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STANDARDS
CCSS: 6.RP.A.2, 6.RP.A.3.B, MP1, MP2, MP3
TEKS: 6.4B, 7.4B, 7.4D
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Running the Great Wall
YOUR MISSION: As you read, use rates to explore China’s Ten-Thousand-Mile-Long Wall—today known as the Great Wall of China. It was built to protect the country from invaders. The Mongols were the main threat during the Ming Dynasty (1368-1644). Round answers to the nearest tenth when necessary on the online answer sheet.
A rate is a type of ratio that compares two quantities with different units.
x Unit A y Unit B
A unit rate is a rate with a denominator equal to 1.
x Unit A → x ÷ y Unit A → x ÷ y Unit A per Unit B y Unit B y ÷ y = 1 Unit B
Workers regularly survey the wall to see where it needs repairs to protect the capital from Mongol attacks. It takes them 30 minutes to survey 150 square feet. How many square feet do they survey per minute?
A. It takes 10 bricks to make up 5 feet along the base of the wall. How many bricks are there along 35 feet of the wall?
B. It takes 70 bricks to make up the wall’s height. Each brick is 0.3 feet tall. How tall is the wall?
It takes 4 jars of ink to record the store’s inventory for 12 weeks. At that rate, how many jars of ink do you need to keep track of inventory for 33 weeks?
To make 3 pots of tea, you need 2 ounces of tea leaves. How many ounces of tea would you need to purchase to make 14 pots of tea?
You spend 42 minutes buying supplies. If you spent the same amount of time in 3 different stores, how many minutes were you in each store?
A. You overhear the Mongol scouts saying that they traveled for 3 days and covered 72 miles. How many miles did they travel per day?
B. But it will take the main Mongol raiding party 5 days to cover the same distance. How many miles per day does the main raiding party travel?
The emperor’s palace is about 250 miles away from your village. How many days will it take for the main Mongol raiding party to reach the palace, rounded to the nearest hundredth?
The Piantou Pass is 22 miles away. Riding your horse at a rate of 19 miles per hour, how long will it take you to reach the Piantou Pass?
The Yanmen Pass is 33 miles away, but the path is easier to travel. At a rate of 22 miles per hour on horseback, how long will it take to reach Yanmen Pass?
Ningwu Pass is 18 miles away but over rougher terrain, so your horse can go only 11 miles per hour. How long will it take to reach Ningwu Pass?
Which pass should you choose? Explain.
The guards send runners to two passes, which are each 10 miles away, to raise the alarm for Mongol raiders. One runner heads east and travels 2.5 miles in 5 minutes. Another runs west traveling 6.25 miles in 15 minutes. Which arrives first?
A group of soldiers leaves to catch the scouts. They travel at a rate of 18 miles per hour. They spot the raiders 21 miles away. How long will it take them to reach the raiders?
Your horse is exhausted! A soldier offers one of their spare horses for you to ride home. It takes you 1 hour and 7 minutes to travel the 20 miles home. What was your rate in miles per hour?
Use any of the numbers from this story to write your own rate question.
Year Construction Started:
221 b.c.
Range in Height of the Wall:
16 to 26 feet
Total Length of the Wall:
13,170.7 miles
Highest Elevation of the Wall, Near Beijing:
4,722 feet