Geometry Comes Alive with Cultural Explorations!

The theme of this unit focuses on respect for cultural traditions and on identifying various aspects and categories of quadrilaterals.

Students will create objects inspired by Native American Indian artifacts, including a local Indian tribe, which contains quadrilaterals in their designs. Students will understand attributes of quadrilaterals and then incorporate them into a final creation that represents their own culture.

Educational outcomes

  • Lesson 1 — Empathy:   Students will investigate, record, and share what they know about Native American Indian cultures and traditions.
  • Lesson 2 — Define: Students will recognize categories and shared attributes of quadrilaterals on  Navajo blankets and then design a “blanket” of their own with quadrilaterals.
  • Lesson 3 — Define: Students will investigate local Native American Indian tribes, then recreate and report on an artifact from a local tribe that contains symbolic quadrilaterals in its design.
  • Design Challenge — Ideate, Prototype & Test: students iterate designing, prototyping, testing, and retesting a model until a final object containing quadrilaterals that symbolizes their own culture is made. They will present all they have learned about cultures and quadrilaterals to an audience.

STEAM INTEGRATION

In the Empathy phase of Lesson 1 students focus on identifying and valuing traditions and symbols of different Native American Indian cultures. In the Define phase of lesson 2, students recognize attributes and categories of quadrilaterals (3.G.A.1) along with symbolic meanings that appear on traditional Navajo blankets. Students understand that shapes come in different categories, may share attributes, and that the shared attributes can define a larger category. Students will also recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.  In the Define phase of lesson 3, students investigate American Indian nations in their local region long ago and in the recent past and recreate an artifact from a local tribe that uses quadrilaterals in its design to describe traditional significance (SS 3.1.2  and 3.G.A.1 ). In the Design Challenge students Ideate, Prototype, Test, and reiterate to create an object that describes their own cultural traditions and contains different quadrilaterals within its design.  Students share what they have learned about quadrilaterals, cultural traditions, and their own culture with an audience.

Click on the “+” icon to open each section

Unit Materials

Building Materials

RAFT Makerspace-in-a-box       -or-

A variety of recycled items: plastic bags, fabric, paper (8.5 x 11 inch sized), cups, straws, cup lids, plates, string, file folders, etc.

Connecting Materials

Paper clips, rubber bands, tape, velcro, glue, etc.

Please Click on the Following Links:

Tech  (videos):

Background Information: 

Handouts:

Other:

Various examples (pictures or actual) of cultural artifacts

 

Design Thinking Overview

Our design thinking units have five phases based on the d.school’s model. Each phase can be repeated to allow students to re-work and iterate while developing deeper understanding of the core concepts. These are the five phases of the design thinking model:

EMPATHIZE: Work to fully understand the experience of the user for whom you are designing.  Do this through observation, interaction, and immersing yourself in their experiences.

DEFINE: Process and synthesize the findings from your empathy work in order to form a user point of view that you will address with your design.

IDEATE: Explore a wide variety of possible solutions through generating a large quantity of diverse possible solutions, allowing you to step beyond the obvious and explore a range of ideas.

PROTOTYPE: Transform your ideas into a physical form so that you can experience and interact with them and, in the process, learn and develop more empathy.

TEST: Try out high-resolution products and use observations and feedback to refine prototypes, learn more about the user, and refine your original point of view.

The Design Thinking Process | ReDesigning Theater. (n.d.). Retrieved April 2, 2016, from http://dschool.stanford.edu/redesigningtheater/the-design-thinking-process/

STEAM Integrated Standards

CCSS.Math.Content.3.G.A.1  Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Social Studies Standards 3.1.2  Students describe the American Indian nations in their local region long ago and in the recent past.

 

 

 

Lesson 1 Overview

How do people observe cultural traditions?

This lesson focuses on students valuing Native American Indian customs and cultural traditions, and examining designs on some traditional artifacts. Students share what culture means to them; whether a school culture, home or family culture, place of origin or other type of culture. (SS 3.3.1)

Essential Questions:

  • What does culture mean to you?
  • What is a tradition?
  • Why do people have traditions?
  • How do people show respect for their culture?
  • How do Native American Indians celebrate their cultures?
  • What traditions do you have in your family?
  • How do objects help tell the story of a culture?
  • What is different about cultures? The same?

LESSON PROCEDURE 

Professional Preparation : 

Lesson Format (Students sit with teams):  

Whole group discussion:

  • Start with an open discussion about cultures in general.
  • Show the video: Cultures Around the World
  • Discuss what we know about Native American Indian cultures and traditions (ask essential questions listed above)
  • Watch the video  Native American Regions in the United States
  • Explain what an artifact is and show examples of artifacts (pictures, real artifacts, and/or visit a museum) from different Native American Indian cultures.
  • Ask questions about Indian artifacts: encourage points of view on student understandings about cultures.
  • Pass out Maker Journal binders and the first Maker Journal page.
  • Students record about their own cultures:  Lesson 1 Maker Journal Page: How I celebrate my culture & its traditions
  • Students share what they entered into their journals.

Student Directions (Click + to open)

A Sample Teacher/Student(s) Dialog:  The following is a sample dialog between the teacher & the students for this lesson.

(Note:  T stands for teacher, and S stands for student, with additional advice in parenthesis).

Observing Native American Indian Cultures & Traditions — whole group discussion

T:      To “empathize” means to understand a real-world situation and to feel what another person is feeling.  Can you think of a time when you understood how another person felt about something?

S:  (students share scenarios …)

T:  Thank you for sharing examples of empathy!  A custom (a tradition) is anything which lots of people do, and have done for a long time.  If something is usually done the same way, you might say that is the “customary way” of doing things. Let’s look at some examples together…

T: What is meant by culture?  By Traditions? (take answers, then show the video: Cultures Around the World)

T: What do you know about Native American Indian cultures and traditions?

(Show the video: Native American Regions in the United States )

T:   How did this video help you empathize Native American Indian cultures and traditions?  What customs are similar to your own?  What are not?  (if possible, allow students time to research different Native American Indian Regions to find out more about customs and traditions)

S:  (answers vary: different tribes, homes, clothing, art, food, etc.)

T:  An artifact is an item or object that tells a story, has symbolism, or gives information about a cultural or its society.   Can you see anything in this classroom that shows people who we are as a class?

S:     (various answers: school mascot, US Flag, etc.)

T:  What do culture and tradition mean to you?

S:  A culture is where my family comes from: a tradition is something people do to remember their culture!

T:  Why do people have traditions?

S:  To pass on stories about their family …

T: What traditions do you have in your family?

S: (various answers: specific holidays, birthdays, special events)

T: How can artifacts help tell the story of a culture? (show artifacts)

S: (various answers: quilts tell a family history, Mexican sugar candy skulls respect the dead, etc.)

T:  (Pass out Maker Journal binders/folders and the first page: Lesson 1 Maker Journal Page: How I celebrate my culture & its traditions — explain how to number additional pages). Write “1” on the top of this first page of your Maker Journal and then explain how you celebrate your culture and its traditions.  On the bottom, write a story and/or draw a picture about your culture and its traditions. Remember to ask me any time you need more pages.

(students fill in the first page of their journal…)

T: Share what you put in your journal. (students share with whole class and/or pair-share).

T: Now, each team will choose one member to go over to the common area (“Makerspace”) to choose 4 different items, and then bring those items back to their team.  (allow time for students to gather items and return to their teams)

T: (Pass out Lesson 1 Maker Journal Page:My Native American Indian Artifact Idea  ). Open your Maker Journal, number this page and add it to your journal.  Record on it all the items your team has gathered.

T: Discuss with your team ideas for making a Native American Indian artifact out of those items, and then describe and draw your ideas on the lower half of your journal page.  Think about how you can use all or some of these items to create something that represents a Native American Indian culture.

(allow time….. after that call time & refocus teams into a whole group setting. Allow time for student teams to share their ideas with the class)

T: What did you learn about Native American Indian cultures and traditions today?

(students share what they learned with the class).


Concept Quick Reference (Click + to open)

Vocabulary:

Artifact: 

  • a man-made object that has some kind of cultural significance.

Culture:

  • the beliefs, customs, arts, etc., of a particular society, group, place, or time

  • a particular society that has its own beliefs, ways of life, art, etc.

  • a way of thinking, behaving, or working that exists in a place or organization (such as a business)

Custom:

  • also called a tradition, is anything which a lot of people do, and have done, for a long time.

Empathy: 

  • the feeling that you understand and share another person’s experiences and emotions.
  • the ability to understand a real-world situation

 

 

Click on the “+” icon to open each section

Lesson Materials

Building Materials

RAFT Makerspace-in-a-box       -or-

A variety of recycled items: plastic bags, fabric, paper (8.5 x 11 inch sized), cups, straws, cup lids, plates, string, file folders, etc.

Connecting Materials

Paper clips, rubber bands, tape, velcro, glue, etc.

Tech  (Show videos):

Cultures Around the World

Native American Regions in the United States

Other

Various examples (pictures or actual) of cultural artifacts

External Resources

Teacher Notes

Consider selecting a few images of recycled materials. Discuss why some items are recycled and others are not. Model good techniques for safe quality internet searches. Consider pre-selecting sites that yield quality information about traditions and cultures, and about caring for the earth.

Active Classroom

Communication is critical in the design process. Students need to be allowed to talk, stand, and move around to acquire materials. Tips for success in an active classroom environment:

1 –  Students can access any wall, board, or surface to gather and explore ideas — students personalize the working space to meet their needs.

2 – Students have regular opportunities to make choices, including choices about what they learn and how they learn it.

3 –Encourage students to learn and to demonstrate what they’ve learned in ways that best suit their individual learning styles.

4 – It is not a free-for-all!  Amount of prep and planning is evidenced by quality of student work and level of students’ engagement. All is carefully thought out in advance.

5 – A lot of meaningful conversations — between teacher and students and also among students.  Lots of questions asked by and of students. Teacher often manages the conversation, but the students and their thoughts, ideas, and questions determine the scope and direction of the conversation.

6 – Instead of teacher or textbook giving answers or info, students discover ideas through inquiry and exploration.  They figure out solutions and answers on their own.

7 – Tests and quizzes are sometimes needed, but focus assessment on student-created “learning artifacts” — students complete these products to demonstrate in-depth knowledge and understanding key topics.

8 – The focus is on the ultimate goal of student thinking… Every activity, lesson, and project is geared toward deepening and strengthening students’ critical thinking skills.  Students analyze, question, explore, and evaluate on a regular basis.

9 – Help students become successful and care for the success of others by asking them to predict problems that might arise in the active environment and ask them to suggest strategies for their own behavior that will ensure a positive working environment for all students and teachers.

10 – Practice and predict clean-up strategies before beginning the activity. Ask students to offer suggestions for ensuring that they will leave a clean and usable space for the next activity. Students may enjoy creating very specific clean-up roles. Once these are established, the same student-owned strategies can be used every time hands-on learning occurs.

Learning Targets

Students will show they realize:

There are many ways to represent traditions and cultures: Students understand the importance for cultures and traditions, including their own. Students also investigate Native American Indian cultures and traditions.

Assessment

Please click on the following links:

(one per student)

Review all student Makerspace Journal pages for formative assessment.

Conduct a group discussions to allow all students to share, discuss and compare their findings.

 

Lesson 2 Overview

How can you design a Navajo blanket with quadrilaterals?

This lesson focuses on students investigating properties of quadrilaterals (3.G.A.1) that represent traditional symbols on Navajo Indian blanket/rug patterns. Students explore attributes and categories of quadrilaterals, and then use quadrilateral shapes to recreate a Navajo blanket pattern that represents something to them.  During this process, students will observe, analyze, and record properties of quadrilateral shapes that appear in the designs.

Essential Questions:

  • What is the same about squares and rectangles?
  • What is different about squares and rectangles?
  • What is a quadrilateral?
  • What do all quadrilaterals have in common?
  • What are examples of quadrilaterals?
  • Why isn’t a hexagon a quadrilateral?
  • What other shapes are not quadrilaterals?  Why aren’t they quadrilaterals?
  • Why isn’t a cube a quadrilateral?

LESSON PROCEDURE

Professional Preparation:

Lesson Format  (Students sit with teams)

Whole Group Discussion:

Class discussion & student team investigations:

Student Directions (Click + to open)

A Sample Teacher/Student(s) Dialog:  The following is a sample dialog between the teacher & the students for this lesson.  Prepare students into teams of 3 to 4  — either you choose or you allow them to choose their own teams and team names. Pass out or ask students to take our their Maker Journals:  prepare extra pages ahead of time for each student)

(Note:  T stands for teacher, and S stands for student, and additional advice is in parenthesis).

Recognizing Quadrilaterals in Navajo Blanket Patterns — whole group discussion

T:  (review shapes): Is a circle a polygon? …  Why not? What is a polygon?  (review all answers)

T:  An attribute helps explain about someone or about something.  For example: attributes of a square:  4 equal length sides and  4 right angles..

T: The word “Quadrilateral” means “four sides” (quad means four, lateral means side). A Quadrilateral is a polygon that has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides. So, squares and rectangles belong to the same category, or family of quadrilaterals because they share features of having 4 closed straight sides and they are flat. Who can give me another example of a quadrilateral?

S: (answers vary…)

T:  Why isn’t a hexagon a quadrilateral?

S: A hexagon has more than 4 sides!

T:  What other shapes are not quadrilaterals?  Why aren’t they quadrilaterals? (take answers)

T:  Why isn’t a cube a quadrilateral?

S: A cube is 3-dimensional, not flat!

T:  Quadrilaterals can be classified by relationships of their sides and angles. So, what attributes are the same about squares and rectangles?

S: Both squares and rectangles have four sides and four right angles!

T:  What attributes are different for squares and rectangles?

S: A square has all sides the same length and rectangles have 2 opposite sides the same length!

T: So can a square be a rectangle?

S: Yes, but a rectangle cannot be a square.

T:  So a square is a special subcategory of rectangle.

T: (show more examples) : A rhombus is also called a diamond.  How is a rhombus like a parallelogram?

S: A parallelogram has 2 opposite sides the same length, and a rhombus is the same except all the sides of a rhombus are the same length.

S: So that means a parallelogram could have 2 opposite equal length long sides, and the other 2 opposite sides equal but shorter in length?

T:  That’s right!  So, a square, rhombus and rectangle are subcategories of parallelograms! More than one type of quadrilateral could belong to a larger category of quadrilaterals because they have shared attributes!

T:  (continue along this line of conversation, with other categories of  quadrilaterals, identifying quadrilaterals that have or do not share attributes with others, and those that are subcategories of other categories…)

T:  Let’s walk around the room (and/or outdoors) to look for examples of quadrilaterals. (Hand out Finding Quadrilaterals all Around Us.) Please record on this journal page where you find some of these quadrilaterals, number the page, and put it into your Maker Space Journals.

T:  What do you remember about Native American Indian cultures and traditions?  (take answers)…… Today we will be looking at quadrilaterals in blanket/rug designs from the Native American Navajo culture….. (show samples of Navajo blankets and rugs, and the video(s):   Navajo Blankets and/or  More about Navajo Blanket Designs.   Ask students what they think about the designs and then pass out the handout: Examples of Navajo Indian Blanket Patterns ).

T:  (Ask students what they notice about each pattern) …

For example, the “Surrounding design” begins with a simple rectangular inner shape, surrounded by repeated layers of squares— where a layer is a group of smaller squares that together form a larger square or a rectangular ring around the middle of the design.

(pass out the Looking at Quadrilaterals in Navajo Blankets journal page to each student)

T:  Can you predict the number of squares needed in the “Surrounding design” for each layer? Please record your answers and your reasoning on this journal page, then share what you think with your teammates… (give time to record in journals — pass out extra journal pages if needed,  and then have students share ideas).

T:  Tell us the name of the blanket and how many squares you found in each layer of it. (For example, the “Surrounding design” increases by 8 each time a layer is added   2-10-18-26).

T:  Anyone notice anything about the “Zig Zag pattern?”  (students could predict the number of squares needed for each “zig zag” if the overall rectangular pattern is to have 11 squares in length and 5 squares in width or some other such configuration. Encourage students to write what they discover in their journals).

