Last updated: December 19, 2024
Lesson Plan
Equal Exchange Lesson Plan
Trade values were often negotiated through a lengthy process.
NPS/D. Ocheltree
- Grade Level:
- Middle School: Sixth Grade through Eighth Grade
- Subject:
- Math
- Lesson Duration:
- 60 Minutes
- Common Core Standards:
- 6.EE.1, 6.EE.2, 6.EE.2.a, 6.EE.2.b, 6.EE.3, 6.EE.4, 6.EE.6, 6.EE.9
- State Standards:
- 6th Social Studies History 1.2.c. Identify examples of social, political, cultural, and economic development in the Western Hemisphere. 6th Economics 3.1.a. Describe how current economic systems in the Western Hemisphere...developed.
- Thinking Skills:
- Applying: Apply an abstract idea in a concrete situation to solve a problem or relate it to a prior experience.
Essential Question
1. Name three things necessary to make a fair trade.
2. Set up this sentence like an algebra problem: Thomas Fitzpatrick equally traded 1 buffalo robe (b) for 2 chocolates (c). Now solve. If 1 buffalo robe is $3, how much is each chocolate worth?
Objective
Students will identify trade goods and their approximate worth in dollars so that they can establish fair trades as practiced during the fur trade era. They will generate algebraic expressions to represent these exchanges.
Background
Intro:
Bent’s Fort began as a trading post in the southern plains during the 1830s. People who visited the post were either from regional Native American tribes or were traders and merchants traveling along the Santa Fe Trail between Santa Fe (then Mexico) and Independence, MO. The trade at Bent’s Fort centered on the buffalo robe market. Cheyenne and Arapaho members hunted and processed the buffalo into large, warm robes to be exchanged for other useful goods like fabrics, cookware, tools, etc. When Native Americans brought in their buffalo robes, they weren’t interested in receiving coin or paper money. They wanted to trade the robes directly for the other items at the post. This was often a long process that followed Native American custom. It depended on respect and trust being built between the two parties.
Preparation
Materials Needed:
- White board or chart paper
- Equal Exchange Activity Page (Spanish available)
Materials
Companion activity to lesson where equal amounts of trade goods will be exchanged.
Download Equal Exchange Activity Page
Spanish version companion activity to lesson where equal amounts of trade goods will be exchanged.
Download Intercambio Igualitario
Lesson Hook/Preview
*This lesson introduces how to formulate equivalent expressions using variables by using real-world problem-solving examples. Prior knowledge in algebra is not essential.
Begin by discussing a potential trade “reward” you could make with your group. Perhaps, for every person who follows a certain rule (r), you will award 1 minute of free time (m). On the board write 1 rule = 1 minute. Now ask the class, “What do you think should happen if more than one person follows the rule? Let’s say 5 people follow it. 5 rules = ___ minutes. What goes in the blank? Yes, 5 rules or 5 (r) equals 5 (m) minutes. Of course, as a class, we want to try to as many minutes as possible, so how many would that be? (Write the appropriate equivalent expression on the board).”
Explain how the equation relates to today's lesson. Say, "As a group, we just had a negotiation, I offered to trade free time for you following a rule. Today, we’re going to look at trade negotiations that took place back during the fur trade era. Sometimes money was used to buy things at a trading post, but usually one or more trade goods were exchanged for other trade goods."
Procedure
1. Read Background Intro aloud to group (see above).
2. After reading, ask “When you go to the store today, do you have to build trust with the person who takes your money? Why or why not?”
3. Add “Earlier when I offered to trade free time for rule following, do you have to trust that I will do what I say?” (accept volunteer responses)
4. Explain that all relationships, even economic ones are built on trust.
5. Break students into pairs to consider this prompt: “What other things are needed to make a fair trade?” After a few minutes, invite students to share their ideas. Guide them to understand that a fair trade works when both parties get something they want.
