6.RP.A.3: Sugar Packets~ Three-Act Math Task

The trick to successful teaching and learning is getting our students engaged and interested in the lessons we are teaching. So why not connect their lessons to aspects of their lives to which they can relate when possible? Well, unfortunately, that is far easier said than done, but luckily this is not one of those cases. Nearly every day over half of my students (in all of my high school classes) have some sort of soda or energy drink. So, naturally, I went with a lesson that ties their love for soda to my love of their math.

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This particular lesson was found on Mr. Dan Meyer’s website at: http://threeacts.mrmeyer.com/sugarpackets/

(others can be found at https://docs.google.com/spreadsheet/pub?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE&output=html)

The Sugar Packets lesson aligns with the 6th grade common core standard 6.RP.A.3 which states “Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.”

Though I mentioned above that my focus is with high school students, I think that beginning with a more simple lesson and then making modifications later to align with the high school standards would work more effectively for the students with whom I am currently working.

First, the students watch a 37 second video demonstrating that drinking soda, something that is completely acceptable by the majority of society, is equivalent to just eating so many packets of sugar, an act that most people would deem disgusting or unnecessary. So, why then, are we, as a society, so okay with drinking soda? After watching the video the students are to guess how many packets of sugar are in a 20 oz bottle of soda.

Then, the students are shown the so-called nutrition label of a 20 oz bottle of coca cola as well as a standard packet of sugar (the teacher could also bring in a bottle of soda and the 16 packets of sugar to show better proportions).

The third step of this lesson is to show students how many packets of sugar are actually in the bottle of soda.

This lesson could be modified for high school statistics and probability: (Summarize, represent, and interpret data on a single count or measurement variable CCSS.MATH.CONTENT.HSS.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).) by having students find the sugar content of other popular foods/drinks and have them graph the data based on volume of the drink and amount of sugar. Then, the students can see if there is a correlation with mean, median and standard deviation.

7.RP – Ratios and Proportions with iPhones

The picture on the top was found at http://www.geek.com/wp-content/uploads/2012/09/i5i4svs_dimensions.jpg and the picture at the bottom was found at http://www.financetwitter.com/2014/09/apple-pay-iphone-six-watch-welcome-to-the-party-but-you-are-late.html

A possible math problem that students can solve is “identify the size ratio difference among the different iPhones in inches and mm.” This would align with the state standard CCSS.Math.Content.7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Students would be given both pictures so that they could see the dimensions of the four latest versions of the iPhone. With the dimensions given, students should be able to apply prior knowledge of converting ratios to find what the dimensions of the iPhone 4s and iPhone 5 are in mm. Students could then compare the face area of the iPhone 4s to the face area of the iPhone 6 plus since the difference in size is greater between those two phones. Other size ratios can also be found among the other iPhones.

Comparing size dimensions of iPhones, can be a great activity for students because it is something that they can be interested in. Many students might have a version of an iPhone and would find it very interesting to compare the size of their own to others. Other students might find the activity interesting because they are using math skills to compare real-life objects.

Proportional Reasoning Learning Progression

Attached is a learning progression and lesson plan for the common core state standards for mathematics cluster “Reason quantitatively and use units to solve problems” under the domain Quantities. The lesson plan includes an interactive activity for students which involves measuring physical objects and making decision about different units.

2nd learning progression lesson plan

2nd formatted learning progression