Raising Sheep and Rational Numbers


Dine’ Culture Standards (3.PO2) I will develop an understanding of Dine’ way of life through Iina’. I will implement and recognize the Dine’ lifestyle. I will present the stories related to Land and Water Beings.

CCSS.MATH.CONTENT.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals)


45 minutes

Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, phone or tablet


Why would a Navajo sheep farmer need rational numbers? Our sheep farmer wants to build a new sheep corral. He would need to know positive and negative numbers, fractions, and decimals. This middle school lesson on rational numbers is integrated with some Navajo sheep history and is for grades 7 to 8. The examples are detailed and include word problems of rational numbers as applied to finding sheep farming profits. Operation rules are covered along with application of ratio and perimeter skills.


1. Bell ringer: Navajo Sheepherding Life

Have students watch this short spotlight video of Navajo sheepherding life in Arizona.

2. Write answers to prompts

Write a short response to it to keep in their notes for discussion during the history parts of the lesson.

  • What do you notice about the northern Arizona terrain?
  • What do traditional Navajos think of land ownership?
  • How does the grandmother, Helen, care for her animals?

3. Math Lesson on Rational Numbers

This presentation, Raising sheep and rational numbers, introduces the concept of rational numbers as anything that can be explained as a ratio. Negative numbers are illustrated both as loans a sheep farmer would take out and depth of holes in the ground that the farmer needs to consider in selecting the size of posts. Students are given rules of integer addition and subtraction to use as an aid in solving problems.

4. Play Game

Play Making Camp Navajo – Sheep Herding and Rational numbers. AVAILABLE FALL 2021/

Select the game with this icon

Differentiated Instruction

For students who may need a review of the basics, this video on What are Rational provides a good and entertaining refresher.

Related Lessons

Adding and subtracting decimals — Students watch two videos explaining decimal and fraction equivalence. They are then presented with a brief reminder of natural, integer and rational numbers. A slide presentation discusses adding and subtracting decimals. The lesson ends with teacher and student-generated practice problems.


There are five problems within the presentation to be worked as a class. Teachers can present the question and have students write the answers and then present the answers. Alternatively, for students working at home, each slide with questions is followed by worked answers.

Teachers can also see which standards students have attempted and how many problems they have answered correctly in the Making Camp teacher reports.