This lesson uses the context of Wastewater Testing and droplet tests to help students make sense of Virus Load. This real-world situation helps students realize that mathematics—especially ratios—is used by communities to make decisions that impact many people.

Students will learn how to explain whether a virus load described by a part-to-part ratio or as a part-to-whole ratio increases, decreases, or stays the same from card to card. Students will be able to compare ratios using part-to-whole reasoning when the total number of droplets are the same, part-to-part reasoning if the number of virus (or non-virus) droplets are the same, and part-to-whole reasoning when using benchmarks of one-half. 

Students play the game Connect the Drops to develop their fluency with ratios and then the game is used as a jumping off point to introduce three important executive function processes related to learning math: working memory, cognitive flexibility, and inhibitory control.

This lesson introduces students to a module that focuses on comparing ratios (by thinking of them as rates). This lesson encourages students to analyze and compare ratios by (1) generating equivalent ratios by mixing paint, and (2) comparing ratios by thinking about how dark the paint is.

Expanding on the previous lessons’ understanding of how to utilize language to describe ratios, this lesson explores ratios and rates within the real-life contexts of plastic bottle waste at home and school; it is designed for students to extract meaning from relevant situations in order to generate problem-solving strategies.

The context of charging rates for cell phones is used in this lesson to make comparisons among the charging rates of different phone chargers. Students will use charging bars to make connections between what they see on their phones everyday and the concept of a charging rate.  

This lesson uses a social media context to introduce students to ratio tables. Other parts of the lesson focus on proportional reasoning using large numbers and use of ratio language to describe related quantities. 

This lesson starts with a revisiting of executive functions and their relationship to ratio tables. Students explore other related ratios found in social media data; they identify and use various operations that can be used to solve problems with ratio tables.  Unit rates are implicitly found at the end of the lesson. 

‍

This lesson focuses on using (horizontal) ratio tables with an emphasis on multiplicative reasoning. Students are encouraged throughout the lesson to consider multiple perspectives for solving problems with ratio tables.

This lesson focuses on simplifying expressions that represent (un)healthy fast food purchasing decisions; the distributive property with expressions is also explored in problem contexts. 

‍

This is the first of four lessons that focuses on the use of the double number line as a tool for solving ratio and rates problems. The origin of chocolate, and the ratio of cacao beans to cacao pods, is used in a bartering context to motivate solving problems involving ratios and rates. 

This lesson builds on D1 by continuing to build a foundation for what a double number line is and how it can be used to support problem solving. The context for this lesson is grocery shopping and comparing prices of items, leveraging the interactivity of a PhET simulation.

This lesson entends the use of the double number line and other strategies to find unit rates for shopping contexts and solutions to travel scenarios (e.g., cost to fill a gas tank, gallons of gas needed, etc.). Strategies for finding unit rates are explicitly discussed. 

This lesson continues with the car trip theme to investigate problems and related strategies to find unit rates. Both the double number line and division strategies are used to find unit rates. Unit rates are used to support comparison shopping.