Description
Welcome to my interactive, FULLY DIFFERENTIATED Geometry curriculum.
There are access points throughout this course for students in the 1st Grade level all the way up to the 12th grade level and beyond. This is a tried and tested course used in an extremely diverse urban classroom where students are truly at all levels.
The 53rd Lesson is a continuation of our work with the Pythagorean Theorem. Some of the class-wide examples relate the Pythagorean Theorem to Rectangles, and in Module 3 there are two-part examples relating the Pythagorean Theorem to 3-dimensional figures; problems which often appear on standardized tests. After our scaffolded examples, students break into 3 different modules to practice using the Pythagorean Theorem at 3 different levels of difficulty. There is an Exit Ticket at the end of this lesson.
The 54th Lesson is a heavily scaffolded and differentiated approach to the basics of the Trigonometric Ratios of Sine, Cosine, & Tangent. This approach has been proven to be successful in a diverse classroom at the target goal of bringing an understanding of the trigonometric ratios to students of all levels and types. After our scaffolded examples, students break into 3 different modules to practice using basic Right Triangle Trigonometry at 3 different levels of difficulty. In each Module, there are problems that make students revisit their understanding of the Pythagorean Theorem in order to see how it connects to trigonometric ratios. There is an Exit Ticket at the end of this lesson.
The 55th Lesson continues our scaffolded and differentiated approach to the basics of the Trigonometric Ratios of Sine, Cosine, & Tangent. This approach has been proven to be successful in a diverse classroom at the target goal of bringing an understanding of the trigonometric ratios to students of all levels and types. In this 2nd episode of right triangle trigonometry, students are introduced to the idea that they can use known trigonometric ratios to find missing side lengths in right triangles. After our scaffolded group-wide approach, students break into Modules to work on this topic at a level of complexity corresponding to their current level of preparation in mathematics. In Modules 2 & 3, there is a logic exercise in which students get to use their understanding of Sine & Cosine along with the Pythagorean Theorem to discover that Sin^2 + Cos^2 = 1!!
The 56th Lesson continues our scaffolded and differentiated approach to the basics of the Trigonometric Ratios of Sine, Cosine, & Tangent. This approach has been proven to be successful in a diverse classroom at the target goal of bringing an understanding of the trigonometric ratios to students of all levels and types. In this 3rd episode of right triangle trigonometry, students are introduced to the idea that they can use the standard calculator functions Sin, Cos & Tan to calculate the required ratio within a triangle, and then use that ratio in order to solve for missing side lengths. In our scaffolded group approach, we use calculated values of Sin43 & Cos43 to find the two missing sides of a triangle, with which we then discover we can use to correctly calculate Tan43. Afterwards, students break into Modules to work on this topic at a level of complexity corresponding to their current level of preparation in mathematics. There is an Exit Ticket at the end of this assignment. See the PREVIEW!!!!
I encourage participation constantly, and use Grid Grades to quickly notate all participation during class. I save my detailed notes, and can look back and say "Johnny participated 12 times on 9/4/2021, etc"
I don't give tests. Instead, I give a test grade each day called "CLASSROOM PERSEVERANCE." This gets broken down into the following:
1.) Attendance - 20% - arriving on time and remaining in class throughout the period (bathroom breaks excepted of course, as long as they return in a reasonable amount of time)
2.) Attempting the Warmup - 20% - students must attempt the Warmup within 4 minutes of arriving. Depending on the order in which I check students, some on a given day may get 5-6 minutes before I check theirs, but if I catch a student with nothing started 4 minutes in they do not get this 20%. The Warmups are fully differentiated to allow ease of access, and of course I still give the 20% if the student has wrong answers, as long as it is an honest attempt
3.) Notes - 20% - as we go through the notes section together, students are expected to fill in the notes. I make sure there is limited writing in the notes so that students can focus on the concepts. There are lots of digital manipulatives. For students with IEP's, I let some of the more writing-heavy pieces be left blank (i.e. a student with a 1st-grade writing level will be expected to move our digital manipulatives around and fill in vocab words, but will be exempt from writing down a solution to an equation)
4.) Activity - 20% - After the notes are complete, there are 3 Modules: Easy, Medium, & Difficult. Module 1 ranges from a 1st-6th Grade Level. Module 2 ranges from a 4th Grade-9th Grade Level. Module 3 ranges from a 9th Grade-12th Grade Level. Students should complete a Module that stimulates their growth but does not frustrate them. Modules are geared towards specific skills. Module 1 focuses on solving 1-step equations within our geometric space. Module 2 contains more complex logical challenges and focuses on multi-step equations. Module 3 contains the most complex logical challenges and brings in exponential equations, quadratic equations, and radical equations. Often, hardworking students will conquer one level and move to the next. As with the Warmup, to receive this 20% students just have to be working diligently. If they are struggling to answer questions correctly, they may need some help or may benefit from moving down to an easier Module.
