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Nicholas County Elementary & Middle School Curriculum 7/16/2003

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Probability/Statistics--Fifth Grade

Kentucky Core Content

Probability/Statistics Strand Concept MA ­ E ­ 3.1.1 Mean, median, mode, and range of a set of data Probability/Statistics Strand Concept MA ­ E ­ 3.1.2 Probability of an unlikely event (near zero) and likely event (near one)

5th Grade Vocabulary Skills Fifth Grade Program of Students Should Studies Know

Students will develop meaning and interpretation of arithmetic mean (average) for numerical data. Students will pose questions; collect, organize, display data; and choose an appropriate way to collect and represent data. Students will use counting techniques, tree Data Statistics Frequency table Tally marks Pictograph Line plot Cluster Gap Range Find probabilities. Mean Solve problems, including those that involve statistics and drawing a picture/diagram. Find the range, median, and mode for a set of data. Read and interpret data. Organize and display data. Find the mean for a set of data.

Suggested Open Response Questions/Answers

Discuss the advantages and disadvantages of using pictographs and line plots. (Possible answer: Advantage: easy to make comparisons. Disadvantages: difficult to show exact amounts with a pictograph when graphing greater numbers, and line plots are not god for showing large amounts of data and greater numbers.) Explain why it is important to have data in order from least to greatest when finding the range, mode, and especially median. (Possible answer: Range---it makes it easier to identify the greatest and the least number. Mode---the same numbers are grouped together. Median---when numbers are in order,

Nicholas County Elementary & Middle School Curriculum 7/16/2003

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Probability/Statistics Strand Concept MA ­ E ­ 3.1.3 The process of using data to answer questions (e.g., pose a question, plan, collect data, organize and display data,

diagrams, and tables to explore probability experiments. Students will explore how sample size affects the reliability of the outcome. Students will make predictions.

Mode Median Bar graph Horizontal axis Vertical axis Double bar graph Stacked bar graph Venn diagram Line graph Stem-and-leaf plot Stem Leaf Experiment Probability

Solve problems, including those that involve ratio, percent, probability, and conducting an experiment.

the number with the middle value is the middle number in the set of data.) Identify examples of statistics found in everyday life. (Possible answer: weather data, city populations, batting averages.) Explain why you wouldn't always have a mode with the data you collect. (Possible answer: Each value might occur the same number of times.) Suppose you want to display the population of the world's ten largest countries. Would you use a line plot or a bar graph? Explain. (Possible answer: I would use a bar graph. There wouldn't be enough room on a sheet of paper to make an x for each person in each country, but I could draw bars to show millions of people.) Explain how you would decide what scale to use to make a bar graph. (Possible answer: Look at the data and choose a scale that would be small enough for the graph to fit on paper but large enough for the bars to show differences in length.)

Probability/Statistics Strand Skill MA ­ E ­ 3.2.1 Pose questions that can be answered by collecting data

Students will find mean, median, mode, and range for a set of data.

Nicholas County Elementary & Middle School Curriculum 7/16/2003

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Probability/Statistics Strand Skill MA ­ E ­ 3.2.2 Collect, organize, and describe data (e.g., drawings, tables, charts)

Outcomes Less likely More likely Equally likely Event

Identify the kind of data best displayed in a double-bar graph instead of a single-bar graph. (Possible answer: Data that compares two sets of responses are best displayed in a double-bar graph.) Explain how Venn diagrams help you solve problems. (Possible answer: Venn diagrams help me organize information that is hard to keep track of in a word problem. They help me sort out who does what.) Compare and contrast line graphs and bar graphs. (Possible answer: Line graphs differ from bar graphs in that in line graphs change is shown over time and in bar graphs amounts are compared. Both are similar in that data is easily compared.) Discuss the advantages and disadvantages of a stem-and-leaf plot. (Possible answer: Advantage---it helps to analyze data confined to a narrow range. Disadvantage---it is hard to make and read for very large data sets.)

Probability/Statistics Strand Skill MA ­ E ­ 3.2.3 Construct and interpret displays of data (e.g., line graph, bar graph, pictograph, line plot, simple Venn diagram, table)

Nicholas County Elementary & Middle School Curriculum 7/16/2003

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Probability/Statistics Strand Skill MA ­ E ­ 3.2.4 Interpret circle graphs Probability/Statistics Strand Skill MA ­ E ­ 3.2.5 Make predictions and draw conclusions based on data

Analyze. Julia's math test scores are 90, 97, 94, 94, 85, 92. She calculated the range to be 2 and the median to be 94. Explain what went wrong and correct it. (Possible answer: Range---She didn't order the numbers first. She found the difference between the first and the last score instead of the greatest and the least. The range is 12. Median---She didn't order the numbers first. The median is 93.) A spinner has 4 sections. There are a green section, a red section, and 2 blue sections. If you spin the spinner, is each outcome equally likely? Explain. (Possible answer: No. There are more blue sections than any other color.) A spinner has 8 sections with 4 different colors. There are a green section, 2 red sections, 2 yellow sections, and 3 blue sections. (a) Identify how many possible outcomes there are when you spin the spinner. (b) Is each outcome equally likely? Explain. (c) Identify which outcome is most likely. Explain. (d) Identify which outcome is least likely. Explain.

Nicholas County Elementary & Middle School Curriculum 7/16/2003

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Probability/Statistics Strand Skill MA ­ E ­ 3.2.6 Find mean, median, mode, and range of a set of data Probability/Statistics Strand Skill MA ­ E ­ 3.2.7 Generate all possible outcomes in simple probability activities Probability/Statistics Strand Skill MA ­ E ­ 3.2.8 Determine the fairness of games using simple probability activities

(Possible answer: (a) 4 possible outcomes; red, yellow, blue, green. (b) No. The sections are not divided equally. (c) Blue is most likely because it is the largest section. (d) Green is least likely because it is the smallest section.)

Nicholas County Elementary & Middle School Curriculum 7/16/2003

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Probability/Statistics Strand Relationship MA ­ E ­ 3.3.1 How data are used to draw conclusions

Probability/Statistics Strand Relationship MA ­ E ­ 3.3.2 How predictions can be based on probability data

Nicholas County Elementary & Middle School Curriculum 7/16/2003

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Probability/Statistics Strand Relationship MA ­ E ­ 3.3.3 How the type of display is related to data (appropriateness of graphs)

McGraw Hill, Math in My World, Grade 5

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