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Navajo Rug Geometry

Compiled and Written by Rachel Marie Kimball

In Collaboration with the Navajo Nation Department of Diné Education

Supported by the Nizhoni Ranch Gallery

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Note to Teachers: Choose Your Own Adventure

This lesson is designed as a Choose Your Own Adventure for you and your students. Before beginning the lesson or unit, identify which geometric concept to focus on. Use every slide, or pick and choose what you would like to do with your students.

Geometric Concepts:

Angles: Right, Acute, Obtuse

Lines: Parallel, Perpendicular, Intersecting

Shapes: Triangle, Square, Trapezoid

As you analyze the above geometric concepts, consider applying knowledge

of patterns, and symmetry and asymmetry to your observations:

Patterns: Growing, Repeating

Symmetry / Asymmetry

This powerpoint is not a one time lesson.

It can be used several times in unique ways.

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Diné and Navajo

(Slide 5)

Origin of Navajo Rugs

(Slides 6-10)

Warm Up

(Slides 11-12)

MAIN MENU

Use the following buttons to click through a variety of activities and informative slides about Navajo Rug Geometry! You can also simply go through the slides in order without using this menu.

*Look for the button on every slide to return to this main menu as needed.

Rug Examples

(Slides 13-28)

Crystal / Storm

(Slides 14-15)

Ganado - Klagetoh

(Slides 16-17)

Red Mesa

(Slides 18-19)

Eye Dazzler

(Slides 20-21)

Storm

(Slides 22-23)

Historic

Two Gray Hills

(Slides 24-25)

Chinle

(Slides 26-27)

Combined Rug Images

(Slide 28)

Specific Symbols

(Slides 29-35)

Create / Perform

(Slides 36-43)

Respond / Connect

(Slide 44)

Additional Resources

(Slides 45 - 49 )

Diné Music

(Slide 46)

Reference List

(Slide 48)

Standards and Objectives

(Slides 49-50)

Supportive Videos / Lessons

(Slide 47)

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Navajo Rug Geometry

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(Slide 3)

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Diné and Navajo

The names Navajo and Diné can be used interchangeably. We will use both in this lesson. Navajo is the common name in society today, but members of the tribe continue to call themselves Diné--pronounced “Din-eh.”

The following link provides excellent sound pronunciation as well as succinct information about the two words. https://navajowotd.com/word/dineh/

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(Slide 3)

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Origin of Navajo Rugs

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(Slide 3)

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Spider Woman and Diné Rugs

Spider Woman is a deity that holds a special place in the Diné culture. It is believed that she is the one who taught the Navajo to weave. The first loom was made from sky and earth cords, and that the weave itself was made from sunlight, lightning, crystals and white shells.

Link to the narrative of how Navajo rugs came to be and are made

The Navajo use different plants to mix solution together to make dyes so that the colors do not fade and stay vibrant. Different types of wool are also mixed to create textures and colors. Black wool and white to make grey. Like a blueprint, weavers have an image in their mind on what they see the rug design to be. They match the dyes to the colors they envisioned. As a very sophisticated process, math is used throughout the whole process, from making sure they have enough wool spun for the rug to tracking large and small intricate patterns.

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Matriarchal Weaving

The Navajo culture is a matriarchal society (meaning the women hold positions of leadership and power), and the women traditionally owned the sheep and were the ones to weave with the wool. To this day, weaving is sacred, and there are many weavers.

What began with weaving women's dresses, biil (two identical blankets sewn together), eventually became single blankets, then Chief's blankets, and evolved on to different styles and designs of blankets and rugs.

Link to the narrative of how Navajo rugs came to be and are made

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(Slide 3)

Navajo weaving started as a means for survival and it later became a way to earn income for families through trading posts.

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Weaving Today

Navajo weaving is done the same way now as it was on the first Navajo loom:

  • shearing the sheep, carding the wool, spinning the wool into yarn, and dyeing it different colors;
  • using a hand-made upright loom;
  • one continuous warp;
  • each strand of woolen yarn is placed into the warp by hand, one strand at a time.

