Fractions as Relationships and Operations · Weeks 10-18

Interpreting Fractions as Division

Students will interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

About This Topic

This topic examines the Spanish conquest of the Aztec and Inca empires and the subsequent establishment of the Spanish colonial system. Students explore how small groups of conquistadors, led by figures like Cortés and Pizarro, were able to topple massive empires through a combination of military technology, alliances with local rivals, and the impact of disease. The curriculum also covers the encomienda system and the blending of Spanish and Indigenous cultures.

Students analyze the power dynamics and the ethical implications of the conquest. This aligns with standards regarding the impact of colonization on Indigenous societies. Students grasp this concept faster through structured discussion and peer explanation as they analyze primary sources from both the Spanish and Indigenous perspectives.

Active Learning Ideas

Mock Trial: The Fall of an Empire

Students hold a trial to determine the primary cause of the Aztec defeat. 'Witnesses' present evidence for technology, disease, or internal alliances, and a jury decides which factor was most decisive.

⏱ 50 min·Whole Class

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Inquiry Circle: Cultural Blending

In small groups, students look at images of colonial Mexican art or architecture. They identify elements that are clearly Spanish and elements that are clearly Indigenous, creating a 'fusion' chart.

⏱ 30 min·Small Groups

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Think-Pair-Share: The Encomienda System

Students read a short description of the encomienda system. They discuss with a partner how this system benefited the Spanish and how it impacted the rights and lives of Indigenous workers.

⏱ 20 min·Pairs

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Watch Out for These Misconceptions

Common Misconception

A few hundred Spaniards defeated millions of people alone.

What to Teach Instead

The Spanish relied heavily on thousands of Indigenous allies who wanted to overthrow the Aztec or Inca. A mock trial or debate helps students uncover the role of these local alliances in the conquest.

Common Misconception

Indigenous culture disappeared after the conquest.

What to Teach Instead

Indigenous languages, foods, and traditions survived and blended with Spanish culture. A collaborative investigation into modern Latin American culture helps students see the continuity of Indigenous influence.

Frequently Asked Questions

How did the Spanish defeat the Aztec and Inca?

It wasn't just one thing. The Spanish had steel armor and horses, but they also formed alliances with Indigenous groups who were enemies of the empires. Most importantly, European diseases like smallpox weakened the Indigenous armies before the major battles even began.

What was the encomienda system?

It was a labor system where the Spanish crown granted colonists the right to demand labor or tribute from Indigenous people in a certain area. In exchange, the colonists were supposed to protect the workers and teach them Christianity, but it often led to harsh forced labor and abuse.

Who were the Conquistadors?

Conquistadors were Spanish explorers and soldiers who led the conquest of the Americas in the 15th and 16th centuries. Most were motivated by the promise of wealth (gold) and land, as well as the desire to spread the Catholic faith.

How can active learning help students understand the Spanish Conquest?

Active learning, like mock trials or primary source analysis, prevents students from seeing the conquest as an inevitable event. By debating the different factors that led to the fall of Tenochtitlan, students recognize the agency of Indigenous allies and the role of chance, making the history feel more dynamic and less like a foregone conclusion.

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