1. Unit 1 Populations and Samplings Learning Map Unit 1

3. Big Idea : In the real world, people create and analyze various data displays in order to draw conclusions about the data. Unit Essential Question: What makes a data representation useful? Concept: Data Collection Concept: Data Analysis Concept: Probability Concept: Problem Solving Essential Questions: How can data displays be used to answer questions? What are the different data displays and how are they used? Essential Questions: How does mean, median, mode, and range, help you interpret data? Essential Questions: How do you use fractions, percents, and decimals to represent probability? How do you determine if a game is fair or unfair? Essential Questio ns: How do we use problem solving skills to reason mathematically and communicate connections throughout statistics? Vocabulary: data, catagorical data, numerical data, value, varibles Vocabulary: mean, median, mode, typical value, average, range, trend, outlier, data Vocabulary: chance, outcome, impossible, certain, probability, likely, unlikely, maybe Vocabulary: solve, compare, estimate, apply, analyze, strategies, arguments and proofs, evaluate, communicate

4. Vocabulary WordDefinition or SentencePicture or Clue Graph Median 1, 2, 3, 4, 5,6,7 Mode1,1,2,2,2,2,3,3,4,5,5,6 2 occurs the most Probability50% chance of rain Problem solving figuring out a puzzle

5. Vocabulary WordDefinition or SentencePicture or Clue Graph A visual representation (picture) of data (information) Median The number exactly in the middle of a group of numbers used to represent the average. 1, 2, 3, 4, 5,6,7 Mode The number that appears most often in a set of data 1,1,2,2,2,2,3,3,4,5,5,6 2 occurs the most Probability How likely something is to happen (out of 100%) 50% chance of rain Problem solving Finding the answer to a problem figuring out a puzzle

6. Let’s see what you know! In your summary tab, make a KWL chart. Fold in 3rds then fold top down. Watch me! What I think I KNOW What I WANT to learn What I LEARNED

7. Math Unit 1 Populations and Samples

8. Unit 1 Lesson 1 Eyelets In this lesson, students will study the number of eyelets in shoes in the classroom. Students will collect data, organize data, graph data and analyze data on bar graphs. Essential Question: How can data displays be used to answer questions? What are the different data displays and how are they used? Vocabulary – categorical variable – Data – mode – numerical variable – values – variable Big Ideas – Variables – Values – Bar Graphs

9. Vocabulary You Need To Know Survey variable value numerical variable categorical variable data mode

10. Goals for the lesson Gather, organize, graph, and analyze data using variables, making data tables, and drawing bar graphs. Connect math and science to everyday life Work cooperatively with others Math can be fun

11. Brainstorm WHAT IS A SURVEY???

12. What do we know from the data? DO you think the data will help convince Blanca’s mom that slip-ons are not fashionable? Would a graph help? What the most common kind of shoe in Blanca’s class? What would the data look like if we surveyed our school?

13. Blanca & Irma’s Data

14. What is a variable? Things that change or vary in an experiment or survey Example: – kind of shoes – number of shoes

15. Numerical Variables Numerical : Numbers – If I ask how many pairs of high top sneakers you have will the answer be numbers or words? – Your answer would be numbers (1 pair, 2 pairs, 3pairs,etc.) Therefore : Number of pairs of high top sneakers is a numerical value Numerical Variable- a question that has a number for the answer or value

16. Categorical Variables Categorical : Words NOT numbers – Type of shoe is a categorical variable – If I ask you what kind of shoes you have on, you will give me words (sandals, tennis shoes, boots, etc) Therefore, type of shoe is a categorical variable Categorical variable- a question with words for the answers or values

17. Values The answers to the question If I ask what kind of shoes you are wearing (variable), you answer by saying Sandal, sneakers, boots (values) LET’S TRY

19. TIMS Laboratory Method 1. Determine your question 2. Determine the variables 3. Draw 4. Collect 5. Graph 6. Explore

20. Question of the Day How can I use a graph to analyze data? Warm-up: DPP F 1. Be ready to sing “Skip Counting”! 2. Review vocabulary 3. Continue with survey

21. Vocabulary WordDefinition or SentencePicture or Clue Variable The quantity that changes. Question in a survey ? EX: What color eyes do you have? Value The possible outcome of a variable. Variable: Color of Eyes Possible values: green, brown, blue, hazel Categorical Variable Variables with values that are not numbers. Color of Eyes Kind of favorite foods Days of the week Numerical Variable Variables with values that are numbers Number of animals Number of siblings Number of eyelets Data Information collected in a survey 8 people have 2 siblings 10 people have 22 eyelets 3 people have 1 animal