Men are also weavers today. Modern-day craftsmanship use inventive practices (such as using copper pennies to make sage green colors), yet Spider Woman's teachings can still be found.

Link to the narrative of how Navajo rugs came to be and are made

Return to Main Menu

(Slide 3)

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Evolution of Navajo Rugs

From the very first "Black Design Blanket" that Spider Woman created to the gorgeous Two Grey Hills or historic Storm Patterns weavers craft today, each textile has one thing in common: they are carefully and spiritually created by expert hands who understand the value of earth and the gifts it gives us. Navajo weaving is a transformation of what mother nature offers to us to give life, the Navajo have used this gift to live off of the land and prosper for hundreds of years.

Rugs may appear different today, but the tradition of rug weaving carries on.

Link to the narrative of how Navajo rugs came to be and are made

Return to Main Menu

(Slide 3)

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Warm Up: Part I

After sharing the narrative of how Navajo rugs came to be and are made on the previous slides, guide students through a brief exploratory warm up using words to describe the process of preparing to weave an authentic Diné Rug:

  • Shearing--Staying in place, use arms and legs to demonstrate slicing and cutting motions that are symbolic of cutting the wool from a sheep.

Axial Motions: slash, carve, slice, cut

  • Carding--Staying in place, use full-body movement to explore a variety of combing motions (up and down, side to side, etc.) and plucking motions, similar to how one would remove tangles from the wool and clean it.

Axial Motions: brush, pluck, smooth out, untwist, untangle

  • Spinning--Staying in place, try spinning different body parts, and compare it to spinning your entire body! Think about how spinning wool would involve pulling and elongating.

Axial Motions: twist, rotate, spiral, spin

  • Dyeing the wool--Staying in place, imagine you are the newly spun wool, and you are standing near a dish of naturally made dye. Imagine what color it is (don’t tell anyone! It’s your own secret). Now carefully dip different body parts into the dye (legs, arms, head), and eventually immerse your entire self into the dye! Pull yourself out, and stretch out long to dry off.

Axial Motions: dip, soak, immerse, stretch

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(Slide 3)

← Watch this read aloud of The Goat in the Rug to learn more about the process of Navajo weaving.

*Axial movement stays in place

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Warm Up: Part II

1st Time Playing the Video →

Observe the process of weaving. Notice how one strand of yarn from the weft travels between the strands of thread that form the warp. Identify any patterns of how many warp strands are skipped before a weft strand dives back in again.

2nd Time Playing the Video →

Perform weaving motions with your body to the music from the video as you travel through the space.

locomotor motions: skip, slide, jump, roll, hop, leap.

Consider assigning half of the class to create frozen, linear shapes in the room to represent the warp while the other half of the class is the weft, weaving around the frozen students and through the open spaces.

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(Slide 3)

*Locomotor movement travels

through space.

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Navajo Rug Examples

Some rugs are titled after geographic locations and time periods in history, and others are named after important cultural subjects.

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(Slide 3)

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CRYSTAL / STORM DESIGN

What do you see?

Geographic / Subject

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(Slide 3)

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Angles

Lines

Shapes

Symmetry / Asymmetry

Patterns

Practice making right, acute and obtuse angles from this rug with your body by bending different joints (knee, hip, elbow, wrist, etc.).

With a partner, use both of your bodies to create right, acute and obtuse angles from this rug together by respectfully connecting different parts of your bodies.

With a partner, create shapes with your bodies to match the parallel, perpendicular and intersecting lines from this rug.

With the teachers help, create class formations where students stand in assigned spots in parallel, perpendicular or intersecting lines to match this rug.

On your own or with a partner, create shapes with your body to reflect the different geometric shapes you see in this rug (square, triangle, rectangle, diamond, etc.) Use a variety of body parts to creatively make your shapes.

With a partner, stand side-by-side or facing each other, and create shapes with your bodies from the rug that match like a mirror reflection to create symmetry.

Identify a pattern on this rug, for example:

and assign specific shapes or movements to the pattern (i.e. high level shape with pointed hands, low level shape with pointed hands; repeat.) Practice the movement pattern a few times to demonstrate how it repeats.

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(Slide 3)

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GANADO–KLAGETOH DESIGN

Geographic

What do you see?

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(Slide 3)

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Angles

Lines

Shapes

Symmetry / Asymmetry

Patterns

Practice making right, acute and obtuse angles from this rug with your body by bending different joints (knee, hip, elbow, wrist, etc.).

With a partner, use both of your bodies to create right, acute and obtuse angles from this rug together by respectfully connecting different parts of your bodies.

With a partner, create shapes with your bodies to match the parallel, perpendicular and intersecting lines from this rug.

With the teachers help, create class formations where students stand in assigned spots in parallel, perpendicular or intersecting lines to match this rug.

On your own or with a partner, create shapes with your body to reflect the different geometric shapes you see in this rug (square, triangle, rectangle, diamond, etc.) Use a variety of body parts to creatively make your shapes.

With a partner, stand side-by-side or facing each other, and create shapes with your bodies from the rug that match like a mirror reflection to create symmetry.

Look for the small detail in this rug that makes it asymmetrical. How can you and a partner reflect this with your own bodies?

Identify a pattern on this rug, for example:

and assign specific shapes or movements to the growing pattern (i.e small frozen shape, jump once; frozen shape a little bigger, jump twice; frozen shape a little bigger, jump three times; etc. ABABBABBB) Do this a few times to demonstrate how it grows.

Return to Main Menu

(Slide 3)

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RED MESA DESIGN

Geographic

What do you see?

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(Slide 3)

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Angles

Lines

Shapes

Symmetry / Asymmetry

Patterns

Practice making right, acute and obtuse angles from this rug with your body by bending different joints (knee, hip, elbow, wrist, etc.).

With a partner, use both of your bodies to create right, acute and obtuse angles from this rug together by respectfully connecting different parts of your bodies.

With a partner, create shapes with your bodies to match the parallel, perpendicular and intersecting lines from this rug.

With the teachers help, create class formations where students stand in assigned spots in parallel, perpendicular or intersecting lines to match this rug.

On your own or with a partner, create shapes with your body to reflect the different geometric shapes you see in this rug (triangle, rectangle, diamond, etc.) Use a variety of body parts to creatively make your shapes.

With a partner, stand side-by-side or facing each other, and create shapes with your bodies from the rug that match like a mirror reflection to create symmetry.

Identify a pattern on this rug, for example:

and assign specific shapes or movements to the repeating pattern (i.e. jump up from low level, spin, drop down low; repeat. ABCABC...) Practice the movement pattern a few times to demonstrate how it repeats.

Return to Main Menu

(Slide 3)

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EYE DAZZLER DESIGN

Subject

What do you see?

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(Slide 3)

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Angles

Lines

Shapes

Symmetry / Asymmetry

Patterns

Practice making right, acute and obtuse angles from this rug with your body by bending different joints (knee, hip, elbow, wrist, etc.).

With a partner, use both of your bodies to create right, acute and obtuse angles from this rug together by respectfully connecting different parts of your bodies.

With a partner, create shapes with your bodies to match the parallel, perpendicular and intersecting lines from this rug.

With the teachers help, create class formations where students stand in assigned spots in parallel, perpendicular or intersecting lines to match this rug.

On your own or with a partner, create shapes with your body to reflect the different geometric shapes you see in this rug (triangle, rectangle, diamond, etc.) Use a variety of body parts to creatively make your shapes.

With a partner, stand side-by-side or facing each other, and create shapes with your bodies from the rug that DON’T match to create asymmetry. (One partner could be on a low level while the other partner is on a high level; or one partner can make a jagged shape while the other partner makes straighter lines.)

Identify a pattern on this rug, for example:

and assign specific shapes or movements to the pattern (i.e. sharp motions on a high level, sharp motions on a low level; repeat.) Practice the movement pattern a few times to demonstrate how it repeats.

Return to Main Menu

(Slide 3)

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STORM DESIGN

Subject

What do you see?

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(Slide 3)

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Angles

Lines

Shapes

Symmetry / Asymmetry

Patterns

Practice making right, acute and obtuse angles from this rug with your body by bending different joints (knee, hip, elbow, wrist, etc.).

With a partner, use both of your bodies to create right, acute and obtuse angles from this rug together by respectfully connecting different parts of your bodies.

With a partner, create shapes with your bodies to match the parallel, perpendicular and intersecting lines from this rug.

With the teachers help, create class formations where students stand in assigned spots in parallel, perpendicular or intersecting lines to match this rug.

On your own or with a partner, create shapes with your body to reflect the different geometric shapes you see in this rug (square, triangle, rectangle, diamond, etc.) Use a variety of body parts to creatively make your shapes.

With a partner, stand side-by-side or facing each other, and create shapes with your bodies from the rug that are NOT a mirror reflection; asymmetry.

Look for the detail in this rug that makes it asymmetrical. How can you and a partner reflect this with your own bodies?

Identify a pattern on this rug, for example:

and assign specific shapes or movements to the pattern (i.e. face wall, throw hands in the air, quarter jump-turn to next wall, throw hands in the air; repeat.) Practice the movement pattern a few times to demonstrate how it repeats.

Return to Main Menu

(Slide 3)

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HISTORIC TWO GRAY HILLS

TOADLENA DESIGN

Geographic

What do you see?

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(Slide 3)

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Angles

Lines

Shapes

Symmetry / Asymmetry

Patterns

Practice making right, acute and obtuse angles from this rug with your body by bending different joints (knee, hip, elbow, wrist, etc.).

With a partner, use both of your bodies to create right, acute and obtuse angles from this rug together by respectfully connecting different parts of your bodies.

With a partner, create shapes with your bodies to match the parallel, perpendicular and intersecting lines from this rug.

With the teachers help, create class formations where students stand in assigned spots in parallel, perpendicular or intersecting lines to match this rug.

On your own or with a partner, create shapes with your body to reflect the different geometric shapes you see in this rug (square, triangle, rectangle, diamond, etc.) Use a variety of body parts to creatively make your shapes.

With a partner, stand side-by-side or facing each other, and create shapes with your bodies from the rug that match like a mirror reflection to create symmetry.

Identify a pattern on this rug, for example:

and assign specific shapes or movements to the pattern (i.e. high level shape, medium level shape, low level shape; repeat.) Practice the movement pattern a few times to demonstrate how it repeats.

Return to Main Menu

(Slide 3)

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CHINLE DESIGN

Geographic

What do you see?

Return to Main Menu

(Slide 3)

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Angles

Lines

Shapes

Symmetry / Asymmetry

Patterns

Practice making right, acute and obtuse angles from this rug with your body by bending different joints (knee, hip, elbow, wrist, etc.).

With a partner, use both of your bodies to create right, acute and obtuse angles from this rug together by respectfully connecting different parts of your bodies.

With a partner, create shapes with your bodies to match the parallel, perpendicular and intersecting lines from this rug.

With the teachers help, create class formations where students stand in assigned spots in parallel, perpendicular or intersecting lines to match this rug.

On your own or with a partner, create shapes with your body to reflect the different geometric shapes you see in this rug (square, triangle, rectangle, diamond, etc.) Use a variety of body parts to creatively make your shapes.

With a partner, stand side-by-side or facing each other, and create shapes with your bodies from the rug that match like a mirror reflection to create symmetry.

Look for the detail in this rug that makes it asymmetrical. How can you and a partner reflect this with your own bodies?

Identify a pattern on this rug, for example:

and assign specific shapes or movements to the pattern (i.e. slow movement, fast movement, slow movement, fast movement; repeat) Practice the movement pattern a few times to demonstrate how it repeats.

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(Slide 3)

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SPECIFIC SYMBOLS

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CROSSES

Represent Spider Woman and her teachings.

What do you see?

Angles: Right, Acute, Obtuse

Lines: Parallel, Perpendicular, Intersecting

Shapes: Triangle, Square, Trapezoid

Patterns: Growing, Repeating

Symmetry/Asymmetry

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(Slide 3)

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DIAMOND

Represents Navajo homeland with its four sacred corners marked by the four sacred mountains.

What do you see?

Angles: Right, Acute, Obtuse

Lines: Parallel, Perpendicular, Intersecting

Shapes: Triangle, Square, Trapezoid

Patterns: Growing, Repeating

Symmetry/Asymmetry

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(Slide 3)

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TRIANGLES

When placed on top of each other, they can become a series of prayer feathers or songs.

Can also be the backbone of a mountain Yei figure

What do you see?

Angles: Right, Acute, Obtuse

Lines: Parallel, Perpendicular, Intersecting

Shapes: Triangle, Square, Trapezoid

Patterns: Growing, Repeating

Symmetry / Asymmetry

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WHIRLING LOGS

Comes from the Navajo origin story, and can be a symbol of good luck.

What do you see?

Angles: Right, Acute, Obtuse

Lines: Parallel, Perpendicular, Intersecting

Shapes: Triangle, Square, Trapezoid

Patterns: Growing, Repeating

Symmetry / Asymmetry

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LIGHTNING

Symbol of strength and power.

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What do you see?

Angles: Right, Acute, Obtuse

Lines: Parallel, Perpendicular, Intersecting

Shapes: Triangle, Square, Trapezoid

Patterns: Growing, Repeating

Symmetry / Asymmetry

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SPIRIT LINE

A single line of contrasting color extending from the center of the rug to the edge.

Each weaver leaves an opening for their creative spirit to enter and exit the weaving. They make one imperfection as well, as no rug can be perfectly created.

What do you see?

Angles: Right, Acute, Obtuse

Lines: Parallel, Perpendicular, Intersecting

Shapes: Triangle, Square, Trapezoid

Patterns: Growing, Repeating

Symmetry / Asymmetry

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CREATE / PERFORM

Geometric Rug Dances

partnership, small groups, or full class

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Step 1: Pick a Rug

Choose a rug that you would like to create a dance for.

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Step 2: Beginning Shape

Create a Beginning Shape that reflects the geometric concept of focus in your rug.

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Concept Example: Intersecting Lines

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Step 3: Middle Movement

Establish 1 to 3 specific movement ideas for the middle of your dance. The movement ideas can be connected to the geometric concept, or to the process of making a rug (shearing, carding, spinning, dying wool, weaving, etc.), or both.

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Concept Example: Pattern sequence of geometric shapes

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Step 4: Ending Shape

Create an Ending Shape that reflects a geometric concept in your rug. (It can be the same as your beginning shape, or different.)

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Concept Example: Asymmetry

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Step 5: Practice to Perform!

Practice your full dance a few times to then perform it for others.

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Dance Summary

Beginning

Middle

End

After selecting a rug, create a beginning shape that reflects the focus geometric concept in your rug.

Establish 1 to 3 specific movement ideas for the middle of your dance. The movement ideas can be connected to the geometric concept, and/or to the process of making a rug (shearing, carding, spinning, dying wool, weaving, etc.) or both.

Create an Ending Shape that reflects a geometric concept in your rug. (It can be the same as your beginning shape, or different.)

(Practice your full dance a few times to then perform it for others.)

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*Click on your rug of choice to revisit it if needed.

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PERFORM

Perform your dance for others in your class, or prepare your dances for an informace for other classes, parents, or a school assembly!

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Response Questions:

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  • Which math skills did you notice it takes to weave a Diné rug?
  • Was there a style of Diné rug that you like most? Which one? What about this rug style makes it your favorite?
  • Which math skills did you notice you can show with your body and movement? How can you show it?
  • Was there a type of movement that you enjoyed most from this lesson?
  • What else did you learn about the Navajo that you didn’t know before?

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Additional Resources

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Diné Music to Dance With:

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Navajo Weaver: Michele Reyes

Extensions to Other Lessons:

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Native American Round Dance:

https://education.byu.edu/arts/lessons/native-american-round-dance

Navajo Rugs Visual Art Lesson

Lesson soon to be available

More Native American lesson plans found on the BYU Arts Partnership Website

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Images Reference List

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All other images from Nizhoni Ranch Gallery

https://www.navajorug.com

https://www.navajorug.com/collections/historic

Slide 7: Modern Image Creative Commons Image: https://commons.wikimedia.org/wiki/File:Native_American_rug_weaver_at_Hubbell_Trading_Post_National_Historic_Site.jpg

