Category Archives: mathematics

Decimals, Epidemics & Fly Vomit – It’s science!

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📖Standards

CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths

CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

CCSS.ELA-LITERACY.L.6.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Technology

Students will need a phone or tablet to play the game.

Time

75 minutes

Lesson Summary

Learn decimals while weighing a flies and the food they eat. The lesson begins with a game on decimals and the Aztec smallpox epidemic, then moves to another disease spreader – flies. Students learn the role flies play in our ecosystem, how they eat and reproduce.

Lesson

1. Play a game

Play AzTech: Empiric Empire to learn basic conversions from fractions to decimals. Empiric Empire is available free for iPad or iPhone and for Android phones. As an added bonus, students will also learn about epidemics. It’s worth mentioning that the smallpox epidemic was spread by viruses but a lot of other diseases are spread by flies.

Note: For summer learning, you may want to just copy the paragraph above into your Google classroom for students to download the games to their phones.

2. Watch a video

I pasted in a link starting after the first minute because that is mostly telling you to like/ subscribe and comment. Ah, YouTube!

Bell Ringer – What if flies went extinct ?  This 7:33  minute video discusses flies as agricultural pests and disease vectors, but also their benefits as scavengers eating up decaying carcasses, pollinators and animal feed.

Here is the link if you’d like to post in your Google classroom or other CMS for students to watch at home. https://youtu.be/80Iqp6bqc-0?t=76

3. Read about flies & perform a demonstration

Recommended reading: Eat like a house fly. Houseflies and barf

What really happens when a house fly lands on your food? Print out this page from Science World – Canada , include the link in your Google classroom or other CMS for students to read, or just read the page to students during class. The demonstration requires vinegar, jello and a turkey baster – things many people have around the house or can pick up easily at a local store. It also includes a list of vocabulary words and definitions, which fits perfectly with our philosophy of direct teaching of academic language.

4. Complete word journal

This lesson provides the opportunity for students to learn many words, in the reading, in the videos and possibly in the Empiric Empire game as well. 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.

5. Presentation on Decimals in Science (Fly Experiment)

Give this presentation on using decimals to weigh flies, their containers and the food they eat to answer the question, “Do flies really eat 10 times their weight each day?”

Watch a second video

I recommend watching the first 5 1/2 minutes of the Facts About Flies – Secret Nature video  to give the students some idea about both flies as vectors of disease but also important scavengers consuming decaying material. The full documentary is 49 minutes, which I personally found to be more about flies than I wanted to know.

Assessment

Three types of assessment are included in this lesson.

  1. The Word Journal assignment is completed individually and submitted.
  2. Math questions answered within the Empiric Empire game are scored automatically with immediate feedback and student results can be viewed in the teacher reports.
  3. Math questions posed within the presentation can be answered as a whole class, having students hold up a card with their answer or with individual students responding and asking the rest of the class to agree or disagree.


Differentiated instruction

Review of Decimal Addition

One-minute step-by-step video from TeacherTube on Adding Decimals may be helpful for students who need a review of decimal addition.

Watch the whole video

For students who are extremely interested in insects, watching the entire 49 minute video of Facts about Flies will satisfy their curiosity

Experiments with fly larva

Hungry Hungry Hermetia

For teachers who want to do a deep dive into the role flies in consuming food waste, the experiment above uses 100 black soldier fly larvae. I am extremely impressed with this lesson because not only does it include a link to where to buy maggots (on Amazon, of course) but also answers the obvious question of what do you do with 100 fly larvae after your experiment is over. The answer is that you feed these to your class reptile. Would I bring 100 maggots into my classroom? Not in a million years, but that is why I am not an entomologist.

You DO have a class snake, don’t you?

Mean, Median and Mode (Bilingual English & Spanish)

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by Dr. Craig Waddell

📖 Standard

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

⏰ Time

30-40 Minutes 

📲 Technology Required

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

📃 Summary

Students play a game teaching basic statistics and history. Next, they are given a presentation with problems students solve finding mean, median, mode, range and outliers.

📚Lesson

Play a game teaching basic statistics and Latin American history

Meet the jaguars in AzTech: Meet the Maya

Play AzTech: The story begins. Students who have finished this game can continue on in the series in AzTech: Meet the Maya. Allow students 15-20 minutes to play.

Students can click on a button in the left of their screen to choose the language and play the games in either Spanish or English.

Assess knowledge of Mean, Median and Mode as a class

Use this Google slides presentation to present sets of numbers to the class to use for finding mean, median, mode and range. This is also available as a PowerPoint presentation.

This presentation can also be assigned for students to complete at home, if learning remotely. Slides with answers can be deleted, or left in for students to check their work.

Review as Necessary

If students need a review, they can watch this video on how to find the mean

Finding the Average video

Or, watch the video in Spanish

Encontrando el promedio

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. AzTech: The Story Begins and AzTech: Meet the Maya links can be found on this reports page. You should have received a password during the Growing Math training.

