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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 9

Putting it All Together

Lesson 1: Fermi Problems

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topics
Math Video Definitions Collection: Linear Expressions, Functions, and Equations Math Video Definitions Collection: Linear Expressions, Functions, and Equations

Overview

This collection aggregates all the video definitions around the topic of Linear Expressions, Functions, and Equations terms and vocabulary. There are a total of 34 videos. This collection of resources is made up of downloadable MP4 files that you can easily incorporate into a presentation.

 

 

 

Slope-Intercept Form, Applications of Linear Functions, Graphs of Linear Functions, Point-Slope Form, Slope, Standard Form, Solving Systems of Equations, Proportions, Data Analysis, Variable Expressions, Functions and Their Inverses, Special Functions, Polynomial Expressions and Numerical Expressions
Video Definition 26--Linear Function Concepts--Correlation Coefficient Video Definition 26--Linear Function Concepts--Correlation Coefficient Video Definition 26--Linear Function Concepts--Correlation Coefficient

This is part of a collection of math video definitions related to to the topic of linear expressions, equations, and functions. Note: The download is an MP4 video.

Data Analysis
Video Definition 25--Linear Function Concepts--Linear Regression Video Definition 25--Linear Function Concepts--Linear Regression Video Definition 25--Linear Function Concepts--Linear Regression

This is part of a collection of math video definitions related to to the topic of linear expressions, equations, and functions. Note: The download is an MP4 video.

Data Analysis
Video Definition 24--Linear Function Concepts--Least Squares Regression Line Video Definition 24--Linear Function Concepts--Least Squares Regression Line Video Definition 24--Linear Function Concepts--Least Squares Regression Line

This is part of a collection of math video definitions related to to the topic of linear expressions, equations, and functions. Note: The download is an MP4 video.

Data Analysis
Video Definition 23--Linear Function Concepts--Scatter Plot Video Definition 23--Linear Function Concepts--Scatter Plot Video Definition 23--Linear Function Concepts--Scatter Plot

This is part of a collection of math video definitions related to to the topic of linear expressions, equations, and functions. Note: The download is an MP4 video.

Data Analysis
Segmented bar graph Instructional Resource--Segmented Bar Graphs Instructional Resource | Constructing a Segmented Bar Graph

This tutorial goes over the construction of a segmented bar graph, along with how it differs from other chart types.

—PRESS PREVIEW TO VIEW THE ACTIVITY— To see the complete collection of Instructional Resources, click on this link.

Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Data Analysis
Math in the News Math in the News: Issue 120--Will Avatar Repeat? Math in the News: Issue 120 | Will Avatar Repeat?

December 2022. In this issue of Math in the News we look at box office data for he new Avatar sequel. Will it have the same success?

—PRESS PREVIEW TO SEE THE SLIDE SHOW— This is part of the Math in the News collection. To see the complete collection, click on this link.

Note: The download is a PPT file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Data Gathering and Data Analysis
Math in the News: Issue 94--Winter's Impact on Florida's Orange Crop Math in the News: Issue 117--Box Office Hits and Misses Math in the News: Issue 117 | Box Office Hits and Misses

December 2022. In this issue of Math in the News we look at box office hits and misses from Disney. The House of Blockbosters every now and then misfires. It's useful to analyze box office data to see what we can learn from the hits and misses. 

—PRESS PREVIEW TO SEE THE SLIDE SHOW— This is part of the Math in the News collection. To see the complete collection, click on this link.

Note: The download is a PPT file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Data Analysis
Definition--Charts and Graphs--Categorical Data Definition--Charts and Graphs--Categorical Data Definition--Charts and Graphs--Categorical Data

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Continuous Data Definition--Charts and Graphs--Continuous Data Definition--Charts and Graphs--Continuous Data

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Discrete Data Definition--Charts and Graphs--Discrete Data Definition--Charts and Graphs--Discrete Data

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Histogram Definition--Charts and Graphs--Histogram Definition--Charts and Graphs--Histogram

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Two-Way Frequency Table Definition--Charts and Graphs--Two-Way Frequency Table Definition--Charts and Graphs--Two-Way Frequency Table

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Joint Frequencies Definition--Charts and Graphs--Joint Frequencies Definition--Charts and Graphs--Joint Frequencies

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Frequency Table Definition--Charts and Graphs--Frequency Table Definition--Charts and Graphs--Frequency Table

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Scaled Pictograph Definition--Charts and Graphs--Scaled Pictograph Definition--Charts and Graphs--Scaled Pictograph

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Pictograph Definition--Charts and Graphs--Pictograph Definition--Charts and Graphs--Pictograph

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Stem-and-Leaf Plot Definition--Charts and Graphs--Stem-and-Leaf Plot Definition--Charts and Graphs--Stem-and-Leaf Plot