(Suggestions:  For the “Eye Dazzler” pattern, ask students how many triangles of each color their design needed and how many squares of each color were needed. Ask how triangles could be rearranged to make a square or a rectangle.  For the other type of “Zig Zag” ask students if they can find any lines of symmetry in their design).

T:  I’d like one student from each team to gather sets of quadrilateral shapes from the common area. (chose or let them decide who gathers the sets of quadrilateral shapes.  Wait for students to return to their teams and to pass out sets to members).

(Pass out handout Looking for Quadrilaterals in a Ganado design.)

T:  Take a look at the Ganado design on your handout. If you draw lines in the Ganado design, can you find any quadrilaterals? (Encourage them to do this and to explain their reasoning).

S: (answers vary)

T:  Ok, now let’s take a look at this (show or pass out to each student a copy of Finding Quadrilaterals in a Ganado design)   What shapes are not quadrilaterals? (e.g., triangles).

types-of-quads-in-a-ganado

 

 

 

 

 

T:  Each team will have 30 minutes (more if need be) to create a team Navajo blanket made out of quadrilaterals. Your team Navajo blanket pattern must contain at least 3 different types of quadrilaterals in its design. Use the quadrilaterals you brought to your team and combine them to make patterns.  Record and explain in your journals all the quadrilaterals, their attributes, and categories that appear in your team blanket. Give your blanket a name and describe what your blanket represents to your team.

(After time is called …. pass out  the Maker Journal page Our Team Navajo Blanket and ask students to fill it out)

  • Students self assess, and peer assess members of their team.
  • Students  report what they have learned to an audience.


Concept Quick Reference (Click + to open)

Check out A Review of Quadrilaterals for details about quadrilaterals.

Check out  The History of Navajo Blankets  for further information about designs on Navajo blankets/rugs and their symbolic meanings.

Watch the video for more on quadrilaterals: Quadrilaterals for 3rd graders

Click on the “+” icon to open each section

Lesson Materials

Building Materials

RAFT Makerspace-in-a-box       -or-

A variety of recycled items: plastic bags, fabric, paper (8.5 x 11 inch sized), cups, straws, cup lids, plates, string, file folders, etc.

Various quadrilateral shapes made from recycled materials; at least 10 per student different sized rhombuses, rectangles, and squares

Scissors and paper (11″ by 17″)  to adhere shapes onto

Connecting Materials

Paper clips, rubber bands, tape, velcro, glue, staplers, etc.

Please Click on the Following Handout Links:

Other

Various examples (pictures or actual) of Navajo blanket patterns

External Resources

Please Click on the Following Video Links:

Please Click on the Following Links for background information:

Teacher Notes

Decide ahead whether you want to show one or both videos (the video: Navajo Blankets  gives a visual display set to background flute music of different patterns, and the video More about Navajo Blanket Designs  goes into detailed explanations of various patterns).

An option for a team blanket design: students trace quadrilateral shapes onto larger paper, then color, or they make more shapes by tracing and cutting them out of other materials.

Remind students to explain all reasoning, and to use precise mathematical vocabulary.  

If you allow students to research online, make sure to model good techniques for safe internet searches. Consider pre-selecting other sites that yield quality information for this topic.

If possible, introduce Native American Indian guests to the class and/or take a class museum visit that features authentic artifacts.

Active Classroom

Communication is critical in the design process. Students need to be allowed to talk, stand, and move around to acquire materials. Tips for success in an active classroom environment:

1 –  Students can access any wall, board, or surface to gather and explore ideas — students personalize the working space to meet their needs.

2 – Students have regular opportunities to make choices, including choices about what they learn and how they learn it.

3 –Encourage students to learn and to demonstrate what they’ve learned in ways that best suit their individual learning styles.

4 – It is not a free-for-all!  Amount of prep and planning is evidenced by quality of student work and level of students’ engagement. All is carefully thought out in advance.

5 – A lot of meaningful conversations — between teacher and students and also among students.  Lots of questions asked by and of students. Teacher often manages the conversation, but the students and their thoughts, ideas, and questions determine the scope and direction of the conversation.

6 – Instead of teacher or textbook giving answers or info, students discover ideas through inquiry and exploration.  They figure out solutions and answers on their own.

7 – Tests and quizzes are sometimes needed, but focus assessment on student-created “learning artifacts” — students complete these products to demonstrate in-depth knowledge and understanding key topics.

8 – The focus is on the ultimate goal of student thinking… Every activity, lesson, and project is geared toward deepening and strengthening students’ critical thinking skills.  Students analyze, question, explore, and evaluate on a regular basis.

9 – Help students become successful and care for the success of others by asking them to predict problems that might arise in the active environment and ask them to suggest strategies for their own behavior that will ensure a positive working environment for all students and teachers.

10 – Practice and predict clean-up strategies before beginning the activity. Ask students to offer suggestions for ensuring that they will leave a clean and usable space for the next activity. Students may enjoy creating very specific clean-up roles. Once these are established, the same student-owned strategies can be used every time hands-on learning occurs.

Learning Targets

Students will be able to:

Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Investigate Navajo blanket patterns; observe, analyze, and record any quadrilaterals that appear on them.

Explain properties of quadrilateral shapes used to create a Navajo blanket design of their own.

Assessment

Please Click on the Following Links:

 (one per student)

Review all student Makerspace Journal pages for formative assessment.

Conduct a group discussions to allow all students to share, discuss and compare their findings.

