Author Archives: AnnMaria De Mars

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.

Differentiated Instruction

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.

⏰ Time

45- 60 minutes

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

Differentiated 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.

Recommended Related Lesson

The Codex in Latin American history and math

Mean, Median and Mode

by Dr. Craig Waddell

πŸ“– Standard

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

⏰ Time

30-40 Minutes 

πŸ“² Technology Required

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

πŸ“ƒ 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.

πŸ“šLesson

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

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 (Bilingual English and Spanish) – The bilingual version of this lesson plan that includes English and Spanish resources.

Reflections on Ojibwe Migration

by Janna Jensen and AnnMaria De Mars

πŸ“– Standard

CCSS.MATH.CONTENT.5.NF.B.4Β  Β Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

CCSS.MATH.CONTENT.6.SP.A.3Β Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

D2.His.13.3-5Β  Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.

⏰ Time

60 minutes

πŸ“² Technology Required

Students need access to a computer with web browser.

πŸ“ƒ Summary

This lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, computing the average number of miles a character walked per day, followed by watching a video on map reading. As a group, students reflect on the challenges of the Ojibwe migration, compute the distance for just one segment and convert the distance from miles to kilometers.

πŸ“šLesson

Storyboard on the Ojibwe Migration

Begin with this story board on the route and major events of the Ojibwe migration. We recommend having students read each section of the story as it advances. Alternatively, the teacher may read it to the class or students can read it to themselves either on devices in the classroom or at home.

Watch a video on how to find the mean

Warning: bad singing ahead. This short video tells how to find the mean – in song. You may skip this video if you have already used it in a previous lesson.

Play the Forgotten Trail Game

Map from Forgotten Trail

Students should play the game at least through the first level. The game begins with a middle school class learning about the Ojibwe migration. Students will solve math problems related to the average number of miles walked per day and fraction of distance covered.

Watch a video on using scales in maps

This video is 7 minutes and covers what is a scale, how to use one and that different maps have different scales. If you feel your students are already familiar with this information, you may skip this video. In the days of Google maps and GPS we have found students often are not as familiar with this information as you might assume.

Presentation on Reflections on the Ojibwe Migration

In this Google slides presentation, students are asked to reflect on the Ojibwe migration. What would it have taken to survive such a journey? They use their map skills to estimate the distance of one leg of the journey, in both kilometers and miles.

Presentation is also available as a PowerPoint.

Synonyms Video

Now that students have seen synonyms as words for the same thing and miles and kilometers as measures for the same distance, finish up with this short (less than 2 minutes) video on synonyms.

Assessment

Slides 14, 18 and 21 can be printed out for students to answer individually, or can be answered as a group in class. Data are available on activities completed and math problems answered in the Forgotten Trail reports. For more information, check out our reports page.

Buffalo Hunts and Division

πŸ“– Standard

CCSS.MATH.CONTENT.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths

CCSS.MATH.CONTENT.5.NBT.A.4 Use place value understanding to round decimals to any place.

NOTE: Teachers who have not yet covered decimals in their class have an option within the lesson to only teach the first standard.

⏰ Time

25- 30 minutes

πŸ“² Technology Required

Computer or mobile device

πŸ“ƒ Summary

Begin with a video on long division (optional) or a presentation on uses of division from the playground to the buffalo hunt. Watch a short video working long division problems. Finish with practicing long division in Making Camp Dakota. Short videos on Dakota buffalo hunt traditions and related math lessons are also linked.

πŸ“šLesson

Video: Optional for Review

If your students need a review of the steps in long division, we recommend this six-minute video that uses the acronym HMS ↓ to teach students to :

  • Ask How Many
  • Multiply
  • Subtract
  • Bring down

Presentation on Division and Buffalo Hunts

This Google slides presentation gives common factors in buffalo hunts across different tribes and explains how whether it is computing the number of hides a horse can carry or how long each group gets to play at recess, division is always useful.

