Category Archives: mathematics

Better Dirt, Better Lives

📖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 an iPad, Mac or Windows computer with the Fish Lake game installed. A video can be 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

📖 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

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

Fill in the Blank: 3 Digit Dividends

📖 STANDARD

CCSS.MATH.CONTENT.4.NBT.B.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

⏰ LESSON TIME

55 Minutes

📃 SUMMARY

This lesson plan will have students reinforce the previously presented concept of long division of 3 digit dividends by 1 digit divisors through a short review, an animated video, a fill in the blank division word problem activity, and game play.  

📲 TECHNOLOGY REQUIRED

Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium and Dakota are both playable on any web browser on those devices. Students will also need access to the games.

📚LESSON PLAN

  1. Start the lesson by having a short review on dividing 3-digit dividends by 1-digit divisors. It is suggested to review the activity that was assigned in the previous lesson, “Build Your Own Division Problem” lesson. You can find the review copy of the activity here: “Review – Build Your Own Division Problem“. (15 minutes)
  2. How to Use Division to Solve a Problem – Start with this animated video on how to use long division, with 3 digit dividends, to solve different word problems. (Time – 1:24)

3. Have students work on the activity “Fill in the Blank: 3 Digit Dividends“. The activity has students fill in the blanks to complete the division word problem, identify the problem, and solve it. (Corresponding “Fill in the Blank: 3 Digit Dividends” Activity Jamboard that’s also linked in the activity above can be used by students as space to work out their division word problems.) (20 minutes)

4. Have students play Making Camp Dakota: Past & Present using our Games Portal for Kids. The division in Making Camp Dakota will be more practice for students on problems with 3 digit dividends divided by 1 digit divisors. (15 minutes)

ASSESSMENT

The “Fill in the Blank: 3 Digit Dividends” activity is not only allowing students to continue practicing the concepts previously introduced and reviewed in this lesson, but also serves as an assessment of how well the student grasps the concept of division using 3 digit dividends and 1 digit divisors.

Making Camp Dakota Teacher Reports

You can view your students’ progress on mastering these standards by viewing your Making Camp Dakota teacher reports. You can access the Making Camp Dakota reports here.

STATE STANDARDS

Minnesota State Standards

4.1.1.6 – Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.  

5.1.1.1 – Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.  

Build Your Own Division Problem

📖 STANDARD

CCSS.MATH.CONTENT.4.NBT.B.6 

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

⏰ LESSON TIME

50 minutes

📃 SUMMARY

This lesson plan will build upon the introduction to division with 3-digit dividends from the “Dividing 3-Digit Dividends” lesson. Students will be able to continue practicing dividing 3-digit dividends by 1-digit divisors through a short review, an activity where students build their own division problems, and game play.

📲 TECHNOLOGY REQUIRED

Students will need a PC, Mac or Chromebook. Students will also need access to “Making Camp Dakota: Past & Present” using our Games Portal for Kids. “Making Camp Dakota: Past & Present” is playable on PC, Mac, and Chromebook using any browser.

📚LESSON PLAN

  1. Start the lesson by having a short review on dividing 3-digit dividends by 1-digit divisors. It is suggested to review the activity that was assigned in the previous lesson, “Dividing 3-Digit Dividends” lesson. You can find the review copy of the activity here: “Review – On Your Way Home.” (10 minutes)
  2. Students will take the information reviewed and use it to complete the “Build Your Own Division Problem” activity. In this activity, students practice division using 3-digit dividends and 1-digit divisors through using virtual manipulatives. (20 minutes)
  3. To end the lesson, students can play Making Camp Dakota: Past & Present to further practice division. Students can access the game using our Games Portal for Kids. (20 minutes)

ASSESSMENT

The “Build Your Own Division Problem” activity is not only allowing students to continue practicing the concepts previously introduced and reviewed in this lesson, but also serves as an assessment of how well the student grasps the concept of division using 3 digit dividends and 1 digit divisors.

Making Camp Dakota Teacher Reports

You can view your students’ progress on mastering these standards by viewing your Making Camp Dakota teacher reports. You can access the Making Camp Dakota reports here.

STATE STANDARDS

Minnesota State Standards

4.1.1.6 – Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.  
5.1.1.1 Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. 

Related Lesson – Fill in the Blank: 3 Digit Dividends

The “Fill in the Blank: 3 Digit Dividends” lesson plan will have students reinforce the previously presented concept of long division of 3 digit dividends by 1 digit divisors through an animated video, a fill in the blank division word problem activity, and game play.  

Counting ropes and rational numbers

Contributed by Lori Hieresrich

📖 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.

📃 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.

📲 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.

📚Lesson

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.

Mean, Median and Mode

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.

Reflections on Ojibwe Migration

by Janna Jensen and AnnMaria De Mars

📖 Standard

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

D2.His.13.3-5  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

📲 Technology Required

Students need access to a computer with web browser.

📃 Summary

This lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, 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.

📚Lesson

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.

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

📖 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

📲 Technology Required

Computer or mobile device

📃 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.

📚Lesson

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

📖 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

📲 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.

📃 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.

📚Lesson

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.