In Dan Meyers Coke V. Sprite activity, found on http://mrmeyer.com/threeacts/cokevsprite/, students use both mathematical concepts and logic principles to develop an argument. The student defends their position by organizing their reasoning, then communicating a compelling argument with their peers. Students are asked to use several representations when presenting the problem, this allows students to eventually get a better understanding for how to use mathematical procedures related to ratios.

When we completed this task as a group we determined that is was necessary to give a hypothetical amount of equal proportions of the respective sodas in each glass. We then took the dropper of Sprite and mixed it with Coke. This causes a change in the ratio (or concentration) between the amount of Coke and Sprite compared to the whole. We now proceed in solving the ratio in terms of percentages. Taking the amount of Coke and dividing it by total amount of soda, we end up finding that 90.9% of the liquid is Coke and 9.1% is Sprite.

We now take our new mixture and add it to our untouched Sprite. First, we must find out how much of the sample is Coke and how much is Sprite. By using the percentages, we found of the Coke and Sprite mixture, we multiply to find the amount of each soda within the sample.  In conclusion, both glasses contain an equal amount of their respective contents. The Sprite with Coke was 90.9% Sprite and 9.1% Coke. The Coke with Sprite was practically the reciprocal of the Sprite with Coke, 90.9% Coke and 9.1% Sprite.

This activity could be covered in a 6th grade math class towards the end of their study of ratios and proportional relationships (CCSS M 6.RP 3.c.) to help the students understand percentages, and how to use percentages in a situation where they need to understand what ‘100%’ of something is that isn’t directly given as 100 units, for example. This might be quite complex for this level, however, and could also be used as a lesson for 7th grade students (CCSS M 7.RP 3.) where the students are to be expected to solve problems with multiple steps.