NOTE: This presentation includes two slides that reference converting a fraction to a decimal. If you have not yet introduced this concept, those slides can be deleted.

Video: Long Division by Guessing

For those students who don’t know where to start with long division – guess!

Play a Game – Making Camp Dakota

Select the Buffalo Icon (top left corner) in the first MATH screen to practice long division.

Math Screen #1 from Making Camp Dakota

Related Lessons

For more instruction on division check out these two lessons:

Related videos

These two videos, each about 1 minute in length, give more information on traditional Dakota buffalo hunts.

Becoming a buffalo hunter

Dakota deer and buffalo hunting

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.

Differentiated 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.

What is a statistical question?

πŸ“– Standard

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers

πŸ“² Technology Required

Computer with projector, for students learning in class. For students learning at home, materials can be accessed on any device with a browser and application to read PDF files or can be printed out and sent home with students.

⏰ Time Required

2 hours (We recommend doing this over two class periods)

πŸ“ƒ Summary

Teachers begin the lesson with a Google slides presentation explaining the requirements for a statistical question. Students complete an assignment identifying whether or not a question qualifies as a statistical question. After class discussion, students complete a second assignment using a small data set shown on a map. In Part 3, students write and answer their own statistical questions using a data set provided, giving an explanation for their answers. Optionally, students can complete a more challenging assignment drawing conclusions from a graph and/or play a game and identify statistical questions.

πŸ“š Lesson

Before you begin, you should have printed out or added to your Google classroom and shared with students the STUDENT handout from the U.S. Census Bureau, “What is a statistical question?” The student version is 11 pages. If you are short on printer paper, you can skip printing page 1. Also, pages 7 and 8 are an optional activity.

You should also print or download the TEACHER version of the Census Bureau handout, “What is a statistical question?” which includes answers to questions in the first two assignments and explanations why each answer was or was not a statistical question.

Introduce students to definition of a statistical question

Begin with the Google Slides presentation, “What is a statistical question?” which breaks down the two components of a statistical question – it must be answered by data and the data must vary.

Students complete assignment on identifying a statistical question

Have students complete Part 1 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Students complete Part 2, assignment on identifying a statistical question using real data

Have students complete Part 2 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Then, continue with the Google slides presentation and have students complete Part 2 of the student handout from the U.S. Census Bureau (linked above). Have students discuss their answers with one another.

Either correct the answers as a class or collect these to correct yourself. Remember, the teacher handout, linked above, has the correct answers.

We recommend you end the first day’s lesson here and begin the next lesson after students have had the assignments from Part 1 and Part 2 corrected.

Students complete part 3, creating their own statistical questions from data.

Students complete Part 3 of the handout on “What is a statistical question?”

Discuss students’ answers in class. Provide feedback on whether a question really is a statistical question and whether students’ answers to their questions are correct. Allow students time to explain their conclusions.

Optional: Students Complete Part 4

First, use the Google slides presentation, starting on Slide 24, to explain how to read an area chart.

Next, have students complete Part 4 from the student handout, “Drawing conclusions from a graph.”

AzTech: Empiric Empire

Optional: Play Empiric Empire

After students have completed Parts 1 to 3 of the student handout (and, optionally, Part 4), have them play the game Empiric Empire. As an additional optional assignment, ask students to identify statistical questions asked and answered during the game.

If students do not have phones but have Chromebooks, they can play Disaster Deduction Detectives instead – available June, 2022.

Assessment

For assignments in Parts 1 and 2 the teacher version of the handout has correct answers and explanations. For assignments in Parts 3 and 4 of the student handout, examples of correct responses are given but these will vary as students provide their own statistical questions.

For the Empiric Empire game, the teacher reports show student responses to questions. It should be noted that this game does begin with fractions and decimals, which are a prerequisite to statistics.

Teach Ratio with Math Snacks

πŸ“– Standard

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

πŸ“² Technology Required

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

⏰ Time

90 minutes

πŸ“ƒ Summary

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

πŸ“š 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.