Graphics Math, Social Studies, & Science

1. Graphics Math, Social Studies, & Science Georgia’s 2016 Adult Education Fall Conference

2. GED Assessment Targets & Practices Lots and Lots of Graphics!!! Math bar graphs, circle graphs, dot plots, histograms, data tables, box plots, scatter plots, graphs Science cladograms, food webs, energy pyramid Social Studies process diagrams, tables, charts, political cartoons, scatterplot, line graphs, bar graphs, circle graphs,

3. Scatterplot • Consists of an X axis, a Y axis, and a series of dots. • Each dot represents one data point. • A best fit line, or trend line, is sometimes drawn to show the general tendency. Use it to find a value based on the trend that the graph is showing. Best Fit Line Y Axis X Axis

4. Scatterplot Use the best fit line, not the individual points, to find a value based on the trend of the graph. What grade could a student expect to make on a test if he studies 4 hours? Base your answer on the trend shown on the scatterplot. 70% 0% 50% 100% 0 1 2 3 4 5 6 7 Hours of Study

5. Scatterplot • Shows the relationship, or correlation, between the two variables. • With or without a best-fit line, this relationship is easy to spot. No Correlation Positive Correlation Negative Correlation

6. Examining Data & Correlation As hours of exercise per week increase what do you think would happen to percentage muscle mass? As hours of exercise per week increase what do you think would happen to weight? As hours of exercise per week increase, what do you think would happen to height? No Correlation Negative Correlation Positive Correlation

7. Examining Data & Correlation As hours of exercise per week increase, weight decreases . As hours of exercise per week increase, percentage muscle mass increases. As hours of exercise per week increase, height is not affected. Height (in) 0 50 100 Weight 0 100 200 Muscle Mass 0% 25% 50% 0 1 2 3 4 Weekly Hours of Exercise 0 1 2 3 4 Weekly Hours of Exercise 0 1 2 3 4 Weekly Hours of Exercise No Correlation Negative Correlation Positive Correlation

8. Correlation Practice / Science What type of correlation is shown in the graph above in which the reaction times for children of different ages is plotted? Negative Correlation

9. Correlation Practice / Social Studies • What approximate profit would be expected for a revenue of $250,000,000? $50,000,000 • What relationship is shown between revenues and profits? Positive relationship (correlation)

10. Let’s scatter and do some Plotting!!

11. scatter & Plot activity • Grab your dots. • Move with your group to each graph and plot your data. • At the last graph, answer the following: • What is the independent variable? • What is the dependent variable? • What type of relationship does the graph depict? • Draw a best-fit line or curve to show the trend • depicted by the plotted points.

12. Line Graphs • A type of graph useful for • showing change over time. • seeing patterns and trends in data. • Made up of POINTS connected by LINE SEGMENTS.

13. This data table depicts the monthly sales figures for a company. • What if you needed to answer the following questions using the information presented this way? • What month had the highest sales? • How many times did sales drop in consecutive months? • Between which months did sales rise the most? • Between which months did sales drop the most? • What is the range in sales for the months shown. WAIT!! Before you answer, let’s look at another way to show the data.

14. Compare the two graphics The left column of the data table, Months, is graphed on the horizontal, or X , axis. The data graphed on the X axis is also to referred to as the INDEPENDENT VARIABLE. The right column, Sales, is graphed on the vertical, or Y , axis. The data graphed on the Y axis is also to referred to as the DEPENDENT VARIABLE. Months Dependent Variable Months Independent Variable

15. Same Data on a Line Graph What month had the highest sales? How many times did sales drop in consecutive months? Between which months did sales rise the most? Between which months did sales drop the most? What is the range in sales for the months shown. What month had the highest sales? July How many times did sales drop in consecutive months? 4 times Between which months did sales rise the most? November - December Between which months did sales drop the most? July - August What is the range in sales for the months shown. Approx. $4,400 - $1,000 = $3,400

16. Look at the changes in the graphs. What do they mean?? • Does it start low and rise? • Does it fall as you move left to right? • Are there places where the line is steeper than others? • Are there places where the line is horizontal, or nearly so? • Does the line change direction? • Try to understand what each of these mean. You will have to pay close attention to what is changing by using the labels on the axes.

17. Important tips for using a line graph to answer a question. • Read the title. • Look at the labels on each axis. • How are the numbers spaced? • What units are used for measurement? • Does each axis start at zero? • Look at the key – on multiple line graphs it is given to show what each line represents. Shows that the axis has a break in the numbering.

