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
In this video lesson, students encounter situations in which using a double number line poses challenges and for which a different representation would be helpful. Students learn to organize a set of equivalent ratios in a table, a more abstract but also a more flexible tool for solving problems. Students see that a table accommodates different ways of reasoning about equivalent ratios. They notice (MP8) that to determine an unknown quantity, they can find the multiplier or find an equivalent ratio with one quantity having a value of 1. Allowing students to use any representation that accurately represents a situation and encouraging them to compare different methods will develop their ability to make strategic choices about representations (MP5).
The video lesson strengthens students’ understanding of the multiplicative relationships between equivalent ratios. It also builds students’ awareness of how a table can facilitate this reasoning to varying degrees of efficiency, depending on the approach.
Grade 6, Episode 4: Unit 2, Lessons 11 & 12 | Illustrative Math
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.
Students will watch African dance and identify tempo. Three options are provided for this lesson depending on the class time allotted. The options include recording heartbeat at rest, calculating tempo in terms of stomps per minute, and choreographing an original dance with tempo changes.
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.
In this interactive activity, students will be led through steps to generate ratios in word form, fraction form, and ratio form. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.
This is a free resource from PBS. Teachers will need to click on Procedure to access the directions for the activity. Note: Sohu/African/African-American Culture has been substituted for Drum-Beating, Foot-Stomping African.
There are three options for this lesson, depending on class needs and time available:
