Illustrative Math Alignment: Grade 7 Unit 9

This is a collection of Holiday-Themed math activities. 

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The collection of definitions on the topic of circles provided by Media4Math is an invaluable resource for students and educators alike. This comprehensive set includes essential terms such as radius, diameter, circumference, chord, and tangent, each explained with clarity and precision. Understanding these fundamental concepts is crucial for students as they form the building blocks for more advanced studies in geometry and algebra.

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The Fractions definitions collection from Media4Math is an invaluable resource for students and educators aiming to master or teach the fundamental concepts of fractions. This comprehensive set includes 20 essential terms, each presented as a downloadable PNG image card, making it easy to integrate into classroom presentations or study materials.

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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.

Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river’s length to its straight-line distance tell us? In this segment the geological forces that account for a river’s motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

Description

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

The following section reviews the basics of algebra tiles. Use this material as background material, and also as a supplement to the video series.

Video Tutorial: Integers: Variable Expressions with Integers. In this video, students simplify various variable expressions that use integers. A

This is part of a series of videos on the topic of Integers. This includes defining integers, modeling integers, integer operations, and integer expressions.

The following section includes background information on integers (and also rational numbers). Refer to this section as you view the videos, or as review material afterward.

Video Tutorial: Ratios: Fraction-Percent Conversion. In this video learn how to convert percents to fractions to simplify percent operations.

This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. 

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Video Tutorial: Ratios and Proportions: Scale Drawings. In this video, we look at the properties of similar figures and use proportions to find lengths of corresponding sides.

Video Tutorial: Ratios and Proportions: Solving Proportions. In this video, we solve proportion problems algebraically.

Video Tutorial: Ratios and Proportions: What are Proportions?. In this video, we solve proportion problems using equivalent ratios.

Video Tutorial: Ratios and Rates: Converting Measurement Units. In this video, we show how to use conversion rates to convert from one unit of measurement to another. Students are shown how to create a conversion rate.

Video Tutorial: Ratios and Rates: Rates and Slopes of Lines. In this video we connect the concept of rate of change for a set of linear data to the concept of slope. We use the slope formula to find the rate of change.

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.

Video Tutorial: Ratios and Rates: Ratios as Decimals. In this video, students explore ratios whose terms are decimals. Students are shown techniques for simplifying these types of ratios in ;the context of solving real-world ratio problems.

Video Tutorial: Ratios and Percents: Calculating Percents. In this video, students will see the relationship between ratios, proportions, and percents. A percent formula is derived and used to solve several real-world percent problems.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

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Circles

Definition

An arc length is the distance along the curved line making up the arc.

Description

The arc length is a crucial concept in geometry, particularly when dealing with circles. It is calculated using the formula 

L = rθ

Topic

Circles

Definition

The area of a circle is the space contained within its circumference, calculated as 

A = πr2

Description

The area of a circle is a fundamental concept in geometry, representing the space enclosed by the circle's boundary. This concept is widely applicable in fields such as physics, engineering, and design, where understanding the area is crucial for tasks like calculating material quantities or designing circular components. The formula 

A = πr2 

Topic

Circles

Definition

The center of a circle is the point equidistant from all points on the circle.

Description

The center of a circle is a pivotal concept in geometry, serving as the reference point from which the radius is measured. It is crucial in defining the circle's position in a plane and is used in various applications such as navigation, where the center can represent a central point of rotation or balance. In mathematical terms, the center is often denoted as the point (h , k) in the Cartesian coordinate system, where all points on the circle satisfy the equation 

Topic

Circles

Definition

A chord is a line segment with both endpoints on the circle.

Topic

Circles

Definition

A circle is a set of all points in a plane equidistant from a given point, the center.

Description

The circle is one of the most fundamental shapes in geometry, characterized by its symmetry and uniformity. It is used extensively in various fields, including engineering, design, and astronomy, where its properties are applied to create wheels, gears, and orbits. Mathematically, a circle is defined by its center and radius, and its equation in a plane is 

(x − h)2 + (y − k)2 = r2 

Topic

Circles

Definition

A circle inscribed in a square touches all four sides of the square at exactly one point each.

Topic

Circles

Definition

An inscribed circle in a triangle is tangent to each of the triangle's sides.

Topic

Circles

Definition

Circles on a coordinate plane are defined by their center coordinates and radius.

Description

Understanding circles on a coordinate plane is essential for analyzing geometric shapes in a mathematical context. This concept is widely used in computer graphics, navigation systems, and physics simulations, where precise positioning and movement of circular objects are required. The standard equation of a circle in the coordinate plane is 

(x − h)2 + (y − k)2 = r2

Topic

Circles

Definition

A circular arc is a portion of the circumference of a circle.

Description

Circular arcs are segments of a circle's circumference, used extensively in design, architecture, and engineering to create curved structures and paths. The length of an arc is determined by the central angle and the circle's radius, calculated using the formula 

L = rθ

Topic

Circles

Definition

Circular composite figures are shapes that include circles or parts of circles combined with other geometric figures.

Topic

Circles

Definition

Circular cross-sections are the intersections of a plane with a solid that result in a circle.