, the students will be numbered off and will split up into groups of 5 to create a song or rap similar to the one we heard at the beginning of class. Each group will write lyrics to a tune they are already familiar with, or a rap, to demonstrate their knowledge of the mean, median and mode and how to calculate these from a set of given data.

10. Students all must have a part in the creation of these lyrics. Students must write their contributions to the lyrics on the back in order to ensure all members participated and understand the content.

Monitoring/Check for Understanding:

11. To check for understanding in this lesson I will be able to collect the independent practice worksheets as well as the lyrics to their M’s song/rap. Some groups that finish will be able to make moves to go along with their lyrics and turn their song into a music video.

12. I will also collect informal assessments through observation during the whole group instruction and practice before they go off to independent practice.

Closure:

13. Students that finish with the independent practice and the lyrics to their song/rap will be able to turn their song into a music video like the one we saw in class.

14. Students when finished may also meet with their groups to conduct their surveys for their group project.

Independent Practice:

15. Students will continue to practice calculating the mean, medians, and modes of data as they collect data to their group survey question and calculate the central tendencies of this data.

Sources: EnVision Material and YouTube

Grade 6 Length: 45 minutes

Shapies- Analyzing Data by its Shape:

Standards:

CCSS:

Statistics and Probability 6.SP

4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

CASS:

1.0 Students compute and analyze statistical measurements for data sets:

1.1 Compute the range, mean, median, and mode of data sets.

Standards for Mathematical Practice:

• Reason abstractly and quantitatively

• Model with mathematics

• Attend to precision

• Look for and make use of structure

• Look for and express regularity in repeated reasoning

Learning Outcomes/Objectives:

1. Students will create a stem and leaf plot, a frequency chart, and a histogram for their set of data for their topic.

2. Students will understand how the shape of data can be analyzed to make predictions about the sample and population.

3. Students will use the shape of their sample data to make predictions about the overall population.

Vocabulary: histogram, frequency table, stem and leaf plot, outlier

Assessment: To assess student progress toward these objectives as well as the unit objectives, I will collect students’ math journals that include answers to critical thinking questions. I will also be able to check their progress towards their final project goal. Students should have at this point their question, data, central tendency calculations, and 2 visual representations.

Materials: Poster board or butcher paper for student projects, markers, construction paper, glue, whiteboard, Math Journals

Room Environment: Students will be seated lecture style for the entire beginning portion of the lesson. Students will work at group tables when it comes time for the Guided Practice.

Modifications for diverse learners:

EL- EL students will be given a guided notes sheet to follow along with the instructional process.

Special Needs- Special needs students will also be given a guided notes sheet to help keep them focused and follow along with given visuals.

GATE- GATE students will be encouraged to create a biased graph along next to a fair graph at each station.

Procedure:

Anticipatory Set:

1. DO NOW activity: Students will read the directions on the board that direct them to look at the visual representations on the board and write in their math journals what similarities and differences they notice about them. They will take 3 minutes to do this.

2. On the board will be a visual of a histogram, stem and leaf plot, and frequency chart, all for the same set of data. We will enter into a time of discussion where students point out several of the things they noticed about these representations.

Teaching/Instructional Process:

3. Teacher will go over the properties of each visual representation explaining what each visual might be most effective for in representing data.

4. We will discuss the issue of misrepresentations with this data as we look at biased graphs that are misleading to data.

5. We will discuss what an outlier is and how we can spot it in these graphical representations.

6. Students will be taking notes on this information in their Math Journals.

Guided Practice and Monitoring:

7. Students will participate in making visual representations by rotating through stations around the room. Students will rotate based on their table groups.

8. There will be 6 stations around the room (2 stations for each visual representation/organization of data to account for the large number of students in the class).

9. Students will rotate through 3 stations (1 of each representation). They will bring their Math Journals with them as they will be creating each of the representations by following simple guiding directions at the station. They will then answer the critical thinking questions that follow.

Monitoring/Check for Understanding:

10. I will be walking around during the stations to see if students are having trouble with any of the visuals in particular. I will be able to check their Math Journals to note how well they constructed the visual and check their understanding by the answers they give to the critical thinking questions.

