IV. Unit 4-Working with Data: Probability and Statistics

Abstract

In this unit students review how to collect, organize and display data using appropriate statistical and graphical methods.  Students review methods for analyzing data sets and making predictions.  Basic concepts of combinations, permutations, and probability are investigated. 

Essential Question:     How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decisions?

Focus Questions:

  1. How are we personally affected by graphs that we encounter in our daily lives?

  2. How can we meaningfully utilize probability computations in our every day lives?

  3. What is the difference between a combination and a permutation?

Benchmarks:

  1. Collect real data and create meaningful graphical representations of the data. (F1, PSCore: 4.1.1)

  2. Use data from samples to make inferences about a population. (F1, PSCore: 4.2.2)

  3. Define and calculate statistical terms such as range, mode, median and mean. (F1, PS8: 4.2.3)

  4. Analyze and interpret data using descriptive statistics including range, mode, median and mean. (F1, PS8: 4.2.3)

  5. Calculate the probabilities of complementary events. (F2, PSCore: 4.3.1)

  6. Calculate the probabilities of mutually exclusive events. (F2, PSCore: 4.3.1)

  7. Solve real world problems involving the probabilities of mutually exclusive events.  (F2, PSCore: 4.3.1)

  8. Solve real world problems involving the probabilities of complementary events. (F2, PSCore: 4.3.1)

  9. Define and calculate combinations. (F3, PS8: 4.3.2)

  10. Define permutations. (F3, PS8: 4.3.2)

  11. Use combinations in a variety of contexts. (F3, PS8: 4.3.2)

Required Activities (Common Experiences):

  1. Collect data and clearly represent with stat plot, line graph, bar graph, and/or circle graph.  Data should be selected in accordance with student interest. (F1, PSCore: 4.1.1) 

  1. Given circle graph with percentages and total number surveyed, find a specific number representing a particular population.  “Types of Books”, Math 10 CAPTest, p.163. (F1, PSCore: 4.2.2)

  1. Calculate median, mean, mode and range of a set of data.  “Museum Visitors”, CAPT Coach, Grade 10, p.237, #1-2. (F1, PS8: 4.2.3)

  1. In context, calculate the probability of complementary events.  “Cards”, and “Marbles”, Math 10 CAPTest p.153 (F2, PSCore: 4.3.1)

  1. In context from line plot data, calculate the probability of a mutually exclusive event. “Summer Country Day Camp”, CAPT Coach, Grade 10, p.239, #15. (F2, PSCore: 4.3.1)

  1. Determine whether situation is a combination or permutation and then calculate.  “Team Task Assignment”, Approach and Connect  (level 7), p.41 (F3, PS8: 4.3.2)

  1. Calculate total number of combinations.  “Shoe Order”, CAPT release item (F3, PS8: 4.3.2)

Suggested Activities:
Calculate and solve real world problems involving permutations.

Student Portfolio Unit Assessments:

  1. Collect data (student’s choice) that can be represented by a stat plot, line graph, bar graph, or circle graph.  Create an open-ended question involving prediction, which could be answered using the graphed data.  For example, collect and organize census data.  (F1, PSCore: 4.1.1)

  1. Collect sale price data for a product of the student’s choosing.  Calculate mean, median, mode, and range of the data.  Decide which measure of central tendency might be used for an advertisement.  For Example, “Earnings”, CAPT Coach, Grade 10, p. 233, Example 9 (F1, PS8: 4.2.3) 

  1. Given an organized set of data, calculate the probability of a random event occurring, the probability of mutually exclusive events occurring, and calculate the total number of combinations that can be made in the context of the problem.  “Leslie’s Helpers”, Math 10 CAPTest, p.169  (F2, F3, PS8: 4.3.2, PSCore: 4.3.1, F3)

Instructional Resources and Materials:
CAPT release items

Math 10 CAPTest

CAPT Coach grade 10

Mathematical Investigations, Book One
Mathematical Investigations, Book Two
Mathematical Investigations, Book Three
Approach and Connect, Level 7
Approach and Connect, Level 8
Graphing Calculator

Connections:  Models real-world problem solving situations.

Pacing:  10 block class meetings

Notes to Teacher:   

 

Approved by Instructional Council on 12/5/05
BOE 1/18/06