MAT 152 Mathematics in the Modern World Module 7 PDF

MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________...

MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Lesson title: Interpreting Different Graphs Materials: Student Activity Sheets Learning Targets: References: At the end of the module, students will be able to: Tomankin, F. Topics in Applied Statistics, 1. Determine different graphical presentations. 2010 2. Draw out information from graphs. www.thefunctionalart.com 3. Apply critical thinking skills to analyze graphs to come up www.wolframalpha.com with ethical and unbiased data interpretation. https://assets.cengage.com/gale/docs/pro duct/HS_06ws_Graphs.pdf Productivity Tip: More about data today! Manage your time well! Motivate yourself by thinking positive so that you can easily understand the facts presented in the graph. A. CONNECT A.1 Lesson Preview/Review Welcome again to data management. Get ready to learn how to interpret different graphs. Let’s start! Graphs are a common method to visually illustrate relationships in data. The purpose of a graph is to present the data that are too numerous or complicated to describe adequately in the text and with less space. There are plenty of data presented on social media nowadays, make sure you only believe those from reliable sources and always double-check information before you believe it. Remember that sharing personal Data online increases the risk of data cloning, so limit making your information public. B. COACH B.1 Content Notes Topic: Interpreting Different Graphs Reading Comprehension Strategy: Definition and Description In this lesson, you are going to read and learn about how to interpret graphs. To help us understand what we read, we will use the comprehension strategy Definition and Description applied in SAS #06. Instructions: Step 1: Read the content notes carefully to understand the context in which the preselected/underlined words are used. Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Different Graphical Presentations When we want to show information in a picture, we must pick the right kind of picture, just like choosing the right words in a story. Imagine you have different tools for different jobs: a hammer for nails, a screwdriver for screws, and so on. Graphs are like tools for showing information. There are many types of graphs, like bar graphs, line graphs, pie charts, histograms, and scatter plots. Each one is good for different things. For example, a bar graph is great for comparing things, like how many students like different colors. A line graph is good for showing how things change over time, like how the temperature changes throughout the day. Histograms are like bar graphs, but they're used to display the distribution of continuous data, like representing the distribution of test scores in a class. Pie charts are about showing parts of a whole, like illustrating the percentage of different genres in a music collection or the breakdown of expenses in a budget. Scatter plots are a way to see if there's a relationship between two variables by plotting points on a graph, like studying the correlation between study time and exam scores. When we pick a graph, we need to think about who will see it and what they need to understand. We also want it to be clear and easy to read, like a book with big letters. So, just like picking the right tool for a job, we pick the right graph to show our information clearly and easily. Step 2: Write the preselected/underlined words in the words column. Step 3: Define the preselected/underlined words by getting the key ideas from the content notes read. Step 4: Write the importance of learning the preselected/underlined words and its use to you as a student or in the future. WORDS DEFINITION IMPORTANCE Graphs A graph is like a visual map made of dots Graphs are like picture maps that show us and lines. The dots represent things, and information in a simpler way and understand the lines show connections between them. things better and make it easier to share information with others. Bar graph A bar graph is a type of graph that uses Bar graphs are important because they help rectangular bars to represent data us see and compare information easily Line graph Line graph is good for showing how things It helps us to understand how things change change over time. over time, helping us spot patterns and trends quickly. Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Histogram It is a special type of bar graph that shows It is important because it visually shows how often different numbers or ranges of how often different values occur in a numbers appear in a dataset. dataset, making it easier to see patterns, compare groups, and understand the data. Pie Graph It is a circular chart divided into slicesPie graphs are important because they to show how different parts make up ahelp us quickly understand the whole. proportions of different categories within a whole. Scatter Plot It is a type of graph that uses dots to Scatter plots are important because they show how two different things are help us see if there's a pattern or related. connection between the two things. Let’s use again definition and description comprehension strategy step by step for the last content notes. Let’s do this! Understanding Data Ethically When analyzing graphs critically, there are several key concepts to keep in mind, such as data integrity, transparency, fair representation, choosing the right type of graph, respect for privacy and consent, accountability, responsibility, and considering societal impact. First, let's talk about data integrity. It's important to make sure the data in the graph is accurate and reliable. Always verify that the information is correct by asking questions like: Where did the information come from? How was it collected? Is there anything that might make it not true? Next, transparency is essential for ethical interpretation. Graphs should clearly label axes, provide appropriate units, and include necessary context or notes to help us understand them. This makes the information easy to follow and trustworthy. Fair representation means that graphs shouldn't hide anything. They should tell the whole story, not just parts of it. Sometimes people show only parts of the graph to make things seem different than they really are. Always make sure the graph is showing the complete picture. Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Choosing the right type of graph is also important. Graphs come in different forms like bar graphs, line graphs, and pie charts. Each type is good for showing different kinds of information. Pick the one that best represents the data. If a graph looks tricky or doesn't seem right, ask questions! Respect for privacy and consent is crucial. If the graph has information about people or private things, it should keep those secrets safe. Don't show things that could make people feel embarrassed or unsafe. Accountability and responsibility mean always thinking about what the graph means. Ask if it tells the whole story or if something is missing. Make sure you are being honest and responsible with the information. Finally, consider the societal impact. Reflect on how the information in the graph might affect different groups of people or society. By following these steps, we can understand graphs better and make sure we're being fair and honest with the information we see. WORDS DEFINITION IMPORTANCE Data Integrity It means making sure that the information It helps us trust the information we use. we use is correct and true Transparency It is being open and clear about how we It helps build trust and confidence in the collect and use information. information we're using. Fair Representation It means showing information accurately It helps us understand things better and make and without bias. fair decisions based on what we know. Use the right picture It means choosing the best type of graph It is important because it helps people see the or chart to show information clearly and true story the data is telling without being honestly. misled or confused Respect for privacy It means being careful to protect people's It is important because everyone has the right and consent personal information and asking for to keep certain things about themselves permission before using it. private, like their name, address, or health information. Accountability and It means being honest and careful with the It is important because when we collect or Responsibility information we use. share data, we need to make sure we're doing it in a fair and trustworthy way. Consider the societal It means thinking about how our actions It is important because the things we do with impact with data might affect other people and data can have a big impact on society. the world around us. And we’re done! Good work! Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Definition and description strategy will help us understand the content better. This strategy can be used in any subject! It takes practice to do this well. Keep trying! The more you practice, the better you'll get at it. Strategy Review 1. What is the title of the text we read? _______________________________________________________________________________ 2. What reading comprehension strategy did we use? _______________________________________________________________________________ 3. What are the four steps in this strategy? _______________________________________________________________________________ B.2 Skill Building Activity Activity B.2.1 Drawing out information from graphs involves several steps to ensure clarity and accuracy. Here's a step-by-step process you can follow: Step 1. Identify the type of graph. Is it a line graph, bar graph, pie chart, scatter plot, etc.? Each type of graph represents data differently. Step 2. Look at the Lines and Labels. Pay attention to the lines (like the lines going across or up and down) and the labels (words) on the bottom and side of the graph. They tell you what the graph is about and what the numbers mean. (x-axis: horizontal and y-axis: vertical) Step 3. Read the Title. The big title at the top of the graph usually tells you what the graph is showing. Step 4. Find Patterns. Identify patterns or trends in the graph. For example, are the lines going up, down, or staying the same? increasing or decreasing trends. Step 5. Do Math if Needed: Sometimes you might need to do a little bit of math to figure out more about the graph, like finding averages or percentages. Step 6. Consider Context: Think about the broader context of the data. Understanding the context helps in drawing accurate conclusions. Step 7. Check for Outliers or Anomalies. Check if there are any numbers or points on the graph that seem different from the others. These could be important, or they might be mistakes. Step 8. Summarize Findings. Finally, talk about what you found out from the graph. Describe what it's showing and what you think it means Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Example: Draw out information from the given graph below using the step-by-step process. Step 1. Identify the type of graph. It