This lesson will allow students to become familiar with the concept of equivalent ratios and similar objects. Through an open investigation, students will develop methods to find equivalent ratios. This is a lesson to be used as part of a unit with Painter Problems and How Far Can You Leap found in ALEX.
This is a College- and Career-Ready Standards showcase lesson plan.
This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?"
This lesson will allow students to become familiar with ratios. In this investigative lesson students will compare ratios and determine equivalent ratios. This is an introductory lesson to be used as part of a unit.
In this activity, the students will visit the website, Math Interactives, to reinforce a lesson on proportions. The students will demonstrate their knowledge of proportions by calculating missing values that will develop photographs. For completion, the students will arrange the photographs to view the final product.
This activity results from the ALEX Resource GAP Project.
This video lesson focuses on finding “A% of B” as efficiently as possible. The numbers in this lesson are purposefully chosen to be difficult for students to calculate mentally or to represent on a double number line diagram, in order to motivate them to find the simplest way to do the calculation by hand.
Grade 6, Episode 8: Unit 3, Lesson 15 | Illustrative Math
In this video lesson, students see that scaling a recipe up (or down) requires multiplying the amount of each ingredient by the same factor, e.g., doubling a recipe means doubling the amount of each ingredient (MP7). They also gain more experience using a discrete diagram as a tool to represent a situation. Additionally, they work with equivalent ratios more abstractly, both in the context of recipes and in the context of abstract ratios of numbers. They understand and articulate that all ratios that are equivalent to a:b can be generated by multiplying both a and b by the same number (MP6).
By connecting concrete quantitative experiences to abstract representations that are independent of a context, students develop their skills in reasoning abstractly and quantitatively (MP2). They continue to use diagrams, words, or a combination of both for their explanations.
Grade 6, Episode 1: Unit 2, Lessons 3 & 5 | Illustrative Math
Students explore percentages of quantities other than 100 and 1 in a variety of contexts. All of the tasks use comparison contexts—describing one quantity relative to another quantity—rather than part-whole contexts.
Students can continue to use the double number lines as a reasoning tool. The equal intervals on the double number line are useful for reasoning about percentages. In addition, using the same representation that was used for other ratio and rate reasoning reinforces the idea of a percentage as a rate per 100 (MP7). Students should also be encouraged to use other strategies to solve percentage problems.
Grade 6, Episode 7: Unit 3, Lesson 11 | 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 Cyberchase media gallery, learn about ratio and proportion and how to use an algebraic shortcut to solve proportion problems. In the accompanying classroom activity, students play a game called the "Pom-Pom Nose Push," in which they collect data and determine the ratio of time to distance. This resource is part of the Math at the Core: Middle School Collection.
In this video from Cyberchase, Harry describes ratio as a fixed relationship between two quantities and then provides examples to explain the concept further.
Investigate a situation where math plays an important role in art. This video focuses on the equation to calculate the correct weights and distances of the components necessary to balance a mobile. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
Be sure to view the activity, The Art of Math - Activity (found under Support Materials for Teachers), to use with the video.
Observe what happens to an image when the scale changes. This interactive exercise focuses on visually comparing multiplicative and additive relationships.
Think about the relationships between the weight and size of similar objects. This interactive exercise focuses on using critical thinking skills and estimation skills to predict how many mini and regular gummy bears it takes to have the same mass as a super bear and then requires using data to complete calculations to see if your prediction was accurate.
This resource is part of the Math at the Core: Middle School collection.
In this infographic, learn about the impact of drought on agriculture in California. In the accompanying classroom activity, students use the information on one of the infographic graphs to compare the share of production value to the share of water usage for different crops and consider the implications for the choice of crops to grow in times of drought. To get the most from this lesson, students should be comfortable interpreting percentages and double bar graphs and familiar with ratios and rates.
The CyberSquad works with an area to figure out how to power a skate park using solar panels in this interactive from WNET. In the accompanying classroom activity, students view and analyze a series of video clips from Cyberchase and complete an activity using area and ratio. Students take what they’ve learned and put it to the test by designing their own solar power dream house. This resource is part of the Math at the Core: Middle School Collection.
This classroom resource provides a video that introduces percents as "parts of one hundred." It explains that percents can be written as a fraction, as a decimal, as a ratio, or with a percent sign. After utilizing this resource, the students can complete the short quiz to assess their understanding.
