Category Archives: ratios and proportions

Cross-curricular lesson on Native American vets

CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

CCSS.ELA-LITERACY.WHST.6-8.1 Write arguments focused on discipline-specific content.

CCSS.ELA-LITERACY.WHST.6-8.6 Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas clearly and efficiently.

⏰ Time

Three to four hours. Time varies depending on the time allowed for research online and whether presentation will be submitted in writing or include presentation or video.

📲 Technology Required

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

Summary

This cross-curricular lesson includes history, mathematics, English language arts, computer applications and physical education. Students play a game which teaches about Native American veterans in World War I. They are given a presentation on the accomplishments of veteran, Joseph Oklahombi. In P.E. class, students sprint 210 yards to simulate Oklahombi’s attack. They are assigned to create a presentation to nominate Oklahombi for the Congressional Medal of Honor. This may include Google Slides, PowerPoint or video presentations.

Lesson

Presentation in Social Studies

Use the Google slides presentation to teach information about Joseph Oklahombi and Native American participation in World War I. They are given a presentation that includes information on the accomplishments of veteran, Joseph Oklahombi, including the ratio of enemy prisoners captured to American soldiers in his unit. The presentation also discusses the failure of the U.S. government to recognize soldiers like Oklahombi as citizens and the subsequent congressional acts that addressed this issue.

Have students play the Native American veterans game and select the section on World War I veterans.

Screenshot of menu with 5 choices, World War I , Women Veterans, War Stories, Famous Veterans and one, unlabeled, picture of a man in a war bonnet

Writing Assignment

The writing assignment and an outline for a guide are included in the presentation. This can be printed or copied and distributed to students through Google Classroom, Schoology or other CMS.

Physical Education

During P.E., have students measure out 210 yards, set out obstacles to dodge and jump over (backpacks with stacks of books would be a good choice) and sprint down the course, simulating Oklahombi’s attack on the machine gun nests.

Mathematics

Two ratios are computed in the presentation. The teacher may ask students to compute these individually and then present the answer. This lesson may be included as part of the ratio and proportion unit.

Computer Applications

Students will need to access the internet for their research. There are many reputable sites with information on Joseph Oklahombi, including the Smithsonian Museum of the American Indian, Oklahoma Historical Society, Veteran’s Administration and more. Optionally, students may submit their assignment as a video or slide presentation or write it using a word processor.

Differentiation

For students who have learning disabilities or other limits on writing ability, an oral presentation or video may be submitted in lieu of the written assignment.

The Codex in Latin American History and Math

Standards

CCSS.ELA-LITERACY.RH.6-8.2 Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source distinct from prior knowledge or opinions.

CCSS.MATH.CONTENT.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations

CCSS.ELA-LITERACY.W.7.1 Write arguments to support claims with clear reasons and relevant evidence.

Technology required

Device with a browser for AzTech Game. Printer for printing codex and related worksheet and activity pages.

Time

4-5 hours

Lesson Summary

This is an augmentation of a lesson from the Library of Congress uses a primary source – the Huexotzinco Codex – as a basis for document analysis, inquiry and applied mathematics. Students analyze pages documenting tribute paid to Spanish administrators, compute the tribute paid, read a one-page overview of the codex and analyze the codex. A presentation is given on connections between Aztec, Mayan and contemporary methods. Students begin or end classes playing a game that includes Mayan history and middle school mathematics.

Lesson

First, some background for the teacher. The Huexotzinco Codex was part of the evidence in a case brought by the Nahuas, Indigenous people of what is now Mexico, against the Spanish administrators, alleging excessive taxation (tribute). This case was won by the Nahuas. In this lesson, students do not learn the full story until the third or fourth class period.

Analyze Documents

Begin with this link to the Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 1, Document Analysis. This should take one class period- approximately one hour.

NOTE TO THE TEACHER: Allow at least 30 minutes before using this lesson the first time, to read through the Library of Congress lesson, download and print out documents for students.

Play a game

Have students sign in and begin the game, AzTech: Meet the Maya. Students should play for about 15 minutes.

Computation – How much was the tribute?

Continue with the second part of Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 2, Computation. After students have completed one tribute sheet and corrected their answers, use this slide presentation to show the connection between the Aztec and Maya codices and our modern system of numbers and graphs. Optionally, have students complete one or two more tribute sheets from the linked lesson. This should take one to two class periods.

Play a Game

At the beginning of class, have students continue the AzTech: Meet the Maya game. Students should play for 15-20 minutes by which time some of the students should have reached the codex activity and explanation in the game.

