Graphing Real-Time Temperature Data in An

Graphing Real-Time Temperature Data in an Investigative Middle or High School Statistics Lesson

Peggy Bertrand and Nita Ganguly Master Teachers, VolsTeach, University of Tennessee, Knoxville UTeach Annual Conference 2015

Lesson Title: What’s the Weather NOW? Subject: Math Author(s): Peggy Bertrand Topic: Illustrating Data Spread with Box-and-Whisker Plots Reviewer(s): Nita Ganguly Grade: Lesson Source: Lesson #: Mentor’s Name: Date lesson will be taught: Mentor’s School: Length of lesson: Subject / Grade: Concepts / Main Idea: In paragraph form, write the concepts and vocabulary of this activity. Explain how your lesson connects to major science or math concepts, builds upon student prior learning or real-world experience, integrates with other subjects, and/or promotes critical thinking by your students. In this lesson, the students will make predictions regarding what they think temperature averages and extremes are for various regions within the USA, and then test those predictions by collecting temperature data. The students will use a box plot generator to develop a visual model of their temperature data. It is anticipated that this lesson is the first time the students are exposed to a box-and-whisker plot. As part of the lesson, the students will infer, on a conceptual and semi-quantitative level, what the parts of the box-and-whisker plot represent. The focus of the lesson is to allow the students to interpret a common visual model used in statistics, and not to generate the model themselves. Appropriate use of models and tools are important mathematical practices. The ability to interpret a visual model or graph and use it as a tool, even if one does not yet know how to generate the model using calculations, is an important skill. Standards: Available online at http://www.state.tn.us/education/curriculum.shtml. Common Core Math Standards CCSS.MATH.CONTENT.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. CCSS.MATH.CONTENT.7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. CCSS.MATH.PRACTICE.MP4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Learning Targets: Translate the science or math standards above into student-friendly, grade-appropriate language. “I can…” statements are useful for younger students. I will be able to collect actual weather data from the USA and graph it. I will be able to compare weather from different regions in the USA and interpret the differences in weather. Measurable Objective(s): Write measurable objectives in SWBAT form, Evaluation: Write at least one question for each measurable based on the state standards: objective. (These may be formative or summative) TSWBAT  Interpret a box plot to find the average temperature. Students  infer from the appearance of a box-and-whisker plot that is will not be required to identify average as median or mean until a automatically generated from numeric input how this plot subsequent lesson. communicates information about the average (median) and the  Interpret box plots to find highest and lowest temperature range of the data extremes, and to calculate temperature range.  to justify claims about temperatures for various USA regions  Use box plots as evidence to support or refute claims. with evidence from box-and-whisker plots  Apply box plots to temperature variations, and connect this to geographical and meteorological phenomena. Materials List: Include material from the VolsTeach library, material Differentiation and Accommodations: What instructional strategy you bring from home. Also include any ancillary documents you must will you use for students who finish early or work more slowly? Are have to teach, such as a PowerPoint presentation, a video you will show, there any students who have special learning needs? If so, indicate how a handout, etc. you will accommodate those needs. Materials List Students will be working in heterogeneous groups of three, so students Verizon Tables, iPads, Laptops, or other devices with internet access will be sharing ideas and expectations throughout the lesson. Role (two devices per group of three) assignment will be rotated, to give each student an opportunity to act in Map of the USA regions (one copy per group of three) different capacities. Multiple opportunities for peer instruction within Explore! handout groups, as well as whole-class discussion, will facilitate the development How is the weather today in the good old USA? of conceptual understanding. (one copy per group) Explain! Handout (one copy per student) Pre- and Post-assessment sheets (one copy per student) Advance Preparation: What must you prepare in advance? Include Safety: List precautions to avoid possible injury during this lesson. If activities such as making copies or filling baggies at UTK, or writing there are no safety concerns, please indicate that below. learning targets on the board at your school. Prior to class, the teacher will configure the tablets so a browser and Students should handle the technology with care. Normal classroom URLs for Weather Underground (www.wunderground.com) and the safety procedures should be followed. Shodor Box Plot Generator (www.shodor.org/interactive/activities/BoxPlot/) are visible on a tablet screen. This is best done via tablet control software, if available. Note that as an alternative, students can type URLs from the explore sheet) into the browser to find the appropriate sites. Grouping Students: How will your students be grouped during the Giving Student Instructions: How will you give instructions during the lesson? What roles will you assign within the group? How will you lesson so that visual, auditory, and kinesthetic learners are all able to ensure that all students are involved in the activity? understand? Where in the lesson will you model something for the students using “I do, We do, You do” or a related modeling strategy? Students are in groups of three. Clear roles are assigned, as described in I Do: Model finding the temperature of one city using Weather the handout (Research Director, Meteorologist, Statistician). Students Underground and recording it in Shodor Box Plot Generator, as periodically change roles to insure