# Application of 2D and 3D volume and area formulas to Native American homes

## Overview

A five day unit for use after student have learned area and volume formulas for 2D and 3D shapes. This series of lessons connects geomery with history as students explore the size of traditional Native American homes and the space each person would have had within the home.

# Lesson plans Days 1-5

**Day 1: Wigwam**

**Read the summary below. Suggest to put it on a Smartboard, Smart TV, or Overhead.**

**Pass out the template, review the formulas needed for surface area, volume, area of the base, and how to calculate the area per person. Have students write formulas in the appropriate boxes.**

**Divide the class into pairs or small groups; then have them reread the summary and highlight the numbers they need to use for their calculations. Next the small groups or pairs should work together to solve the problems; then combine smaller groups into larger groups to compare answers, finally regroup as a class and discuss. **

**Challenge the class to see how many examples of tribes they can find that lived in this type of home and share them maybe in Google classroom or using another electronic media.**

**Wigwam**

**Wigwam**

**Tribes indigenous to the Northeast United States traditionally lived in wigwams. These homes had a hemisphere shape and could stand up to the harsh winter conditions they faced. The homes were constructed using the young green tree saplings of almost any type that were 10 to 15 feet long. The saplings were cut down and bent around a circle that had been drawn in the Earth. The diameter of the circle varied from 10 to 16 feet and the bent saplings were placed around the circle with one end touching each side to form the support for the wigwam. The finished home was 8 to 10 feet tall with a hole in the center for the smoke from the fire to escape. Another set of saplings was placed over the first for structural support. The outside of the wigwam was then covered in bark strpped from trees. As many of 60 people lived in a wigwam together. **

**For the wigwam:**

**Find the surface area:**

**Smallest diameter wigwam****Largest diameter wigwam**

**Find the volume:**

**Smallest diameter wigwam****Largest diameter wigwam**

**Find the amount of area of the base (space)**

**Smallest diameter wigwam****Largest diameter wigwam**

**Find the amount of space each person would get if 40 people lived in the largest diameter wigwam.**

**Day 2: Longhouse **

**Today students will be learning about another type of home that Native Americans lived in; The Longhouse. They will use many of the same formulas as they priors day lesson; however, today the skill of finding the area of a combined shape is used. **

**Divide students into groups, pass out the templates, read the summary, have students either draw cards to determine their width, how far apart their hearths were placed, and how many people lived in the home or pass out template sheets with this information written in the box that is different based on how many groups you will have. **

**Similar to yesterday have the groups reread the summary and highlight the numbers they need to use for their calculations. Next the small groups or pairs should work together to solve the problems. At the end of class compare how changing the width and/or height impacts the overall volume of the structure. **

**Challenge the class to see how many examples of tribes they can find that lived in this type of home and share them maybe in Google classroom or using another electronic media.**

**Summary of The Longhouse **

**Longhouse**

**Longhouse**

**Longhouses were constructed by Indigenous people who were native to the Northeastern United States and Eastern Canada. These homes often housed members of an extended family with new members being added as daughters married bringing their new husbands into the home and starting families of their own. A typical long house was 20 to 23 feet wide and up to 246 feet in length. They had a 9.8 ft-wide central aisle and a 6.6 ft wide compartment at each end. Hearths were spaced about 20 to 23 ft apart down the aisle with smoke holes in the roof. Most longhouses were made with wooden poles tied together with leather and covered with bark. The bottom had a rectangle shape with a rounded (semi-circle) roof. It was very common for 20 individual families (80 to 100 people) that all were related to one common individual to live in one longhouse. **

**For the longhouse:**

**Find the total surface area using the given measurements**

**Find the volume using the given measurements**

**Find the amount of area of the base using the given measurements**

**Find the area of the roof (half-circle) using the given measurements****Find the combined storage area in the long house****Find the area of the central aisle**

**Find the amount of space (area) each person would get if _____ people lived in the largest size longhouse.**

**Days 3 and 4: Tipi**

**Divide the class into 6 groups (2 of each group A-C). Group A will be finding the measurements of the smallest tipi, group B the medium tipi, and group C the largest. Day three will focus on the calculations and checking with another group who did the same letter to make sure they found the same answers.**

**Day four will be application of the measurements to make a model. Students will use construction paper and wooden dowels or straws to make a model of a tipi. Each group should decide on a scale that fits their measurements best; ie 2 feet = 1 in for the pole and 2 ft³ = 1 in³**

**Summary: **

*Tipi *

*Tipis were traditionally used by Indigenous people of the Plains in the Great Plains and the Canadian Prairies of North America. The frame was usually made from trees made into 13 poles that were 15 to 18 feet long. After being tied together at the thin ends the poles they were raised upright with a twist so the poles crossed above where they were tied together. At the bottom the poles were pulled apart (large ends) to form a circle usually ten feet in diameter. Tanned or untanned buffalo hides that had been stitched together to form the outer covering were stretched over the poles to form the covering for the frame. At the bottom of tipi the poles are secured to the ground with tent pins, a doorway was created using extra buffalo hide, and at the top extra buffalo hides were used to create a smoke flap. Typically 30 to 40 people would live in one tipi comfortably.*

**For the tipi:**

**Find the length of the center pole (hint: use the pythagorean theorem)**

**Find the volume of the tipi**

**Find the surface area of the tipi**

**Find the area of the base of the tipi**

**Find the amount of space (area) each person would get if 30 people lived in your tipi**

**Day 5 Earthlodge**

**This is the culmination of the unit and the day I have students work independently to see how much they have learned. I allow students to use their notes and formula sheets and have them complete the calculations below. I have attached a rubric I use for this unit. **

**For the earthlodge: **

**Find the volume of the roof area only****Find the area of the base (the living space) and how much each person would get if 15 people lived there****Find the surface area of the roof; then find how much mud or clay would be needed to build the home if each square foot of the home required one pound of mud/clay mix.**

**Summary for Earthlodge: **

*Earth Lodge*

*Earth lodges were homes that were constructed partly into the ground around them. They were built by Indigenous people who lived in the Great Plains and Eastern Woodlands. These homes were built using a technique weaving branches together and pressing mud or clay into the weave. The branches were woven together to make a dome like shape and support posts (made from tree trunks) were added under the roof as construction progressed. The digging, building of the roof, and adding of support posts occured at the same time resulting in homes that would be as big as 50 feet across and had a center height of 15 feet. Typically between 15 and 20 people would live in each home. *

### See lesson plans above

Students will get different templates each day