Write a Narrative Explanation

Continue with the third part of Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 3, Narrative Explanation.

Assessment

Four types of assessments are included; observation of student understanding of historical document analysis in the class discussion, student self-corrected math computation, student written assignments (analysis sheet, observations and scenario outlines) and the math problems in the AzTech game which are scored automatically with data available in teacher reports.

Differentiated instruction (optional)

Advanced Students who complete their assignments early can continue with the AzTech: Meet the Maya game. If they complete this game, they can choose to play AzTech: The Story Begins or AzTech: Empiric Empire.

English learners can play the AzTech : Meet the Maya and AzTech: The Beginning games in English or Spanish.

Recommended Related Lesson

Counting ropes and rational numbers

Ratio and Proportion Unit

2 Replies

Note: When we surveyed teachers from the 2021-22 academic year, the most requested addition to the site was to combine the lessons into units. Of course, your average teacher could do this but your average teacher is also short of time.

📖Standards

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

CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

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

⏰Time Required

About 4 hours for all seven lessons

📲Technology Required

Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning. Presentation could be printed for students at home without computer access.

🧾Unit Summary

This seven-lesson unit teaches sixth- and seventh-grade standards on ratio and proportion using real-world problems. Complete unit requires about 4 hours and includes multiple hands-on activities.

Lesson 1: Teach Ratio with Math Snacks (90 Minutes)

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

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 2: Ratios as Fractions (10 Minutes)

Summary

Standard: CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

Yes, this lesson plan is just a video. We watched LOTS of boring videos on ratios and rates to find this one! This video can be used before or after the lesson on Introduction to Ratio and Proportion, either as an introduction for students who need more preparation or a second look for students who could benefit from having the material presented in a different way.

Lesson 3: Introduce Ratios and Proportion (30 minutes)

Standard: CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

Summary: Students are presented with definitions of ratio and proportion along with multiple examples and ways to solve these problems. This presentation includes multiple explanations for multiple levels of understanding. There is a solution using algebra, with cross-multiplication and an explanation of why cross-multiplication works. There is also an explanation using equivalent fractions. If you are teaching an algebra class, use the first explanation and delete the second. For a more basic math class, delete the first explanation and just use equivalent fractions. Also includes a baking activity, not required but highly recommended.

Lesson 4: Ratio, Proportion and Animal Identification (65 Minutes)

Standard: CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

Students hear or read a presentation on ratio, percentage decrease, rate and proportion. They watch a short video on ratio. Students collect data either outdoors or using images provided. They then compute ratio, rate, increase and proportion using the data.

Lesson 5: Introducing Ratio and Proportion with Making Camp Navajo (30 Minutes)

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

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 6: Rates, Ratios and Proportions with Fractions (40 Minutes)

Standards: CCSS.MATH.CONTENT.7.RP.A.1 Compute unit rates, including those that involve complex fractions, with like or different units.
CCSS.MATH.CONTENT.7.RP.A.2.C. Represent proportional relationships by equations

Students watch a 4-minute video giving examples of finding unit rates by simplifying fractions. They solve a problem together as a class and are given a short lecture on solving rate problems with complex fractions. Problems provided can be worked by students individually or done together in class.

Lesson 7: Discover Dairy – Ratio in the Cow Life Cycle (65 Minutes)

Standards:CCSS.Math.Content.6.RP.A.1 Understand ratio concepts and use ratio reasoning to solve problems.
CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities
CCSS.ELA-LITERACY.RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.

This cross-curricular lesson is from Discover Dairy. Students read a passage on the life cycle of dairy cows. A guided class discussion answers questions on the life cycle. The lesson concludes with a challenging lab in which students create a healthy cow diet.

Discover Dairy: Cow Life Cycle

1 Reply

📖 Standards

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

CCSS.ELA-LITERACY.RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.

📲 Technology Required

Computer with printer to print lab work sheets, for in-class use. Computer or tablet with Internet access for home use.

Heads up! For the lab in this lesson you will need spinach, carrots, cheese sticks, orange juice, and a weight scale and/or measuring cups. It is not required to do the lab 2 component but recommended.

⏰ Time

60-70 minutes

📃 Summary

Lesson

NOTE: While we create most lessons on the Growing Math site ourselves, we do include links to other lessons that are exemplary in their cross-curricular, standards-based design. This lesson is one of two “lessons we love” from Discover Dairy. The entire 14-page guide with two lessons can be downloaded here, including reading passages, lab assignments and answer keys.

