Mathematics with Harish Kumar

Harish Kumar Sharma, Jan 7, 2023

geogebra applets

Table of Contents

  1. chapter I
    1. Circle Area (By Peeling!)
    2. Triangle Angle Theorems
    3. Parallelogram: Area
    4. Triangle Exterior Angle
    5. Right Triangle Trigonometry: Intro
    6. Exploring Polygon Angles: Triangle through Octagon
    7. Triangle Angle Sum Theorem
    8. Circle Terminology
    9. Area of Circles
  2. chapter II
    1. Battleship in the Coordinate Plane!
    2. Complementary Meaning?
    3. Proof Without Words
    4. Supplementary Angles (Quick Exploration)
  3. CHAPTER III
    1. AA Similarity Theorem
    2. SAS: Dynamic Proof!
    3. ASA Theorem?
    4. SSS: Dynamic Proof!
  4. CHAPTER IV
    1. Surface Area: Intuitive Introduction
    2. Sections of Cylinders
    3. Sections of Cones
    4. Net of a Cone
  5. CHAPTER V
    1. Graph the Line
    2. Graphing Linear Equations: Question Generator (V2)
    3. Solving Linear Systems by Graphing: Quiz (V1)
    4. Writing Equations of Parallel and Perpendicular Lines
  6. CHAPTER VI
    1. Trapezoid: Area (I)
    2. Circumcenter (& Questions)
    3. TRUE MEANING of π
  7. CHAPTER VII
    1. Area of a Triangle (Discovery)
    2. 1 Radian: Clear Definition

1.

chapter I

  • 1. Circle Area (By Peeling!)
  • 2. Triangle Angle Theorems
  • 3. Parallelogram: Area
  • 4. Triangle Exterior Angle
  • 5. Right Triangle Trigonometry: Intro
  • 6. Exploring Polygon Angles: Triangle through Octagon
  • 7. Triangle Angle Sum Theorem
  • 8. Circle Terminology
  • 9. Area of Circles

1.1.

Circle Area (By Peeling!)

[b][color=#c51414]Questions for Extension and Application:[/color][/b][br][br][color=#1551b5]1) Was the "triangle" formed truly a triangle? Explain why or why not. [br][/color][br][color=#1551b5]2) What would we need to do to the number of "peels" in order to make the so-called "triangle" formed look[br] more smooth (like a true triangle) vs. a "choppy" triangle? [/color][br][br][color=#1551b5]3) Suppose an above-the-ground circular swimming pool has a radius of 12 feet. What is the area of the exposed surface of the water it contains? [br][br]4) Suppose a circular track (that surrounds grass) has a circumference of 500 feet. If 3 bags of grass seed are needed to be spread out across every 100 square feet of grass in the circular region inside this track, determine how many entire bags of grass seed will be needed to cover the entire area of the circular region surrounded by this track. [br][br]5) Suppose a 12-inch pizza (pizza with diameter = 12 inches) costs $12.00. Suppose a 24-inch pizza costs $24.00. Which pizza is the better buy? Explain why this pizza is the better buy. (Assume both pizzas have the same thickness.) [br][/color]
– Tim Brzezinski

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1.5.

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1.7.

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1.8.

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1.9.

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2.

chapter II

  • 1. Battleship in the Coordinate Plane!
  • 2. Complementary Meaning?
  • 3. Proof Without Words
  • 4. Supplementary Angles (Quick Exploration)

2.1.

Battleship in the Coordinate Plane!

Creation of this activity was inspired by [url=https://twitter.com/alicekeeler]Alice Keeler[/url]'s blog article "[url=http://www.alicekeeler.com/2016/01/14/game-based-learning-google-slides-coordinate-plane-battleship/]Game Based Learning: Google Slides Coordinate Plane Battleship[/url]".
INTRODUCTION:
[b]This game is played JUST LIKE the old Milton-Bradley game BATTLESHIP. [br]Yet here we'll be playing within the context of the COORDINATE PLANE. [br]The goal is to to SINK ALL 5 of your opponent's ships before he/she sinks all 5 of yours. [/b][br][br][b]When it is YOUR TURN, be sure to state the following: [/b][br][br][b]1) Quadrant Number[br]2) The Ordered Pair[br][br][/b]For example, stating "Quadrant 2: Negative 3 comma 2" indicates the ordered pair (-3, 2). [br]If it's a "MISS", plot a white point on your game board at that location. [br][color=#cc0000]If it's a "HIT", plot a red point on your game board at that location. [br][br][/color]Once you sink one of your opponent's ships, he/she needs to announce this fact to you. [br]When this does happen, use the SEGMENT tool to mark a sunken ship. [b][color=#ff00ff][i]Have fun! [/i][/color][/b]
How to Move Your Ships (at the Beginning); How to Mark Opponent's HITS (RED) and misses (yellow)
How to Plot YOUR OWN HITS (RED) and MISSES (WHITE) & How to Mark a Sunken Ship
YOUR GAME BOARD:
OPPONENT'S GAME BOARD: KEEP TRACK OF YOUR HITS & MISSES HERE.
– Tim Brzezinski

