This video lesson introduces graphs as an important way of representing a proportional relationship. Students plot points on the graph from tables and start to see that the graph of a proportional relationship always lies on a line that passes through (0,0). They match tables and graphs of given situations and articulate their reasons for each match (MP3).
Grade 7, Episode 5: Unit 2, Lesson 10 | Illustrative Math
In this video, students visit a small-town festival that features the world’s largest stainless steel skillet. In addition to a question about scaling recipes, they also are asked how increasing or decreasing the radius of a circle affects its area. The accompanying classroom activity requires students to compare the areas of the world’s largest skillet and a standard 12-inch skillet through reasoning and computation and to explore the meaning of pi through a hands-on activity. This resource is part of the Math at the Core: Middle School Collection.
Although the Scaling Up Recipes and Circles in Practice video ("Greetings from the World’s Chicken Festival") and the Scaling Up Recipes and Circles in the Real World interactive ("Sunnyside Up") can be used independently, they are deliberately designed to complement each other.The video takes students to a small-town fall festival that features the world’s largest stainless steel skillet as well as food preparations for a crowd of 8,000 people. They are asked how they can use proportional reasoning to scale recipes and how increasing or decreasing the radius of a circle affects its area.The interactive explores the questions asked in the video as students scale up recipes and food portions to feed a family reunion of 108 people and as they discover the mathematical relationship between the length of a circle’s radius and its area. To enhance classroom use, refer to the Interactive Guide handout and Questions worksheet that students can reference and complete as they work through the interactive.
Be sure to use the Scaling Up Recipes and Circles in the Real World Activity that can be found in the Support Materials for Teachers section for a great activity that teaches the standard(s).
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.
Although Inverse Proportions and Shadows in the Real World and the Inverse Proportions and Shadows in Practice interactive ("Shadow Puppets") can be used independently, they are deliberately designed to complement each other.
The video takes students to "Sky-Vue Drive-In" to explore what happens to the size of shadows as an object moves further away from a light source.
The matching interactive simulates three figures of different heights standing at various distances in front of a movie projector, allowing students to measure the corresponding shadows of the figures on the movie screen and to see how the relationship between the distance from the light source and the height of the shadow is represented graphically.
Be sure to use the Inverse Proportions and Shadows in the Real World Activity that can be found in the Support Materials for Teachers section for a great activity that teaches the standard(s).
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.
Although Proportions and Music in the Real World ("Belle of Louisville") and the Proportions and Music in Practice interactive ("Musical Scales") can be used independently, they are deliberately designed to complement each other.
The video introduces students to the relationship between music and mathematics, specifically how the length of a pipe or string is related to its frequency, as they learn about the calliope aboard the Belle of Louisville steamboat, a massive pipe organ, and a variety of instruments at a recording studio.
The matching interactive allows students to play a virtual pan pipe, measure the length of its pipes, record their frequency, and understand the inverse proportional relationship between these frequencies and the instrument’s corresponding pipe lengths.
Be sure to use the Proportions and Music in the Real World Activity that can be found in the Support Materials for Teachers section for a great activity that teaches the standard(s).
In this lesson, students learn about scaling an object, first smaller (1/10) and then larger (2x). This Cyberchase activity is motivated by two video clips in which the CyberSquad travels to Proporciona, where they visit a land of giants and a land of tiny people (similar to Gulliver's Travels).
Observe what happens to an image when the scale changes. This interactive exercise focuses on visually comparing multiplicative and additive relationships.
In this lesson, students are asked to figure out the dimensions of enlargements of rectangular photographs (and some reductions), based on the percentage of the enlargement. This Cyberchase activity is motivated by a For Real segment in which Bianca, working at a new job, has the task of enlarging a photograph into a poster-sized wall decoration.
In Topic A, students examine situations carefully to determine if they are describing a proportional relationship. Their analysis is applied to relationships given in tables, graphs, and verbal descriptions. At the end of the unit, students will use proportional and non-proportional relationships to solve real-world problems.