You can also go to the Discover Dairy site, which requires a free registration and login to download individual parts of the lesson and see the other lessons they have available.

Read a passage on the life cycle of a dairy cow

You’ll find this on page 14 of the handout linked above or download both reading assignments here (it’s only two pages) or copy the link to assign in your Google classroom to read on line.

Class Discussion on Life Cycle

Using the discussion questions on page 4 of the complete lesson plan, discuss the dairy cow life cycle with students based on their knowledge from the reading.

Lab Exercise #2 Feeding a Dairy Cow

Each student or group will need a scale or measuring cup and the following:

1 cup spinach
Baby or whole carrots
1 cheese stick
One 12 oz. cup of orange juice

Distribute the materials needed and the lab assignment (pages 11 and 12 of the complete lesson plan or you can link directly to those here, if you want to assign in Google classroom or other management system. Note that link includes both labs 1 and 2.) Lab explanation from page 5 of the complete lesson plan.

Teachers should explain that a healthy, well-cared-for cow will give more milk. The way farmers care for their cows and how they feed them has helped to increase the amount of milk cows give over the past 50 years.  Just like our diets, a cow’s diet must be balanced based on her stage of life. For instance, a baby calf requires higher energy foods to fuel her rapid growth.  A cow that has just given birth requires higher levels of certain nutrients to replenish her body. Farmers must adjust rations to accommodate those needs.  Farmers work closely with an animal nutritionist and use a variety of feed products to balance cows’ diets to meet their precise nutrient needs using a variety of feed products.  Farmers use a large feeding scale to make sure each cow gets the right amount of each feed. Those feeds are blended together to provide a balanced diet called a Total Mixed Ration (TMR). During the lab, students should use the carrots, celery, cheese and orange juice to balance a diet to meet the required nutrients listed on the lab worksheet. They should use a weight scale to measure the right amount of each feed. If they don’t have a weight scale, they can use measuring cups to determine the amount. Complete the ratios in the worksheet.
– Discovery Dairy

Answer keys for this lab exercise as well as for the lab for the selective breeding lesson can be found here.

Review and Summarize Dairy Cow Life Cycle: What We’ve Learned

Review questions and summary can be found on pages 5 and 6 of the complete lesson plan.

ASSESSMENT

This lesson includes three types of assessment – the initial class discussion gives an estimate of the general class understanding of the dairy cow life cycle. The lab provides individual student data on mastery of both the science and math concepts. The concluding review questions can be poised to the whole class or given to students as a quiz.

Related lesson

Discover Dairy: Selective Breeding

Analogies with sheep and goats

📖Standard

CCSS.ELA-LITERACY.L.7.5.B Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words.

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)

⏰LESSON TIME

25 -30 minutes including game play

📲TECHNOLOGY REQUIRED

A device with a web-browser – PC, Mac or Chromebook – or phone or tablet.

📃Summary

Students play a game which teaches about raising lambs, the uses of sheep and the ratio of single to twin lambs. The lesson ends with definitions of sheep and goat vocabulary and examples of analogies with sheep and goats. Optionally, students may complete a word journal assignment.

📚Lesson

Start with a game

Students begin by playing Making Camp Navajo. You can just copy and paste these instructions into your Google classroom or other system, or just copy and show in a projector on the board – old school rules!

You can assign your students usernames and passwords or you can send us a list and we will register your students for you. Email the list to growingmath@7generationgames.com . Your students can create their own usernames and password but we do not recommend this, mostly because they will forget what they entered.

Play Making Camp Navajo

There are three activities students should play. If you have not played before, the game will start you at the introduction. If you are a returning user, log in and click on the Life tab.

Earn page with choices of Numbers, life and random

Learn about sheep in Navajo daily life

On the LIFE page, you’ll see two photos with sheep in them. Play both of those sections.

Next, go to the numbers page and pick this option to learn a little more about sheep.

Now that you have read the instructions, here is the link to go to Making Camp Navajo.

Learn the vocabulary

Now that students have learned about sheep, let’s learn some sheep and goat vocabulary using this Google slides presentation. The presentation ends with two examples of analogies, then asks the students to give their own examples of analogies.

Assessment

This lesson has two types of assessment. Making Camp Navajo automatically records students answer to problems in the three game activities, assessing the Diné and math standards. The analogies produced by students address the ELA standard.

