Math at the Core: Middle School

Grade 8


  • Volume of a Cone

    Watch an animated demonstration of finding the volume of a cone and cylinder with the same base and height in this video from KCPT. In the accompanying classroom activity, students estimate the relative volume of a cone and cylinder with the same base and height. They test their estimates by filling the cone and pouring the contents into the cylinder and then use the cylinder volume formula as a basis for predicting the cone volume formula. To get the most from the lesson, students should know the formulas for the area of a circle and volume of a cylinder.

    Grades: 6-8
  • Translations and Reflections

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    Watch an animated demonstration of translating and reflecting a triangle on the coordinate plane in this video from KCPT. In the accompanying classroom activity, students watch the video and then consider the effect of translating and reflecting on the coordinates of the vertices of the triangle. Next, they draw translations and reflections of a triangle and identify the number of units and direction of translation as well as the lines of reflection in classmates drawings. To get the most from the lesson, students should be comfortable graphing points on the coordinate plane. Prior exposure to reflection is helpful.

    Grades: 8
  • Rotation and Dilation

    In this video from KCPT, watch an animated demonstration of rotating and dilating a triangle on the coordinate plane. In the accompanying classroom activity, students watch the video; draw rotations and dilations of a triangle; and identify center of rotation, angle of rotation, and scale factors in classmates drawings. To get the most from the lesson, students should be comfortable graphing points on the coordinate plane and reproducing a drawing of a geometric shape at a different scale. Prior exposure to rotation and dilation is helpful.

    Grades: 8-12
  • Geometry of Shapes in Kapa Design

    Explore the beauty of geometrical shapes and find the patterns that a Hawaiian kapa quilt maker incorporates into her designs in this video from the Center for Asian American Media. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-8,13+
  • Pythagorean Theorem in Kapa Design

    Listen to a master quilt maker discuss the relationship between art and mathematics as she demonstrates how the Pythagorean theorem is an important part of the pattern design process in this video from the Center for Asian American Media. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-8,13+
  • Hiking Mt. Majestic: The Pythagorean Theorem to the Rescue

    Learn how the Pythagorean theorem can help you calculate the distance of a hike through the mountains. This video focuses on breaking down an irregular figure into a series of right triangles so you can calculate the actual distance of the hike, then use similar steps to calculate the distance of the hike at Perilous Peak to compare the two hiking adventures.

    This media gallery 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: 7-8
  • Applying the Pythagorean Theorem

    In this video, watch an animated demonstration of using the Pythagorean theorem to find an unknown side of a right triangle. In the accompanying classroom activity, students solve problems in which they apply the Pythagorean theorem to find the sides of right triangles and to determine whether a set of triangle sides form a right triangle. To get the most from this lesson, students should be comfortable using a calculator to find square roots. They should also have experience solving equations involving an unknown square.

    Grades: 8
  • Applying the Pythagorean Theorem

    In this video, learn how using the Pythagorean theorem can help people solve real-world problems involving distances. In the accompanying classroom activity, students develop their problem-solving, spatial reasoning, and geometry skills by putting the Pythagorean theorem to use. After a brief discussion about how to use the theorem to find the distance between two points on a coordinate grid, students partner up and play a game in which they generate (and then calculate the distance between) two or more points on the grid. As the game increases in complexity, students begin working in all quadrants and begin identifying multiple triangles that they can use to determine the distance between points.

    Grades: 8
  • Football and the Pythagorean Theorem: There's Math in Sports?

    Explore how the Pythagorean theorem can be used to determine the distance that a pass and a kick in football actually travel in this interactive from Alabama Public Television.

    Grades: 6-8,13+
  • Equivalent Expressions Using Exponents

    Apply your critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to get you to recognize patterns and determine a rule.

    This resource is part of the Math at the Core: Middle School collection.

    Grades: 8-9
  • Comparing Powers of 10

    Use powers of 10 to investigate scientific notation. This interactive exercise focuses on determining which of a series of numbers written in scientific notation is larger and by what magnitude then you need to use your critical thinking skills to determine methods for general cases.

    This resource is part of the Math at the Core: Middle School collection.

    Grades: 6-8
  • Meatballs: Volumes of Spheres and Cylinders

    Use your problem solving skills to find out if the pot will overflow when Dan adds meatballs to his pasta sauce. This interactive exercise focuses on using the volume equations for cylinders and spheres to figure out the multistep problem of how many meatballs it would take to fill the space left in the pot.

    This resource is part of the Math at the Core: Middle School collection.

    Grades: 8-9
  • You Pour, I Choose: Volumes of Cylinders

    Compare the volume of varied cylindrical glasses filled to different heights. This interactive exercise focuses on using what you know about cylinders to make a prediction about their volume and then requires calculating the actual volume to see if your prediction was accurate.

    This resource is part of the Math at the Core: Middle School collection.

    Grades: 8-9
  • Popcorn Picker: Volumes of Solid Shapes

    Experiment with the volume of two cylinders made from the same size paper. This interactive exercise focuses on using what you know about cylinders to make a prediction about their volume and then requires calculating the actual volume to see if your prediction was accurate.

    This resource is part of the Math at the Core: Middle School collection.

    Grades: 8-9
  • The Lowdown | Time for A Raise? What You Need to Know About the Minimum Wage

    Explore the numbers at stake in the debate over raising federal minimum wage in this interactive from KQED. The interactive compares nominal and real wages adjusted for inflation and how minimum wage rates differ throughout the country. In the accompanying classroom activity, students graph the data to find trends and patterns and learn that understanding the numbers can help them come to their own conclusions about the issue. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-8
  • The Lowdown | Made in America: The High Cost of Fashion

    Investigate data on changes over time in where our apparel is made and how much we spend on it in these images from KQED. In the accompanying classroom activity, students use the interactive and graph the data. They also look for patterns and relationships. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 8
  • The Lowdown | Counting Undocumented

    Explore the number of undocumented immigrants living in California by county and compare populations and labor force to the rest of the United States in this interactive from KQED. In the accompanying classroom activity, students look at the numbers in their own state and compare the center and variability to the rest of their region. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-8
  • The Lowdown | What You Need to Know about Immigration Reform

    Interpret graphs showing changes over time in the percentage of foreign-born US residents and in annual deportations in this interactive from KQED. In the accompanying classroom activity, students use the interactive and look at how rates have changed over the decades. They also extrapolate to future years. To get the most from this lesson, students should be comfortable interpreting slope as rate of change over time. They should also be able to find the equation of a line when given two points. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 8
  • The Lowdown | Poverty Trends: What Does it Mean to Be Poor in America?

    Use math to learn about changes in US wealth distribution and poverty rate over time in this interactive from KQED. In the accompanying classroom activity, students interpret the graphs and consider how the poverty rate spike following the Great Recession of 2008 differs from poverty rate spikes of previous eras. To get the most from this lesson, students should able to interpret data involving percent increase and decrease, and they should be familiar with slope as rate of change over time. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6
  • Modeling the Linear Relationship Between Fahrenheit and Celsius

    Explore the relationship between degrees Fahrenheit and degrees Celsius. This video focuses on developing an expression to model the relationship between the temperature scales using a line graph to calculate slope and the y intercept.

    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: 6-8

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