A second form of assessment is available through this the questions in the presentation.

Related lesson/ Differentiated Instruction

If your students need instruction on computing the mean, try this lesson, Understanding the mean, with skunks. This review can be done with the entire class or assigned to individual students as needed.

Mean, Median and Mode – The English only version of this lesson plan that includes English resources.

10-Minute Multiplication Practice with Ojibwe History (Bilingual English & Spanish)

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📖Standards

CCSS. Math 3OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. 

CCSS.MATH.CONTENT.3.OA.C.7– Fluently multiply and divide within 100

NCSS The study of people, places, and environments enables us to understand the relationship between human populations and the physical world. 

⏰Time Required

10 minutes

📲Technology Required

Computer/tablet with internet access for reporting student assessment data from Making Camp Bilingual.

📃Summary

Ojibwe History Integrated with Math If your students are like most people, you’re having a hard time getting them to focus. Each of these three activities only takes a few minutes and teaches Native American history or multiplication. These 10-minute lessons can be done as stand-alone activities at the beginning or end of a class to raise student engagement, or the three in this unit can be combined for a single 30-45 minute lesson.

📚Lesson

Activity 1

Matching Multiplication

Step 1: Have students open Making Camp Bilingual. If you need more detailed instructions on how to access Making Camp Bilingual, student usernames and logging in, please go to this lesson plan. 

Step 2: If students are playing the game for the very first time, they will watch the two introductory videos that talk about Native Americans and how to play the game (5 minutes). Then you will see the Making Camp choice screen.

Step 3: Have students click the NUMBERS (NÚMEROS) box to view the six math challenges. You can press the round, green button at the bottom left with white squares to return to the choice screen at any time.

Step 4: Have students click on the top left box (with cards) to play a memory game. In this game, you match multiplication problems with their answers. You may assign this activity for 5 minutes of multiplication drills.

Activity 2

The Multiplication Dog

Step 1: Have students click on the icon with the dog. 

  • This lesson opens with a paragraph explaining that some tribes used dogs to haul heavy loads, using a type of sled called a travois. The player then has the opportunity to earn a dog and items for their dog in the game by answering multiplication problems. The game resets when it is finished, and also takes about 5 minutes.

Activity 3

Reaping the Rewards of Math Practice at the Wigwam 

The player should now have enough points to get a wigwam and at least two items to supply their wigwam. 

Step 1: Click on the wigwam icon on the bottom left. This will play a video on how a wigwam was built, followed by a second video that briefly discusses that trading existed between and within tribes long before the settlers came.

Step 2: The player then has an option to trade points for items for their wigwam.

Clicking on the wigwam in the lower left corner will bring the player to their wigwam. Purchased items appear here for decoration and interaction. 

  • Clicking on an item brings up a text box with information on how that item was used or obtained by the Ojibwe people.
  • Some items also perform actions when clicked. For example, the parfleche opens to show pemmican inside; when clicked, the dog walks across the wigwam.

Assessment

Making Camp Bilingual offers Data and Reports for teachers to access after students are finished playing. 

State Standards

Minnesota History Substrand 2, Standard 3. Historical events have multiple causes and can lead to varied and unintended outcomes.

Related: 10-Minute Multiplication Practice with Ojibwe History

The lesson above has a companion lesson for English Only Learners. 10-Minute Multiplication Practice with Ojibwe History is the same lesson from above but provides the resources in English only, featuring Making Camp Premium.

Analogies with sheep and goats

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📖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.

Many lambs

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.

Related lesson

The Navajo-Churro: America’s first domestic sheep

Food Deserts, Indigenous Seeds and Data Stories

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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.

Teaching frequency tables with Indigenous communities’ data

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STANDARD

CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

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

Technology Required

Students will need either a computer or tablet to play the game. Teachers will need a computer connected to a projector or smart board to show the presentation or video.

Time

60-75 minutes including presentation, analysis, and game.

Summary

With a Google slides presentation, students are introduced to the concept of answering a question with data. A video is also provided for review. Using a data set of all tribal leaders in 2019, they are walked though an example of using Google Sheets to create frequency table and plots of data. Students then use the data set to create their own tables and plots. Students finish the lesson by playing a game where they learn about computing distributions in Mayan history.

Lesson

1. Presentation on primary sources and frequency distributions with Google sheets.

Give students a slide presentation that asks the question “How wired are tribes?” . This also gives the definitions of data, primary sources, secondary sources and frequency table. Students will learn how to create a frequency table with Google sheets.

Differentiated Instruction: If needed, students can review the information by watching this video on their own.

You can also assign students who were absent to watch the video on their own.

2. Assign Students to Create Their Own Frequency Distribution

A Google doc with the assignment and link to video.

You’ll need the 2019 Tribal Leaders Data Set to complete this assignment. Copy the link into Google classroom for students to access.

Here is the answer key for the teacher

If your students completed the assignment correctly, it will match the answer key here.