5.) Participation - 20% - I am HUGE on participation. From the beginning of class until the end of the notes, I encourage, AND REWARD, constant participation. All students must participation twice (10% each) to get this 20%. Any additional participation is a 1% bonus. It is important to allow students to complete each slide of the Notes independently before going over them. The Notes are designed carefully with hints and scaffolding to allow students to teach themselves, with the teacher as a guide only. Even the slides with vocabulary in them have word banks and hidden clues. Every time you get to a new slide in the notes, give students a reasonable amount of time (30 s - 2 minutes depending on the exercise) to try on their own, and then share out answers together.
Too often in classrooms filled with struggling learners do students walk into class on the first day already discouraged. A grading system where tests are replaced with everyday willingness to succeed has strong positive results. On one hand, students feel empowered in that if they show up on time and try they cannot be unsuccessful. And I believe in my differentiation techniques to the extent that I know if they do the 5 things listed above, they will learn. On the other hand, students watch their excuses taken away by this system. ("Mom math is hard for me you know that and the teacher is confusing" - "Well ma'am i give 20% each day for showing up on time and your child chose to be late 3 times this week. Furthermore, twice this week did not take Notes, which consists of filling in the blanks on slides. That's also 20%. ) - You get the idea! I promise you your students of all types (advanced, Learning-Disabled, English Language Learners, etc.) will find success and appropriate challenges if they show up and try on these slides.
You will discover that the Notes are at a lower level. When we are working together we construct the basics. You might say, "Well my advanced students may be bored while we are going over these notes." They might be, unless you have them teach the class. Once the students get accustomed to our Participation-based curriculum and approach, I offer to exempt the advanced kids from taking the notes (they can figure them out on their own) if they stand up, go through the Slides, and lead the discussion just as I would. Less work for you, and you can roam the classroom and provide support.
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Description
Welcome to my interactive, FULLY DIFFERENTIATED Geometry curriculum.
There are access points throughout this course for students in the 1st Grade level all the way up to the 12th grade level and beyond. This is a tried and tested course used in an extremely diverse urban classroom where students are truly at all levels.
The 53rd Lesson is a continuation of our work with the Pythagorean Theorem. Some of the class-wide examples relate the Pythagorean Theorem to Rectangles, and in Module 3 there are two-part examples relating the Pythagorean Theorem to 3-dimensional figures; problems which often appear on standardized tests. After our scaffolded examples, students break into 3 different modules to practice using the Pythagorean Theorem at 3 different levels of difficulty. There is an Exit Ticket at the end of this lesson.
The 54th Lesson is a heavily scaffolded and differentiated approach to the basics of the Trigonometric Ratios of Sine, Cosine, & Tangent. This approach has been proven to be successful in a diverse classroom at the target goal of bringing an understanding of the trigonometric ratios to students of all levels and types. After our scaffolded examples, students break into 3 different modules to practice using basic Right Triangle Trigonometry at 3 different levels of difficulty. In each Module, there are problems that make students revisit their understanding of the Pythagorean Theorem in order to see how it connects to trigonometric ratios. There is an Exit Ticket at the end of this lesson.
The 55th Lesson continues our scaffolded and differentiated approach to the basics of the Trigonometric Ratios of Sine, Cosine, & Tangent. This approach has been proven to be successful in a diverse classroom at the target goal of bringing an understanding of the trigonometric ratios to students of all levels and types. In this 2nd episode of right triangle trigonometry, students are introduced to the idea that they can use known trigonometric ratios to find missing side lengths in right triangles. After our scaffolded group-wide approach, students break into Modules to work on this topic at a level of complexity corresponding to their current level of preparation in mathematics. In Modules 2 & 3, there is a logic exercise in which students get to use their understanding of Sine & Cosine along with the Pythagorean Theorem to discover that Sin^2 + Cos^2 = 1!!