Lesson 3 Overview

What can you make with quadrilaterals that symbolize a local Native American Indian culture?

In this lesson, students explore artifacts characteristic of local Native American Indian tribes from long ago and  in the recent past that contain quadrilateral designs. Students then recreate an artifact influenced by a local tribe that includes quadrilaterals in its design. Students will observe, analyze, and record properties of quadrilateral shapes that appear in their artifact and use this information to describe the American Indians in their local region (SS 3.3.1 and 3.G.A.1).

Essential Questions:

  • How can you research information about local Native American Indians?
  • Can you identify a local Native American Indian tribe?
  • What are some traditions of local tribes?
  • What local tribal artifacts can you reproduce that have quadrilaterals in their design?
  • What attributes and categories of quadrilaterals appear on the recreated artifacts?
  • How and why does your design illustrate the traditions of a local American Indian tribe long ago and in the recent past?

LESSON PROCEDURE

Professional Preparation:

Lesson Format  (class discussion and student team investigations)

  • Students gallery walk all materials in the common area and then sit with teams.
  • Review Native American Indian cultures and traditions from prior lessons.
  • Review quadrilaterals; especially different categories (e.g., rhombuses, rectangles, etc.) that share attributes and whose attributes can define a larger category. Also review why some shapes are not quadrilaterals.
  • Watch the video:  Native American Indian Children
  • Pass out Student Makerspace Journal page: Lesson 3 Investigating Quadrilaterals on a Chumash Breastplate
  • Explain that a breastplate is a device worn over the torso to protect it from injury, as an item of religious significance, or as an item of status. Many Native American tribes, such as the Plains Indians, created breastplates out of bone, “hair pipe beads”, buckskin, and other materials.  In California the Chumash Indians created breastplates too. Ask students to investigate the breastplate inspired by a Chumash breastplate on their Makerspace Journal page and to answer questions about the shapes it is made of.
  • Introduce Native American Indians in your local region from long ago and in the recent past.
  • Discuss ways to research information about local Native American Indians.
  • Watch the video with class:   Native American Indian History
  • Ask essential questions about the video, including local native traditions and local examples of quadrilaterals appearing on clothing and other artifacts.
  • Student teams obtain quadrilateral materials from the common area, and recreate a local Native American Indian artifact containing quadrilaterals in its design with the materials.
  • Pass out Student Makerspace Journal page: Lesson 3 Exploring Local Native American Indian Artifacts
  • Ask students to report about their artifact, including the quadrilaterals it contains, and their attributes.
  • Students prepare a presentation to the class about their local Native Indian artifact and report on the quadrilaterals within its design and cultural significance.

Student Directions (Click + to open)

A Sample Teacher/Student(s) Dialog:  The following is a sample dialog between the teacher & the students for this lesson.  Prepare students into teams of 3 to 4  — either you choose or you allow them to choose their own teams and team names. Pass out or ask students to take out their Maker Journals:  prepare extra pages ahead of time for each student)

(Note:  T stands for teacher, and S stands for student, and additional advice is in parenthesis).

Quadrilaterals in local Native American Indian artifacts —

whole group discussion

T:  (short review of what have learned so far. Give students examples of local Native American Indian artifacts from your area.  If possible, bring in tribal representatives to speak with the class. Include preparing time for further student research;  online, museums, etc.)

S:  (answers vary — e.g., Native American Indian culture, quadrilaterals in designs, quadrilateral categories, attributes, etc.)

(show the video: Native American Indian Children )

T: Did you find any quadrilaterals in this video?  Where?

S:  (answers vary — e.g., clothing, various artwork, musical instruments, etc.)

T:  (students get into teams.  Pass out Makerspace Journal page to each student:

Lesson 3 Investigating Quadrilaterals on a Chumash Breastplate ).

T:  Does anyone know what a breastplate is? (take answers)  …. a breastplate was worn over the chest to protect it from injury, as an item of religious significance, or as an item of status. Many Native American tribes, such as the Plains Indians, created breastplates out of bone, “hair pipe beads”, buckskin, and other materials.  In California the Chumash Indians created breastplates too.

(Ask students to investigate the breastplate inspired by a Chumash breastplate on their Makerspace Journal page and to answer questions about the shapes it is made of. Share results).  Some questions might be:

T:  What shapes do you recognize on this Chumash breastplate?  Which shapes are quadrilaterals?  Which shapes are not quadrilaterals?  Why aren’t they quadrilaterals?

S:  (answers vary)

T: In (name of your state or local region) we have local Native American Indians that have lived here long ago and even recently. What are some ways could you research information about a local Native American Indian tribe?

S:  (answers vary — e.g., videos, books, online, museums, interviews, etc.)

T: (discuss ways to research and to identify local Native tribes — e.g., plan a trip to a local museum; invite experts to talk with students; provide books on the subject, have students research local tribes via internet, books, etc., bring in sample artifacts and/or pictures of artifacts from local tribes. These activities may include other class days. As time allows, investigate these options …. and then return to the following discussion)

(show the video: Native American Indian History )

T:  What did you notice about native traditions?  Did you notice any quadrilaterals appearing on Native American Indian clothing and artwork?

S:  (answers vary)

T: (Pass out at least 10 per student: different sized rhombuses, rectangles, and squares).  Besides the quadrilateral shapes I just passed out to you, I want one person from each team to go to the common table and choose 1o other items  — then return them to your team. (allow time for this … )

T: (once teams have materials, pass out one Makerspace page per student of

Lesson 3 Exploring Local Native American Indian Artifacts )

T: I want you to use the quadrilaterals and materials your team has collected to recreate one “team” artifact from a local Native American Indian tribe.  It must include at least 3 different types of quadrilaterals. I also want each of you record information on your own Makerspace page, including describing the quadrilaterals it contains and their attributes.

