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Distributions and Mayan Trading (Bilingual English & Spanish)

📖Standard

7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Minnesota State Standard – History Sub-strand 4, Standard 15 “North America was populated by indigenous nations that had developed a wide range of social structures, political systems, and economic activities, and whose expansive trade networks extended across the continent.”

Time

20- 30 Minutes 

📲Technology Required

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

📃Summary

The two videos here combine math and social studies, because, clearly, the Maya understood math. The concept of distributions is introduced in the context of trading, explaining why some objects are more valuable. Students play AzTech: The Story Begins, which reviews fractions and measures of central tendency. The lesson concludes with a question and another video on distributions.

📚Lesson Plan

1. Watch video – Mayan Trading (1:57)

Also available in Spanish! – El Comercio Maya (1:58)

El Comercio Maya

The Mayan trading video is based on an idea from one of my favorite history teachers, who says that history is more than just names and dates but also how people lived, what they used, what they did. It also has a bar chart of the relative value of objects. It explains that the Maya traded less common items for more common ones and that items that were more difficult to obtain were more valuable.

2. Play AzTech: Meet the Maya

Next, have students start the AzTech games series. They can play AzTech: Meet the Maya online or using an iPad. We recommend downloading the game onto your iPhone or iPad for better performance.

3. Question to test understanding

José tried to trade a banana for a quetzal feather and a villager threw a spear at him. Why would the villager do that? Explain using math. Extra points if you can discuss distributions in your explanation.

José ofreció intercambiar un plátano por una pluma de quetzal y un aldeano le lanzó una lanza. ¿Por qué haría eso? Explica usando la matemática. Puntos extra si puedes hablar de distribuciones en tu explicación.

4. Video giving the answer to the word problem on distributions (5:15)

Also available in Spanish! (5:15)

Explicando distribuciones y variabilidad

This five-minute video introduces distributions and variability and gives an example of computing a weighted mean from a frequency distribution.

OPTIONAL You can also copy this Google slides presentation to your own classroom if you’d rather modify the explanation for your own lecture. The slides can also be printed out and sent home with students who do not have Internet access.

Spanish Google Slides presentation – Introduciendo Distribuciones

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. The link to the teacher dashboard for AzTech: Meet the Maya student reports can be found on this page. You should have received a password during the Growing Math training.

State Standards

Minnesota State Standard 6.4.1.1 – Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

Related Lesson

Distributions and Mayan Trading – This lesson is the English Only version of the lesson above.

PERIMETER OF RECTANGLES, SQUARES AND TRIANGLES (Bilingual English & Spanish)

📖Standard

CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

LESSON TIME

30 minutes without gameplay, 45 minutes with gameplay

📃 SUMMARY

In this lesson plan, students will learn how to compute perimeter, apply those skills in game-based practice problems and solve perimeter problems using an interactive web-based activity with virtual manipulatives. 

📲 TECHNOLOGY REQUIRED

Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with access to Google apps. 

📚 Lesson Plan

1. Video: How to Find the Perimeter and Polygons (3:00)

Watch this animated video that explains how to find the perimeter of different polygons, including rectangles, triangles and squares.

Or watch it in Spanish: ¿Cómo encontrar el perímetro de un polígono? (3:12)

2. INSTRUCTIONAL ACTIVITY WITH ASSESSMENT: Interactive perimeter problems activity

This digital activity walks students through calculating the perimeter of different shapes including a rectangle, a square and a circle in a narrative-driven context around the farm and integrates virtual manipulatives. Students are provided in-activity instruction as they are presented with and explained the formulas to use when they need to use them. Additionally, with in-activity scaffolding, students can “get a hint” on each problem. 

You may elect to read and work through it during class time, giving students time to complete the problems or assign it as an individual assignment. 

If your students have not used virtual manipulatives with Google slides previously, here is a 30-second introduction.

Video: Use Virtual Manipulatives in Google Slides (0:27)

Or watch the video in Spanish: Usar manipulativos en Google Slides (0:27)

 Estimated time to complete: 20-25 minutes

3. GAME: Making Camp Premium or Spirit Lake 

Have students play Making Camp Premium games for 15-20 minutes (remainder of the lesson time) specifically including these icons. 

Perimeter is also covered in the second half of Spirit Lake: The Game.

Assessment

In addition to the virtual manipulative activity above,  remember that you can always see your students’ performance on the problems in Making Camp Premium and Spirit Lake by accessing the reports page. You will need to enter the password you received during training.

State Standards

Minnesota Math Standard 3.3.2.2 – Find the perimeter of a polygon by adding the lengths of the sides.

Minnesota Math Standard 3.3.2.3 – Measure distances around objects.

Related Lesson

“PERIMETER OF RECTANGLES, SQUARES AND TRIANGLES” – The English only version of the lesson plan above with English only resources.