Slide 8: Pueblo Woman with Child Creative Commons Image: https://picryl.com/media/a-pueblo-woman-and-child-757d85

Pueblo Woman Among Pueblos Creative Commons Image: https://commons.wikimedia.org/wiki/File:Everyday_life_in_Taos_Pueblo.jpg

Slide 9: Warp and Weft Creative Commons Image: https://commons.wikimedia.org/wiki/File:Gauzeweave.svg

Modern Woman Weaving Creative Commons Image: https://en.wikipedia.org/wiki/File:Navajo_loom_desert_view.jpg

Slide 10: Images from Mandi White and her grandmother.

Slide 38: Creative Commons Image:

https://www.empoweredacro.com/home-typical

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Utah State Standards and Objectives (basic list)

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2nd Grade

Dance: 2.D.CR.3

Mathematics: 2.MP.4, 2.MP.7, 2.G.1, 2.G.3

Social Studies: 1.1.a, b, c, 1.2.a,b,

3rd Grade

Dance: 3.D.P.1

Mathematics: 3.MP.4, 3.MP.7, 3.G.1, 3.G.2

Social Studies: 2.1.b, 2.1.c, 3.1.a,

4th Grade

Dance: 4.D.CO.2

Mathematics: 4.MP.4, 4.MP.7, 4.MD.5, 4.G.1, 4.G.2, 4.G.3

Social Studies: 2.1.b, 2.1.c

5th Grade

Dance: 5.D.P.7

Mathematics: 5.MP.4, 5.MP.7, 5.G.3

Social Studies: 1.2.a-b

6th Grade

Dance: 6.D.CO.3

Mathematics: 6.G.1

Social Studies: 1.4.c, 2.2.a

1st Grade

Dance: 1.D.CO.2

Mathematics: 1.MP.7, 1.MP.8, 1.G.1, 1.G.2.a,b.

Social Studies: 1.1.a, 1.1.b

Kindergarten

Dance: K.D.CO.2

Mathematics: K.MP.4, K.G.2, K.G.3, K.G.4

Social Studies: 1.1.d,

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Diné Standards

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4th -6th Diné Character Building Standards

Standard: K’ é hwiinidzin dóó ádáhozdílzin bee hadínísht’ée dooleełígíí bóhwiideesh’ááł.

I will develop and apply critical thinking to establish relationships with the environment.

Concept 2- Ádáhozdílzin. I will maintain the sacredness of self-identity.

PO 1. Íínísts’ ą́ą’go binahjį’ bínashidi’neeztą́’ígíí choosh’į́į dooleeł. I will listen to and apply Diné teachings.

4th -6th Diné Culture Standards

Standard: K’é dóó nitsáhákees dóó nahat’á náásgóó iiná bee siih hasingo ádoolnííł.

I will develop an understanding of Diné way of life.

Concept 1: Nitsáhá kees

Shintsáhákees shił nilį́į go bee ádaa ákonisdzin dool eeł. I will acknowledge and value my thoughts and personality.

PO 1: Diné be’é’ooĺįįł bóhoosh’aahgo binahjį’ ádił nishdlį́į dooleeł. I will develop my cultural knowledge to build self worth.

PO 3: Nitł’iz ałtaas’éi baa ákonisin dóó baa hashne’ dooleeł. I will explain the significance of my cultural possessions.

4th -6th Diné History Standards

Standard: Diné bibee’é’ool’įįł dóó ádahóót’įįdígíí shił nilį́įgo ádídíínísht’i’ dooleeł.

I will understand historical/factual events, people and symbols that influence my family.

Concept 3: Nihinaagóó bitsį’ yishtłizhii kéédahat’ínígíí dóó shidine’é bahane’ ahąąh naashnilgo baa hashne’ dooleeł. I will compare and contrast major historical events of Diné and neighboring tribes.

PO 2: Ałk’idą́ą́’ dóó dííshjį́įjį’ ádahóótįįdígíí ałhąąh naashnil dooleeł. I will compare Diné and a neighboring tribe’s historical timeline.

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Navajo Rug Geometry

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