Unit Rate

This comprehensive video tutorial serves as an intensive review for the ACT Math section, covering a wide array of topics crucial for high school students preparing for college entrance exams. The content is structured as a series of 31 practice problems that mimic the style and difficulty of actual ACT questions. It progresses through various mathematical domains including pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. The video adopts a pause-and-practice format, encouraging active participation where viewers attempt each problem before watching the detailed step-by-step solution. Key themes explored in this review include solving linear and quadratic equations, working with functions, understanding geometric properties of polygons and circles, applying trigonometric ratios (SOH CAH TOA) and identities, and analyzing statistical data. The video also places a strong emphasis on real-world application problems involving percentages, sales tax, discounts, and unit conversions. Particular attention is given to algebraic manipulation strategies, such as solving systems of equations and simplifying complex expressions, as well as test-taking tactics like identifying key information in word problems. For educators and students, this video is a valuable resource for standardized test preparation. It allows teachers to identify specific areas of weakness in student understanding by isolating problem types (e.g., if a student struggles with problem 10, they need more support with circle geometry). The step-by-step explanations model clear mathematical reasoning, demonstrating not just *how* to get the right answer, but *why* specific methods work. This makes it an excellent tool for flipped classrooms, homework support, or intensive boot-camp style review sessions prior to test dates.

This educational video provides a clear, step-by-step guide on how to calculate the three fundamental variables of motion: speed, distance, and time. Through a series of six progressive word problems, an animated teacher guides students through the formulas for each variable, demonstrating not just the arithmetic but also the importance of unit analysis and cancellation. The video utilizes the popular "DST triangle" mnemonic to help students memorize the relationship between the variables. The content is structured into three distinct sections, with two examples provided for each concept: calculating distance (Speed × Time), calculating speed (Distance ÷ Time), and calculating time (Distance ÷ Speed). Specific attention is given to defining each term—explaining speed as a scalar quantity, distance as total length, and time as duration—and verifying the correct units of measurement for the final answers. For educators, this resource serves as an excellent direct-instruction tool for upper elementary or middle school math and science classes. It effectively models problem-solving behaviors, such as identifying given values, selecting the correct formula, substituting numbers, and checking units. The video's pacing allows for "pause-and-solve" interactivity, making it ideal for introducing the concepts or reviewing them before a test.

This instructional math video bridges the gap between theoretical graphing concepts and real-world problem solving. It demonstrates how to interpret key features of linear graphs—specifically slope, x-intercepts, and y-intercepts—to answer practical questions about distance, profit, and physical measurements. The video uses three distinct scenarios to illustrate these concepts: a hiker walking home, an ice cream vendor seeking a profit, and a river's water level decreasing over time. The video focuses on three primary mathematical themes: (1) Understanding slope as a unit rate and using it for unit conversion (dimensional analysis), (2) Identifying the x-intercept as a "break-even point" where a value reaches zero, and (3) Recognizing the y-intercept as an initial value or starting condition (when x=0). It emphasizes distinguishing between mathematical values (like a negative slope) and their physical interpretations (speed is positive). For educators, this video is an excellent resource for Applied Algebra or Pre-Algebra classes. It moves beyond rote calculation to conceptual understanding, helping students see *why* we calculate slope or intercepts. The visual overlays showing dimensional analysis provide a strong cross-curricular link to science, while the business application offers a practical financial literacy moment. It effectively models how to extract hidden information from a visual representation.

This educational video demystifies the concepts of slope and intercepts by connecting them to real-world scenarios. Through two distinct examples—a hiking trip and trends in paper billing—the narrator demonstrates how abstract mathematical features on a graph translate into tangible information like speed, starting position, and rates of change over time. The video uses clear visuals and step-by-step calculations to bridge the gap between algebraic formulas and practical understanding. The content focuses on key algebraic themes including linear functions, calculating slope using the rise-over-run formula, and interpreting both x and y-intercepts in context. It specifically addresses how a positive slope represents an increase (hiking distance) while a negative slope represents a decrease (preference for paper bills), providing a well-rounded view of linear relationships. For educators, this video serves as an excellent tool for Algebra 1 or pre-algebra classrooms. It moves beyond rote calculation, encouraging students to analyze what specific points and lines on a graph actually mean. Teachers can use this to introduce the topic of linear modeling or as a reinforcement tool to help students struggling to extract meaning from word problems and their corresponding graphs.