Closure:

11. I will close the lesson by giving students directions to meet with their project teams in order to create 2 visual representations of their data. During this time, I will be meeting with each team to ensure they have appropriate data for their project. If the students do not have data, they will at this time collect data from a class sample.

Independent Practice:

12. Students will choose 2 of the visual representations to create for their data.

13. They will creatively put together a poster displaying these two visual representations of their data for their final project. They will also write up an explanation as to why they chose these two visuals to represent their data.

14. Students who finish early may use the computer to find graphs or other visual representations in media which are biased and misleading.

Grade 6 Length: 45 minutes

Measuring Data Accurately

Standards:

CCSS:

Statistics and Probability 6.SP

5c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

CASS:

1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.

1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency.

1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context.

Standards for Mathematical Practice:

• Reason abstractly and quantitatively

• Model with mathematics

• Look for and express regularity in repeated reasoning

• Construct viable arguments and critique the reasoning of others.

Learning Outcomes/Objectives:

1. Students will choose the central tendency that best represents their set of data and be able to explain why orally or in writing.

2. Students will be able to list 5 reasons for biased data or inappropriate uses of statistics.

Vocabulary: (no new vocabulary) Review: bias, representation, outliers

Assessment:

Materials: rope, 3 hats to represent Mean, Median, and Mode

Room Environment: Desks will be pushed back to allow room at the front for the model data representation. Students will be in and out of seats to participate in the simulation.

There will be a long rope set up at the front of the room in front of the white board. With “fair-sticks” I will call up 4 students to be our Center Stage Stars for the simulation. They will wear tall hats decorated by me to signal that they are the center value.

Modifications for diverse learners:

EL and Special Needs- The visuals and simulation in this activity is catered toward both EL students and those with special needs. This activity allows students to visualize the information, review the information, act out the information, move around and express themselves through words orally and in writing.

GATE Students- GATE students will be asked to write down their thoughts and conclusions of this activity as they relate to other data. During class discussion I will be sure to call on these students only occasionally so they do not dominate conversation.

Procedure:

Anticipatory Set:

1. DO NOW activity: Students will calculate the mean, median, and mode of a data set on the board in order to review how to make these calculations. They will then predict why these measures of center are of different values and not the similarities and differences between the values.

2. Students will also come into the classroom to find the rope and hats at the front of the room which will engage them in the instructional activity later on in the class.

Teaching/Instructional Process:

3. First, the teacher will have set of data up on the board that the students have just calculated the mean, median, and mode for.

4. Teacher will call on students to ask them how they have found these calculations.

5. The students will then discuss how these calculations are similar or different.

6. Finally, they will discuss why these differences may be there.

7. The teacher will then call upon 3 volunteers using fair-sticks to be the Center Stage Stars.

8. Students will then also be chosen to represent the data on the board, each student receiving a point of the data. (1 student will volunteer to be the videographer/photographer at the back of the classroom so students may later see the visual representation as a whole.)

9. Students will stand on the number line taped on the ground in order to represent their place within the data. This will simulate the shape of the data with clusters and outliers. The Center Stars will then take their place on the number line based on the calculations we made. The students will take a picture of this position as we discuss which Center Star most accurately represents the shape of the data.

10. We will add a few more points to the data, and as a class we will re-calculate the mean, median, and mode with these new points of data to determine how the new data has affected the shape of the graph and the different points of center.

11. We may repeat this process several more times in order to test our theories of which central tendencies are influenced by outliers.

Guided Practice and Monitoring:

12. The pictures taken by the photographer will be immediately posted up on the projector as we have a class discussion about how the mean, median, and mode changed with the new points of data.

13. Some of the questions asked of the students in this time will be, “How much did the mean move when we added this point of data?” (as pictures are shown), and “Do we have any outliers in this data? What might their role be?” “How much is the median affected by the new data?” etc.

