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PA-D-1-1

Page history last edited by Tashe Harris 6 years, 1 month ago

PA.D.1.1 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet and use a calculator to examine this impact.


In a Nutshell

Students should develop a complete understanding of actual middle (median) and calculated middle (mean). With the introduction of a new data point, or eliminating one, students need to be able to anticipate how this change will affect median and mean. Using a computer based spreadsheet program on a PC, laptop, iPad or calculator, students can list and sort data with ease. Most of the programs also have 1-variable data analysis to help find median and mean, assisting in data analysis.

Student Actions

Teacher Actions

  • Develop a Productive Mathematical Disposition by collecting data sets to calculate mean, median, and mode problems with real-life context (grades, heights, allowance, etc…).

  • Develop a Deep and Conceptual Understanding by analyzing measures of central tendency on data sets in various forms (tables, graphs, lists, etc…) to gain a deeper understanding of the role of mean, median and mode as measures that can be used to efficiently describe the entire data set.

  • Develop Mathematical Reasoning by using multiple methods (logical reasoning, technology, computation, graphic comparisons, etc…)  when removing any number in the data set or adding a number to the data set to analyze and describe the effect that this has on the mean and median of that data set.

  • Facilitate meaningful mathematical discourse by having  students create meaningful data sets with real life context to compute mean, median and mode with context. Allow students time to discuss this data and what the mean, median and mode represents with either a partner or group.

  • Pose purposeful questions and tasks by creating discourse, such as “If I remove your lowest test score, how would that affect your overall grade for this course? Does a low test score cause an increase or a decrease in your overall grade? Explain a situation where dropping the lowest test score might not help a student’s grade.”

  • Promote procedural fluency by allowing students to review the steps of calculating mean, median and mode.

  • Facilitate meaningful mathematical discourse by allowing students to share and discuss their suggestions for how to differentiate between mean, median and mode (ex...median in driving is in the middle of the road and median in math is the middle number)

  • Use and connect mathematical representations by allowing students to use one or more technological apps to represent a data set and calculate 1-variable data analysis.

  • Implement tasks that promote reasoning and problem solving by providing students with multiple methods to model and describe the effect on mean and median when any number is added or removed from the data set. Allow for multiple opportunities and various real-world situations for students to discuss the effects of changing the mean and median.

Key Understandings

Misconceptions

  • Calculate mean, median, and mode

  • Understand the impact of inserting or deleting data has on the mean and median

  • Use technology to create data displays

  • Students will  think the median is the middle number in the order the data is presented and not order the data from least to greatest.

  • When calculating the mean students may input the data wrong using the incorrect order of operations

  • Students may think that when they delete a low number in their data set it will decrease the mean. 

OKMath Framework Introduction

Pre-Algebra Introduction

 

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