Measuring Your World
Description
For this project, we looked at and observed different shapes, polygons, and 3-dimensional objects. We learned about different ways we could measure these shapes and objects. We measured these by using formulas. The formulas we used solved for the area and/or volume of the shapes and objects.
Formulas
Pythagorean's Theorem: a² + b² = c²
Distance Formula: d = √(x₂ - x₁)² + (y₂ - y₁)²
Equation of a Circle: x² + y² = r²
Sine, Cosine, and Tangent:
SinΘ = Opposite/Hypotenuse
CosΘ = Adjacent/Hypotenuse
TanΘ = Opposite/Adjacent
Area of a Polygon:
For this project, we looked at and observed different shapes, polygons, and 3-dimensional objects. We learned about different ways we could measure these shapes and objects. We measured these by using formulas. The formulas we used solved for the area and/or volume of the shapes and objects.
Formulas
Pythagorean's Theorem: a² + b² = c²
Distance Formula: d = √(x₂ - x₁)² + (y₂ - y₁)²
Equation of a Circle: x² + y² = r²
Sine, Cosine, and Tangent:
SinΘ = Opposite/Hypotenuse
CosΘ = Adjacent/Hypotenuse
TanΘ = Opposite/Adjacent
Area of a Polygon:
Area of a Circle: A = ∏r²
Volume of a Prism: Volume = base (main polygon/shape: rectangle, triangle, etc.) x height
Examples:
Rectangular Prism: (l x w) x height
Triangular Prism: (1/2 b x h) x height
Volume of a Prism: Volume = base (main polygon/shape: rectangle, triangle, etc.) x height
Examples:
Rectangular Prism: (l x w) x height
Triangular Prism: (1/2 b x h) x height
"Design Your Own Project"
Group
Claire, Emily, Kelaiah
Description
For the "Design Your Own Project," in groups or by ourselves, we had to measure the volume of anything we wanted. It could be the volume of an object or of something we wanted to create. The object or project we measured had to be of something that isn't a common shape, for example, rectangular prisms, cylinder prisms, etc. We had to challenge ourselves.
What My Group Chose to Measure
For our project, my group and I chose to bake a cake. We chose to bake a cake because we wanted to create a project we would enjoy making. My group and I realized, just measuring the volume of the shape of a cake, a cylinder, wasn't challenging enough. So we decided to measure the frosting that covered the cake.
Math
Group
Claire, Emily, Kelaiah
Description
For the "Design Your Own Project," in groups or by ourselves, we had to measure the volume of anything we wanted. It could be the volume of an object or of something we wanted to create. The object or project we measured had to be of something that isn't a common shape, for example, rectangular prisms, cylinder prisms, etc. We had to challenge ourselves.
What My Group Chose to Measure
For our project, my group and I chose to bake a cake. We chose to bake a cake because we wanted to create a project we would enjoy making. My group and I realized, just measuring the volume of the shape of a cake, a cylinder, wasn't challenging enough. So we decided to measure the frosting that covered the cake.
Math
Reflection
During this project, we faced a couple of challenges. One of the first challenges we faced was, we had to change our project idea from what we originally wanted. We wanted to create two layers of cake and measure the frosting around it as a more challenging project, but as we were taking the 1st layer of the cake out of the pan, it broke into pieces. We couldn't measure the 1st layer of the cake, so for our project, we decided to just measure the amount of frosting that was on the 2nd layer. A second challenge we faced during this project was figuring out how to do the math. We dealt with this problem by using the habit of a mathematician, starting small. Instead of solving the whole problem first, we researched and found each individual formula needed to solve it. Then we once we were able to understand how to solve each formula, by using all of them put together, we solved for the frosting. A success we had in this project was time management. We were able to create, measure, and finish our project on time without any stress and the overall project went smoothly.
During this project, we faced a couple of challenges. One of the first challenges we faced was, we had to change our project idea from what we originally wanted. We wanted to create two layers of cake and measure the frosting around it as a more challenging project, but as we were taking the 1st layer of the cake out of the pan, it broke into pieces. We couldn't measure the 1st layer of the cake, so for our project, we decided to just measure the amount of frosting that was on the 2nd layer. A second challenge we faced during this project was figuring out how to do the math. We dealt with this problem by using the habit of a mathematician, starting small. Instead of solving the whole problem first, we researched and found each individual formula needed to solve it. Then we once we were able to understand how to solve each formula, by using all of them put together, we solved for the frosting. A success we had in this project was time management. We were able to create, measure, and finish our project on time without any stress and the overall project went smoothly.