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3.

CHAPTER III

  • 1. AA Similarity Theorem
  • 2. SAS: Dynamic Proof!
  • 3. ASA Theorem?
  • 4. SSS: Dynamic Proof!

3.1.

AA Similarity Theorem

[color=#000000]The [/color][b][color=#0000ff]AA Similarity Theorem[/color][/b][color=#000000] states:[/color][br][br][i][color=#0000ff]If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.  [/color][/i][br][br][color=#980000]Below is a visual that was designed to help you prove this theorem true in the case where both triangles have the same orientation.  (If the triangles had opposite orientations, you would have to first [b]reflect[/b] the white triangle [b]about any one of its sides[/b] first, and then proceed along with the steps taken in the applet.)  [/color][br][br][color=#000000]Feel free to move the locations of the [/color][color=#38761d][b]BIG GREN VERTICES[/b][/color][color=#000000] of either triangle before slowly dragging the slider. [/color][b] [/b][i][color=#ff0000]Pay careful attention to what happens as you do.[/color][/i]
Quick (Silent) Demo
– Tim Brzezinski

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3.3.

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4.

CHAPTER IV

  • 1. Surface Area: Intuitive Introduction
  • 2. Sections of Cylinders
  • 3. Sections of Cones
  • 4. Net of a Cone

4.1.

Surface Area: Intuitive Introduction

TEACHERS:
For an introductory class activity related to this, [url=https://www.geogebra.org/m/mgwejudc]click here[/url].
– Tim Brzezinski

4.2.

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5.

CHAPTER V

  • 1. Graph the Line
  • 2. Graphing Linear Equations: Question Generator (V2)
  • 3. Solving Linear Systems by Graphing: Quiz (V1)
  • 4. Writing Equations of Parallel and Perpendicular Lines

5.1.

Graph the Line

Drag points A and B so the line matches the equation.
– Steve Phelps

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6.

CHAPTER VI

  • 1. Trapezoid: Area (I)
  • 2. Circumcenter (& Questions)
  • 3. TRUE MEANING of π

6.1.

Trapezoid: Area (I)

1.
[color=#000000]In the [/color][color=#ff00ff][b]trapezoid[/b][/color][color=#000000] above, suppose base_1 = 6 cm, base_2 = 3 cm, and height = 5 cm.[br]What would the area of the [/color][color=#ff00ff][b]trapezoid[/b][/color][color=#000000] be? [/color]
2.
Without looking up the formula on another tab in your internet browser, describe below, in your own words, how you could find the [b][color=#ff00ff]area of ANY TRAPEZOID[/color][/b] in terms of both its bases and its height.
Quick (Silent) Demo
– Tim Brzezinski

6.2.

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7.

CHAPTER VII

  • 1. Area of a Triangle (Discovery)
  • 2. 1 Radian: Clear Definition

7.1.

Area of a Triangle (Discovery)

[color=#000000]Interact with the applet below for a few minutes.  [br][br][i]Be sure to move the [/i][b]VERTICES[/b] [i]of the triangle around each time [b]before you move the slider. [br][/b][/i][/color][br]Answer the questions that appear below the applet.
1
What LARGER FIGURE was formed when the slider reached its end? How do we know this to be true?
2.
How does the area of the original triangle compare with the area of this LARGER FIGURE?
3.
How do we find the area of this LARGER FIGURE? What is the formula we use to find it?
4.
Given your responses to (2) & (3), write a formula that gives the area of JUST ONE of these congruent triangles.
Quick (Silent) Demo
– Tim Brzezinski

7.2.

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