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Introducing Ratio and Proportion with Making Camp Navajo

πŸ“– STANDARD

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

⏰ Time

30 minutes

πŸ“² 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.

πŸ“ƒ 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.

πŸ“š 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.

Geometry and Ledger Art

by Avis Prentice and AnnMaria De Mars

πŸ“– Standards

CCSS.MATH.CONTENT.7.G.A.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

⏰ Time

90-120 minutes, including time students spend on creating shapes, measurement and creating winter count artwork

πŸ“² Technology Required

A computer with project/ smart board for viewing as a class or computer or mobile device for viewing videos at home is required. Art project can be done on Google Slides or PowerPoint or with markers and paper or construction paper, glue and scissors. Paper bags (optionally) can be used to simulate a hide background.

πŸ“ƒ Summary

Students begin by watching two videos that appear to be unrelated – on Native American ledger art and using a protractor to measure angles. These are explained in the presentation, that art can take many forms. Vocabulary and basic facts regarding angles are introduced. Students use an online app to create angles with different lengths of lines. After measuring lengths and angles of their shapes, students create artwork for their own event and a classroom ‘winter count’. Use of angles in computer animated art is explained. The session ends with assessment of students’ knowledge of measurement of angles.

πŸ“š Lesson

Watch video on Native American Ledger Art

Watch to 5:07

Students will watch the video to the point of 5:07 , where the curator says to think of an event you really want to remember.

Watch video on using a protractor

Explain basic concepts and vocabulary of measuring angles

This 31-slide deck explains degrees as a measure of rotation, defines acute, obtuse and right angles and obtuse, acute and right triangles. Instructions are given for students creating their own ledger art. Available as Google slides here or as a PowerPoint Presentation here.

Students use an online app to create triangles from different lengths of lines.

Example from the GeoGebra app

In this exploratory activity, students should learn that a triangle cannot be created from any three lines. They will also get practice creating different angles and seeing the shapes of triangles with different angles. This activity is recommended but can be skipped if students do not have access to devices. Alternatively, the teacher or a student can create angles with result shown on a smart board/ projector.

Students create and measure shapes

As instructed in the presentation, students create lines, triangle and circles. They measure the diameter or radius of circles, length of lines and angles of triangles. Students write a description of their shapes using mathematical terms.

Students create their own artwork to commemorate an event

Students will use the shapes created in the previous activity to create original work. They will present their artwork to the class and explain its meaning.

Students watch a video on winter count

Emil Her Many Horses explains the creation and meaning of the winter count

Students combine their events to form a classroom record

Individual student events can be combined on poster board, included in a single Slides or PowerPoint document. Dr. Vivian Young recommends using large brown paper bags to simulate hides, crumpling and tearing around the edges to give more of a hide appearance.

End with presentation

Finish the slide presentation by informing students that their measurements are the first step a software developer would take in turning their artwork into computer animation for a game or website. They have been programming and did not even know it!

Assessment

An assessment of students’ knowledge of measurement of angles and types of triangles is included here as :

Google doc file for assessment

PDF version of assessment

ANSWER KEY FOR ASSESSMENT

Making a Calendar with Google Slides

πŸ“– Standard

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.

CCSS.ELA-Literacy.RH.6-8.1 Cite specific textual evidence to support analysis of primary and secondary sources.

⏰ Time

200 minutes (approximately 5 class periods)

πŸ“² Technology Required

Students will use the Internet to find a minimum of 12 appropriate images to represent their topic. Students will need access to a device with Google Slides to create calendar.

πŸ“ƒ Summary

This lesson plan allows students to explore a topic of interest to create an informational calendar. Students are to pick a topic, include an image for each month, brief explanation and source for that image. At the end of the project, students perform a self-assessment.

πŸ“š Lesson

Introduce Assignment to Students

Calendar Assignment

In this assignment, you will be creating a personalized calendar using Google slides. Your calendar must consist of a minimum of 13 pages an include the following:

  1. A title slide with introduction of the topic.
  2. A page for each month with:
    1. An image related to your topic
    2. Text explaining the image and its relationship to the topic.
    3. A link to a source for the image and information on the page.

Presentation to Explain Modifying Template

Use this brief presentation to explain how to change the background on a slide and how to add images. It uses the 2022 calendar template as an example.

There are many, many Google Slides calendar templates you can find on the web. Many of these are great, some cost money, some are for 2021 and some have broken links. So, we added an example here that you, on the topic, “Indigenous”, that you can copy into your Google classroom and modify, just to make sure you would have a free template that is available and up to date. It uses a variety of methods of citing sources, from a simple web link in January to APA style in May.

The sample calendar as a PDF is found here.