(Allow students time to investigate local Indian tribes and to choose an artifact from their tribe to recreate on their own made out of quadrilaterals. Allow time for students to recreate team artifacts and record on journal pages).

T:  (ask student teams to report to the class about their local artifact).

S: (Student teams prepare presentations to the class about their local Native American Indian artifacts).


Concept Quick Reference (Click + to open)

Check out the following web sources to look for information about local Native American Indian tribes:   

Engage students in sharing ideas, reasoning, and approaches, using a variety of representations. Include presenting and explaining ideas and reasoning to one another in pair, small group, and whole class discourse.

Motivate students to listen carefully to and critique the reasoning of peers, using examples to support or counterexamples to refute arguments.

Ask clarifying questions; try out others’ strategies and approaches.

Help identify how different approaches to solving a task are the same and how they are different.

Click on the “+” icon to open each section

Lesson Materials

Building Materials

RAFT Makerspace-in-a-box

-or-

Various quadrilateral shapes made from paper or other materials, at least 10 per student: different sized rhombuses, rectangles, and squares.

Scissors and paper (11″ by 17″)  to adhere shapes onto

Connecting Materials

Various adhesives and fasteners (glue, tape, staplers, etc.)

Other

Various examples (pictures or actual) of local Native American Indian patterns and artifacts.

 

 

 

External Resources

Teacher Notes

If you do not wish to show the Chumash breastplate from California, consider creating a different handout/journal page for your students that displays an artifact with quadrilaterals from a more applicable local region near where you live; 1 per student. 

Remind students to explain all reasoning, and to use precise mathematical vocabulary.  

If you allow students to research online, make sure to model good techniques for safe internet searches. Consider pre-selecting other sites that yield quality information for this topic.

If possible, introduce Native American Indian guests to the class and/or take a class museum visit that features authentic artifacts.

Active Classroom

Communication is critical in the design process. Students need to be allowed to talk, stand, and move around to acquire materials. Tips for success in an active classroom environment:

1 –  Students can access any wall, board, or surface to gather and explore ideas — students personalize the working space to meet their needs.

2 – Students have regular opportunities to make choices, including choices about what they learn and how they learn it.

3 –Encourage students to learn and to demonstrate what they’ve learned in ways that best suit their individual learning styles.

4 – It is not a free-for-all!  Amount of prep and planning is evidenced by quality of student work and level of students’ engagement. All is carefully thought out in advance.

5 – A lot of meaningful conversations — between teacher and students and also among students.  Lots of questions asked by and of students. Teacher often manages the conversation, but the students and their thoughts, ideas, and questions determine the scope and direction of the conversation.

6 – Instead of teacher or textbook giving answers or info, students discover ideas through inquiry and exploration.  They figure out solutions and answers on their own.

7 – Tests and quizzes are sometimes needed, but focus assessment on student-created “learning artifacts” — students complete these products to demonstrate in-depth knowledge and understanding key topics.

8 – The focus is on the ultimate goal of student thinking… Every activity, lesson, and project is geared toward deepening and strengthening students’ critical thinking skills.  Students analyze, question, explore, and evaluate on a regular basis.

9 – Help students become successful and care for the success of others by asking them to predict problems that might arise in the active environment and ask them to suggest strategies for their own behavior that will ensure a positive working environment for all students and teachers.

10 – Practice and predict clean-up strategies before beginning the activity. Ask students to offer suggestions for ensuring that they will leave a clean and usable space for the next activity. Students may enjoy creating very specific clean-up roles. Once these are established, the same student-owned strategies can be used every time hands-on learning occurs.

Learning Targets

Students will be able to:

Describe American Indian nations in their local region long ago and in the recent past.

Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category.

Recognize rhombuses, rectangles, &  squares as examples of quadrilaterals, & draw examples of quadrilaterals that do not belong to any of these subcategories with a local Native American Indian artifact.

Assessment

Please Click on the Following Links:

 (one per student)

Review all student Makerspace Journal pages for formative assessment.

Conduct a group discussions to allow all students to share, discuss and compare their findings.

Design Challenge Overview

Illustrate Your Own Culture with Quadrilaterals

In the culminating lesson, each student ideates, prototypes, tests, reiterates, and finally creates an artifact (containing quadrilaterals) that symbolizes their own culture.  Students will report all they have learned about quadrilaterals and Native American Indian cultures, and explain the cultural significance of their final artifact design to peers and/or another audience. (SS 3.1.2 and 3.G.A.1)

Essential Questions:  

  • How does your culture celebrate its traditions?
  • How do artifacts help tell the story of a culture?
  • How can you categorize different types of quadrilaterals?
  • What is the same, and what is different about your culture compared to a local Native American Indian tribe’s culture?
  • What have you learned about local Native American Indian tribes from the recent past or long ago?