This video provides a clear and practical guide to solving word problems involving average rate of change. It bridges the gap between abstract mathematical concepts and real-world scenarios by demonstrating that while real-life functions (like hiking speeds or fuel consumption) are rarely perfectly linear, the average rate of change allows us to calculate a single, useful rate over a specific interval. The narrator, Justin, walks viewers through three distinct examples: a distance-time graph, a fuel consumption graph, and a data table relating temperature to campground attendance. Key themes include identifying input and output variables, interpreting graphs of non-linear functions, understanding positive versus negative slopes in context, and calculating slope using the "rise over run" formula. The video specifically emphasizes how to handle fractional answers in word problems, teaching students to interpret them meaningfully (e.g., "2 campers for every 3 degrees" rather than "0.66 campers"). It also reinforces the difference between instantaneous speed at a single moment and average speed over a duration. For educators, this resource is excellent for Algebra I or II classes transitioning from linear equations to general functions. It serves as a vital conceptual building block for calculus by introducing the idea of secant lines. The clear visuals and step-by-step calculations make it an ideal tool for direct instruction, review, or as a flipped classroom assignment to help students grasp why slope formulas are relevant beyond straight lines.

This educational video provides a clear, step-by-step guide to understanding linear graphs, slope, and the critical distinction between dependent and independent variables. Narrated by Kaylee, the lesson begins by reviewing how to calculate slope using "rise over run" on a coordinate grid, demonstrating how a constant slope allows points to form a straight line. It then transitions into real-world applications, using examples like running speed and dog walking wages to show how linear relationships appear in everyday life.

This comprehensive video tutorial provides a thorough review of fundamental arithmetic concepts essential for middle school math success. It begins by grounding students in the basics of addition and subtraction using number lines to explain integer operations, before progressing to multi-digit column arithmetic with carrying and borrowing. The video systematically covers all four major operations—addition, subtraction, multiplication, and division—using varied strategies like standard algorithms, mental math tricks, and real-world analogies involving money to make abstract concepts concrete. Beyond basic operations, the video transitions into more complex topics including operations with decimals, long division leading to decimal answers, and operations with fractions having unlike denominators. The instructor demonstrates clear, step-by-step methods for finding common denominators and converting improper fractions to mixed numbers. The visual style mimics a blackboard, allowing students to follow the handwriting and procedural flow of each problem naturally. The final section of the video focuses on practical applications of percentages, specifically calculating tips and sales tax. It teaches powerful mental math strategies—such as finding 10%, 5%, and 1% separately to build up to complex percentages like 15% or 18%—which are invaluable life skills. This video serves as an excellent refresher for students transitioning to pre-algebra or for those needing remediation in core numeracy skills.

This clear, high-contrast instructional video provides a visual and algebraic explanation of slope, specifically focusing on the difference between positive, negative, zero, and undefined slopes. The narrator breaks down the fundamental definition of slope as "rise over run" (change in y divided by change in x) and uses dynamic visual diagrams to demonstrate how changes in rise and run affect the steepness of a line. A key feature of this video is its use of trigonometry (tangent/arctangent) to connect slope values to specific angles in degrees, offering a deeper conceptual understanding than standard Algebra 1 tutorials. The video culminates in a comprehensive "starburst" diagram that simultaneously displays lines with slopes of 0, 1, 2, 3, undefined, -1, -2, and -3, allowing students to visually compare steepness and direction relative to the origin. For educators, this resource serves as an excellent bridge between basic graphing concepts and more advanced trigonometric applications. It is particularly useful for visual learners who need to see how numerical slope values correspond to the physical "steepness" of a line. The clean blackboard style makes it easy to replicate the diagrams in class, and the inclusion of the angle calculations provides a natural extension for advanced students or geometry classes.

