Project Description
In this project students learned what geometric transformation dilation. Most people understand dilation by something getting smaller and bigger. For example you zooming in and out on a computer. We also explored the skills and functions of geometry. During this project students had to do all the benchmarks that were given.
Bench-1 The Scale Model. Proposal: Students can work individually or in a group of 2-3 people to propose a scale model.
Bench-2 The Mathematical Calculations: Students document the mathematical calculations that prove their model truly be a scale model.
Bench-3 The Scale model Exhibition: Students construct and present their scale models.
Bench-4 Digital Portfolio Update: Students fully document the project on their DPs.
Bench-2 The Mathematical Calculations: Students document the mathematical calculations that prove their model truly be a scale model.
Bench-3 The Scale model Exhibition: Students construct and present their scale models.
Bench-4 Digital Portfolio Update: Students fully document the project on their DPs.
Handouts
No. Activity Must Include
1 Similar Problems
2 Inventing Rules
3 Polygon Equations
4 More Similar Triangles
5 Ladder Crossing
6 The Shortest Path
7 Now You See It
8 Dilating with Rubber Bands
9 Enlarging on a Copy Machine
10 Repeated Dilations
11 Billy Bear Grows Up
1 Similar Problems
- For each pair of figures, state an equation to find the length
- State (or show the steps) on how you found the missing lengths
2 Inventing Rules
- Documented all three possibilities
3 Polygon Equations
- For each pair of figures, state the equations to find the lengths labeled by variables
- Show how you solved the equations
- Explain or show how you solved for any remaining lengths of either figure
4 More Similar Triangles
- Show how you found the unknown lengths
- Show how you solved for the unknown variable in the proportion
5 Ladder Crossing
- Show how to find the height at which the ladders intersect
6 The Shortest Path
- Show how to find the shortest path
- Show how to calculate the actual distance of the point along the line
7 Now You See It
- Question 1: The answer and explanation of how you obtained it
- Question 2: A diagram clearly showing how you found the point and answers to both questions given in the ptoblem
8 Dilating with Rubber Bands
- A diagram with your original image, the dilated image and the center of dilation clearly labelled.
- Answers to all questions in Parts 5, 6 and 7.
9 Enlarging on a Copy Machine
- For each proposal, determine whether it will result in a 300% enlargement. Explain your reasoning.
10 Repeated Dilations
- For Questions 1-8, be sure to justify your answers (how you know)
- For Question 9-10, fully defend your answer
11 Billy Bear Grows Up
- Billy Bear at Week 4 drawn on isometric graphic paper
- The table with all data filled in for the first eight weeks
- The answers to Question 3 and 4 with a clear explanations
Topics covered include:
Similarity and Congruence
Proportional Reasoning and the Algebra of Proportions
Polygons and Angles
Logical Reasoning and Proof
Modeling
Similarity and Congruence
- Developing unique ideas about the meaning of “same shape” and learning the math definition of similar
- Discovering the special properties of triangles in connection with similarity, as well as special polygons
Proportional Reasoning and the Algebra of Proportions
- Understanding proportionality in connection with similarity
- Proportionality.situations involving similar figures
- Understanding the role of proportionality in non geometric situations
- solving equations involving fractional expressions
Polygons and Angles
- Developing formulas for triangles and other polygons
- Learning the properties of angles formed by a traversal across parallel lines
- Understanding the triangle inequality and investigating its extension to polygons
Logical Reasoning and Proof
- Working with the concept of counterexample in understanding the criteria for similarity
Modeling
- Using a geometric diagram to represent a real-world situation
- Students made scale drawings to solve problems
- Learning properties of similar triangles to real-world situations
- Exploring how models provide insight in a variety of situations
- How making a model can help you learn more about the problem. And help you understand further into the problem.
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Exhibition Video Game
During the process of making my video game I had trouble making the game. It was my first time programing something by myself. It was also my first time seeing a programing website. It was stressful for me to make this game becaise