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Charts and Graphs--Scatterplot Definition--Charts and Graphs--Scatterplot Definition--Charts and Graphs--Scatterplot

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Math Example--Combinatorics--Factorial Expressions: Example 1 Math Example--Combinatorics--Factorial Expressions: Example 1 Math Example--Combinatorics--Factorial Expressions: Example 1

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

Data Analysis and Combinatorics
Instructional Resource: Quadratic Regression on Desmos Instructional Resource: Quadratic Regression on Desmos INSTRUCTIONAL RESOURCE: Tutorial: Quadratic Regression on Desmos

In this tutorial we walk students through the steps of doing a quadratic regression on a Desmos graphing calculator. The steps include showing how to create pseudo-quadratic data on a spreadsheet.

This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link. 

Quadratic Equations and Functions and Data Analysis
Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 5 Math Example--Charts, Graphs, and Plots--Estimating the Line of Best Fit: Example 5 Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 5

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

Point-Slope Form, Slope-Intercept Form and Data Analysis
Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 4 Math Example--Charts, Graphs, and Plots--Estimating the Line of Best Fit: Example 4 Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 4

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

Point-Slope Form, Slope-Intercept Form and Data Analysis
Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 3 Math Example--Charts, Graphs, and Plots--Estimating the Line of Best Fit: Example 3 Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 3

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

Point-Slope Form, Slope-Intercept Form and Data Analysis
Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 2 Math Example--Charts, Graphs, and Plots--Estimating the Line of Best Fit: Example 2 Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 2

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

Point-Slope Form, Slope-Intercept Form and Data Analysis
Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 1 Math Example--Charts, Graphs, and Plots--Estimating the Line of Best Fit: Example 1 Math Example--Charts, Graphs, and Plots-- Estimating the Line of Best Fit: Example 1

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

Slope-Intercept Form and Data Analysis
Video Tutorial: Line of Best Fit Video Tutorial: Line of Best Fit Video Tutorial: Line of Best Fit

This video looks at the Line of Best Fit. A real-world data set is analyzed, from which a linear function in slope-intercept is derived. Students are shown how to find the line of best fit using a TI graphing calculator. Strategies for estimating the line of best fit are also explored.

Slope-Intercept Form and Data Analysis
Math in the News: Issue 116: The 2021 Olympics Math in the News: Issue 116: The 2021 Olympics Math in the News: Issue 116: The 2021 Olympics

August 2021. In this issue of Math in the News we look at various charts and statistics about the Tokyo Olympics. Students are shown a series of charts and are then asked questions to encourage them to analyze the data. This is an excellent back-to-school activity with the focus on real-world data.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Data Analysis
INSTRUCTIONAL RESOURCE: Algebra Application: The Rise of K-Pop INSTRUCTIONAL RESOURCE: Algebra Application: The Rise of K-Pop INSTRUCTIONAL RESOURCE: Algebra Application: The Rise of K-Pop

In this Algebra Application, students examine the music industry, specifically the rise of Korean pop music, or K-Pop. Using industry data students examine tables and graphs of categorical data before identifying possible functional relationships. A mathematical model is developed to explore the relationship between viral videos and sales. Topics covered: Mathematical modeling, Linear regression, Categorical data, Functions.

Applications of Linear Functions and Data Analysis
INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable? INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable? INSTRUCTIONAL RESOURCE: Algebra Application: When Will Space Travel Be Affordable?

In this Algebra Application, students examine the budding industry of commercial space travel. Using data from the Bureau of Transportation Statistics, students build a mathematical model from historical airfare data. This model is used to predict when commercial space travel will become affordable. This also includes a discussion of inflation-adjusted costs and the future value of money. Topics covered: Mathematical modeling, Linear regression, Exponential functions, The time value of money.

Applications of Exponential and Logarithmic Functions, Applications of Linear Functions and Data Analysis
INSTRUCTIONAL RESOURCE: Algebra Application: Why Are Receipts So Long? INSTRUCTIONAL RESOURCE: Algebra Application: Why Are Receipts So Long? INSTRUCTIONAL RESOURCE: Algebra Application: Why Are Receipts So Long?

In this Algebra Application, students gather data to study the lengths of paper receipts. They also learn to estimate the total number of receipts produced worldwide using industry data. From this they can study the environmental impact of having to produce so many paper receipts. The math topics covered include: Measures of central tendency (specifically the mean), Scientific notation, Rates, Converting different units. The culminating activity is for students to make a persuasive case to retailers about finding alternatives to paper receipts, using the data they gathered and analyzed. This is a great back-to-school activity for middle school or high school students. A relevant real-world application allows them to review math concepts.

