From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

CONTENTS OF CURRICULUM UNIT 17.05.04

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Background
  4. Content and Objectives
  5. Teaching Strategies
  6. Classroom Activities
  7. Example Problems
  8. Resources
  9. Appendix – State Standards
  10. Biography for Teachers
  11. Endnotes

Math World Problems and the Diné Hooghan

Jolene Rose Smith

Published September 2017

Tools for this Unit:

Example Problems

  1. The male alchi’ adeez’a, forked hooghan has been a home for the Dine people use since the early 1400’s and the female hooghan nimaz, hooghan was use first during the early 1800’s. Approximately how many centuries older is the alchi’ adeez’a, male hooghan?
  2. The male alchi’ adeez’a, hooghan has been a home for the Dine people use since the early 1400’s and the hooghan nimaz, female hooghan was used starting in the early 1800’s. Approximately how many times older is the male alchi’ adeez’a, hooghan?
  3. The male alchi’ adeez’a, hooghan has three main posts constructed to hold the foundation, whereas the female hooghan has eight posts. How many more posts are used in the hooghan nimaz, female hooghan, than in the male?
  4. The male alchi’ adeez’a, hooghan has three main posts constructed to hold the foundation, whereas the hooghan nimaz, female hooghan has eight posts. How many times more posts are used in the hooghan nimaz, female hooghan, than in the male?
  5. It takes a 5 day week, of 8 work hours each day, to chop and haul 500 cedar logs to construct a hooghan nimaz, female hooghan. Whereas the male alchi’ adeez’a, hooghan take 2 ½ days. What is the difference in the number of hours required for chopping the logs for the two hooghans?
  6. Constructing a hooghan takes many hours and numerous logs and thousand pounds of dirt. It takes about four days to haul all the cedar logs needed and about 2 days to haul the dirt. When working continuously, the completion of the hooghan will take two weeks. What is the total number of hours from the beginning to completion of a hooghan?
  7. Four workers are needed to strip the cedar bark off the logs. There are 500 logs, how many logs will each worker strip?
  8. Some men were stripping barks off the cedar logs. 8 men were stripping the logs. Then 12 men came to help strip logs. How many men are stripping logs now?
  9. Some cedar logs need to have notches so the logs connect at the end of each post. Two men chopped notches into the logs. The first man is able to chop notches onto 8 logs per hour and the second man is able to chop 12 logs per hour. What is the total number of notched logs they can complete within eight hours?
  10. The distance between neighboring posts when constructing the hooghan nimaz, female hooghan’s base, is measured in 8 feet intervals. There are 8 posts in all, what is the total perimeter of the hooghan?
  11. Between each neighboring pair of posts in the hooghan nimaz, female hooghan there are 15 logs. What are the total number logs between the eight main posts?
  12. The ceiling of the hooghan is built into levels. The first level is constructed onto the vertical posts. The first level has 8 main beams and additional 32 beams to form the first level of the ceiling. How many logs are needed for the first level?  
  13. Two men worked 8 hours every day for 2 weeks and 3 days to complete a conical roof of a female hooghan. How many hours did it take for the two men to complete the roof?
  14. The central height of a female hooghan is 12 feet and the central height of a male alchi’ adeez’a, hooghan is 15 feet. What is the difference in height between the two hooghans, expressed in inches?
  15. The interior perimeter of a female is 2 times larger than the perimeter of the male alchi’ adeez’a, hooghan. The male hooghan has an interior perimeter of 32 feet. What is the female hooghan’s interior perimeter?
  16. A sand and clay mixture is used to cover the outer section of the hooghan. It takes about 2/3 of a bucket of sand and 1/3 bucket of clay dirt to make a mixture in one bucket. A five gallon bucket is used to measure the amount of sand and clay. About 150 buckets of the mixture is needed to cover the first layer of the hooghan. How many gallons of sand and clay mixture are needed?
  17. Mud clay is used to seal the holes and cracks between the logs. A bucket carries 25 pounds of mud clay. To seal the holes and cracks, 30 buckets are filled with clay. What is the total number of pounds of clay they contained?
  18. Two men begin to seal the cracks and holes on the lower portion of the hooghan. The first man begins on the outside and the second man begins on the inside of the hooghan. The interior used 11 ½ buckets of clay, and the exterior used 18 ½ buckets. How many more buckets of mud clay were used on the exterior?
  19. The distances between two hooghans are determined by where a clan family resides. When two clan families conduct a 3-night ceremony known as Ndaa’, the families live 15 miles apart from each other. The families determine the midpoint between the two hooghans, and this is where the second night of ceremony is conducted. How far from the two hooghans does the second night ceremony take place?
  20. During a ceremony 8 women sit on the north side of the hooghan and 11 men sit on the south side of the hooghan. The patient and the medicine man sit on the east side. What is the total number of people in the hooghan?
  21. 12 women were sitting on the north side of the hooghan. After the third song is sung, some women left the hooghan to prepare the meal. There were 8 women still in the hooghan. How many women left the hooghan?
  22. Certain prayers and songs are performed in the hooghan between when sun sets and the early dawn. How many hours is this when the sun sets at 9:50 p.m. to early dawn at 3:30 a.m.?
  23. Four trucks travel to Black Mesa to get cedar logs. It takes 6 hours to chop and haul the cedar logs into each truck. What is the total number of minutes to load logs into one truck?
  24. Four short logs are used make a square frame of the smoke hole. Then 16 shorter logs are added to cover gaps around the frame of the smoke hole. How many logs are used to frame the smoke hole?
  25. Three main cedar posts are used to form the perimeter of the male alchi’ adeez’a, hooghan. Then 20 additional posts are added between each of the 3 posts. How many posts are added?
  26. A boy is carrying an arm load of wood for the fire in the hooghan, four arm loads to the main cooking fire, and three arm loads to the fire for boiling water. How many trips did he make from the wood pile to the three fire sites?
  27. 11 horse riders came from the east and 21 horse riders came from the south. How many more horse riders came from the south than the east?
  28. Bit’ahnii’s water tank has 30 more gallons than the Tódích’íi’nii’s water tank. Tódích’íi’nii’s have a 25 gallon water tank. How many gallons does the Bit’ahnii’ have?
  29. Tódích’íi’nii’s have 30 fewer gallons of water in their tank than the Bit’ahnii’. Bit’ahnii’s have 55 gallons in their water tank. How many gallons do the Tódích’íi’nii’ have?
  30. At the end of the Ndaa ceremony, 150 bags of yarn were purchased. Each bag contains 100 skeins. If the skeins are distributed among 10 families, how many skeins will each family receive?

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