unit 4 desmos project
Here is the LINK to my graph.
No annotated picture :( Sorry.
Reflection:
How did you go about drawing this image? (Did you plan? Did you use patterns,reflections of curves? Did you experiment? Did you consult with peers/teacher?) (3-5sentences)
At first I struggled finding out what I wanted to do but as time progressed I decided to do what is called Nyan Cat. I had a lot of help from Caitlyn on this project and through that help came something really good looking, as seen in the link. I did a lot of trial and error throughout this project, inputting equations then changing them so they fit better.
b. How did using Desmos and creating this drawing help you understand function families and their transformations? (Be specific and discuss two types of functions and what you learned about them - for example, discuss how you understand linear and quadratic functions.) (3-5 sentences)
I think that doing this project helped me understand visually how certain functions work. I think the most useful equations were the linear and quadratic, I used so many that, if I had annotated my photo, it would be full of words and arrows. This also helped me by teaching me how to make equations stop at a certain point on the coordinate plane.
No annotated picture :( Sorry.
Reflection:
How did you go about drawing this image? (Did you plan? Did you use patterns,reflections of curves? Did you experiment? Did you consult with peers/teacher?) (3-5sentences)
At first I struggled finding out what I wanted to do but as time progressed I decided to do what is called Nyan Cat. I had a lot of help from Caitlyn on this project and through that help came something really good looking, as seen in the link. I did a lot of trial and error throughout this project, inputting equations then changing them so they fit better.
b. How did using Desmos and creating this drawing help you understand function families and their transformations? (Be specific and discuss two types of functions and what you learned about them - for example, discuss how you understand linear and quadratic functions.) (3-5 sentences)
I think that doing this project helped me understand visually how certain functions work. I think the most useful equations were the linear and quadratic, I used so many that, if I had annotated my photo, it would be full of words and arrows. This also helped me by teaching me how to make equations stop at a certain point on the coordinate plane.
Unit 3
Q1: What content/skills have been most interesting to you?
The most interesting skill I learned was how to generalize a formula. I thought this was the most interesting because I didn't enjoy working on any of the other content or skills. Also this part was interesting because I had never realized how easy it was to generalize a formula.
Q2: How have you grown mathematically?
I have grown mathematically in many ways. I have gotten a better root in Geometry this year than last year, I think this year has made me more prepared for algebra 2 and that I will not struggle as much as I did with geometry last year.
The most interesting skill I learned was how to generalize a formula. I thought this was the most interesting because I didn't enjoy working on any of the other content or skills. Also this part was interesting because I had never realized how easy it was to generalize a formula.
Q2: How have you grown mathematically?
I have grown mathematically in many ways. I have gotten a better root in Geometry this year than last year, I think this year has made me more prepared for algebra 2 and that I will not struggle as much as I did with geometry last year.
Unit 2
Q1: What has been the work you are most proud of in this unit?
I am really proud of the entire shadow sub-unit that we did. I think I worked well with my partners and by myself as well. I liked that I can now no longer wonder about how tall something is because I can figure it out
Q2: What skills are you developing in geometry/math? Skills can be applied across mathematics – think graphing, creating tables, creating diagrams or mathematical models, approaching problems in different ways (by testing cases, by testing extreme examples, by setting up a table initiating/approaching hard problems, e), or learning how to use your graphing calculator to fit equations to data.
I am developing crucial problem solving skills that will help me for years to come. I'm learning to accept challenges, not give up when I come across them.
Q3: Choose one topic: similarity (ratios) or trigonometry. Explain what it is. Provide an example of how it is used in mathematics to solve problems. State an application of the topic in the adult world (i.e. scaled replicas of sculptures, scaled models for architecture, trigonometry in construction or blood splatter analysis, etc).
Similarity - the comparison of like shapes
Trigonometry - the measure of triangles and angles
Both of these can be used together in math and science to calculate the dimensions and dilations of a shape. A real world example would be a bridge architect. He has to compare all sorts of similar shapes and angles to support as much weight as possible with as little money as possible.
I am really proud of the entire shadow sub-unit that we did. I think I worked well with my partners and by myself as well. I liked that I can now no longer wonder about how tall something is because I can figure it out
Q2: What skills are you developing in geometry/math? Skills can be applied across mathematics – think graphing, creating tables, creating diagrams or mathematical models, approaching problems in different ways (by testing cases, by testing extreme examples, by setting up a table initiating/approaching hard problems, e), or learning how to use your graphing calculator to fit equations to data.
I am developing crucial problem solving skills that will help me for years to come. I'm learning to accept challenges, not give up when I come across them.
Q3: Choose one topic: similarity (ratios) or trigonometry. Explain what it is. Provide an example of how it is used in mathematics to solve problems. State an application of the topic in the adult world (i.e. scaled replicas of sculptures, scaled models for architecture, trigonometry in construction or blood splatter analysis, etc).
Similarity - the comparison of like shapes
Trigonometry - the measure of triangles and angles
Both of these can be used together in math and science to calculate the dimensions and dilations of a shape. A real world example would be a bridge architect. He has to compare all sorts of similar shapes and angles to support as much weight as possible with as little money as possible.
Burning tent lab
Question 1: Once you have a minimal path, what appears to be true about the incoming angle and the outgoing angle?
They are the same measure.
Question 2: Why is the path from points Camper to TentFire the shortest path? Briefly explain. (Think about the shortest distance between two points.) Because the distance from Camper to River to TenFire is just a straight line, and if you move the River point then you are putting a bend in the line.
Question 3: Where should the point River be located in relation to segment Camper to TentFire' and line AB so that the sum of the distances is minimized? The point river should have the same measure angles on both side.
They are the same measure.
Question 2: Why is the path from points Camper to TentFire the shortest path? Briefly explain. (Think about the shortest distance between two points.) Because the distance from Camper to River to TenFire is just a straight line, and if you move the River point then you are putting a bend in the line.
Question 3: Where should the point River be located in relation to segment Camper to TentFire' and line AB so that the sum of the distances is minimized? The point river should have the same measure angles on both side.
Batman Tesselation
I chose to do Batman™. I started with a square then I cut two slants coming down from the sides to a curve making the head then translated it to the top of the square. I then translated, from the top right, Batman™ left and down 3, 6, 9, 12, and 15 inches, only 12 inches to the left.
I don't believe that tessellations are art or math but a combination of both. I think that you have to apply both art and math to create this type of creation.
I don't believe that tessellations are art or math but a combination of both. I think that you have to apply both art and math to create this type of creation.
Snail Trail
First I constructed a circle. I then created a diameter. Then I reflected the line twice which gave me sixths. I created a point in one of the sections, then reflected it until there was one point in every section. I turned trace on and labels off, then made a check box to show/hide the circle and lines. It shows reflectional symmetry and rotational symmetry.