Differentiated Instruction

For students who struggle with vocabulary, including English learners, you may wish to include a word journal assignment. Some teachers call it a personal dictionary. Regardless, the goal is the same, for students to record new words, give a dictionary definition and “make the word their own”. This can be done by rewriting the definition in their own words, using the word in a sentence or including an illustration of the word.

Two dictionary sites to recommend for definitions are below. An added bonus to mention to students is that they can hear words pronounced.

Since students often ask for an example, here is an example you can link in your lesson.

The personal dictionary assignment, with all links, can be found here. Feel free to copy and paste into your Google classroom or other site, or print out for your class.

Food Deserts, Indigenous Seeds and Data Stories

1 Reply

Standard

CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.

CCSS.ELA-LITERACY.RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

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

⏰ Time

70 – 90 minutes, including cooking activity

📲 Technology Required

A computer with projector or smart board is required to show the video and presentation to students.

Summary

This truly cross-curricular assignment begins by watching a video about seed rematriation, that is returning Indigenous seeds to their original lands. They read a short booklet on cooking and nutrition, then do a cooking activity at school or home. A presentation on food deserts includes definitions, data and actions students can take. Students add new words or phrases to their word journal and complete a math assignment using data from the presentation. Advanced students play a game to learn more math and Navajo culture.

📚 Lesson

Watch this video seed rematriation, that is, growing Indigenous seeds in the lands from which they came originally.

Read a short booklet on cooking and nutrition

Scrambled eggs and spinach – available here as a free pdf from the U.S. Department of Agriculture, is directed at parents but should be at the reading level of most sixth- or seventh-graders.

Make some eggs

It will be a lot more fun for your class if you can actually go to the school kitchen and cook some eggs. Reading the booklet above will give the recipe, optional ingredients and much more. The only 3 ingredients you absolutely need are eggs, spinach and vegetable oil or butter.

Alternative assignment

If you absolutely cannot go to the kitchen at school because of scheduling, safety regulations or other reasons, here are two other options.

Assign this activity for students to do with their parents at home. Here is the link for the recipe. You can make this an extra credit activity because not everyone has parents who have time or money to run out for eggs and spinach. Optional: If students have access to a phone or tablet, have them record themselves/ their parent cooking.
You can watch a video of kids making the recipe , but doing it with your class will be more fun.

Listen to/ read presentation on food deserts

What if there was nowhere to buy eggs, spinach or even seeds near where you live? You can use this Google slides presentation to present to students in class or assign them to read on their own.

Complete word journal

Students add words or terms with which they are unfamiliar to their word journal. Some teachers call it a personal dictionary, to others it’s a word journal. Regardless, the goal is the same, for students to record new words, give a dictionary definition and “make the word their own”. This can be done by rewriting the definition in their own words, using the word in a sentence or including an illustration of the word.

Two dictionary sites to recommend for definitions are below. An added bonus to mention to students is that they can hear words pronounced.

Since students often ask for an example, here is an example you can link in your lesson.

The personal dictionary assignment, with all links, can be found here. Feel free to copy and paste into your Google classroom or other site, or print out for your class.

Math assignment: Using statistics and ratio to answer questions

Copy the assignment into your Google classroom or other system or print out for students. Students will use the data from the Food Deserts presentation to answer questions about percentages. They will also create pie charts (circle graphs) and bar charts. You can have students do this with a calculator or pencil and paper or using Google sheets.

ANSWER KEY for assignment

If you’d like a spreadsheet where these tables and graphs were created, you can find it here.

Differentiated Instruction: For Advanced Students

Challenge more advanced students to watch this video on Making Mounds for Three Sisters Gardens. The vocabulary is a little more advanced than the typical sixth-grade with terms like “nitrogen”, “fish emulsion”. In the first farm, they planted 80 mounds. Students should watch the video and figure out from the information given how wide the plot must be .

More advanced students can also play the Making Camp Navajo game, available from the Games for Kids portal on this site, to learn more about farming and expand their knowledge of ratio and proportion.

Assessment

Word journals are graded based on correct or incorrect definition. Data analysis assignments assess student achievement of math standards above.

Introducing Ratio and Proportion with Making Camp Navajo

1 Reply

📖 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

📚 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

Go to the Games Portal for Kids page – here https://www.growingmath.org/games-portal-for-kids/
Select the icon for Making Camp Navajo. You may need to scroll down to see it. The icon looks like this:
Login with your username and password your teacher gave you.
Play through the introduction and until you get to the page with Numbers, Life and Random as choices, click on the Numbers box.
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

2 Replies

📖 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

📚 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 and show the video again, 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

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.

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.