22. Let’s Begin How many eyelets are on the shoes of the students in your class? What are the variables? Number of Eyelets Number of Pairs of Shoes

23. Let’s Draw Include both variables Include possible values LABEL EVERYTHING!

24. Collect the Data

25. How can I use a graph to analyze data? 9-1-10 – Warm-up: Compare your homework with your partner. Do your charts and or graph look alike or different? 1.Check the data (slide) 2.Analyze the data 3.Describe the graph –

26. Let’s Check The Data Did we include everyone? How do we know?

27. Graph the Data All graphs must include: – Title – Label both Axis with the correct values and variables – Values must be equally spaced on the axis – Put the value 0 where the axis meet

28. What will we do in math today? Question of the Day: How do I use a graph to analyze data? Warm-up: Drop in the Bucket worksheet side 1 problems #7 and 8 only Worksheet p. 63-65 Homework: DPP H

29. Explore: Analyze the Data How many have 20 eyelets? 8? 0? What is the MODE? (most common number of eyelets) What are the values for number of eyelets? What do we notice about those values? Alexis said she had 14 eyelets on her pair of shoes. Do you think she is correct? Why or why not?

30. Describing the graph using words. 4 things to include: How many bars are on the graph? What is the tallest and shortest bar? Where are the bars located? – Beginning of the graph – Middle of the graph – End of the graph What is the mode (tallest bar) on the graph?

31. Let’s Try It! Use question/answer format: – The number of students that have 20 eyelets on their shoes is 2. – 0 students have 8 eyelets on their shoes. – 2 students have 0 eyelets on their shoes. The mode for number of eyelets is 24 because it is the tallest bar on the graph. You can find the mode on the graph by looking for the tallest bar on the graph.

32. The values for number of eyelets with bars above them are 0, 4,12,16,20,22,24,28,30, and 32. All of the numbers are even numbers and all of the numbers except 22 and 30 are multiples of 4. 14. **DESCRIBING A GRAPH** The graph has 10 bars. The highest bar is 24 eyelets on 7 pairs of shoes. The lowest bars are 2, 6, 8, 14, 18 and 26 eyelets on 1 pair of shoes. The tallest bars are near the end of the graph. The mode of the graph is 24 eyelets. 17. 4+12+16+20+20+22+22+24+24+24+24+24+24+24+28+28+28+ 28+28+30+32= 486 eyelets in room 210

33. Describe the Eyelets graphs for: A professional basketball team in uniform. The basketball team wears high top sneakers which have a lot eyelets. There would not be a lot of bars because they all wear the same type of shoe. The tallest bars would be at the end of the graph. Vacationers on a beach Most people wear flip-flops to the beach, so the tallest bars will be at the beginning with 0 eyelets. Some people will wear sneakers, so there will be some eyelets shown on the graph. Where would the tallest bars be on the graph? Would there be many bars or just one or two?

34. Questions What is the total number of eyelets on all the shoes of all the students in your class? 486 eyelets in room 210 Estimate (about) the total number of eyelets for the entire 5 th grade. About 500 eyelets in room 210, so 500 x 2= 1,000. There are about 1,000 eyelets in the 5 th grade at SIMA. How did you make your estimate? How would the graph be different if you gathered data from all the fifth graders in your school?

35. There are about __1,500 eyelets on 5 th graders at Fred Douglas. 500 eyelets per class x 3 classes= 1,500 eyelets 500 +500+500= 1,500 eyelets SIMA = 1,000 eyelets 500 x2 Fred = 1,500 eyelets 500 x 3 West= 1,000 eyelets 500 x2 Blades = 2,000 eyelets 500 x 4= 2,000 Central = 1, 500 eyelets 500 x 3 TOTAL = 7,000

36. Did we reach our goals? Gather, organize, graph, and analyze data using variables, making data tables, and drawing bar graphs. Connect math and science to everyday life Work cooperatively with others Math can be fun

37. Think and Write About It! What would happen if some students counted the eyelets on only one shoe while other students counted the eyelets on both sides? – Write your response in your math journal. – Include your answer to the question and support your answer with facts and examples. – Remember to strive for five!

38. How will my response be graded?

39. Vocabulary Quiz Fill in the blank with the correct vocabulary word. Only write the answer on your paper. data mode variable value graph categorical variable numerical variable 1.How many pets do you have in your home is an example of a ___________ ______ 2.A __________ is a way to show information in a visual format. 3.________ is another word that describes information. 4.The most common number in a set of data is called the ______________________. 5.A ________________ is the question in a survey. 6.Blue would be a possible ___________________ for the variable, “what color are your eyes? 7.“What color are your eyes?” is a ______________ _______________.