maximum participation. described on the handout. The temperature and a regional designation must both be added. Note that when you first use the box plot program, you must clear default data. We Do: Model finding and recording several temperatures for one region while the student teams follow along. After a few temperatures are added, instruct students to click the Update Box Plot button. Teacher also points out the Graph All The Data and Graph By Category buttons. You Do: Instruct the teams, working under the direction of their research director, to complete collecting their data for the first region. Circulate during the activity, monitor that students are collecting and recording data correctly, and ask questions about the graphs. When a group is finished with the first region, instruct them to change roles, select a new region, and interpret it as well. Engagement: Estimated time: 5 minutes Motivate students with a “hook” to engage their attention and focus on the learning. Personally meaningful and relevant. Should be fairly short. Learning targets should be introduced. Teacher actions and directions Probing teacher questions that create a need to know Instruct students they are not to touch the tablets until instructed. What is a conjecture we can form about how the temperature varies according to the US regions? Give each student an Explore! handout. Each group also gets one color The further north, the colder! (if possible) map of the USA showing cities, states, and regions. Ask Hawaii will be the warmest. students to find their city and state on the map, and to identify the US Which region do you think will have the broadest range of region in which they live. Be prepared to give students a little help temperatures, from warmest to coldest, right now? interpreting the regional map. The Midwest, because it’s pretty far from north to south. The West looks further from north to south, and it has mountains. As you ask questions about regional temperature variations, write student Students may not understand what constitutes a temperature range, and conjectures on the board – warmest region, coldest region, region with they may not have a rationale for deciding which US region might have the widest temperature difference, region with the smallest temperature a broad temperature range. difference, etc. How can we test our conjectures? We can go to Weather.com or the Weather channel. We can collect data in a table and we can graph the data. Transition… What will you say or do to make a clear and smooth transition from the Engagement to the Exploration section? Today we’re going to gather temperature data from the regions of our country. Then we’ll compare the regional temperature differences using a method of graphing that will help us test our predictions. Exploration: Estimated Time: 25 minutes Student-centered activity intended to induce curiosity and suspense. Should provide choices and student-to-student interaction. Rigorous and relevant learning segment that clearly supports the lesson objectives. This part of the lesson is the heart of the 5E Inquiry-based lesson format. Teacher actions and directions Probing teacher questions that guide students to a common set of experiences Throughout Exploration, students have access to the Explore! hand-out and map. Students are in groups of three, with two tablets per group. See Grouping Students and Giving Student Instructions, above, for further elaboration. What do you think the parts of the graph represent? I think this line is an average. Say: Do not touch the tablets yet. I will model what I want you to do. This part is the highest, and lowest temperature. Follow along on your handout. If students don’t know what the parts of the graph represent, that’s OK; Proceed with I Do. this activity will help them get a conceptual feel for Box Plots an Say: You may now turn over the tablets and turn them on. Research their meaning. directors, please ask your meteorologist to go to Weather Underground and your statistician to go to the Box Plot program. Signal me when your Why do you think I’ve asked you to distribute the cities across the team is ready. region, rather than picking cities that are really close to each other? Proceed with We Do. If we pick them close together, they might be too similar and not Say: This is a special type of graph, called a Box-and-Whisker plot. As represent the whole region. you work on your graphs, try to figure out what they are telling you. We might be looking at averages, and to get a good average, we need to Proceed with You Do. look at the entire region. Transition… What will you say or do to make a clear and smooth transition from the Exploration to the Explanation section? It’s time for us to see what our graphs are telling us about differences in temperature across the regions of our country. Explanation: Estimated Time: 10 minutes Student-centered activity in which students explain the results from their exploration above. Teacher encourages generation of ideas and alternatives, analysis, evaluation, and explanation from multiple perspectives and viewpoints. Teacher actions and directions Probing teacher questions that help students clarify their understanding and introduce information related to lesson concepts and vocabulary Throughout explanation, students should have access to the tablets, I see that you think Hawaii has the smallest temperature range. “Explain!” hand-out, and the map. Students are still in their groups. What is the evidence that makes you say so? It has the smallest box. Say: Now I want you to consider the questions on the handout. I want It’s the smallest distance from the end of the right whisker to the end of you to work in your groups for 10 minutes to see how you would answer the left whisker, and the ends of the whiskers are the highest and each question and explain your answer to the class. These questions will lowest temperatures. help you when we discuss our class’s findings. Make sure each member If I asked you to calculate the temperature range as a number, how of your group can speak for your whole group, because I may call on would you do this? Show me your calculation. anyone in your group to speak for