6. Ask group, “Is rule following for free time a fair trade? and What does the group and the teacher get if the trade goes well?”
7. Pre-read Equal Exchange Activity Page. Assign and circulate through room to check for understanding.
8. Explain that at Bent's Fort in the 1830s and 1840s interpreters were often needed because of the many languages spoken. Similarly, math can be thought of as another language. We express math by using number symbols the way words use letter symbols. However, some types of math use both numbers and letters just like the expression I wrote on the board earlier: 5 r = 5 m.
9. State "the letters in algebra problems are called variables. 5 r = 5 m is a type of equation is called an equivalent expression. It means whatever is on the left side of the equal sign has exactly the same value as whatever is on the right side of the equal sign. Most math problems you’ve already done in school are equivalent expressions. 3 + 2 = 5. Three plus two is the same as 5. How about 4 x 6 = 24? Four times six is the same as 24.”
10. Say, “When people trade items they want things to be equal or fair. Look at the ‘My Account’ example on the Activity Page. Notice that the kettle has a value of $8 and the blanket has a value of $9. Is that equal? (No.) What could we do to make this an equal trade?” (Guide students to find combinations of equal value for either $8 or $9.)
11. Read through the rest of the example to show that the items to trade on the left equal the items traded for on the right. $14 = $14.
12. Write an expression for the example:
1 k (kettle) + 2 r (robes) = 1 b (blanket) + 2 c (chocolate) + 1 t (tin cup).
1 k + 2 r = 1 b + 2 c + 1 t.
Point out that when a number (coefficient) is next to a letter (variable) with no operation sign in between, that means to multiply. So in this equation, 2 r means 2 times the value of r and 2 c means 2 times the value of c.
13. Demonstrate solving this expression by filling in the values for the variables as given on the activity page. ($8 + $6 = $9 + $3 + $2).
14. For the activity page, have students generate their own algebraic expression based on their traded items. Circulate through the room to check for understanding. After 15 minutes or so, regroup and call on volunteers to share their equivalent expression.
15. Recall the historical context of this activity and note how having strong math skills would have been important to traders.
16. Summarize the lesson and hand out the Exit Ticket.
17. Give group feedback on the progress they made during this lesson in reaching their free time fair trade.
Vocabulary
Indian Agent – an official representative of the U.S. government to negotiate policies related to Native American interests
Variable – a letter or symbol that represents an object or quantity in an equation
Coefficient – a numerical quantity that is placed before a variable
Equivalent Expressions – mathematical statements that look different, but have the same value
Assessment Materials
Equal Exchange Exit TicketAssessment Exit Ticket containing the two essential questions from the Equal Exchange Lesson.
- Name three things necessary to make a fair trade?
- Set up this sentence like an algebra problem: Thomas Fitzpatrick traded 1 mule (m) for 4 tin cups (c). Now solve. If one mule is $8, how much is each tin cup worth?
Assessment Exit Ticket for Equal Exchange Lesson containing the two essential questions.
Rubric/Answer Key
Equal Exchange Exit TicketAnswers to Exit Ticket essential questions for Equal Exchange Lesson.
1. Name three things necessary to make a fair trade?
- Negotiation skills, math skills, interpretive skills, and products of close value that people want or need.
1 m = 4 c or 1(m) = 4(c) or 1 x m = 4 x c
Now solve. If 1 mule is $8, how much is each tin cup worth?
$8 = 4 c
8 = 4 x c
8 = 4 x 2
Each tin cup is worth $2
Supports for Struggling Learners
For Activity Page, use student pairs or mixed small groups for collaboration and peer support. Check for understanding with all groups while they are working.
Enrichment Activities
Social/Emotional Enrichment:
Discuss the obstacles to fair trade and relate them to fair relationships. Consider how the level of respect and trust create or maintain a friendship. Give personal examples of how peer relationships can be one-sided and what a person can do to either prevent that from happening or to make it more equal, such as self-advocacy or increasing awareness of the dynamic.