Differentiated Instruction: For more advanced students

You may wish to have them compute an additional frequency distribution to show the frequency distribution of tribal entities by BIA region. That answer is also provided in the file above.

3. Play a game that teaches distributions

When students have completed their assignments that can play AzTech: Meet the Maya, a game which teaches statistics, including frequency distributions.

Assessment

Two types of assessment are available, their answers to the assignment with Google sheets, and their responses to the in-app math challenges in AzTech: Meet the Maya, which are graded automatically with data available from the. teacher reports.

Learn 4 Math Facts at Once with Google Slides

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Standard

CCSS.MATH.CONTENT.3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. 

CCSS.MATH.CONTENT.3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares.

CCSS.MATH.CONTENT.4.NBT.B.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm.

TIME

45-60 minutes

Technology Required

Students will need access to a computer or tablet and Google slides.

Summary

Start with a video as an ice breaker. Then, students read or listen to a presentation explaining how each math fact is actually four. Students complete an activity where they create their own math facts slides. A recommended video explains features of Google slides. Students complete the lesson playing Making Camp Dakota, solving word problems using division.

LESSON

Watch a video : Four Math Facts in One

In 4 minutes, this video explains how each time you learn a math fact, you are really learning four facts

Listen to/ Read a presentation on four math facts at a time

This presentation explains how one math fact is actually four because 7 x 6 = 42 means that 42 ÷ 7 = 6 and also that 6 x 7 = 42 and 42 ÷ 6 = 7. As an added bonus, it includes some ranch vocabulary like cattle, steer, heifer and bull.

Example from presentation

After the teacher has given the first part of the presentation, students are challenged to first show how a given math fact is actually four math facts, using steers. Next, students create their own examples. The easiest way to do this is through assignment in Google classroom or other system, including email, giving students their own copies of the slides to modify.

Recommended Video: Math Facts with Google Slides

If your students are unsure how to copy and paste, how to select multiple elements at a time, rotate objects or insert a duplicate slide, it is all in this video. Why not watch the video first? Because students often pay more attention once they realize they have questions that can be assigned by the assigned video.

How do you copy 84 chickens?

Play Making Camp Dakota

Making Camp Dakota
Making Camp Dakota teaches division of two- and three-digit dividends

Play Making Camp Dakota: Past and Present to learn about Dakota history and culture and solve division problems, such as dividing the people on the buffalo hunt. Students can be assigned to go directly to the game here or to access it by selection in the games portal for kids.

Assessment

Two types of assessment are included in this lesson:

  1. Students create their own math facts slides, and in-game assessment.
  2. Problems are scored automatically in Making Camp Dakota and data are available through the teacher reports.

Differentiated Instruction

Many students with learning disabilities have stronger achievement in one area than another, for example their grade level in reading is higher than in mathematics. For these students in higher grades, an assignment to learn to use presentation software such as Google slides is age appropriate and intrinsically interesting and at the same time increases their knowledge of basic math facts.

Better Dirt, Better Lives

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📖STANDARD

CCSS.MATH.CONTENT.4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

📲Technology Required

Students will need a Mac or Windows computer with the Fish Lake game installed. A video can be a substitute for students who do not have access to one of these devices.

⏰Time

30 minutes

📃Summary

Begin with playing the Fish Lake game. A video of the section on crop rotation may be used by schools that don’t have Fish Lake installed. Give a presentation (included) on crop rotation. Watch a video on “What is one-half” and end the lesson with a presentation (included) on whether one-half is fair.

📚Lesson

Play Fish Lake or watch video of game play

Even though you can use this lesson without playing the game, I urge you to install Fish Lake on your iPads, Mac or Windows computers. You can download it for free for computers. For iPads, email support@7generationgames.com for a discount code and we’ll get back to you the same day. Seriously, even if you normally use Chromebook, it will be a nice break and your students will love it. We recommend letting them play for 15 minutes.

Play the game Fish Lake, (available to Growing Math schools, on iPad, Windows or Mac computers). If students do not have devices to access the game, students can watch a video here.

Slide presentation on crop rotation

Use this Google slides presentation to explain crop rotation as more than just being sure each farmer did her fair share of the work or had a fair share of the fields. It was good science.

Watch a short video: What is half ?

This short (1:40) video explains that one-half is two equal parts, with examples of one-half as a distance between two points or as a shape divided into two parts.

Slide presentation on one-half as fair

Use this Google slides presentation to show two halves are equal and that 2/4 = 1/2. Multiple examples of dividing something in half are given, from six blankets to half a deer. Students can also read the presentation and manipulate the examples on their own.

Half a deer

Assessment

Fish Lake data reports are available for teachers to access after students have finished playing.  

Introducing Ratio and Proportion with Making Camp Navajo

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📖 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.

Geometry and Ledger Art

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by Avis Prentice and AnnMaria De Mars

📖 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

📲 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.

📃 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.

📚 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