Make a personalized gift

Janna Jensen, IT specialist from North Dakota, laminates each page in the calendar and binds the pages for a personalized gift from students to parents or other special people in their lives. If you have limited funds, you can just laminate the first and last page for durability, or skip lamination altogether if you don’t have a laminator.

If, like me, you don’t have a binding machine, you can just use a 3-hole punch and twist ties from cables or bags of bread. Ask the lunchroom staff to save some for you.

My first time ever using a laminator.

Make this assignment your own!

I highly recommend encouraging your students to improvise with this assignment. They can find another template on line, insert pages in between months so that each month has a large scale image at top – the possibilities are endless.

Assessment 

Students perform a self-assessment shown below. 

Related Lesson

You may wish to use this lesson to introduce students to the concepts of primary and secondary sources.

Individualized Learning

Advanced students may wish to complete these six online lessons to become more proficient with Google slides.

State Standards: North Dakota

K-5.IAI.9 Organize information using technology and other tools.


TE.K-5.MTL.11 Use technology to gather and share information with a variety of audiences in ways that others can view, use, and assess.

Calendar example with grazing lands

Making a Calendar with PowerPoint

by Janna Jensen

πŸ“– Standard

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

200 minutes (approximately 5 class periods)

πŸ“² Technology Required

Students will use the Internet to find appropriate images to reflect tasks typically accomplished during a specific month. Students will need access to a device with PowerPoint to create calendar.

πŸ“ƒ Summary

This lesson plan allows students to explore agricultural subjects of interest to create an informational calendar. Students are to pick a field in agricultural and create a calendar outlining the big tasks performed each month. At the end of the project, students perform a self-assessment.

NOTE: While this assignment focuses on agriculture, it could be modified for any subject – science, social studies, literature, and, certainly, art.

Don’t have PowerPoint but you use Google Slides? Check out this lesson.

πŸ“š Lesson

Introduce Assignment to Students

Calendar Assignment

In this assignment, you will be creating a personalized calendar using PowerPoint. Your calendar must consist of a minimum of 13 pages an include the following:

  1. A title slide with introduction of the topic.
  2. A page for each month with:
    1. An image related to your topic
    2. Text explaining the image and its relationship to the topic.

See the Agriculture Calendar for an example.

Video or Presentation on Creating Calendar with PowerPoint

Classroom Presentation

Use this PowerPoint of Instructions on how to create a calendar with PowerPoint. It is a brief 3-5 minute explanation. Instructions are also available in Google Slides format.

Video

This video is only 1:33 and shows using PowerPoint to create a calendar

Students can watch the video above, which has only music, no voice over, so it will be usable even if your students don’t have headphones or your computers don’t have speakers. It is also a good review if students are learning at home or need an extra reminder.

Make a personalized gift

I laminate each page in the calendar and bind the pages for a personalized gift from students to parents or other special people in their lives. If you have limited funds, you can just laminate the first and last page for durability, or skip lamination altogether if you don’t have a laminator.

If you don’t have a binding machine, you can just use a 3-hole punch and twist ties from cables or bags of bread. Ask the lunchroom staff to save some for you.

Assessment

Students perform a self-assessment shown below.

State Standards: North Dakota

K-5.IAI.9 Organize information using technology and other tools.


TE.K-5.MTL.11 Use technology to gather and share information with a variety of audiences in ways that others can view, use, and assess.

Counting ropes and rational numbers

Contributed by Lori Hieresrich

πŸ“– Standard

CCSS.MATH.CONTENT.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

πŸ“ƒ Summary

The lesson begins with a discussion of record keeping methods in Indigenous cultures. Students will watch video on Incan counting ropes. Students will create their own number line counting rope. Students watch another video on number lines. Students will use their number line to find Absolute Value of an integer. Students will demonstrate understanding of adding and subtracting integers on number line.

πŸ“² Technology Required

The videos can be watched on any computer, phone or tablet. Not technology, but each student needs 2 yards of cord. ( As long as needed for all the knots with even spaces between.) Thicker cord is better to make it more tactile. Cord that works could be hemp, leather strips, or twine.

πŸ“šLesson

Start with this PowerPoint presentation. Also available as a Google Slides presentation.

NOTE: If you are using it as a PowerPoint presentation, download it before making any changes. Making changes to the PowerPoint in Google Drive will delete the animations and one of the embedded videos and you don’t want to do that.

The first five slides introduce the topic of how people from different Indigenous cultures in the Americas measured time and other quantities.

2. Watch this video on Quipu accounting

3. Make a counting rope

Students make their own counting ropes using rope, string or twine. Instructions to give students are provided in the PowerPoint.

4. Use the counting rope to solve math problems

Students follow along in the presentation to solve problems using positive integers , fractions and negative integers. The concept of absolute number is introduced, as well as the fact that adding the same number but with the opposite sign will always equal zero. If students are learning at home, they can complete the problems on their own.

