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Step 1: Determine the tool you will use to create this assignment.

I will be using the recordex for this assignment and will use the video sharing site, Math Nation and Geogebra for this assignment.

Step 2: Gather your resources

To complete this project, you will need to use the following: MathNation.com

https://web.algebranation.com/#/

• An evaluation of three available tools at your school including their affordances and limitations (Use what you created in Week 2).
• Your adaptation assignment from Week 3.
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• The current TIM level is Adaptation: The teacher facilitates students in exploring and independently using technology tools. The students are required to use their cell phones, iPad, computers or laptops to increase or decrease the similar figures. This is also Active adoption as the setting is arranged for direct instruction and individual seat work. Students work in very limited and regulated access to the computers/

Introduction

This task is intended to assess how well students are able to solve problems involving scale and similarity. The task also extends the concept of similarity and scale to include area of a rectangle Standards Assessed & State Item Specifications

 

Domain	Geometry
Standards	MAFS.7.G.1.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Item Types	Equation Editor    GRID  Matching Item  Multiple Choice  Multi-select
Assessment Limits	Geometric figures must be two-dimensional polygons.
Calculator	Yes
Context	Allowable

 

 

Habits of Mind 

 

1. Persisting: Sticking to task at hand; Follow through to completion; can and will remain focused.

 

4. Thinking Flexibility: Able to change perspective; Consider the input of others; Generate alternatives; Weigh options.

 

6. Striving for Accuracy: Check for errors; Measure at least twice; Nurture a desire for exactness, fidelity & craftsmanship.

 

7. Questioning and Posing Problems: Ask myself, “How do I know?” Develop a questioning attitude; Consider what information is needed, choose strategies to get that information; Consider the obstacles needed to resolve.

Standards for Mathematical Practices

 

MAFS.K12.MP.1.1: Make sense of problems and preserve in solving them.  

MAFS.K12.MP.4.1: Model with mathematics.

 

MAFS.K12.MP.5.1: Use appropriate tools strategically.

MAFS.K12.MP.7.1: Look for and make use of structure.

Enduring Understanding

• Analyzing geometric relationships develops reasoning and justification skills.

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• Geometry and spatial sense offer ways to interpret and reflect on our physical environment.

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• Understanding the attributes of two dimensional shapes to analyze, represent, and model geometric relationships in the real world.

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• Measurement describes the attributes of objects and events.

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• Standard units of measure enable people to interpret results or data.

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        Diagram 1                                                                Diagram 2

Sample Answer:   For diagram 2, the height for the larger picture is 6, so the smaller pictures are 3 inches wide. The ratio for width is 4/3, so the height would be 4.5 inches.

Sample Answer:    For diagram 1, the height is 6 for the regular photo, so each other one has to be 3 inches high and the smaller photo has a ratio of about 3/6, so it would be half wide so it is 2 inches wide.

 

2. Find the size of the sheet of paper for each arrangement.

        Diagram 1                                                                 Diagram 2

The measurements of the sheet of paper are  8.5 wide and 6 high.

The measurements of the sheet of paper are 6 wide and 6 high.

 

3. Looking at only the smaller copies of the photos, are the areas the same? Justify it.

No, because in diagram one 4.5 inches x 3 inches= 13.5 square inches. In diagram 2,. 3 inches x  2 inches = 6 square inches

4. Is the ratio of the area of one small photo to the entire sheet of paper the same? Explain how you know.

         Check student responses, student responses may vary.

Evaluation

Level	Understanding	Strategies, Reasoning and Procedures	Communication
Beginning	There is no solution, or the solution has no relationship to the task.   Inappropriate concepts are applied and/or procedures are used.   The solution addresses none of the mathematical components presented in the task.	No evidence of a strategy or procedure, or uses a strategy that does not help solve the problem.   No evidence of mathematical reasoning.   There were so many errors in mathematical procedures that the problem could not be solved.	There is no explanation of the solution, the explanation cannot be understood or it is unrelated to the problem.   There is no use or inappropriate use of mathematical representations (e.g. figures diagrams, graphs, tables, etc.)
Developing	The solution is not complete indicating that parts of the problem are not understood.   The solution addresses some, but not all of the mathematical components presented in the task.	Uses a strategy that is partially useful, leading some way toward a solution, but not to a full solution of the problem.   Some evidence of mathematical reasoning.   Could not completely carry out mathematical procedures.   Some parts may be correct, but a correct answer is not achieved.	There is no use, or mostly inappropriate use, of mathematical terminology and notation.   There is an incomplete explanation; it may not be clearly presented.   There is some use of appropriate mathematical representation.
Accomplished	The solution shows that the student has a broad understanding of the problem and the major concepts necessary for its solution.   The solution addresses all of the mathematical components presented in the task.	Uses a strategy that leads to a solution of the problem.   Uses effective mathematical reasoning.   Mathematical procedures used.   All parts are correct and a correct answer is achieved.	There is some use of mathematical terminology and notation appropriate of the problem.   There is a clear explanation.   There is appropriate use of accurate Mathematical representation.   There is effective use of mathematical terminology and notation.
Exemplary	The solution shows a deep understanding of the problem including the ability to identify appropriate mathematical concept and the information necessary for its solution.   The solution completely addresses all mathematical components presented in the task.   The solution puts to use the underlying mathematical concepts upon which the task is designed.	Uses a very efficient and sophisticated strategy leading directly to a solution.   Employs refined and complex reasoning.   Applies procedures accurately to correctly solve the problem and verify the results.   Verifies solution and/or evaluates the reasonableness of the solution.   Makes mathematically relevant observations and/or connections.	There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.   Mathematical representation is actively used as a means of communicating ideas related to the solution of the problem.   There is precise and appropriate use of mathematical terminology and notation.

 

STEP 3

The current TIM level is Infusion: The teacher provides the learning concept and the students choose the technology tools to achieve the outcome. Students will use computers or laptops to increase or decrease the similar figures. This is Goal-Directed Adaption. Students will have access to computers that will facilitate the construction of increasing or decreasing the size of similar figures.

The technology tool(s) students will use to complete the lesson.

The lesson will be modified to include Geogebra and Math Nation to dilate the picture. The picture will be enlarged then decreased in size.

This tool enhances the lesson because the students are able to use measure to increase or decrease the image thus having a real picture of what actually happens in dilation.

The changes made to the lesson to move it up to the Infusion Level on the Matrix. The students now have the learning context and choose technology tools to achiever the outcome. The can experiment with Geogebra or Math Nation to learn about dilations. This is both active learning as the student is engaged in using technology as a tool to learn. It is also constructive learning as students use technology to connect new information to their prior knowledge.

Students are able to easily navigate these tools that I use in my classroom. Each student has an account, by logging in with their student numbers. This  tool helps to create a more personalized learning experience for my students. Students are able to access this tool on their cell phones, on the schools’ computers and at home on their computers.

STEP 4

Reflection.

This course has taught me the many tools available to teach, facilitate and create valuable lessons for my students. It also taught me how to enhance the use of the technology in my classroom. It is important that with the implementation of technology in the classroom comes great responsibility and planning.

At the start of the class, my level was Active Adaption. Today, my level has moved to Active infusion as I allow my students to learn and explore using these tools. As I prepare my lessons ow I take into consideration the what, when, how and why I am using the tool and try to make it useful to out students.

Find the measurements of the small photographs for each arrangement.  Show your calculations and explain how you figured it out.