your group. GO! I take these two numbers on the ends of the whiskers and subtract. I can read them on the graph. Circulates to answer procedural and vocabulary questions, but refrain Does it surprise you some of Alaska’s temperatures are warmer than from directly answering questions about the box plots. Monitor group some of the temperatures in the Midwest? Why do you think this is discussion formatively. the case? Some of Alaska is pretty far south. Some of the Midwest is pretty far north! Also, Alaska has some cities on the ocean, and that helps temperatures stay moderate. Transition… What will you say or do to make a clear and smooth transition from the Explanation section to the Elaboration section? Now let’s share our thinking. Some of the questions I ask might require you to think beyond mathematics, to what you know about geography and weather patterns. We’ll see how much we can figure out together. Elaboration: Estimated Time: 15 minutes Another learning segment that is connected to the Explore/Explain above and encourages further application and extension of the essential concepts of the lesson. Teacher actions and directions Probing teacher questions that help students extend or apply their newly acquired concepts / skills in new situations Throughout Elaboration, students should have access to the tablets, Which region has the widest temperature variation? Use evidence “Explain!” handout upon which they have recorded notes, and the map. from the box plots to support your claim. Students are still in their groups. Teacher calls on volunteers and non- The box plot for Alaska is wider from the end to end, so this means the volunteers to answer questions and begin discussion, using the box plots temperature extremes are farthest apart. as a model for average temperature and temperature ranges. A document Some students may not use the full range of the box and whisker plot, camera is helpful for students to be able to show evidence, using their using only the shaded area. box plots. What do the ends of the “whiskers” represent? The lowest temperature is the end of the left whisker, and the highest Ask students to use the box plots as evidence to support claims. Note that temperature is the end of the right whisker. depending on the time of year, the time of day, and the cities selected by How do you know that? the students, the appearance of the box plots will be different. We can look at the temperature data, and read the numbers off the graph, and compare them to each other. This would be a good time to refer back to conjectures about regional What does the vertical line in the middle represent? temperatures made at the beginning of the lesson. The average temperature. How can we tell if this average is a median or a mean? We can calculate the median and the mean, and see which one the number represents. What feature of a region is likely to cause wider temperature variation? Why is this? How far north it is, or how big it is. How far apart the north and south are in a region. North tends to be cool, and south tends to be warm. How would you predict these box and whisker plots would change later today? How can we test our prediction? They would shift to the right; temperatures might be warmer. We would collect the data again, later. We would need to use the same cities! Transition… What will you say or do to make a clear and smooth transition from the Elaboration section to the Evaluation section? Let’s find out what we learned today about Box-and-Whisker plots, and what they say about variation of data. Evaluation or Exit: Estimated Time: 5 minutes Lesson Closure. Summary of what was learned in lesson, final connections of lesson concepts to prior learning or real-world application, reflections about the learning, readdressing the learning targets, self-assessment or teacher assessment of student understanding Teacher actions and directions Probing teacher questions that help students understand what was learned in the lesson Hand out post-test. See Post-Test (Note that a pre-test is also included, which may be given if the goal is to See Post-Test key measure learning that occurred as a result of lesson. Assessment Summary Formative assessment(s): Occurs throughout the lesson. How will you determine the student’s learning within this lesson (i.e. observations, student responses / elaborations, white boards, student questions, etc. …)? During the collaborative learning segment, ask students to interpret the box plots as they construct them. Teachers should remind students to update their box plots frequently, and to switch between viewing all the data and data by category. The teacher can assess students’ ability to read the graphical axis by asking for average or extreme values from the box plots. Teachers should emphasize claim/evidence thinking; e.g., which region has the highest temperature average, and what is your evidence? Since predictions were made at the beginning of class, students must be reminded to collect data that will ultimately test their predictions. Higher level questioning can assess a general understanding of statistics concepts such as sample space and central tendency. As more data is added for a region, the box plots for that region being generated be different groups become more similar. Why? As each subsequent temperature is added, there tends to be less variation in the mean. Why? Continue to press the students to consider why! Summative assessment(s): Usually occurs at the end of the lesson. How will you determine the student’s learning at the end of the lesson? Provide a student copy of the exit questions or post assessment. See attached Pre- and Post-Tests Ancillary Materials Attach all ancillary materials (summative assessments, student instructions, images, worksheets, etc.) to this lesson plan document to create a single file. List the ancillaries below, and indicate in which part of the lesson each ancillary will be used. If an ancillary cannot be attached to this document, include it in the list by name and indicate where it can be found. All are attached. http://edtech2.boisestate.edu/randysmith768/502/webquest/process.html Explore! How is the weather today in the good old USA?