LESSON PROCEDURE

Professional Preparation :

  • Arrange all materials in a common area for students to access. Prepare ahead sets of quadrilateral shapes for students and place in bags or other arrangement for easy and quick access.
  • Prepare methods of final assessment.
  • Provide enough space in the room to form student teams at tables, or in small desk clusters (3 to 4 students per team).  Room arrangement should allow for observation and safety in getting around to students.
  • Make copies of Student Maker Journal page: Design Challenge  My Own Cultural Artifact
  • Decide on Design Challenge constraints:
    • Only use the materials from the Makerspace area in your design.
    • Your artifact must contain at least 3 different types of quadrilaterals in its design.
    • You must complete your Journal page:  Design Challenge  My Own Cultural Artifact

Lesson Format     ( Whole Group Discussion)

  • Pass out Student Maker Journal pages: Design Challenge  My Own Cultural Artifact
  • Review quadrilaterals.
  • Review what they learned about Native American Indian cultures and traditions.
  • Think about the meaning of one’s own culture.
  • Review how to brainstorm ideas.
  • Explain what Ideate, Prototype, and Test mean in the Design Thinking format.
  • Explain that students will create an artifact that represents their own culture, which includes quadrilaterals within its design and meets criteria.
  • Ideate  Investigate models that represent your own culture, and then brainstorm, sketch, and rapid prototype ideas for making an artifact that represents your own culture. Share ideas teammates.
  • Prototype & Test —  design how to create a representation of your own culture with materials from the Makerspace common area. Prototype, test,  and then test over and over to make sure your design meets all the criteria.
  • Final Design — Once your design has met all criteria, create the final design and be prepared to share information about it.

Introduce the Design Challenge (Click + to open)

A Sample Teacher/Student(s) Dialog:  The following is a sample dialog between the teacher & the students for this lesson.

(Note:  T stands for teacher, and S stands for student, with additional advice in parenthesis).

T:  What have you learned so far about quadrilaterals?

S: (answers vary…. make sure to review types of quadrilaterals, attributes, categories, and subcategories)

T: What have you learned about cultures and traditions?

S: (answers vary…. review Native American Indian cultures, and in local areas, and the artifacts that represented those cultures)

T: Think back about what your own culture means to you…. (share out with a partner, or at teams)…..

T: You will create/design/model an artifact that represents your own culture, which includes quadrilaterals within its design and meets criteria.  Explain Criteria and Constraints (see below):

Criteria & Constraints

T: Engineers design things using some rules about how the designs must behave or work.  These rules are called criteria.  Engineers can run out of materials, money, time to build, or space in which to build something.  In other words there are limits on how something can be built.  These limits are called constraints.  The criteria and constraints for this challenge are below (list on a chart or copy onto handouts for students):

Criteria (design requirements) Constraints (design limitations)
  • Model is portable
  • Model must represent your personal culture
  • Must complete the Journal page:  Design Challenge  My Own Cultural Artifact
  • Present final design to an audience.
  • Model must be built with materials provided in the Makerspace
  • Model must be completed and tested in the given time
  • Model must include at least 3 different kinds of quadrilaterals

T:  (explain the Ideate, Prototype, and Test phases of the Design Challenge to students. See sections below with sample student & teacher dialogs)

Click on the “+” icon above to open this dialog section

Ideate

  • Investigate models that represent your own culture (be it school, religion, ethnicity, etc.), and then brainstorm, sketch, and rapid prototype ideas for making an artifact that represents your own culture. Share ideas with teammates.
  • Allow students time to look through sources for information about their culture (books, online sources, outside of class, etc.).  You could decide to make this a separate time and then at another time bring students together to brainstorm, to sketch ideas, and to rapid prototype.
  • Have teams keep track of time, record ideas, and share thoughts with one another.

 

Student Directions (Click + to open)

A Sample Teacher/Student(s) Dialog:  The following is a sample dialog between the teacher & the students for this lesson.

(Note:  T stands for teacher, and S stands for student, with additional advice in parenthesis).

T:  So far you looked, listened, and learned about your culture by doing research.  Now you will ideate.  What does it means to ideate?

S: It means to come up with some ideas quickly about how I want my model, or design, to look!

T: What are some ways you could quickly come up with ideas?

S: My teammates and I could set up a short time to jot down ideas on post-its! A teammate could keep track of time.

T: And then you brainstorm ideas!

S: Yes, when we brainstorm, any idea is fine, no matter how silly it seems!  We could draw pictures, write words, and show what we have in mind on our post-its. With each idea, we could quickly put our post-it ideas on one big poster! After time is called, we look at all the brainstorm suggestions and decide what we like or don’t like about them.

T: Does that means you’ll be asking a lot of questions?

S: Yes!  Questions help us to understand better what we want to create!

T: And they help you get closer to your design idea! What do you do when you have an idea for your artifact model?

S: We sketch it out, think about what materials we’ll need, and get ready to make sample models!

T: That’s right! You start to prototype!

Click on the “+” icon above to open this dialog section

Prototype

Students design representations of their culture using materials from the Makerspace area. They may choose to or need to return to this prototype phase through a series of iterations of models. 

Student Directions (Click + to open)

A Sample Teacher/Student(s) Dialog:  The following is a sample dialog between the teacher & the students for this lesson.

(Note:  T stands for teacher, and S stands for student, with additional advice in parenthesis).

T: Now that each person in your team has decided on a model that could represent their culture, it’s time to prototype a design!

S: To prototype means to start making a model, or design,  with the Makerspace materials!

T: What helps you in designing your prototype?

S: I think of all the sketches and ideas I made in the Ideate phase, and use them as best as I can to create a final prototype.

T: Are there any other techniques to help you get started?

S: I could first draw all the parts I think it will need, then gather the materials to make it!

T:  Do you think you’ll get your model exactly how you want it the first time?

