Illustrative Math Alignment: Grade 6 Unit 8

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. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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In this application of arithmetic, students analyze the changing population of bison in the Americas. Using real-world data and applying key math concepts, students will do some sophisticated analysis using basic skills.  These are the key math concepts covered: Place value Skip counting Doubling Data analysis Given the wide disparity in the population of bison over several centuries, students will be analyzing data in the millions but using place value to gain a clear understanding of the numbers involved. Skip counting will be used to analyze changes to populations, including patterns than involve doubling. Students will be actively engaged with the subject matter and will develop a mathematical mindset around data. This is an excellent preparation for the data analysis developed in upper elementary and middle school.

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.

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Topic

Sequences and Series

Definition

A finite series is the sum of the terms of a finite sequence.

Description

A finite series is a significant concept in mathematics, representing the sum of the terms of a finite sequence. This concept is essential in various mathematical and scientific applications, including statistics, finance, and computer science.

In real-world applications, finite series are used in financial calculations, such as determining the total amount of payments over a fixed period. They are also used in data analysis to find the sum of a dataset. Algebraically, a finite series can be expressed as  

Topic

Sequences and Series

Definition

A sequence is an ordered list of numbers that follow a particular pattern or rule.

Description

Sequences are fundamental concepts in mathematics, representing ordered lists of numbers that follow a specific pattern or rule. This concept is crucial in various mathematical applications, including algebra, calculus, and computer science.

Topic

Sequences and Series

Definition

A finite sequence is a sequence that has a limited number of terms.

Description

A finite sequence is a sequence with a specific number of terms, making it a crucial concept in the study of sequences and series. This concept is fundamental in various mathematical applications where the number of elements is limited, such as in statistics and computer science.

In real-world applications, finite sequences are used in data analysis, where datasets have a specific number of entries. They are also used in computer algorithms that process a fixed number of elements. Algebraically, a finite sequence can be represented as

Topic

Sequences and Series

Definition

An infinite sequence is a sequence that continues indefinitely without terminating.

Description

An infinite sequence is a fundamental concept in mathematics, representing a sequence that continues indefinitely without terminating. This concept is essential in various mathematical and scientific applications, including calculus and analysis.

In real-world applications, infinite sequences are used in mathematical modeling and simulations where processes continue indefinitely, such as in population dynamics or financial forecasting. Algebraically, an infinite sequence can be represented as  

Topic

Sequences and Series

Definition

A series is the sum of the terms of a sequence.

Description

Series are significant concepts in mathematics, representing the sum of the terms of a sequence. This concept is essential in various mathematical and scientific applications, including calculus, analysis, and financial modeling.

In real-world applications, series are used in financial calculations, such as determining the total amount of payments or investments over time. They are also used in data analysis to find the sum of a dataset. Algebraically, series can be represented in various forms, such as arithmetic series, geometric series, and more.

Topic

Sequences and Series

Definition

An infinite series is the sum of the terms of an infinite sequence.

Description

An infinite series is a significant concept in mathematics, representing the sum of the terms of an infinite sequence. This concept is essential in various mathematical and scientific applications, including calculus and analysis.

In real-world applications, infinite series are used in mathematical modeling and simulations where processes continue indefinitely, such as in signal processing or financial forecasting. Algebraically, an infinite series can be represented as 

Topic

Sequences and Series

Definition

A convergent series is a series whose terms approach a specific value as the number of terms increases.

Description

A convergent series is a critical concept in the study of sequences and series, where the sum of its terms approaches a finite limit as the number of terms increases. This concept is essential in various mathematical and scientific applications, including calculus and analysis.

Topic

Sequences and Series

Definition

A divergent series is a series whose terms do not approach a specific value as the number of terms increases.

Description

A divergent series is a significant concept in the study of sequences and series, where the sum of its terms does not approach a finite limit as the number of terms increases. This concept is essential in various mathematical and scientific applications, including calculus and analysis.

Topic

Sequences and Series

Definition

The binomial series is the expansion of a binomial raised to any integer power.

Description

The binomial series is a powerful tool in mathematics, particularly in the study of sequences and series. It represents the expansion of a binomial expression raised to any integer power, which is essential in various mathematical and scientific applications, including probability, algebra, and calculus.