18. The TREND shown by a graph is the general tendency or direction. The trend can help you make a PREDICTION, or informed guess, about what could be expected to happen next. What is the trend shown by the graph for the amount of milk consumed? The trend shows that as the years progress, milk consumption increased. What could you predict will be true about the amount of milk consumed in 2015? The amount of milk could be predicted at approximately 26 million liters per week. What is shown by the place where the two lines intersect? The consumption of milk and Pepsi was the same, approx. 27,000,000 liters per week. What is the trend shown by the graph for the amount of milk consumed? What could you predict will be true about the amount of milk consumed in 2015? What is shown by the place where the two lines intersect?

19. Circle Graphs • Used to depict parts of a whole • Important for students to realize what the “whole” is. The whole represents 1 day or 24 hours The whole represents the billions of dollars of budget cuts. Sum of the sections equals $1089

20. Circle Graphs Often the “whole” is 100%. Students should look for what number100% represents in each situation.

21. Circle Graphs Practice The graph depicts the blood type distribution of the 480 people who were treated at Centerville Hospital during the month of May. How many of those treated had type O blood? The graph depicts the blood type distribution of the 480 people who were treated at Centerville Hospital during the month of May. How many of those treated had type O blood? = 100X= 40(480) x = 192 192 people

22. Circle Graphs ¼ 25% These parts of a circle are important to remember! ¾ 75% ½ 50%

23. Circle Graphs These part of a circle are important to remember! 2/3 Approx. 67% 1/3 Approx. 33%

24. Circle Graph practice What two items together comprised approximately one-fourth of the budget cuts? What two items together comprised approximately one-fourth of the budget cuts? Interest Payments & Medicare

25. Histograms • Made of adjoining bars with identical widths. • Data is grouped and the length of the bars indicates frequency for each group. • The horizontal axis shows the data in numericalgroups of equal size. • The vertical axis shows the frequencies for the groups. • Easy to see & compare the distribution of the data • Students may be asked to match a histogram with a data set No Gaps Numerical Groupings

26. Histogram Practice Histograms cont. The fifty states were surveyed to ask about average in-state tuition and fees. The results are shown on the histogram. How many states from this histogram have tuition and fees less than $4000? 4 states 3000 4000 5000 6000 7000 8000 9000 10000 11000 Average In-State Tuition & Fees What percent of the 50 states has tuition between $6000 to $8000? 10 states = 10(100) = 50x x = 20% If 2 more states are added to the graph with tuition rates of $5000, the data would be added to which section? They would be added to the section $5000 - $6000

27. Bar Graphs • Used if the data is in categories, such as countries, years, classes, etc. Practice Question: Which year had approximately half the number of tornadoes that occurred in 2007? A) 2005 B) 2006 C) 2008 D) both 2005 & 2006 Gaps A) 2005 B) 2006 C) 2008 D) both 2005 & 2006 Categories

28. Box and Whisker Plots • Statistical tool useful for comparing data • It divides the data set into four equal groupings • Test-takers need to be able identify the parts and understand the implications of the data distribution.

29. Activity: Haircut Boxplot How much do you normally pay for a haircut? Write the amount in large figures on a sheet of paper. Position yourself on the number line according to your haircut price, boys on one number line, girls on the other. Find the: Median Upper & Lower Quartiles Upper and Lower Extremes $45

30. Construct a Box & Whisker Plot • Find the median. Draw vertical line above the number line for this value. • ***If two numbers are in the middle, average them to find the median. • Find the median of the upper values. Draw a vertical line for this value • Find the median of the lower values. Draw a vertical line for this value. • Add horizontal lines to form a box. • Plot points for the lowest and highest values • Draw a line from the box edge to each of these to form the whiskers. 6 28 34 35 38 38 46 54 54 32 0 10 20 30 40 50 60 70 60

31. Box Plot – Name the Parts Median Upper Quartile Lower Quartile Upper Extreme Lower Extreme Q1 Q2 Q3 Q4 0 10 20 30 40 50 60 70 The box plot equally divides the data points into 4 groups, or quartiles - Q1,Q2,Q3,Q4

32. Box Plots – Can be VERTICAL also!! Practice - Label each of the following & give its value M – median UQ – upper quartile LQ – lower quartile UE – upper extreme LE – lower extreme Label the quartiles with Q1, Q2, Q3, Q4 . 5 6.5 UE 3 Q4 12 1 UQ Q3 10 5 0 M Q2 LQ What is the range? Which quartile contains the most data points? Which quartile has data that is spread out the most? 12-1 = 11 Q1 LE All quartiles contain the same number of data points Quartile 4 – from 6.5 to 12

33. Box Plot - Practice Mankens South Mills Hardin 14 14 14 Three elementary schools asked parents to estimate how many hours a week their children spent on homework. 12 12 12 10 10 10 8 8 8 6 6 6 4 4 4 The box plots depict the data received from the parents for each school. 2 2 2 0 0 0