Assessment

In addition to the problems completed as a class in the presentation, students complete this worksheet with problems on using a number line with positive and negative integers and absolute value. Only print the first page. The second page is the answer key.

Number line and absolute value – word doc

Number line and absolute value – pdf

Individualizing instruction (optional)

Knots on a counting rope video or the children’s book by the same name give other examples of using a rope to count. This would be appropriate for younger children or those in the class who are at a lower grade level in reading proficiency.

Ratio, Proportion and Animal Identification

πŸ“– Standard

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

⏰ Time

60-70 minutes

πŸ“² Technology Required

A computer, phone or tablet with Internet connection is required to watch the video and play Making Camp Navajo. If these are not available, the assignment can be printed out and distributed to students or shown in the classroom on a projector with computer.

πŸ“ƒ Summary

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.

πŸ“šLesson

Review the concepts and introduce the assignment

Begin with this presentation that explains ratio, rate, percentage increase/ decrease and proportion. The presentation also introduces the assignment students will complete. There is a video included in the presentation on ratio. If you have difficulty playing the video Atlantean Dodgeball, in the presentation, here is the direct link.

Students complete data collection, ratio, rate and proportion assignment

There are four options for completing this assignment, depending on your environment. Ideally, students would collect data outside, but if you are in the middle of the city or it is winter and there are no animals around, you may want to select one of the other options. Allow students to choose one of the four options or delete whichever does not fit your situation.

If observing animals outside is not an option, here are two images your students can use to identify animals. Click the link for an image you can save in your Google classroom.

Scene 1- Animals in the savanna

Yes, all these animals can be found in the African savanna

Key for scene 1 – Image with animals labeled

Names of the 23 animals in scene 1

If students don’t have a partner, they can use Scene 2, Animals in unexpected places, for their second data collection.

Key for scene 2 – Image with animals labeled

Names of the 24 animals in scene 2

Play Making Camp Navajo

Play the Making Camp Navajo game to learn more about ratio and equivalent ratio.

(Available Fall, 2021). If you’d like access to the beta version, please email us at growingmath@7generationgames.com We’d be happy to provide it to you.

Individualizing instruction (optional)

The presentation discusses the animal kingdom and the six kingdoms many biologists use for classification of living organisms. For students who are particularly interested in this topic, the post, “Are insects animals?” can be provided as supplemental reading or teachers may wish to print this out for students who do not have home Internet access.

RELATED LESSONS

These two lessons are recommended for students prior to this assignment.

Converting fractions to decimals

πŸ“– Standard

CCSS.MATH.CONTENT.7.NS.A.2.D Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

⏰ Time

30-40 minutes

πŸ“² Technology Required

A projector or smart board is required to show the Google slides presentation in class. It can also be shown using any web meeting software for remote learning. The random candy generator can be used by students in anything with a browser, including computers, tablets or phones. This activity is optional. It’s actually more fun with fun-size bags of candy like Skittles or M & M’s.

πŸ“ƒ Summary

Students watch a video or hear a presentation explaining using long division to convert fractions to decimals. A second method of using place value is discussed when the denominator is tenths, hundredths or thousandths. Students then play a game that teaches converting fractions to decimals and end with an activity finding the decimal representing each color in a bag of candy. A simulator is included if no bags of candy are available!

πŸ“š Lesson

EITHER watch the video below

This is a 7-minute video that gives the steps in converting fractions to decimals, with multiple examples, using both long division and place value.

OR Use this Google Slides Presentation

The Google slides presentation covers the same material as the video with the same examples. The steps in the long division problems are animated in the presentation. If you prefer a PowerPoint presentation you can find that here. Both can be viewed from these links or you can copy into your own Google drive or download to modify for your class.

The presentation and video both include two sample problems to work as a class.

NOTE: The presentation includes an activity converting fractions to decimals using candy or a random sample application.

Play a Game

Play the Empiric Empire game for 10 minutes. This game teaches fractions and decimals in the context of concepts from epidemiology such as prevalence, incidence and mortality rate.

Simulated Candy Bag

Convert fractions with Candy

The Google Slides/ Powerpoint ends with an activity where students use a pack of candy to find fractions, convert those fractions to decimals and graph the result. If you don’t have time / forgot to buy bags of candy, you can use a simulator here. Random fact: The average fun-size bag contains 12 pieces of candy. There is a link for plain graph paper in the slides. If you’d prefer graph paper with fractions and decimals already entered, this page is divided into sixteenths.

Assessment

This lesson includes three types of assessment. There are the problems completed together in class, included within the presentation or video. There are the problems completed within the Empiric Empire game which you can see in the teacher reports. There is also an assessment at the end of the slides using different colors of candy to convert fractions to decimals and chart the results.