S:  Probably not!  I mean, I think I might change my mind and recreate the model differently…

T: That’s what we mean by iterating!  You may choose to or need to return to the prototype and make changes to it many times. It’s ok to make changes, and mistakes are actually good for us! 

S: How are mistakes good for me?

T: You learn to think in different ways from making mistakes, and mistakes help your brain to grow!  Changing the ways we look at ideas helps us expand our thinking!

S: WOW!

T: Are you ready for some fun? Ok students, go forth and prototype!

Click on the “+” icon above to open this dialog section

Test your Design

Students test their designs,  and then test over and over to make sure the design meets all the criteria. (Keep in mind students may choose to or need to return to this phase as the iterate). A final design is chosen after all tests are complete. 

Student Directions (Click + to open)

A Sample Teacher/Student(s) Dialog:  The following is a sample dialog between the teacher & the students for this lesson.

(Note:  T stands for teacher, and S stands for student, with additional advice in parenthesis).

T:  Now that you’ve made prototypes, it’s time to test them!

T: Did get your model exactly how you want it the first time?

S:  No!  I changed my mind and recreated the model differently a few times…

T:  So it might have taken several sample models before you choose the final one?

S: Yes!  And I have to make sure my model meets all the criteria and constraints!

T: That’s right!  Not only are you just making a model of your culture, you have certain criteria and constraints. Who can remind us what the criteria and constraints are for this design challenge?

S:  (answers… check to make sure all criteria and constraints are completely covered)

T: Ok, now I want you to test and retest  your models to make sure they meet all the criteria! Once you have your final design, make sure to fill out your Student Maker Journal page!

(allow time for students to finish the Design Challenge….. supplement with your chosen forms of assessments: Click on the “+” icon to open  “Assessment” section on right sidebar)


Concept Quick Reference (Click + to open)

Students understand the fundamentals of quadrilaterals: A Review of Quadrilaterals

Watch the video with students:  Quadrilaterals for 3rd graders

Click on the “+” icon to open each section

Design Challenge Materials

Building Materials

RAFT Makerspace-in-a-box       -or-

A variety of recycled items: plastic bags, fabric, paper (8.5 x 11 inch sized), cups, straws, cup lids, plates, string, file folders, etc.

Connecting Materials

Paper clips, rubber bands, tape, velcro, glue, etc.

 

External Resources

Please Click on the Following Video Link:

 

Maker Journal Pages

Please Click on the Following Link:

Teacher Notes

Model good techniques for safe quality internet searches. Consider pre-selecting sites that yield quality information for this topic.

Check for proficiency in the final Design Challenge: 

Suggestion: students prepare a more in-depth report describing what they learned about cultures and traditions, and explain how quadrilaterals were used in this inquiry unit to represent cultural traditions, including their own culture.

Students present their findings to their peers, and/or a parent audience, including describing and classifying quadrilateral shapes in their designs and organization of shapes by their properties, categories and subcategories, and why their design illustrates the traditions of their own culture.

Students compare and contrast quadrilaterals in their design with those from Native American Indian cultures. How are the cultures and traditions alike and how are they different?

Students discuss any changes to their design they could have made and why?

Assess each student’s progression over the course of this Unit Inquiry and to the final Design Challenge.

Active Classroom

Communication is critical in the design process. Students need to be allowed to talk, stand, and move around to acquire materials. Tips for success in an active classroom environment:

1 –  Students can access any wall, board, or surface to gather and explore ideas — students personalize the working space to meet their needs.

2 – Students have regular opportunities to make choices, including choices about what they learn and how they learn it.

3 –Encourage students to learn and to demonstrate what they’ve learned in ways that best suit their individual learning styles.

4 – It is not a free-for-all!  Amount of prep and planning is evidenced by quality of student work and level of students’ engagement. All is carefully thought out in advance.

5 – A lot of meaningful conversations — between teacher and students and also among students.  Lots of questions asked by and of students. Teacher often manages the conversation, but the students and their thoughts, ideas, and questions determine the scope and direction of the conversation.

6 – Instead of teacher or textbook giving answers or info, students discover ideas through inquiry and exploration.  They figure out solutions and answers on their own.

7 – Tests and quizzes are sometimes needed, but focus assessment on student-created “learning artifacts” — students complete these products to demonstrate in-depth knowledge and understanding key topics.

8 – The focus is on the ultimate goal of student thinking… Every activity, lesson, and project is geared toward deepening and strengthening students’ critical thinking skills.  Students analyze, question, explore, and evaluate on a regular basis.

9 – Help students become successful and care for the success of others by asking them to predict problems that might arise in the active environment and ask them to suggest strategies for their own behavior that will ensure a positive working environment for all students and teachers.

10 – Practice and predict clean-up strategies before beginning the activity. Ask students to offer suggestions for ensuring that they will leave a clean and usable space for the next activity. Students may enjoy creating very specific clean-up roles. Once these are established, the same student-owned strategies can be used every time hands-on learning occurs.

 

 

Learning Targets

Students will be able to:

Explain all phases of the Design Thinking process:  Empathy, Ideate, Prototype, Test, and Design.

Design an artifact that represents their own culture. The artifact will incorporate several different types of quadrilaterals in its design.

Compare and contrast their artifacts with sources to build knowledge about expressing their own culture.

Report on the significance of their artifact, of the attributes, categories, and subcategories of quadrilaterals it contains, and how this helped them understand about cultures and traditions.

Assessment

Please Click on the Following Links:

 (one per student)

Review all student Makerspace Journal pages for formative assessment.

Conduct a group discussions to allow all students to share, discuss and compare their findings.