34. Box Plot - Practice Which school has the highest median number of homework hours per week? What are the medians for each school? Which school has the highest median number of homework hours per week? Mankins Elementary What are the medians for each school? South Mills– 5 hour Mankins – 8 hours Hardin – 2 hours Hardin Mankens South Mills 14 14 14 12 12 12 10 10 10 8 8 8 6 6 6 4 4 4 2 2 2 0 0 0

35. Box Plot - Practice Mankens South Mills Hardin 14 14 14 Which schools(s) has the greatest range in number reported weekly homework hours? Both South Mills and Hardin have ranges of 12. Which school(s) has the greatest range in the number of reported weekly homework hours? 12 12 12 10 10 10 8 8 8 6 6 6 4 4 4 2 2 2 0 0 0

36. Box Plot - Practice Which represents the greatest number of students whose study hours were reported? 3rd quartile of South Mills 4th quartile of Hardin 2nd quartile of Mankens All quartiles represent the same number of students Which represents the greatest number of students whose study hours were reported? 3rd quartile of South Mills 4th quartile of Hardin 2nd quartile of Mankens All quartiles represent the same number of students Mankens South Mills Hardin 14 14 14 12 12 12 10 10 10 8 8 8 6 6 6 4 4 4 2 2 2 0 0 0

37. Dot (or Line) Plots • Used to organize data above a number line by placing a dot (or X) to represent each occurrence of a value. • Easy way to show and compare frequencies • Usually used with a small (less than 50) set of values. • Might see as a hot spot or drag & drop question X X X X X X X X 5 10 15 20

38. Job Survey Twelve adult ed students were asked how many jobs they have had in their lifetimes so far. The results are as follows: 2, 5, 0, 4, 6, 2, 3, 13, 0, 1, 1, 2 Complete the dot plot that is shown by adding any dots needed to include all data. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number of Jobs

39. Job Survey Questions: What is the mode of this data set? What is the median of this data set? What point could be considered an outlier? 2 2 13 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number of Jobs

40. Job Survey Questions continued: How many people in the survey had fewer than two jobs? If the outlier in this data set were dropped, which of the following would NOT change? mean median mode range 4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number of Jobs

41. Organizational Charts The 3 Branches of Government and Separation of Powers

42. Checks and Balance Contest Be the first team to place all the cards with the correct branch of the government. Executive Legislative Judicial

43. Visuals in Science: Cladograms • Used to show evolutionary relationships. The original characteristic is placed at the bottom and it pertains to all of the organisms on the diagram. Derived traits are placed above and pertain only to some of the organisms.

44. Visuals in Science: Cladograms Going up/right on a cladogram indicates more recent times. Organisms are considered to be more closely related if they share more recently evolved characteristics. Time Flows

45. Cladograms Practice What is the original trait? vertebrae 2. Which organism(s) have the greatest number of derived traits? Crocodiles & birds Which organism has four limbs but does not develop in an amniotic egg? Amphibian (frog)

46. Cladograms practice 4. Which two organisms are most closely related? Sharks & Amphibians Crocodiles & Birds Primates & Crocodiles Amphibians & Crocodiles 4. Which two organisms are most closely related? Sharks & Amphibians Crocodiles & Birds Primates & Crocodiles Amphibians & Crocodiles

47. Cladograms practice Place letters in the blanks to correctly label the diagram with the characteristics shown. 1. ______ Wings2. ______ 6 Legs3. ______ Segmented Body4. ______ Double set of wings5. ______ Cerci (abdominal appendages)6. ______ Crushing mouthparts7. ______ Legs8. ______ Curly Antennae F C A G E D B H

48. Teaching Social Studies – Political Cartoons • Students should analyze the cartoonist’s point of view and the message being conveyed by looking at: • Symbols • Exaggerations • Irony • Stereotypes • Text/Labels

49. Teaching Social Studies – Political Cartoons Which of the following best summarizes the message of the cartoon ? The Supreme Court’s job is to correct the government’s mistakes. The three branches of our government work together effectively. Passing a law is the job of all three governmental branches. The three branches of our government do not work together very effectively. Which of the following best summarizes the message of the cartoon ? The Supreme Court’s job is to correct the government’s mistakes. The three branches of our government work together effectively. Passing a law is the job of all three governmental branches. The three branches of our government don’t often work together effectively.

50. Food Web – It is all about what eats what!! Energy flows from the producers (plants) to the consumers (animals). Each step away from the producers results in less available energy. Arrows point from what is eaten to what eats it. A grasshopper is eaten by _______________ and it eats _________________. Arrows point from what is eaten to what eats it. A grasshopper is eaten by birds & mice and it eats plants.