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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 8

Data Sets and Distributions

Lesson 1: Got Data?

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Definition--Measures of Central Tendency--Quartile Definition--Measures of Central Tendency--Quartile Quartile

Topic

Statistics

Definition

Quartiles divide a ranked data set into four equal parts.

Description

Quartiles are used to summarize data by dividing it into four parts, each representing a quarter of the data set. They provide insight into the spread and center of data, helping to identify the distribution and variability. Quartiles are used in box plots to visually represent data distribution, making them valuable in fields such as finance and research for analyzing data trends.

Data Analysis
Definition--Measures of Central Tendency--Geometric Mean Definition--Measures of Central Tendency--Geometric Mean Geometric Mean

Topic

Statistics

Definition

The geometric mean is the nth root of the product of n numbers, used to calculate average rates of growth.

Description

The geometric mean is particularly useful in finance and economics for calculating compound interest and growth rates. Unlike the arithmetic mean, it is appropriate for data sets with values that are multiplicatively related. For example, the geometric mean of 2, 8, and 32 is calculated as (2 × 8 × 32)1/3 = 8. In mathematics, the geometric mean is essential for understanding exponential growth and decay.

Data Analysis
Definition--Measures of Central Tendency--Population Mean Definition--Measures of Central Tendency--Population Mean Population Mean

Topic

Statistics

Definition

The population mean is a measure of central tendency that provides an average representation of a set of data.

Description

The Population Mean is an important concept in statistics, used to summarize data effectively. It is meant to represent the mean for a given statistic for an entire population. For example, the mean length of a salmon.

Data Analysis
Definition--Measures of Central Tendency--Sample Mean Definition--Measures of Central Tendency--Sample Mean Sample Mean

Topic

Statistics

Definition

The sample mean is the average of a sample, calculated by summing the sample values and dividing by the sample size.

Description

The sample mean is a measure of central tendency that provides an estimate of the population mean based on a sample. It is widely used in statistics for making inferences about populations from samples, playing a crucial role in hypothesis testing and confidence interval estimation. The sample mean is used in fields such as economics, biology, and psychology to analyze data and draw conclusions about larger populations.

Data Analysis
Definition--Measures of Central Tendency--Average Speed Definition--Measures of Central Tendency--Average Speed Average Speed

Topic

Statistics

Definition

Average speed is the total distance traveled divided by the total time taken.

Description

This concept finds application in areas such as physics, transport, and everyday scenarios like calculating travel time. For example, if a car travels 300 km in 3 hours, the average speed is Average Speed = 300 km / 3 hours = 100 km/h. Understanding average speed is key in mathematics as it helps contextualize rate and distance problems in real-life situations.

Data Analysis
Definition--Measures of Central Tendency--Weighted Mean Definition--Measures of Central Tendency--Weighted Mean Weighted Mean

Topic

Statistics

Definition

The weighted mean is the average of a data set where each value is multiplied by a weight reflecting its importance.

Description

The weighted mean is used when different data points contribute unequally to the final average. It is commonly applied in finance to calculate portfolio returns, in education to compute weighted grades, and in various fields where data points have different levels of significance. The weighted mean provides a more accurate representation of data by considering the relative importance of each value.

Data Analysis
Definition--Measures of Central Tendency--Weighted Average Definition--Measures of Central Tendency--Weighted Average Weighted Average

Topic

Statistics

Definition

A weighted average is an average that takes into account the relative importance of each value, calculated by multiplying each value by its weight and summing the results.

Description

The weighted average is used when different data points contribute unequally to the final average. It is commonly applied in finance to calculate portfolio returns, in education to compute weighted grades, and in various fields where data points have different levels of significance. The weighted average provides a more accurate representation of data by considering the relative importance of each value.

Data Analysis
Definition--Measures of Central Tendency--Average Definition--Measures of Central Tendency--Average Average

Topic

Statistics

Definition

The average is a measure of central tendency, calculated by dividing the sum of values by their count.

