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).
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.