Raising Sheep and Rational Numbers

πŸ“– 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

πŸ“² Technology Required

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

πŸ“ƒ 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.

πŸ“š 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.

Google Slides and Math

πŸ“–Standards

CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

CCSS.ELA-LITERACY.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

⏰ Time

120 – 180 minutes (You may wish to use 2-3 class periods)

πŸ“² Technology Required

The games used here require a Chromebook, Windows or Mac computers or iPads.

πŸ“ƒ Summary

Students play three games that teach fractions and statistics. Students learn enhanced features of Google slides. They then create a Google slides presentation stating which is their favorite game and why.

πŸ“š Lesson

0. Optional: Google Slides Basics

If students are not familiar with Google Slides, begin with the Google Slides Basics lessons. If students know how to create slides document, select a theme, add text, images, transitions and animations, you can skip this step.

1. Introduce the assignment

Explain to students that they will be playing three different educational games and making a recommendation for future classes. If there is only time to play one of these games, which should the teacher choose. A copy of the assignment is here with both Chromebook and iPad games included. Save to your Google classroom or other system and delete whichever device is not available to your students. If your students have access to both devices, no editing is required. Since their presentation will be made with Google Slides and they want it to be as convincing as possible, they should include images and video to support their points.

2. Play AzTech: The Story Begins

This game teaches fractions and basic statistics, integrated with social studies terms and Latin American history.

Allow students 10 -15 minutes to play the game.

3. Learn about Google Slides Advanced Features

This presentation has links to six videos beyond Google slides basics.

Click on the links on the left side of the screen to learn about:

  • Modifying the theme
  • Inserting video
  • Adding effects to text and images

Allow 10-15 minutes to watch videos and start on their presentations.

4. Play Forgotten Trail or Fish Lake Adventure

Students play Fish Lake Adventure (iPad) a game that teaches fractions or Forgotten Trail (Chromebook), a game that teaches fractions and statistics.

Allow 10-15 minutes to watch videos and continue their presentations.

5. More Google Slides Advanced Features

Continue with more Google slides basics. Watch three videos on the right side of the screen on :

  • Customizing with Word Art
  • Publishing to the web
  • Presentation notes

Allow 10-15 minutes to watch videos and continue their presentations.

6. Play AzTech: Meet the Maya

Allow students the option of playing AzTech: Meet the Maya or continuing one of the two previous games. Meet the Maya continues the game series that teaches fractions and basic statistics, integrated with social studies terms and Latin American history.

Allow 10-15 minutes to play and continue their presentations.

7. Finish !

It’s decision time. Students will select one game to finish for their presentation. Students who finish ahead of the class may play the other games.

Allow 30 minutes to finish the game they have chosen and continue their presentations.

8. Optional (extra credit) Present or publish

Depending on your class and your own objectives, you may want to end this lesson with students either publishing their presentations to the web or presenting in class and trying to convince their classmates that the game they have chosen is the one students should be using to learn next year.

Allow 30 minutes to finish the game they have chosen and continue their presentations.

Google Slides Basic Skills

⏰ Lesson Time

15-20 minutes EACH for two lessons

πŸ“² Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, iPhone or iPad

πŸ“ƒ Summary

There are 6 short videos on Google Slides topics like adding images and choosing a theme. We recommend breaking the first four videos into two separate lessons that students complete during class.

πŸ“š Lesson

These lessons from Google for Education provide a good overview to Google Slides. These are part of the Applied Digital Skills program for which you can register your class and/or yourself or you can just select individual lessons. In our experience, students do better when the lessons are split over 3 or more days.

Day 1: Watch videos 1, 2 and 3

Learn Google Slides while creating a presentation about you. This lesson can be used as is or modified for other topics. The default assignment is for students to create an “All About Me” presentation. The first three videos explain creating a presentation, choosing a theme, inserting a title, adding text and images. You can copy the link and paste it into your Google classroom or other site used for assignments or have students watch these together as a group in class.

For younger students, these three videos may be adequate for your class requirements.

Day 2: Create a Presentation (Bells and Whistles optional)

Watch this five-minute video on Animation and Transition in Google Slides.

Create Your Own Presentation

After watching this 5-minute video, students are ready to create their own presentation. Students can create an “About Me” presentation as suggested in the Google slides or teachers can assign their own preferred topic.

Assessment

Rubric for assessment includes:

  • Student created Google slides presentation
  • Presentation includes the following elements: headers, text and images
  • Presentation uses at least one animation and one slide transition

For younger students, you may wish to eliminate the last requirement.

Related lesson:

Google Apps Basics for Hamsters — As the name implies, a super-basic introduction to Google Drive and Google Docs.