Description

In statistics, the average is crucial for analyzing data sets, revealing trends, and providing insight into overall performance. It’s applicable in various fields, from school grades to business metrics. For example, if a student scores 80, 90, and 100 on three exams, the average can be calculated as follows: Average = (80 + 90 + 100) / 3 = 90. The average is essential in math education as it forms a foundational concept for more advanced statistical analyses.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 12 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 12 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 12

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 1 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 1 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 1

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 2 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 2 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 2

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 3 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 3 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 3

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 4 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 4 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 4

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 5 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 5 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 5

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 6 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 6 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 6

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 8 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 8 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 8

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 9 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 9 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 9

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 10 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 10 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 10

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 11 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 11 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 11

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 13 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 13 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 13

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 7 Math Example--Charts, Graphs, and Plots--Reading and Interpreting Scaled Graphs--Example 7 Math Example--Charts, Graphs, and Plots-- Reading and Interpreting Scaled Graphs--Example 7

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Subtraction Facts to 100 and Data Analysis
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability

What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 1 Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, 1 Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 1

In this Investigation we explore uncertainty and randomness. This video is Segment 1 of a 4 segment series related to Data Analysis and Probability. Segments 1 and 2 are grouped together.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 3 Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, 3 Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 3

In this Investigation we look at real-world data involving endangered wolf populations. This video is Segment 3 of a 4 segment series related to Data Analysis and Probability. Segments 3 and 4 are grouped together.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Applications: Data Analysis Closed Captioned Video: Algebra Applications: Data Analysis Closed Captioned Video: Algebra Applications: Data Analysis

In this episode of Algebra Applications, students explore the dramatic events of 2008 related to the mortgage crisis. Brought about principally through mortgage defaults, the effect on the overall economy was severe. Yet, this situation offers an ideal case study for the exploration of key concepts in data analysis and probability. By exploring these questions students get a front row seat to the historical events of the world's largest economy.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Applications: Data Analysis, Segment 1: Introduction Closed Captioned Video: Algebra Applications: Data Analysis, 1 Closed Captioned Video: Algebra Applications: Data Analysis, Segment 1: Introduction

In this introductory segment students learn about the mortage crisis of 2008. In the process they get a brief introduction to what a mortgage is.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Applications: Data Analysis, Segment 2: What Is a Mortgage? Closed Captioned Video: Algebra Applications: Data Analysis, 2 Closed Captioned Video: Algebra Applications: Data Analysis, Segment 2: What Is a Mortgage?

The time value of money is at the basis of all loans. Students learn about the key factors that determine monthly mortgage payments and use the TI-Nspire to create an amortization table. This table is used throughout the rest of the program to explore different scenarios.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Applications: Data Analysis, Segment 3: What Is a What is a Subprime Mortgage? Closed Captioned Video: Algebra Applications: Data Analysis, 3 Closed Captioned Video: Algebra Applications: Data Analysis, Segment 3: What Is a What is a Subprime Mortgage?

Having learned the general features of a mortgage, students learn the specifics of a subprime mortgage. With this comes the notion of a credit score, and with credit scores come the probabilities for a loan default. Students use the amortization table to run probability simulations to determine possible loan defaults on subprime mortgages.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Applications: Data Analysis, Segment 4: What is an Adjustable Rate Mortgage? Closed Captioned Video: Algebra Applications: Data Analysis, 4 Closed Captioned Video: Algebra Applications: Data Analysis, Segment 4: What is an Adjustable Rate Mortgage?

Another factor in the mortgage crisis was the use of adjustable rate mortgages. Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration Closed Captioned Video: Algebra Applications: Linear Functions, 3 Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration

Linear Expressions, Equations, and Functions

Linear Exp
Special Functions and Applications of Linear Functions
Closed Captioned Video: Ratios and Rates: Rates from Data Closed Captioned Video: Ratios and Rates: Rates from Data Closed Captioned Video: Ratios and Rates: Rates from Data

Video Tutorial: Ratios and Rates: Rates from Data. In this video, we look at linear data sets that can be used to find the rate of change.