The 56th Lesson continues our scaffolded and differentiated approach to the basics of the Trigonometric Ratios of Sine, Cosine, & Tangent. This approach has been proven to be successful in a diverse classroom at the target goal of bringing an understanding of the trigonometric ratios to students of all levels and types. In this 3rd episode of right triangle trigonometry, students are introduced to the idea that they can use the standard calculator functions Sin, Cos & Tan to calculate the required ratio within a triangle, and then use that ratio in order to solve for missing side lengths. In our scaffolded group approach, we use calculated values of Sin43 & Cos43 to find the two missing sides of a triangle, with which we then discover we can use to correctly calculate Tan43. Afterwards, students break into Modules to work on this topic at a level of complexity corresponding to their current level of preparation in mathematics. There is an Exit Ticket at the end of this assignment. See the PREVIEW!!!!
I encourage participation constantly, and use Grid Grades to quickly notate all participation during class. I save my detailed notes, and can look back and say "Johnny participated 12 times on 9/4/2021, etc"
I don't give tests. Instead, I give a test grade each day called "CLASSROOM PERSEVERANCE." This gets broken down into the following:
1.) Attendance - 20% - arriving on time and remaining in class throughout the period (bathroom breaks excepted of course, as long as they return in a reasonable amount of time)
2.) Attempting the Warmup - 20% - students must attempt the Warmup within 4 minutes of arriving. Depending on the order in which I check students, some on a given day may get 5-6 minutes before I check theirs, but if I catch a student with nothing started 4 minutes in they do not get this 20%. The Warmups are fully differentiated to allow ease of access, and of course I still give the 20% if the student has wrong answers, as long as it is an honest attempt
3.) Notes - 20% - as we go through the notes section together, students are expected to fill in the notes. I make sure there is limited writing in the notes so that students can focus on the concepts. There are lots of digital manipulatives. For students with IEP's, I let some of the more writing-heavy pieces be left blank (i.e. a student with a 1st-grade writing level will be expected to move our digital manipulatives around and fill in vocab words, but will be exempt from writing down a solution to an equation)
4.) Activity - 20% - After the notes are complete, there are 3 Modules: Easy, Medium, & Difficult. Module 1 ranges from a 1st-6th Grade Level. Module 2 ranges from a 4th Grade-9th Grade Level. Module 3 ranges from a 9th Grade-12th Grade Level. Students should complete a Module that stimulates their growth but does not frustrate them. Modules are geared towards specific skills. Module 1 focuses on solving 1-step equations within our geometric space. Module 2 contains more complex logical challenges and focuses on multi-step equations. Module 3 contains the most complex logical challenges and brings in exponential equations, quadratic equations, and radical equations. Often, hardworking students will conquer one level and move to the next. As with the Warmup, to receive this 20% students just have to be working diligently. If they are struggling to answer questions correctly, they may need some help or may benefit from moving down to an easier Module.
5.) Participation - 20% - I am HUGE on participation. From the beginning of class until the end of the notes, I encourage, AND REWARD, constant participation. All students must participation twice (10% each) to get this 20%. Any additional participation is a 1% bonus. It is important to allow students to complete each slide of the Notes independently before going over them. The Notes are designed carefully with hints and scaffolding to allow students to teach themselves, with the teacher as a guide only. Even the slides with vocabulary in them have word banks and hidden clues. Every time you get to a new slide in the notes, give students a reasonable amount of time (30 s - 2 minutes depending on the exercise) to try on their own, and then share out answers together.
Too often in classrooms filled with struggling learners do students walk into class on the first day already discouraged. A grading system where tests are replaced with everyday willingness to succeed has strong positive results. On one hand, students feel empowered in that if they show up on time and try they cannot be unsuccessful. And I believe in my differentiation techniques to the extent that I know if they do the 5 things listed above, they will learn. On the other hand, students watch their excuses taken away by this system. ("Mom math is hard for me you know that and the teacher is confusing" - "Well ma'am i give 20% each day for showing up on time and your child chose to be late 3 times this week. Furthermore, twice this week did not take Notes, which consists of filling in the blanks on slides. That's also 20%. ) - You get the idea! I promise you your students of all types (advanced, Learning-Disabled, English Language Learners, etc.) will find success and appropriate challenges if they show up and try on these slides.
You will discover that the Notes are at a lower level. When we are working together we construct the basics. You might say, "Well my advanced students may be bored while we are going over these notes." They might be, unless you have them teach the class. Once the students get accustomed to our Participation-based curriculum and approach, I offer to exempt the advanced kids from taking the notes (they can figure them out on their own) if they stand up, go through the Slides, and lead the discussion just as I would. Less work for you, and you can roam the classroom and provide support.
