Expressions and Equations


  • Slope and House Construction

    Discover how math is required for quality construction when a Master Carpenter shares his experience and expertise. This video focuses on explaining slope as rise over run and shows how slope comes into play when building homes to take math out of the classroom and into real world problem solving. This resource is part of the Math at the Core: Middle School collection.

    Grades: 6-8
  • Commutative and Associative Properties of Addition

    Generate equivalent expressions using two additive properties. This video focuses on using the associative and commutative properties of addition to combine like terms, simplify expressions, and create equivalent expressions.

    This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

    Grades: 3-7
  • Scale City | Reviewing Ratios, Proportions, and Scale

    In this interactive, students put quarters into a virtual vending machine and solve 16 problems involving ratios and proportions in order to receive “treats.” In the accompanying classroom activity, small groups of students take turns solving the problems to see which group is quickest to finish the game. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-7
  • Scale City | Proportions and Music in Practice

    In this interactive, students explore the relationship between sound frequencies and the length of pipes on a pan flute. By answering questions about the values of ratios and completing a chart, students are introduced to the concept of an inverse proportional relationship. The accompanying activity helps students explore the mathematical relationships that exist among musical notes and their frequencies. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-7
  • Determining Surface Area with Unit Blocks

    Use your spatial reasoning skills to calculate the surface area when given a 3D figure. This video focuses on a right rectangular prism and shows you how unit blocks can help you visualize, then calculate the surface area. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers. This resource is part of the Math at the Core: Middle School collection.

    Grades: 5-7
  • Scale City | Proportions and Music in the Real World

    In this video—through footage of the calliope aboard the Belle of Louisville, a church pipe organ, and various instruments at a recording studio—students are introduced to the mathematical concept that the length of a musical pipe or a string has a proportional relationship with the sound it produces.  In the accompanying activity, stringed instruments are used to demonstrate the concept presented in the video. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-7
  • Scale City | Proportional Relationships Among Time, Distance, and Speed

    In this interactive, students compare the speed of the racehorse Man o’ War to other famous racehorses, a cheetah, a track star, and a middle school student. Students discover the direct proportional relationship between distance traveled in a set time and speed, and the inverse proportional relationship between speed and the time it takes to travel a set distance. In the accompanying activity, students complete a chart based on data from the interactive and make observations about the relationships that the data represent. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-7
  • Scale City | Proportional Relationships in the Real World

    In this video, students visit the Kentucky Horse Park where they are introduced to the question How are speed, time, and distance interrelated? The accompanying activity builds on a demonstration from the video of the length of Man o’ War’s stride versus the length of a person’s stride by allowing students to measure their own strides versus that of the great racehorse. This resource is part of the Math at the Core: Middle School Collection.

     

    Grades: 6-7
  • Scale City | Inverse Proportions and Shadows in the Real World

    In this video, students take a quick trip through the history of drive-in theaters and are then asked to consider the question, "What is the relationship between the size of an object’s shadow and the object’s distance from a light source?" In the accompanying classroom activity, students do a hands-on experiment about the size of their own shadows at different distances from a projector or other light source. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-7
  • Scale City | Inverse Proportions and Shadows in Practice

     In this interactive, students explore what happens to a figure’s shadow on a movie screen as the figure moves away from the projector. They also use approximate measurements to complete a chart of distance from light source versus height of shadow on the screen. As the chart is completed, students see how the relationships are represented graphically. The accompanying activity provides discussion questions for students to consider as they work through the interactive, as well as a chart for them to complete as they measure and compute values based on the interactive. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-7
  • Scientific Notation

    This animated Math Shorts video from UEN explains the term scientific notation and provides several examples in converting extreme numbers to and from scientific notation. It also demonstrates how to multiply numbers using scientific notation. In the accompanying classroom activity, students practice writing numbers in scientific notation and develop real-world problems for each other to solve. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-9
  • Bivariate Data and Analysis: Anthropological Studies

    Investigate how skeletal populations can help determine the impact of slavery on the height and health of African American males. This video focuses on the measurements and equations Mark Mack is using to explore relationships between the length of the bones in the leg and height while discussing how statistics is a useful tool to analyze data and make inferences taking math out of the classroom and into real world problem solving. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-8
  • Finding Patterns to Make Predictions

    Make predictions then explore the patterns found in everyday objects like stairs. This interactive exercise focuses on developing an equation to represent a mathematical rule and working with virtual manipulatives to visualize a concept, taking math out of the classroom and into the real world. This resource is part of the Math at the Core: Middle School collection.

    Grades: 3-8
  • Piano Tuning and Balancing Equations

    Examine how one innovator is working to improve the way concert pianos are designed and tuned. This video focuses on the balance that needs to occur in an ideally tuned piano key and explores how David Stanwood calculated the balance range through data analysis of measurements and ratios, taking math out of the classroom and into real world problem solving.
    Grades: 5-7
  • Valentine Cards: Exploring Relationships Between Variables

    Determine how many valentines will be exchanged depending on the number of students in each class. This interactive exercise focuses on examining data to find a pattern and extending the pattern until a rule can be realized, taking math out of the classroom and into the real world.
    Grades: 5-9
  • Balancing Scales To Solve Equations

    Predict the number of blocks you need to equal the weight of one bag and then test your theory. This interactive exercise focuses on using critical thinking skills to add and subtract items on the scales to achieve balance and visual problem solving. This resource is part of the Math at the Core: Middle School collection.

    Grades: 5-7
  • One-Variable Equations: How Much Did He Read?

    Visualize a word problem in multiple ways to develop your problem solving skills. This video focuses on converting a problem with fractions into a one-variable equation and alternately modeling it using unit blocks.

    This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

    Grades: 4-6
  • Distributive Property with Variables

    Model with algebra tiles to generate equivalent expressions. This video focuses on visualizing the distributive property.

    This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

    Grades: 6
  • Approximating Square Roots of Nonperfect Squares

    Visualize a strategy for approximating the square roots of nonperfect squares through modeling. This video focuses on a ratio, the number of extra tiles over the number of tiles for the next square that will give you a fractional approximation of the square root of a number. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers. This resource is part of the Math at the Core: Middle School collection.

    Grades: 8
  • Order of Operations

    Discover the importance of order of operations when solving an expression. This video focuses on implementing PEMDAS and demonstrates the reason we need order of operation by solving a single expression in three different, two incorrect, ways. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
    Grades: 4-6

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