Ratios and Rates
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 10 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 10 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 10

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 9 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 9 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 9

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 8 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 8 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 8

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 7 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 7 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 7

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 6 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 6 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 6

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 5 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 5 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 5

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 4 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 4 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 4

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 3 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 3 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 3

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 2 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 2 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 2

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 1 Math Example--Charts, Graphs, and Plots--Analyzing Scatterplots: Example 1 Math Example--Charts, Graphs, and Plots-- Analyzing Scatterplots: Example 1

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Definition--Measures of Central Tendency--Probability Distribution Definition--Measures of Central Tendency--Probability Distribution Probability Distribution

Topic

Statistics

Definition

A probability distribution describes how the values of a random variable are distributed.

Description

Probability distributions are fundamental in statistics, providing a mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. They are used in various fields such as finance, science, and engineering to model uncertainty and variability. For instance, the normal distribution is a common probability distribution that describes many natural phenomena.

Data Analysis
Definition--Measures of Central Tendency--Outlier Definition--Measures of Central Tendency--Outlier Outlier

Topic

Statistics

Definition

The outlier is is an extreme value for a data set.

Description

The Outlier is an important concept in statistics. While it doesn't represent the average data set, it does set the range of extreme values in the data set. An outlier can be extremely large or small. 

In mathematics education, understanding outlier is crucial as it lays the foundation for more advanced statistical concepts. It allows students to grasp the significance of data analysis and interpretation. In classes, students often perform exercises calculating the mean of sets, which enhances their understanding of averaging techniques.

Data Analysis
Definition--Measures of Central Tendency--Normal Distribution Definition--Measures of Central Tendency--Normal Distribution Normal Distribution

Topic

Statistics

Definition

The normal distribution is a measure of central tendency that provides an average representation of a set of data.

Description

The Normal Distribution is an important concept in statistics, used to summarize data effectively. In real-world applications, the Normal Distribution helps to interpret data distributions and is widely used in areas such as economics, social sciences, and research.

Data Analysis
Definition--Measures of Central Tendency--Categorical Data Definition--Measures of Central Tendency--Categorical Data Categorical Data

Topic

Statistics

Definition

Categorical data refers to data that can be divided into specific categories or groups.

Description

Categorical data is essential for organizing and analyzing information that falls into distinct categories, such as gender, race, or product type. This type of data is often used in market research, social sciences, and public health studies to identify patterns and relationships between groups. In mathematics, understanding categorical data is crucial for interpreting bar charts, pie charts, and frequency tables.

Data Analysis
Definition--Measures of Central Tendency Definition--Measures of Central Tendency Measures of Central Tendency

Topic

Statistics

Definition

The measures of central tendency is a measure of central tendency that provides an average representation of a set of data.

Description

The Measures of Central Tendency is an important concept in statistics, used to summarize data effectively.

In real-world applications, the Measures of Central Tendency helps to interpret data distributions and is widely used in areas such as economics, social sciences, and research.

For example, if a data set consists of the values 2, 3, and 10, the mean is calculated as (2 + 3 + 10)/3 = 5.

Data Analysis
Worksheet: The Language of Math: Multiplication Equations, Worksheet 3 Worksheet: The Language of Math: Multiplication Equations, Worksheet 3 Worksheet: The Language of Math: Multiplication Equations, Worksheet 3

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
Numerical and Algebraic Expressions
Worksheet: The Language of Math: Multiplication Equations, Worksheet 1 Worksheet: The Language of Math: Multiplication Equations, Worksheet 1 Worksheet: The Language of Math: Multiplication Equations, Worksheet 1

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
Numerical and Algebraic Expressions
Worksheet: The Language of Math: Multiplication Equations, Worksheet 2 Worksheet: The Language of Math: Multiplication Equations, Worksheet 2 Worksheet: The Language of Math: Multiplication Equations, Worksheet 2

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
Numerical and Algebraic Expressions
Worksheet: The Language of Math: Multiplication Equations, Worksheet 4 Worksheet: The Language of Math: Multiplication Equations, Worksheet 4 Worksheet: The Language of Math: Multiplication Equations, Worksheet 4

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
Numerical and Algebraic Expressions