Apply fraction operations to real-world and complex historical word problems.
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Introduce Shulbasutra example of non-unit fractions.
Some of the oldest examples of working with non-unit fractions occur in humanity's oldest geometry texts from India, called the Śhulbasūtra (c. 800 BCE). Let's look at a historical problem posed by Baudhāyana.
Real world contexts and historical geometric construction require visualization.
When multiple sources fill a container at different rates, fraction division helps us calculate their combined rate.
Chaturveda Prithudakasvami's cistern problem.
Problem. This problem was posed by Chaturveda Pṛithūdakasvāmī (c. 860 CE). Four fountains fill a cistern. The first fountain can fill the cistern in a day. The second can fill it in half a day. The third can fill it in a quarter of a day. The fourth can fill the cistern in one fifth of a day. If they all flow together, in how much time will they fill the cistern?
Maria decorating bags with lace.
Maria bought of lace to decorate bags. She used for each bag. Which expression correctly finds the number of bags she decorated?
Amritpal's train vs plane travel time.
List the given travel times with units.
What math operation finds the 'time saved'?
Convert the mixed number to an improper fraction and write the subtraction.
Find a common denominator, subtract the numerators, and simplify the fraction.
Convert the simplified improper fraction back to a mixed number with units.
Does the magnitude of the time saved make sense?