Author: juanfuentes

Trigonometry Ratios G.SRT

juanfuentes CCSS-Math Learning Progressions, HS Algebra, HS Geometry

This learning progression will take place at a 9th grade Algebra 1 classroom. The class is consisted of 32 students where the students have an individual sitting arrangements. This allows the students to work on their own and makes it easy to work with a partner as well. The book use for this class is “Geometry: Integration, Applications, and Connections” by Glencoe and McGraw-Hill. The lesson will cover chapter 8: Applying Right Triangles and Trigonometry but will focus on using sine, cosine, and tangent ratios in order to solve/find the sides and angles of a right triangle.

CCSS.Math:

1.) CCSS.Math.G-SRT.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

2.) CCSS.Math.G-SRT 7

Explain and use the relationship between the sine and cosine of complementary angles.

3.) CCSS.Math.G-SRT.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Learning Progression Trigonometry Ratios-1fej0wt

 

 

Exponential Decay Functions F.LE

juanfuentes CCSS-Math Learning Progressions, HS Functions

The learning progression will be based upon Exponential Decay Functions where the students will be able to understand the properties and used it to solve real-life problems. At this point, the students have prior knowledge of solving Exponential Growth Functions and will be able to build upon that knowledge and use it to understand how Exponential Decay Functions work. The CCSS.Math standards that are align with the learning progression are:

  1. Math.HSF-LE.A.1: Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.
  2. Math.HSF-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

3. Math.HSF-LE.B.2: Interpret the parameters in a linear or exponential function in terms of a context.

 

Learning Progression for Practice edTPA-1lavusr

 

Surface Area & Volume of 3D shapes 6.G.A.4

juanfuentes Assessment of CCSS-Math

6.G.A.4: Solve real-world and mathematical problems involving area, surface area, and volume.

Tasks: Students will have to properly use the equations provided in order to calculate the surface area and volume of the following shapes.

When calculating the surface area of an object (examples 1, 2, and 4) how many faces are there in order to get the right answer?

Commentary

The goal of this task is for students to understand the concepts behind 3D shapes and have a visual representation of shapes. During the lesson is taken place, the teacher will require to show students how to properly label the parts of the shape in order to correctly use the information in the equations provided to them. This will allow the students to understand the different dimensions and sides of a shape. Once the students are able make connections, the students will be able to determine the surface are and volume of a shape. With this being said, it’s common that students make simple mistakes such as forgetting to add the right number of faces of a shape. At this point, the teacher will need to use this task to make sure that students are able to understand the dimensions of a figure and how they differ from a different shape. The teacher will provide the properties and cover example problems in order to calculate the surface are of the shapes and volume. The students will also have a visual representation of the shapes.

Solution:

  1. By looking at the shape, we can see that there are four faces/sides with the same dimension of 3×2. This implies that the dimension of 3×2 will be multiply by 4 or simply add (3×2=6) 4 times. This will result of 24 in². The remain 2 faces/sides have a dimension of 2×2 resulting in 8 in². To a total surface are of 32 in².In order to calculate the volume of the figure (Length x width x height) we get 2in * 3in * 2in = 12 in³.
  2. To calculate the surface area of this shape, the same procedure as solution 1 will be follow with the exception that in order to calculate the surface area of triangle will require the equation of (base*height)/2. To a total surface area of 29.6 in². In order to calculate the volume of shape the picture on the right illustrate the equation needed to do so and volume = 8 in³.
  3. In order to calculate the volume of a cylinder the picture on the left illustrate how to do it. The volume of the shape will be 230.91 in³. To calculate the surface area of the cylinder, it will require students to use the equation. Surface area = 209 in².
  4. In order to calculate the surface area, we can see that the shape has a right triangle and two of the faces make up a square resulting in 49 in². By adding to other 3 sides/faces we get a total of 240.2 in². To calculate the volume of the figure the equation of Volume = area of base x height will be needed. This indicates that area of the base is (7*7)/2 and the height is 8 in where the volume = 196 in³.

Laws of Sine & Cosine (Shadows) SRT.10&11

juanfuentes HS Geometry, Picture Problems
Image result for building and shadow
Problem: Mike is looking at a building that is 300 feet away from him. If the angle of elevation between his position and the building is 25 degrees, how tall is the building?
HSG-SRT.D.10 Prove the Laws of Sines and Cosines and use them to solve problems.
HSG-SRT.D.11 Understand and apply the Law of Sines and the Law of Cosines in right and non-right triangles.
The purpose of this picture is to guide the lesson of the day. By using the shadow of a building students can relate the usage of the Law of Sines and Cosines to real life scenarios. This will provide a better understanding of the properties of the laws and provide a visual representation.

Weight Versus Time A-REI.B.3

juanfuentes HS Modeling, Technology Teaching Issues
How is the volume of water changing over time? When it comes to explaining volume and rate of change there are many possible ways to do this. By simply collecting weight data for a draining funnel students will be able to develop a model to illustrate the data collected. As the picture illustrate, it will be simple set up using a dual-range sensor to accomplish this lesson. 

The idea of the lesson is for the students to be able to understand rate of change and how it can be represented. Students will be able investigate using the proper equipment to answer questions such as at what rate is the water level decreasing? How long will it take for the funnel to drain completely?

Overall, students will be able to meet the objectives of recording the weight versus time data for a draining funnel and describe the recorded data using mathematical understanding of slope of a linear function.

Common Core State Standard:

HSA-REI.B.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HSS-ID.C.7 Interpret the slope (rate of change) and the intercept in the context of the data.

HSS-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a liner fit.