Your goal is to explore the current temperatures of various US cities, and to use temperature data to draw conclusions about temperature variance across different US regions this morning.

Your team consists of a meteorologist, a statistician, and a research director. Rotate these roles during the activity.

Your tools are  A map of the USA divided into seven different regions.  A tablet with access to 4G and the internet.  Weather Underground (www.wunderground.com)  Shodor Box Plot Generator (www.shodor.org/interactive/activities/BoxPlot/).

Roles and Rules:  The research director picks the cities, and guides the other team members.  The meteorologist uses Weather Underground to get the current temperature for the cities.  The statistician records the temperature data in the Shodor Box Plot Generator data field. If the temperature in a northeast city is 23 degrees, enter “23, northeast” (without the quotes, please). Record each data point on a separate line.  Your team should obtained and record temperature data for at least seven cities in each region. Once you have seven temperatures, switch roles and repeat the process for another region.  Periodically, try clicking the Update Box Plot button. You can choose to Graph All The Data or Graph By Category. You will get an error message if you try to graph too few data points.

Explain!

Use your graphs for evidence as you answer the following questions. Be prepared to explain your answers in class discussion. (This form is for notes only.)

1. Which region had the largest temperature range? Why do you think this region had such a large variation in temperature?

2. Which region had the smallest temperature range? What factors might explain this small temperature variation?

3. If we were to repeat this experiment later today, what changes in the graphs would we be likely to notice?

4. If we were to repeat this experiment in the middle of the summer, what changes in the graphs would we be likely to notice?

5. Compare the box plot for Hawaii with that for the South. What differences do you observe? What could account for those differences?

6. What are some of the advantages of using a box and whisker plot instead of a table of numeric data? What are some disadvantages? Pre-test

The graph above shows temperature variations for three separate regions in the United States at one specific time. Use the graph to answer the following questions. Explain each answer using evidence from the graph.

1) What was the highest temperature measured, and which region was it in?

2) Which region has the lowest average temperature, and what is it?

3) Calculate the temperature range for the region with the largest variation in temperature.

4) Which region is likely to be farthest south? What is your reasoning?

5) Is it more likely the temperatures for all three regions were measured in summer or in winter? Explain your answer. Post-test

1) What was the lowest temperature measured, and which region was it in?

2) Which region has the highest average temperature, and what is it?

3) Calculate the temperature range for the region with the largest variation in temperature.

4) Which region is likely to be farthest north? What is your reasoning?

5) How likely is it that Region B represents the southern region of the USA in summertime? Explain your answer.