During our Tuesday, April 18th CAMI meeting, Gina Cortez and Amy Vickers facilitated a conversation around shadows.
Notice/Wonder
We showed this slide and asked the group what they noticed and wondered.
| What do you notice? | What do you wonder? |
| Interesting exercise in perspective. To figure out/draw an object’s shadow would be very complicated – time of day and year, location, size and shape of object, “internal” object structure. Is this possible with a mathematical formula? What would that look like? Probably easier to do it intuitively! | If I marked the top of the lamppost in chalk throughout the day, what shape would I end up with? (I don’t think it would be a circle)I wonder why the shadow seems to move away from poleI wonder if I would see a building shadow if the picture showed more. |
| The length and direction of the shadow changes. | How the snow would feel on my feet 🙂 |
| I notice I can see the shape of the parking sign in some of the shadows (on the right), but in others it just looks like the shadow of a pole (on the left). | Where is the sun at the moment when the photo was taken? |
| I notice that some shadows are longer and some shorter for the same sign post.— that when the sunlight shines from the front of the sign post, the shadow captured the top of the sign post.— that when the sunlight shines from the side of the signpost, the shadow captured is the pole. | I wonder which way the sunlight is hitting the object to get each length of shadow. —– where must I stand when I take the picture to get the shadows in the photo. Far away or close up to the object. |
| In the lamppost sequence, the image on the left has the longest shadow – I’d thought at first that the shadow of the post would move in a circle, but that image makes me see that it wouldn/t | Was the photographer standing in the same place in each photo (of the respective signs)? |
| The direction of the shadow changes in each picture | I wonder how much time passed between different photos. |
| The color of the brown sign changes. | Were some of the photos cropped to keep the shadow of the photographer out of the picture? Or where did the photographer stand? |
| I wonder what time each picture was taken. | Are shadows ever the same exact shape and size as the thing that produces them? |
| I notice the signpost has holes in it. | I keep thinking about the proportional math problems. “If a man stands next to a tree and the man is x inches tall and his shadow is z inches, how tall is the tree. |
| The lamppost makes light and also shadow. | How does the length of the shadow change as the sun moves? |
| It is so beautiful to just watch the shadow of something move over the course of a day and just think about how its caused by this flaming orb 8 minutes away | I wonder how the sequence of pictures would differ at different times of the year. |
| There is only one shadow per object. | Is there only one light source? Or is it that when up against the sun all others get drowned out in the sun’s light? |
| The lamppost looks like it is tilted at different angles in the pictures, but so is the ground. | I wonder if the photos would be the same at the same time of day on a different day/month. |
| The lamppost is on a strip of lighter colored bricks, but it isn’t centered on that strip. | How do the degrees between shadows change at different times of day |
| It looks like the stone work and design in the lamp post photo were not designed with the lamppost’s shadow in mind | I wonder if the pictures were taken on the same day or different days. |
| The lamppost pictures are so different from each other, while the sign pictures look very similar, except for the shadows (time of day taken). | Is the angle between the lamp post and its shadow always the same? How could you even measure that? |
| I notice that the top of the shadow of the sign is not visible at certain times of day. | What time of year were these photos taken? I assume they were taken in the last couple weeks. |
| I notice the right angles of the shadow to the object projecting the shadow. | In which compass direction are the shadows pointing? |
| Shadow are like mysteries art intriguingly beautifully dark but… |
What new questions do you have?
Then we discussed these shadows photographed on the CUNY Lehman College campus.
In this discussion we wondered if the shadows were in order or taken on the same day. We wondered about the 3D configuration of the building creating the zigzag shadow. We wondered why some shadows were darker. We noticed the reflections of the windows on the shadow.
Then, after showing this slide that measured shadows of sticks in the snow over time, we asked about noticing, wondering, and exploring mathematical ideas.
| What do you notice? | What do you wonder? | What math would you like to explore? (from any part of our discussion today) |
| There is an extra shadow. One bigger than the sticks in the second image. | Does this mean that on the left, the two twigs are the same length (6 inches), but are producing such different lengths (being fairly close together)? Why would a stick of the same size, at the same time, result in a shadow that different in length? Does the shadow of every object make a different shape | How you would come up with a formula to predict the size, shape and location of different objects’ shadows. |
| The length of the shadows do not change with texural changes in the snow. It does look different though. They would though if the “holes/craters” were large enough I think – shadow displacement? (Whoever wrote this, I love it) Thank you, I wrote this! | Do the little sticks mark the end of each shadow at different moments in time? | How many (or what kind of) shapes can you make as shadows of the same object? (Like if you have a cube and hold it in front of a light in different orientations, what kinds of shapes can the shadow make?) |
| I’m seeing the smaller twigs seem to be in a bit of a line (but maybe not). | How much time passed between each little stick marking? | What is the shape of the path traced by the tip of a shadow throughout the day? |
| I noticed in the first image the first stick look a little taller than the other stick | Why two different sticks? Wouldn’t they provide the same information? | Graph shadow length and number of minutes? |
| One set of 1,2,3,4 points seems to be in a straight line. The other set seems to be a curve? | do the 2s (and 1s and 3s and 4s) correspond to the same time? | How do you make a sun dial? |
| The shadow of the bottom stick appears to be the same length as the shadow at the 4th stage. | Why does the shadow marks create two different shapes? The top seems more like a line. The bottom seems more like a curve. | If you pick up a stick from the snow would the shadow long gate as you pull away from the ground? Maya: What math would you use to determine the length of a shadow given that shadows are not static objects but ephemeral? |
| With help, I noticed that the light source is not moving because it’s the sun. | If I will ever get to play in the snow again! | I wonder how to determine if shadows on opposite sides of the earth have the same combined sum at all times of day. For example, when one object has the longest shadow possible, would the same object on the other side of the earth have no shadow at that exact same time? |
| Would whatever shape gets created be symmetrical? And would it have a gap? | ||
| How is it possible for the 1st shadow at one stage of the day the same length as the 4th shadow at a different stage of the day? | ||
| If two identical objects are on exact opposite sides of the earth, does the combined lengths of their shadows equal the same thing at all times? | ||
| Where are the footprints of the person who laid the smaller twigs? |
Small Groups
We split into three small groups and discussed the following questions. Each group created the image shown below. A favorite tool of this meeting was the interactive shade map.
Group 1
How do shadows look on opposite sides of the Earth at the same time of day? How are they mathematically related?
Group 2
When measured every 20 minutes, how does the tip of the shadow of the Washington Monument move over time?
Group 3