is a line graph comparing the number of vehicles manufactured by two companies, A and B, over a period from 1997 to 2002. Step 2. Look at the Lines and Labels. x-axis (horizontal): Represents the years from 1997 to 2002. y-axis (vertical): Shows the number of vehicles manufactured in thousands. Lines: Company A and Company B. Step 3. Read the Title. The title is "Number of Vehicles Manufactured by Two Companies From 1997 to 2002 (in Thousands)". Step 4. Find Patterns. Company A: Starts at 119, decreases to 99 in 1998. Peaks at 141 in 1999, then drops to 78 in 2000, then rises smoothly from 120 in 2001 to 159 in 2002. Company B: Starts at 139, decreases to 120 in 1998. Falls at 120 to 100 in 1999, peaks at 128 in 2000. Drops to 107 in 2001, then increases to 148 in 2002. Step 5. Do Math if Needed. Averages: Calculating the average production over the years could provide additional insight. Company A: (119 + 99 + 141 + 78 + 120 + 159) / 6 ≈ Approximately 120,000 vehicles. Company B: (139 + 120 + 100 + 128 + 107 + 148) / 6 ≈ Approximately 124,000 vehicles. Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Step 6. Consider Context. The graph shows trends in vehicle manufacturing over six years. Maybe they had new models, changes in management, or economic issues. Step 7. Check for Outliers or Anomalies. Company A made a lot fewer vehicles in 2001 (78,000) than in other years and both companies made a lot more vehicles in 2002. Step 8. Summarize Findings. Company A experienced significant fluctuations in production, with a notable drop in 2001 and a dramatic increase in 2002 and Company B had more stable production numbers but also saw a significant increase in 2002. Both companies showed a positive trend in vehicle manufacturing by the end of the period, especially in 2002. Conclusion: Company A had big changes in the number of vehicles they made each year, especially in 2001 and 2002 and Company B was steadier but also made a lot more vehicles in 2002. Something important might have happened in 2002 that made both companies increase their production. By following these steps, you can understand and explain the information in the graph. Now, Try this. Examine the graph provided below using the step-by-step process. Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Step 1. Identify the type of graph. ____________________________________________________________________________ ____________________________________________________________________________ Step 2. Look at the Lines and Labels. ____________________________________________________________________________ ____________________________________________________________________________ Step 3. Read the Title. ____________________________________________________________________________ ____________________________________________________________________________ Step 4. Find Patterns. ____________________________________________________________________________ ____________________________________________________________________________ Step 5. Do Math if Needed. ____________________________________________________________________________ ____________________________________________________________________________ Step 6. Consider Context. ____________________________________________________________________________ ____________________________________________________________________________ Step 7. Check for Outliers or Anomalies. ____________________________________________________________________________ ____________________________________________________________________________ Step 8. Summarize Findings. ____________________________________________________________________________ ____________________________________________________________________________ Conclusion: ____________________________________________________________________________ ____________________________________________________________________________ Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Now, Let's have a scenario where we analyze a graph comparing loan interest rates among different lenders. Here's how we can apply critical thinking skills to ensure ethical and unbiased data interpretation. Graph Details: Title: Internet Provider Speed Comparison (2024) y-axis: Average Download Speed (Mbps) x-axis: Internet Providers (Provider A, Provider B, Provider C, Provider D) Source: Independent Network Testing Data Average download speeds for each internet provider are as follows: Provider A: 100 Mbps Provider B: 150 Mbps Provider C: 120 Mbps Provider D: 90 Mbps 1. Understand the Context: Where Does Data Come From? Independent network testing data was used to assess download speeds of various internet providers. Why Are We Looking at It? We're seeking the internet provider with the highest download speeds to ensure efficient online access. Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ 2. Examine the Data Presentation: Does It Show the Full Picture? Yes, the graph clearly displays each provider's download speed. It privide insights into each provider's download speeds. 3. Identify and Avoid Misleading Elements: Does Anything Look Weird? The data is straightforward and easy to understand. 4. Compare with Other Sources: Does This Match What We Know? *Note: Check What Others Say. The download speeds seem consistent with industry standards. 5. Interpret the Data Ethically: What Do the Download Speeds Tell Us? Provider B offers the highest average download speed, while Provider D has the lowest. Are Some Providers Better? Provider B's superior speed may result from infrastructure or network management investments. 