Searching for Shapes in Architecture (Day 1)
Lesson 3 of 9
Objective: SWBAT find simple mathematical patterns in architecture and examine the ways in which different 2 dimensional shapes and 3 dimensional solids interact with one another to create new polygons and 3 dimensional solids. UPDATED 8/10/15.
Refresh and Review
In order to leverage and grow through students’ application of their prior knowledge to a situation, it is important to make sure they are reminded of all of the "tools" (knowledge) at their disposal. We open with a review. Here you will see students making a Connection to Prior Knowledge.
First, the attributes of simple polygons:
- Can you measure the interior area of the shape? (Is the shape "closed"?)
- Do the lines defining the shape meet at their ends to form vertices (corners)?
- Do the lines defining the shape cross each other?
- How many edges meet at each vertex (corner)? More than two?
- How many edges? How many vertices (corners)? Are they the same number?
We actively look for the differences between regular and irregular pentagons, hexagons and octagons. This can be done much like a dichotomous key, or by sorting.
- What number of sides does the shape have? (sorting) or What is the same between these two shapes? What is different? (dichotomous key)
- Are the shape’s sides congruent (same length)?
- Are the interior angles congruent (same size)?
This has been a review of both vocabulary and basic shape knowledge. In order to facilitate knowledge transfer, it is important to apply the review immediately. I have students draw and name/label several different quadrilaterals on their whiteboards, draw parallel and intersecting lines, draw a right triangle and a rectangle, and identify the 90 degree angle.
- Students can examine the 4 right angles of a rectangle and calculate their cumulative measurement.
- Students can compare the angles in a triangle and a rectangle. Making comparisons is more rigorous than simply listing attributes of a given shape because students have to reason through their thinking, and put that thinking into words. Facilitate the comparison to bring students to the point of noticing and then proving that the measurement of angles in a triangle is 1/2 that of the angles in a rectangle.
The DK book - The Story of Architecture by Jonathan Glancey and Sir Norman Foster has a powerful, lyrical introduction from which I read the first 4 paragraphs. I try to provide experiences with language that address the latency period of language learning. This gives the students the opportunity to simply listen and to recognize and enjoy beauty and meaning without being forced through a comprehension activity. This is an important stage not only for my English Language Learners but for ALL learners, especially when many of them have parents who are unable to read aloud much due to other responsibilities.
I know for a fact that who I am today was in many ways shaped by all the hours of listening to my parents read to me not only from children's books, but from high-level literature. So I read this short introduction to give my students that same type of experience; a brief moment of floating down a river of beautiful, meaningful language. So while I don't interact with them much about this short text excerpt, I believe this is a critically important instructional choice.
Students are challenged immediately to bring the power of architectural design into their thinking by answering the questions on the Shapes in Architecture: Entrance Ticket.
These questions are designed help them think about connections between local architecture and the natural and cultural environment. This Entrance Ticket Visual Companion shows four photos of southwestern architecture with accompanying questions that I use to support students in completing the entrance ticket.
I show students the Simple Polygons PowerPoint as a quick review of specific vocabulary we have discussed in the previous two lessons. It also introduces some enrichment terms for the geometrically curious!
I've included my Vocabulary List. I've indicated essential (Tier 1) terms in blue. I use this list to insure that I'm checking on my ELL students and to provide as-needed extra support. I also included Tier 3 words to provide spelling and syllabication support for students who want to challenge themselves. with these out of level words. If time permits, I sort these words by part of speech to assist language learners in using them in oral sentences for their explanations and debates about polygons in architecture.
I guide students in an investigation of architecture around the world using these shapes. I made notes to remind myself of key ideas/prompts I want to use to guide children in answering literal and open-ended questions about architectural math and the relationship between culture, landscape and architecture. Here is a short clip that shows how I integrate these questions: Classroom Video: ELL Students.
Guided practice notes are provided to assist students in organizing their notes by each building. I intentionally do not list the questions on this page because the questions I ask my students will vary depending on their readiness level, their language skills, and their need for enrichment and integration of content.
Optional Video Clips:
This video on Habitat 67 has some great exterior views and provides visual support for a discussion of how architecture interacts with nature. Obviously the architect felt strongly about providing residents views of the St. Lawrence River, and also about providing privacy. Observe that no windows face each other. Possible questions for students:
- What about the boxes? Do they fit in with the river? Does it matter?
- This was designed as low-income housing, but because it is so unique it ended up being luxury condominiums. Is that fair?
- Should only wealthy people have the opportunity to live in beautiful and unusual places?
This is an interesting view of the Waldespirale. It is a quite unique structure, and worth spending some time looking in order to engage students in a dialogue about what they see!
Throughout this activity I confer with students about what they find interesting, focusing on developing their understanding of polygons within this real-world context. They work in partnerships or small groups to discuss what they see. Here's a bit of what this looks like in action: Classroom Video: Student Led Inquiry.
I split students into two groups, a computer and a book group. (They will rotate).
Computer Group: This group works with photos of buildings from around the world which I’ve shared with them via Google Drive. The students use good Google Draw to overlay simple polygons on the different features of the building. They can take notes on circles and curves but at this time they do not label them, because that's not our focus during this set of lessons. As students work, I prompt them with these questions about patterns, function and aesthetics:
- What patterns do you notice about how polygons are used in buildings?
- What do you think about how polygons are used to make a building beautiful?
- What do you think about how polygons are used to make a building strong and useful?
These are subjective evaluations, and I encourage students to develop their own point of view.
I also encourage students to reflect upon architectural clues that hint at the local environment, climate, and culture.
Book Group: This group uses a note taking page to record basic information about some notable buildings and/or architectural styles. Their first focus is to examine how polygons and the resulting 3D solids are used in different buildings, natural settings, and cultures. The second focus will be to jot down some basic information about the buildings - name, location, when built, special features, cultural importance and so on.
Lesson Materials: This document contains 41 photos (my own and Wikipedia) that can be used in this activity. It is an open word document, so it can be downloaded and revised to suit your needs.
Some students prefer to work on paper and sometimes the technology can get in the way of the learning. I also have 5 black and white printable images whose different polygons can be traced with a ruler and color pencils or crayons. I recommend thin tipped pencils!
Today has been quite a learning journey, one I want students to reflect upon. I ask my students to think silently about one math pattern they noticed in the architecture they looked at today. Then I reintroduce the word structure, and ask them to think silently about what role certain shapes play in buildings - are they functional, (for support), aesthetic, or does it depend on the building? During the lesson I saw that students needed additional support for the word functional, so I point out the rectangular frame around our classroom door. That is an example of something that is functional. It's strong and we can infer it is cheap because rectangular doors and door frames are easy to find.
At the conclusion of these architecture lessons, students will be writing about their observations. This kind of dialogue (Classroom Video: Writing Across the Disciplines) provides support for clear, concise sentences that accurately portray what they have learned. Students are expected to discuss the polygons (and resulting 3d solids) they find in each building, the purpose they think these shapes fulfill (functional, aesthetic, both). They are also expected to state their inferences regarding details of how the building is adapted to the natural environment, how it is a reflection of the culture, and support their claims.