Investigation 2.2 - any polygon angle sum

Focus Question: What is the angle sum of any polygon with n sides?

Helpful site:
Math is Fun - Polygon angles

Application problem of understanding triangle angles.

Investigation 2.1 - Regular Polygons angle and angle sum formulas

The focus question is: What is the size of each angle and the sum of all angles in a regular polygon with n sides?

The students will review what is important in a polygon and how regular and irregular polygons compare.  The goal is for students to develop formulas the sum of interior angles for a polygon of n sides.


S - Sum of all angles
S = 180 (n - 2)  
when n = any number of sides of a polygon


A - measure of one angle
A = 180 (n - 2)/ n
OR  
A = 180 - 360/n   
when n = any number of sides of a polygon

Link to Geometry and Regular Polygon Site

Click here to access

Check - up #1 - Need to Know

Investigation Focus Questions:

Problem 1.1

1. What properties do all polygons share?

2. What properties do some sub-groups of polygons share?

Problem 1.2

1. What are some common benchmark angles?

2. What part of a full turn is each angle equal to?

Problem 1.3

1. When a drawing shows two rays with a common endpoint how many rotation angles are there?

2. How would you estimate the measure of each angle?

Problem 1.4

1. How do you measure and angle with an angle ruler and a protractor?

Problem 1.5

1. In a triangle, what measures of sides and angles give just enough information to draw a figure that is uniquely determined?


Need to Know:
1. Finding angle measurements using a protractor.
2. Properties of shapes
3. Drawing angles and polygons given specific measurements
4. Investigation Vocabulary: polygon, regular polygon, rotation. supplementary and complementary angles, obtuse and acute angles, straight angles, reflex angles, right angles
5. Correctly naming and labeling an angle

Skills #3

Attached here is Skills #3 and also the notes on questions students had on Skills #3 from class.

Skills #3 Worksheet

Skills #3 Notes for Questions.

Investigation 1.5 - Drawing Challenge

Focus Question: In a triangle, what measures of side length and angles give enough information to draw a figure?

We completed Investigation 1.5 together in class and the students need to complete B #2-6 for homework.

Notes from class- click here to access

(These notes cover the Investigation Questions A and B from class.)

Investigation 1.4 - Measuring Angles

Investigation 1.4

Important vocabulary:

• supplementary angle - angles that add up to 180˚
• 
  
• complementary angle- angles that add up to 90˚

Here are the notes from today's class and the 1.3 and 1.4 homework.

Click here to access the notes.

Here is a sheet to help with benchmark angles.  This was given as a hard copy to all the students.

Click here to access the worksheet.

Answer Key for ACE Problems Inv 1.4 Level I or II

Click here for access.

Investigation 1.2 - Shapes and Designs

Focus Question: What are some common benchmark angles? 

Today students looked at the question, "What are some of the benchmark angles?"

Students were exposed to vocabulary words such as:

• acute
• obtuse
• initial side
• terminal side
• degrees
• right angle 
• straight angle

Here are some of the notes taken from today class.

We ended by playing a connect four game.  Lets see if our students can defeat their parents!

Estimating Angles Online Games:

Enrich-Math - Estimating Angles

Alien Angles- Estimating Angles

Banana Hunt - Oswego.edu

Homework Expectations

Today, we talked about producing quality homework. This year, students will receive a grade for homework. However, the grade will not be based on the number right or wrong, but on the work's completion, quality, and correction/reflection. Approximately one assignment per week will be collected and contribute to an overall term homework grade.

Here is the homework descriptor that was handed out to students:

7th Grade Math Homework Expectations

1. Completion - All assigned problems have been attempted and completed with work shown.  If there are incomplete or partially completed problems, questions should be written in place of work and contact with your teacher should be made (email, face-to-face prior to or at the beginning of class).

2. Quality - Work has your name, assignment title (page number, problems and investigation), and date at the top of the page.  Work is legible and organized.  

3. Correction & Reflection - Work is not erased and corrections (if needed) are done in a different color.  At the bottom of the page rank yourself from 1- 5 (1 = not understanding the content, 5 = solid understanding of content) and write a thought about the work you completed.

• If you did well, what was the key to your success on this work?
• If you found the work challenging, what do you need to do to better understand the material? This is a strategy to help you get better at the material covered in class. The sooner you identify that you're finding work challenging, the sooner you're able to get the help you need.

Shape Set

Here is the shape set from today's lesson.  It can be found on page 9 of Investigation 1.1 in your text.

Investigation 1.1- Shapes and Designs

Focus Question: What properties do all polygons have?  

Diving into polygons!

In the first section of Shapes and Designs, students spent time defining the characteristics of polygons. Ask your student, "What makes a shape a polygon?" These shapes have some specific properties!

Next, everyone got some hands-on time, looking at a variety of shapes and categorizing them. Most groups categorized the shapes by the number of sides they had, but then many expanded those further into sub-categories. How many different categories can there be for quadrilaterals (four-sided polygons)?

Here are some pictures of the students in action with the shape sets.

Our First Unit! Shapes and Designs

This year, we begin our math studies with an exploration into two-dimensional geometry. The parent letter below outlines what students and parents can expect from this unit.

Here is a pdf version for a clearer view. I particularly enjoy the resources listed on the second page.

Skill Sheet #1

7th Grade Math Skill Sheets are given out once a week to build on the students' math skills.  Skill Sheet #1 was handed out today and is due Friday September 11th.

Click here to access a copy of Skill Sheet #1