Topic

Sequences and Series

Definition

The binomial theorem describes the algebraic expansion of powers of a binomial.

Description

The binomial theorem is a fundamental theorem in algebra that provides a formula for expanding binomials raised to any positive integer power. This theorem is essential in various mathematical disciplines, including algebra, calculus, and probability theory.

Topic

Sequences and Series

Definition

Pascal's Triangle is a triangular array of binomial coefficients.

Description

Pascal's Triangle is a fundamental concept in mathematics, representing a triangular array of binomial coefficients. This concept is essential in various mathematical and scientific applications, including combinatorics, algebra, and probability theory.

In real-world applications, Pascal's Triangle is used in probability calculations, particularly in binomial expansions and combinatorial problems. It is also used in computer science for algorithm design. Algebraically, the elements of Pascal's Triangle can be expressed as  

Topic

Sequences and Series

Definition

A recursive formula defines each term of a sequence using the preceding term(s).

Description

A recursive formula is a fundamental concept in mathematics, representing a way to define each term of a sequence using the preceding term(s). This concept is essential in various mathematical and scientific applications, including computer science and algorithm design.

Topic

Sequences and Series

Definition

An explicit formula for a sequence provides a direct way to calculate any term in the sequence.

Description

An explicit formula for a sequence is a mathematical expression that allows for the direct computation of any term in the sequence without needing to know the previous terms. This concept is fundamental in the study of sequences and series and is widely used in various mathematical applications.

Topic

Sequences and Series

Definition

The common difference is the difference between consecutive terms in an arithmetic sequence.

Description

The common difference is a key concept in arithmetic sequences, representing the consistent interval between consecutive terms. This concept is fundamental in understanding linear patterns and is widely used in various mathematical applications.

Topic

Sequences and Series

Definition

The common ratio is the ratio between consecutive terms in a geometric sequence.

Description

The common ratio is a fundamental concept in geometric sequences, representing the consistent factor by which each term is multiplied to obtain the next term. This concept is crucial in understanding exponential growth and decay, which are prevalent in various mathematical and scientific applications.

Topic

Sequences and Series

Definition

Summation notation is a mathematical notation used to represent the sum of a sequence of terms.

Description

Summation notation is a powerful tool in mathematics, representing the sum of a sequence of terms in a compact form. This concept is essential in various mathematical and scientific applications, including calculus, statistics, and computer science.

Topic

Sequences and Series

Definition

The Fibonacci sequence is a sequence where each term is the sum of the two preceding ones, starting from 0 and 1.

Description

The Fibonacci sequence is a famous sequence in mathematics, where each term is the sum of the two preceding ones, starting from 0 and 1. This sequence is significant in various mathematical and scientific applications, including computer science, biology, and art.

Topic

Sequences and Series

Definition

Triangular numbers are numbers that can be represented by an equilateral triangle.

Description

Triangular numbers are fundamental concepts in mathematics, representing numbers that can form an equilateral triangle. This concept is crucial in various mathematical applications, including algebra, geometry, and number theory.

In real-world applications, triangular numbers are used in combinatorial problems and in determining the number of connections in a network. They are also used in computer algorithms and game design. Algebraically, triangular numbers can be represented as  

Topic

Sequences and Series

Definition

Square numbers are numbers that are the square of an integer.

Description

Square numbers are fundamental concepts in mathematics, representing numbers that are the square of an integer. This concept is crucial in various mathematical applications, including algebra, geometry, and number theory.

In real-world applications, square numbers are used in area calculations, particularly in determining the area of squares. They are also used in computer algorithms and cryptography. Algebraically, square numbers can be represented as n2 , where n is an integer.

Topic

Sequences and Series

Definition

Graphs of arithmetic sequences form a linear graph on a coordinate plane.

Description

Graphs of arithmetic sequences are a visual tool used in mathematics to represent the terms of an arithmetic sequence on a coordinate plane. This concept is crucial for understanding linear patterns and relationships in sequences and series.

Topic

Sequences and Series

Definition

Graphs of geometric sequences visually represent the terms of a geometric sequence on a coordinate plane. These are nonlinear graphs.

Description

Graphs of geometric sequences are a visual tool used in mathematics to represent the terms of a geometric sequence on a coordinate plane. This concept is crucial for understanding exponential patterns and relationships in sequences and series.

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.

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.

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.