This educational video provides a clear and practical introduction to dimensional analysis, a mathematical method used to convert units of measurement. The narrator, Justin, breaks down the process of using known conversion rates to manipulate units, ensuring that unwanted units cancel out to reveal the desired result. Through step-by-step examples, viewers learn how to set up conversion chains for rates, such as changing miles per hour into feet per second. The video explores key themes of unit conversion, ratios, and algebraic thinking. It specifically covers two distinct types of problems: a standard rate conversion involving distance and time, and a more complex multi-variable problem involving currency exchange and mass. The visual presentation emphasizes the importance of placing units correctly in the numerator or denominator to achieve cancellation, a foundational skill for advanced math and science courses. For educators, this video serves as an excellent resource for bridging the gap between basic math skills and applied sciences like chemistry and physics. It demonstrates the "train track" or "fence post" method often used in stoichiometry. Teachers can use this video to introduce the concept of dimensional analysis, reinforce the importance of tracking units during calculation, or as a remediation tool for students struggling with multi-step word problems involving rates.

This instructional video demonstrates the "unitary method" for solving percentage word problems where the goal is to find the whole amount given a specific part and its corresponding percentage. The video walks through three distinct real-world scenarios: calculating the original price of a phone based on a discount amount, determining a weekly allowance based on savings, and finding a total school population based on the number of students playing sports. The content focuses on a consistent three-step algorithmic approach: identifying the known percentage and value, dividing to find the value of 1%, and then multiplying by 100 to find the whole (100%). This systematic repetition helps reinforce the logic behind reverse percentage calculations, moving beyond rote memorization of formulas to conceptual understanding of proportional reasoning. For educators, this video serves as an excellent direct instruction tool for introducing 6th and 7th-grade students to reverse percentage problems. It provides a clear visual model for setting up equations and executing mental math strategies (like dividing by 20 by splitting it into dividing by 2 and then 10). The real-life contexts make the abstract math relevant, demonstrating how these skills apply to shopping, budgeting, and analyzing statistics.

This instructional math video features Justin guiding viewers through the process of constructing linear equations from real-world word problems. Rather than solving given equations, the focus is on the critical skill of translating a text narrative into a mathematical model using the slope-intercept form ($y = mx + b$). The video uses three distinct examples—painting a fence, training for a marathon, and climbing a mountain—to demonstrate how to extract the necessary components from a story. Key themes include identifying the y-intercept as the "initial or starting value" and calculating the slope as the "rate of change." The video explicitly covers both negative slope (decreasing values, like painting a fence) and positive slope (increasing values, like running distance or climbing height). It breaks down the formula for slope ($change in y / change in x$) within the context of the word problems, helping students see the connection between abstract formulas and concrete situations. For educators, this video is an excellent resource for bridging the gap between arithmetic reasoning and algebraic modeling. It directly addresses the common student struggle of "where do I start?" when facing word problems by providing a consistent two-step framework: find the start (y-intercept) and find the rate (slope). This systematic approach helps demystify algebraic modeling and is highly applicable for 8th-grade math standards regarding functions and high school Algebra I curricula.

This instructional math video provides a structured approach to solving distance, rate, and time word problems using rational equations. The narrator, Justin, introduces the fundamental relationship between these variables ($t = d/r$) and outlines a clear four-step process for tackling these often-confusing problems: filling in a data table, setting up the appropriate equation, solving for the unknown, and interpreting the answer in the context of the original question. The video explores key algebraic themes including modeling real-world scenarios, manipulating rational expressions, and solving both linear and quadratic equations that arise from these models. It specifically addresses common scenarios like traveling "with the wind" versus "against the wind," teaching students how to mathematically represent these external forces by adding to or subtracting from a base rate. For educators, this video is an excellent resource for Algebra 1 or Algebra 2 classrooms. It scaffolds complex word problems into manageable visual components, helping students organize their thinking. The step-by-step walkthroughs of two distinct examples—one resulting in a linear equation solved via cross-multiplication and another resulting in a quadratic solved via the LCM method—provide a comprehensive model for students to follow in their own practice.