Ojibwe Clans and Migration (Bilingual English & Spanish)

📖STANDARDS

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

Minnesota State Standard – History Sub-strand 4, Standard 15 “North America was populated by indigenous nations that had developed a wide range of social structures, political systems, and economic activities, and whose expansive trade networks extended across the continent.”

⏰ Time

40 minutes

📲 Technology needed

Internet connection on a PC or Chromebook laptop, tablet, or phone.

📃 Summary

This Ojibwe clan lesson for Grade 3 is focused on Ojibwe culture. Students learn where people and places are located and why they are there. They will become familiar with the causes, patterns and effects of Ojibwe settlement and migration. They will learn of the different population centers in Ojibwe society and investigate the impact of human activities on the environment. 

📚 Lesson

The downloadable Google Slides presentation is available here. This has a digestible summary of the Ojibwe migration, and why and how it happened. The Ojibwe clans are introduced as well as the new lifestyles that the Ojibwe adopted after they migrated to the Great Lakes area and Ontario, Canada.

Game

Making Camp Bilingual can reinforce clans and culture studies using the Life section.

  1. Select the LIFE button from the main choice screen.
  2. From the LIFE choices, click on the box in the middle of the bottom row, the one with the four people, and watch the video about Ojibwe social structure. Answer the questions that follow the video. 
  3. Next, select the box on the bottom right. Watch the overview video on clans and totems. Answer the questions.
  4. Students can also click on each individual clan totem icon to learn more about each Ojibwe clan and answer a question about each of them to earn points.
  5. Return to the wigwam and trade with the points earned in this lesson.

Students can use the language button to switch between English and Spanish while watching the videos.

Alternatively, students may also play Forgotten Trail, which is an adventure game that homes in on the Ojibwe migration. Two kids in the game retrace the Ojibwe migration on their own and learn more about Ojibwe history along the way.

Assessment

Teachers will be able to view student reports for Making Camp Bilingual to view how many modules students completed in the LIFE section and their scores for each one.

Related Lesson

“Ojibwe Clans and Migration” – The English Only version of the lesson plan above featuring Making Camp Premium.

Mean, Median and Mode (Bilingual English & Spanish)

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)

📖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.

Problem-solving Two Ways (Bilingual English & Spanish)

📖 Standard

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

⏰ Time

30-40 minutes

📃 Summary

Students are introduced to the various means of problem solving in a brief presentation. They watch a video on visualization, then solve a problem that asks them to visualize. After watching a video on building a model, students build and/or draw their own model of a multiplication problem or property. Lesson concludes with game play to reinforce these problem-solving strategies and learn more. This lesson assumes that students have some familiarity with multiplication of one-digit numbers and division with one-digit divisors.

📲 Technology Required

If teaching in person, the teacher will need a computer and projector or smart board to show the videos, or students can be given the links to watch on their own devices. Students will need a PC, Mac or Chromebook or tablet. Making Camp Bilingual, Making Camp Lakota and Making Dakota are all playable on any web browser on those devices. Spirit Lake: The Game, playable on Mac or Windows computers also teaches these same concepts. Students will also need access to the games.

📚Lesson

Watch a Video: Visualize (2:38)

Or watch it in Spanish – Visualizar (2:38)

This video teaches you how to visualize a problem. Visualization may help you solve it more easily. If you use objects to imagine quantities of numbers in certain problems, you will be able to find the solution faster.

Short presentation and problem (10 minutes)

After watching the video, teachers can present this short Google slides presentation or assign to students in Google classroom, giving another example of visualizing a problem.

Visualize – Presentation in English

Visualizar – Presentation in Spanish

The presentation ends with asking students to visualize another problem themselves. It then leads into the next video.

Watch a video: Build a Model (1:37)

Or watch it in Spanish – Construyendo un Modelo (1:37)

If you’d rather give a presentation than show a video, here is a Google slides deck you can use as is for copy to your own Google drive and modify.

Build a Model – Presentation in English

Construyendo un Modelo – Presentation in Spanish

Actually Build a Model (10 minutes)

Two possible assignment for building a model are:

  • Have students create a model using Google draw, jam board or simply drawing it on paper.
  • Build a physical model using objects in their home or school

Google slides presentation describing these assignments is given here.

Assignments – Presentation in English

Assignments – Presentation in Spanish

You can simply save to your own Google classroom and then assign to your class to include both types of problems or modify to add more explanation or delete whichever one does not apply to your class before assigning.

Play a game (15 minutes)

Assign students to play Making Camp Bilingual (plays on any device) to practice these problem-solving strategies and more with multiplication and division.

Growing Math Games

Assessment

Two assessments are built into the lesson, on visualization and building a model. Teachers can also see which standards students have attempted and how many problems they have answered correctly in the Making Camp Bilingual teacher reports.

Related: Problem-solving Two Ways

The lesson above has a companion lesson for English only learners. Problem-solving Two Ways is the same lesson from above but provides the resources, videos and Google Slides, in English only.