6.Communicate Findings Transparently: Make It Simple. Provider B delivers the highest average download speed, indicating it's ideal for fast and reliable internet connectivity. *Note: Think about being honest and Fair. Varying speeds prompt consideration of service quality, coverage, and pricing. Consulting experts or further research can clarify speed factors. Interpretation: Provider B offers the highest average download speed, while Provider D provides the lowest. Choosing a provider with faster speeds ensures smoother online experiences. Understanding the graph helps us select an internet provider that meets our need for efficient online connectivity. C. CHECK C.1 Check for Understanding Next, let's have a scenario where we analyze a graph comparing loan interest rates among different lenders. Here's how we can apply critical thinking skills to ensure ethical and unbiased data interpretation. Note: This activity is going to count for 20% of your quiz 2 grade while the remaining 80% is completed through pen and paper tasks. Let's make every moment count and dive right in! Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ Graph Details: ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ Loan Interest Rates Comparison (2022) ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ Step-by-step Analysis: 1. Understand the Context: Where Does Data Come From? ______________________________________________________________________________________________ ______________________________________________________________________________________________ Why Are We Looking at It? ______________________________________________________________________________________________ ______________________________________________________________________________________________ Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ 2. Examine the Data Presentation: Does It Show the Full Picture? ______________________________________________________________________________________________ ______________________________________________________________________________________________ 3. Identify and Avoid Misleading Elements: Does Anything Look Weird? ______________________________________________________________________________________________ ______________________________________________________________________________________________ 4. Compare with Other Sources: Does This Match What We Know? ______________________________________________________________________________________________ ______________________________________________________________________________________________ *Note: We can ask friends or family if these interest rates seem fair. 5. Interpret the Data Ethically: ______________________________________________________________________________________________ ______________________________________________________________________________________________ 6. Communicate Findings Transparently: Make It Simple: ______________________________________________________________________________________________ ______________________________________________________________________________________________ *Note: Think about being honest and fair. Interpretation: ______________________________________________________________________________________________ ______________________________________________________________________________________________ ______________________________________________________________________________________________ ______________________________________________________________________________________________ D. CONCLUDE D.1 Summary / Frequently Asked Questions 1. What are the limitations of a Graph? A graph lacks complete accuracy of facts. It depicts only a few selected characteristics of the data. We cannot use a graph in support of a statement. A graph is not a substitute for tables. Usually, laymen find it difficult to understand and interpret a graph. Typically, a graph shows the unreasonable tendency of the data, and the actual values are not clear. Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.  MAT 152: Mathematics in the Modern World Module #7 Name: _________________________________________________________________ Class number: _______ Section: ____________ Schedule: ________________________________________ Date: ________________ 2. What are some common mistakes to avoid when interpreting graphs ? When interpreting graphs, avoid common mistakes like ignoring the scale, overlooking labels, focusing on specific points without looking at the overall trend, and falling for misleading designs. These errors can distort your understanding of the data. Always check the scale, labels, and overall trends to get the true message. D.2 Thinking about Learning You did a lot! Have you learned a lot? Let’s talk about your learning experience. 1. What routines, behaviors, actions help you work better? Describe how it helps. _________________________________________________________________________________ _________________________________________________________________________________ 2. On a scale of 1-5, 1 being the lowest and 5 being the highest, how successful were you in meeting today’s lesson objectives? Why do you say so? What factors contributed to this? What changes, if any , should you do for your next lessons? _________________________________________________________________________________ _________________________________________________________________________________ Learning Modules by PHINMA Education is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.