Laws of Exponents and Data Analysis
Definition--Measures of Central Tendency--Variance Definition--Measures of Central Tendency--Variance Variance

Topic

Statistics

Definition

Variance is a measure of the dispersion of a set of values, calculated as the average of the squared deviations from the mean.

Description

Variance quantifies the degree of spread in a data set, providing insight into the variability of data points around the mean. It is a fundamental concept in statistics, used in fields such as finance, research, and engineering to assess risk and variability. A high variance indicates greater dispersion, while a low variance suggests that data points are closer to the mean.

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
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--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--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--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--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--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--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--Lower Quartile Definition--Measures of Central Tendency--Lower Quartile Lower Quartile

Topic

Statistics

Definition

The lower quartile (Q1) is the median of the lower half of a data set, representing the 25th percentile.

Description

The lower quartile is a measure of position, indicating the value below which 25% of the data falls. It is used in conjunction with other quartiles to understand the distribution and spread of data. In real-world applications, the lower quartile is used in finance to assess the performance of investments and in education to evaluate student achievement levels.

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

Topic

Statistics

Definition

The upper quartile (Q3) is the median of the upper half of a data set, representing the 75th percentile.

Description

The upper quartile is a measure of position that indicates the value below which 75% of the data falls. It is used in conjunction with other quartiles to understand the distribution and spread of data. In real-world applications, the upper quartile is used in finance to assess investment performance and in education to evaluate student achievement levels.

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

Topic

Statistics

Definition

The interquartile range (IQR) is the range between the first and third quartiles, representing the middle 50% of a data set.

Description

The IQR is a measure of statistical dispersion, indicating the spread of the central portion of a data set. It is particularly useful for identifying outliers and understanding the variability of data. In real-world applications, the IQR is used in finance to assess investment risks and in quality control to monitor process stability.

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

Topic

Statistics

Definition

A symmetric distribution is a probability distribution where the left and right sides are mirror images of each other.

Description

Symmetric distributions are characterized by data that is evenly distributed around the mean, resulting in a balanced, mirror-image shape. The most common symmetric distribution is the normal distribution, which is widely used in statistics for modeling natural phenomena. Symmetric distributions are important for statistical inference, as many statistical tests assume data is symmetrically distributed.

Data Analysis
Definition--Measures of Central Tendency--Box-and-Whisker Plot Definition--Measures of Central Tendency--Box-and-Whisker Plot Box-and-Whisker Plot

Topic

Statistics

Definition

A box-and-whisker plot is a graphical representation of data that displays the distribution through quartiles.

Description

Box-and-whisker plots are useful for visualizing the spread and skewness of a data set, highlighting the median, quartiles, and potential outliers. They are particularly valuable in comparing distributions across different groups. In real-world applications, box plots are used in quality control processes and in analyzing survey data to identify trends and anomalies.

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

Topic

Statistics

Definition

Discrete data consists of countable values, often represented by whole numbers.

Description

Discrete data is commonly used in situations where data points are distinct and separate, such as the number of students in a class or the number of cars in a parking lot. It is crucial for fields like computer science, where discrete structures and algorithms are fundamental. In mathematics, discrete data is used in probability theory and combinatorics, helping to solve problems involving permutations and combinations.

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

Topic

Statistics

Definition

Continuous data is numerical data that can take any value within a range.

Description

Continuous data is vital for representing measurements such as height, weight, and temperature, which can assume an infinite number of values within a given range. In real-world applications, continuous data is used in fields like engineering, physics, and economics to model and predict outcomes. Understanding continuous data is essential for performing calculations involving integrals and derivatives in calculus.

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

Topic

Statistics

Definition

A skewed distribution is a probability distribution that is not symmetric, with data tending to cluster more on one side.

Description

Skewed distributions occur when data is not evenly distributed around the mean, resulting in a longer tail on one side. Skewness can be positive (right-skewed) or negative (left-skewed), affecting the interpretation of data and statistical measures such as the mean and median. Skewed distributions are common in real-world data, such as income levels and test scores, where extreme values can influence the overall distribution.

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

Topic

Statistics

Definition

A histogram is a graphical representation of data distribution using bars of different heights.

Description

Histograms are used to visualize the frequency distribution of continuous data, making it easier to identify patterns and trends. They are widely used in fields such as economics, biology, and engineering to analyze data distributions and detect anomalies. In mathematics, histograms are essential for understanding probability distributions and statistical inference.

Data Analysis
Definition--Measures of Central Tendency--Median of an Odd Data Set Definition--Measures of Central Tendency--Median of an Odd Data Set Median of an Odd Data Set

Topic

Statistics

Definition

The median of an odd data set is one of the terms in the data set.

Description

The Median is the middle term of a data set. If the data set consists of an odd number of terms, no matter how many terms there are, the Median will be the middle term of that set.

In mathematics education, understanding median of an odd data set 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