Category Archives: ratios and proportions

Introducing Ratio and Proportion with Making Camp Navajo

📖 STANDARD

CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities

⏰ Time

30 minutes

📲 Technology Required

Either a project or smart board connected to the computer will be required to view presentation and videos in class or students will need a computer to watch during a web meeting. The game can be played on any computer or tablet with Internet access.

📃 Summary

Students play the Making Camp Navajo game, selecting the activity that explains ratio and proportion. The teacher reviews the activity with the class in a presentation, that includes three more problems to be completed as a group.

📚 Lesson

1. Play Making Camp Navajo and Learn Ratio and Proportion

Begin the lesson with students playing Making Camp Navajo. The following instructions can be pasted into a document linked to an assignment in your Google classroom or other system, or just printed out or written on the board.

Play Making Camp Navajo for an introduction to ratio and proportion

  1. Go to the Games Portal for Kids page – here https://www.growingmath.org/games-portal-for-kids/
  2. Select the icon for Making Camp Navajo. You may need to scroll down to see it. The icon looks like this:
  3. Login with your username and password your teacher gave you.
  4. Play through the introduction and until you get to the page with Numbers, Life and Random as choices, click on the Numbers box.
  5. Play the two activities that have a girl holding a lamb and an ear of corn. These will teach you about ratio and proportion and give you a few example problems and how to solve them. The two activities you are supposed to select are shown below.
Activities introducing ratio and proportion

2. Review definitions of ratio and proportion with more examples

To reinforce the information, in the presentation, use this 30-slide deck.

Google Slides presentation of Introduction to Ratio and Proportion

PowerPoint presentation of Introduction to Ratio and Proportion.

The first 13 slides review the information from the game and the subsequent 17 explain how to solve for an equivalent ratio and provide additional examples to solve as a class.

Assessment

Students’ knowledge of ratio and proportion is addressed by problems within the game and by the problems in the presentation, solved together in class.

Teach Ratio with Math Snacks

📖 Standard

CCSS.Math.Content.6.RP.A.1 Understand ratio concepts and use ratio reasoning to solve problems.

📲 Technology Required

Computer with projector, for in-class use. Computer or tablet with Internet access for home use.

⏰ Time

90 minutes

📃 Summary

Students watch a video from Math Snacks in which Isabella uses the ratio of words she speaks to her date to determine if it was a good or bad day. The video has a companion teacher guide with questions to stimulate students’ thinking about ratios and test their understanding. Students play a game where they brew potions with given ratios to defeat an opponent. Students then complete a learner’s guide assessing and reinforcing their knowledge of ratios.

📚 Lesson

Read the Bad Date Teacher Guide

The Teacher Guide, available from Math Snacks, will give you an overview of the lesson. This guide includes several discussion questions for use with students.

Watch the Bad Date Video

This three- and-a-half-minute humorous video uses the ratio of words in a conversation to show a couple of bad dates and one good one.

Have a class discussion

Use the discussion questions in the Teacher Guide from Math Snacks to check students’ understanding. Note that this will require you to restart a show the video, stopping at specific points.

If you have not yet introduced equivalent ratios to your class, you may want to skip some of these questions and come back later.

Play the Game Ratio Rumble

The Ratio Rumble game can be played online here at the Math Snacks website or downloaded free for iPads. The first game level begins with 1:1 ratios and gets more complex in higher levels.

Students complete the learner guide

It’s called a learner guide, not a worksheet, so that makes it cool! Seriously, the Bad Date Learner Guide, available here from Math Snacks, has two pages of review and assessment items that test understanding. Students are asked to draw a picture of a ratio, complete “what-if” scenarios and give some examples of other situations in which 1:1 ratios would or would not be desirable.

Related lesson

For another introduction of ratio, see the lesson Introduction to Ratio and Proportion.

Raising Sheep and Rational Numbers

📖 Standards

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)

⏰ Time

45 minutes

📲 Technology Required

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

📃 Summary

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.

📚 Lesson

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.

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.

Assessment

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.