40. Big Idea : In the real world, people create and analyze various data displays in order to draw conclusions about the data. Unit Essential Question: What makes a data representation useful? Concept: Data Collection Concept: Data Analysis Concept: Probability Concept: Problem Solving Essential Questions: How can data displays be used to answer questions? What are the different data displays and how are they used? Essential Questions: How does mean, median, mode, and range, help you interpret data? Essential Questions: How do you use fractions, percents, and decimals to represent probability? How do you determine if a game is fair or unfair? Essential Questio ns: How do we use problem solving skills to reason mathematically and communicate connections throughout statistics? Vocabulary: data, catagorical data, numerical data, value, varibles Vocabulary: mean, median, mode, typical value, average, range, trend, outlier, data Vocabulary: chance, outcome, impossible, certain, probability, likely, unlikely, maybe Vocabulary: solve, compare, estimate, apply, analyze, strategies, arguments and proofs, evaluate, communicate

41. Unit 1 Lesson 2 and 3 Analyzing Data Lesson 2 and 3-Review: Representing Data and Analyzing Data In this lesson, students will review bar graphing and use the median to average data. Students will compare and analyze data in graphs. They use median, mode and average to represent data. Essential Question: How does mean, median, mode, and range, help you interpret data? Vocabulary – average – median – numerical variable – value – Variable – Mode – mean Big Ideas – Bar graphs – Averages – Median – Analyzing graphs – Finding median – Using averages to represent data

43. Average A number that can be used to represent a typical value in a set of data. Median Mode Mean 1, 4, 5, 7, 8, 10, 12 77777777 7 1,1,1,3,3,4,5,5,6,7 1 is the mode 1+2+4+5=12/4=3 mean is 3

44. Warm-Up Essential Question: How does mean, median, mode, and range, help you interpret data? 1. On the notebook paper, do DPP L. This will be counted as a grade. Place it in the basket on the red chair when finished. 2. Take out your composition book and copy the following journal prompt for homework. This should be a “hamburger” style paragraph. What did you learn about graphs from doing the Eyelets lab?

46. Vocabulary WordDefinition or SentencePicture or Clue Average Median Mean Mode

47. Mr. Moreno’s Graphs Graph A- Kindergarten-5 th grade students in the cafeteria because the bars are in the beginning, middle and end of the graph. The range of bars is from 40 inches to 60 inches. Therefore, the graph tells us there are short students, average students, and tall students in the cafeteria. Graph B- The kinder garten students because the bars are in the beginning and middle of the graph. The range of heights is 43 inches to 53 inches. Graph C- The height of Mr. Moreno’s 5 th grade class because 51 inches is the shortest and 59 inches is the tallest student. Most 5 th graders are taller than other students in a kindergarten-5 th grade. Most of the bars are in the middle and end of the graph. 51,52,52,53,53,54,54,55,55,56,56,56,57,57,57,58,58,58,58,59,59 $2.10, $2.50, $2.75, $3.00, $3.50 0,1,2,2,3,3 0,20,24,30 20,21,22,23,24

51. Searching the Forest Lab 1. Draw 2. Collect and Organize data 3. Graph 4. Analyze the Graph DRAW – Name the 2 variables in the lab N- Number of tiles (numerical variable) C- Color of the tiles (categorical variable) COLLECT AND ORGANIZE DATA ( see chart)

52. Essential Question: How do you use fractions, percents, and decimals to represent probability? Warm-up: DIB side 4 #1 and 2 Tear out workbook p. 47 Facts race- square numbers Notes on square numbers Vocabulary Review Lab Analyze data

53. Vocabulary WordDefinition or SentencePicture or Clue

54. Vocabulary WordDefinition or SentencePicture or Clue MedianThe number exactly in the middle of a set of data which respresents the average. EstimateAbout or close to; prediction PredictionUsing background knowledge with what you have seen, heard or read to make an educated guess ActualTo find the exact answer FractionThe number of parts out of the whole.

55. Vocabulary WordDefinition or SentencePicture or Clue ProbabilityHow likely something is to happen out of 100%. Problem SolvingTo figure a problemSolving a puzzle

57. Predication/Actual ColorPredictionActual Blue2020 Green00 Red1010 Yellow2020

58. Lin’s Data Red20/50 20 out of 50 Green10/50 10 out of 50 Blue20/5020 out of 50

59. Essential Question: How do you use fractions, percents, and decimals to represent probability? Warm-up: DIB side 4 #3 and 4 Check warm-up and homework Review vocabulary Graded assignment- Joselyn’s Wildflowers