Monitoring/Check for Understanding:

14. During the discussion, students will be asked to pull out their stoplights and switch their light to their level of understanding. This will allow me to monitor understanding as well as give the appropriate independent practice to the students.

Closure:

15. To close the lesson I will have students come together in their groups and review the mean, median, and mode of the set of data they gathered for their team projects. They will discuss which central tendency best represents their set of data for the question they are analyzing. They will submit a paragraph written by the group that explains why they chose this value to represent their data.

16. Once students finish with their teams and submit their paragraph to me, they may continue onto independent practice. As a team they will come up to me to explain their reasoning and I will give them the appropriate differentiated instruction for whatever level they might be on.

Independent Practice:

17. Students will work with 1 of 3 modes of practice depending on how well they understand this material. The “Re-teach” “Practice” or “Enrichment” sheets by enVision for 19-8.

Sources: envision material (Independent practice sheets)

Grade 6 Length: 45 minutes

Wrapping it Up- Constructing Conclusions

Standards:

CCSS:

2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

5. Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations.

b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

CASS:

2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.

2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.

Standards for Mathematical Practice:

• Reason abstractly and quantitatively

• Construct viable arguments and critique the reasoning of others

• Look for and express regularity in repeated reasoning

• Attend to precision

Learning Outcomes/Objectives:

1. Students will demonstrate knowledge of analyzing data as they draw conclusions from their team project data orally in discussion.

2. Students will create a presentation of their conclusions through either a poster or a portfolio that presents their question, data, conclusions, and reasoning.

3. Students will also determine the fairness and accuracy of their analysis in writing as they define any bias in their data.

Vocabulary: conclusions, analyze

Assessment: Final team project (portfolio or poster presentation).

Materials: Materials to create a poster- Poster board, markers, glue, and materials to create a portfolio- Computer, binders, labels

Room Environment:

Room will be set up as normal with project making materials in the back. Students may rearrange desks during independent practice in order to make their projects if necessary.

Modifications for diverse learners:

EL- Students will be placed in groups from the beginning that support their abilities. These students will also be encouraged to have a speaking role during the presentation to increase speech confidence in the classroom. Other contributions may include the visuals of the presentation.

Special Needs- These students will receive guided notes with visuals for the lecture portion of the day (along with EL students).

GATE- GATE students may also choose to add creativity to their final presentation by including the class creatively or designing a follow up question to further pursue their findings.

Procedure:

Anticipatory Set:

1. DO NOW: Students will write in their math journals the question they have asked for the team project along with 3 alternate ways of asking this question. Then they will choose which way to ask the question seems most fair.

Teaching/Instructional Process:

2. Teacher will model why some questions are biased and therefore create misleading results.

3. I will give an example orally and ask students why they might think this type of question is unfair.

4. I will give 3 examples of unfair questions and 3 examples of fair questions as we discuss why these questions are fair or unfair.

Guided Practice and Monitoring:

5. Students will work with a partner to create a fair and an unfair question.

6. We will then share these questions with the class.

7. Students will listen to the two questions presented by the pairs and hold up a 1 if the first question was the biased question or a 2 if the second question was the biased question.

8. This will allow for me to see if students understand biased and unbiased questions.

Monitoring/Check for Understanding:

9. I will check for understanding throughout the guided practice by listening to the questions the students came up with themselves and observing whether they correctly or incorrectly guess the biased question.

Closure:

10. To close this question I will ask the students to define what bias is in their journal. We will then discuss if there are other ways in which they know data could be biased.

11. I will show them a picture of a biased graph and demonstrate the importance of giving an accurate visual representation (as a review for when we learned about making histograms).

Independent Practice:

12. Students will also get together in their group to analyze all of the work they have done so far for their team projects. They will draw conclusions based on this information and be prepared to present their findings tomorrow.

13. With the rest of the time, students will put together their final projects in a professional manner as they will be presented the following week. They may put together either a portfolio or a large poster. They must include their question, data, mean, median, mode, overall analysis, conclusions, and 2 visual representations.

14. They must dress nicely for their presentation to show that they are professionals in this field and make their presentation creative and exciting.

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