Illustrative Math Alignment: Grade 7 Unit 9

This is a collection of Holiday-Themed math activities. 

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This collection of math examples on Ratios and Rates from Media4Math offers a comprehensive resource for students to develop essential mathematical skills. Comprising 32 carefully curated examples, the collection increases in complexity, allowing learners to progress from basic concepts to more challenging applications. Each example utilizes visual models, which serve to simplify the understanding of ratios and rates, making abstract ideas more tangible.

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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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Data Analysis

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Equations

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This segment explores the impact of colony collapse disorder on honey production using statistical data. It introduces box and whisker plots and the calculation of mean as statistical tools to analyze honey yields. Key vocabulary includes colony collapse disorder, box plot, and mean. Applications include modeling bee population declines and their broader ecological and agricultural implications.

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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.

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Percents

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The video explores converting fractions to percents for simplified calculations. Examples include determining cargo contents, rose sales, and motorcycle proportions. Fraction-percent equivalence simplifies arithmetic and provides quick insights into ratios and totals. Applications include logistics, commerce, and urban planning.

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.

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Ratios

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The video explains how proportions are used to create scale drawings, ensuring geometric figures remain proportional. Examples include finding dimensions in similar triangles, scaling architectural models, and solving geometric problems. The concept of proportional relationships is key to accurate scaling.

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Ratios

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This video focuses on solving proportions algebraically, converting them into equations to solve real-world problems. Examples include predator-prey ratios, scaling pizza dough recipes, and creating shades of paint. The video demonstrates methods for handling terms in denominators and simplifying ratios to whole numbers.

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Ratios

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Proportions are explained as equivalent ratios used to solve real-world problems. Examples include matching juice mixtures and adjusting recipes. The video uses ratio tables and number lines to scale ratios proportionally in practical applications.

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Ratios

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This video covers converting units using rates, with examples like speed conversion, currency exchange, and calculating seconds in a year. It emphasizes multiplication by conversion rates to transition between units effectively.

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Ratios

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Rates are linked to slopes in linear functions. The video explores calculating rates of change for graphs of speed, savings growth, and loan repayment. It highlights using the slope formula to interpret and solve practical problems.

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Ratios

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This video demonstrates calculating rates from data sets, focusing on patterns like distance-time relationships and wages. Examples include determining car speeds, hourly wages, and unit costs of gasoline. Data tables are used to visualize and compute rates.

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Ratios

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The video explores working with ratios involving decimals, such as finding unit costs for salmon or recycling rates. Scientific notation and multi-step conversions are used to calculate speeds of spacecraft like Voyager I.

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Ratios

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Ratios are connected to percentages in this video. Examples include finding percentages of colored socks or non-green items in collections. It develops a formula for converting part-to-whole ratios into percentages.

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Ratios

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The video covers practical applications of ratios for measuring slopes of roofs and ramps. Examples include comparing roof pitches, calculating base lengths of roofs, and determining ramp heights. Ratios provide clarity for gradual slopes.

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Ratios

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This video explains generating and comparing equivalent ratios. Examples include simplifying fractions, determining similarity in geometric shapes, and integrating multiple ratios into a comprehensive ratio. Applications extend to geometry and proportional reasoning.

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Ratios

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This video focuses on ratios written with fractions, showing how to convert fractional ratios into whole-number ratios by eliminating denominators. Applications include recipes and ensuring proportions are maintained in measurements. It emphasizes mathematical manipulation to align ratios with practical uses.

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Ratios

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This video introduces rates, a type of ratio comparing different units, such as distance over time (speed) or dollars per hour (wage). Examples demonstrate calculating rates and converting units. Applications include measuring efficiency and performing unit conversions.

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Ratios

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Ratios are compared to fractions, emphasizing differences between part-to-part and part-to-whole relationships. Examples include finding fractions of subsets within a collection and modeling classroom demographics. The video highlights deriving fractional equivalents from given ratios.

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Ratios

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The video explains ratios involving more than two items, such as 1:3:4, and how they encompass multiple pairwise ratios. Applications include recipes where ingredients are combined in specific proportions. It demonstrates working forward and backward with ratios to identify components or adjust quantities proportionally.

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Ratios

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The video focuses on unit rates, where the denominator equals one. It includes practical examples like finding the cost per pound of bananas or determining hourly wages. Applications extend to conversions and scaling calculations for various real-world tasks.

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Ratios

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The video showcases visual representations like tape diagrams, snap cubes, and grids to solve ratio problems. It includes examples such as determining quantities in coin collections and paint mixtures. Applications involve modeling real-world problems using clear, visual methods.

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Ratios

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This video illustrates converting ratios to percents using visual aids like area models and grids. Examples include determining percentages of colored eggs, fruit types, and combinations of colored lights.

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Ratios

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This video introduces the concept of ratios, which describe relationships between quantities. Key concepts include writing ratios in different forms (e.g., 2:3, 2/3, and 2 to 3) and simplifying ratios. It also covers part-to-part ratios and part-to-whole ratios using examples like sports balls and colored shapes. Applications include categorizing objects and exploring numerical relationships in sets.

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Circles

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

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

L = rθ

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Circles

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

A = πr2

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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 

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Circles

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

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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 

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Circles

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

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Circles

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

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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 

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Circles

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

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Circles

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

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Circles

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

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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

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Circles

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

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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

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Circles

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

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Circles

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