Math Tourist: Ratios and The Great Wall

Essential Questions for students (objectives):  How can ratios help us convert measurement and determine scale between distances?

Supplies:   video (length-1:07), access to resources that show distances in North America, calculators, Great Wall problem-solver notemaker

CCSS:  6.RP.3, 7.RP.1, Social Studies:  Ancient Cultures - China
Instructional Format: Video, student problem-solving, group work       Time needed: 20 minutes – 60 minutes
Vocabulary for a Word Wall: ratio, km

Description: There are many ways to use this video in your math class.  First of all, I did film it for a 6th grade class, but you can use it any time that you are working with ratios, proportions, or measurement conversion (or even studying ancient China).   The upshot of this lesson is that the Great Wall of China is 8,000 km long, so if it was cut and put across our border with Canada, would it protect the US?  You could also have students explore where it could be cut and placed and fit perfectly in the US (surrounding Texas or along the Mississippi river?).  The second part of the video is a tie into Social Studies asking whether the students feel that the Great Wall would be a good form of protection against invaders.  I also ask the students to relate The Great Wall to the wall proposed along the border to Mexico.  This way students can explore ancient China and discuss current events.  A note-maker is included to assist students in persevering through the problem-solving process.

1)  You can show this video (1:07) at the beginning of a unit on ratios as a hook that will keep the students interested in learning about ratios.  You can have them work on the problem at the end of daily lessons (or once a week) armed with new knowledge that they are exploring in class.  Or you could revisit the video at the end of the unit as a formative check to see what the students have learned about ratio and whether they can apply that knowledge.

2)  You could show this video as a warm-up activity after the students have learned how to convert between different measurement systems using ratios.  It is a great way to show context to a ratio problem.

Extensions:  Students can research The Great Wall of China.  Do they know that you can see it from space?  How long did it take to build?  How much did it cost?  How might that relate to the proposed wall between the US and Mexico?  Everyone says that The Great Wall was made so that the soldiers could see their enemies coming and be prepared for an attack.  After seeing the growth of trees around The Great Wall, I find that theory tough to believe.  So, what would make it better protection?   In the background of the video, you can see the poor air quality of Beijing (and we are 3 hours out of the city proper).  What can China do about their poor air quality?

Attached worksheets or documents: Great Wall problem-solver notemaker

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