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Geometry-EDC 262

Brenna Maurer, Mar 25, 2021

Lines, Rays, and Segments

1. Congruent Segments Construction (I)
2. Perpendicular Lines Investigation (VB)
3. Rays & Angles
4. Broken Centimeter Ruler

Congruent Segments Construction (I)

I[color=#000000]n the applet below, use the limited toolbar to construct segments that are congruent to the two segments displayed.[br]Use the [b]Distance[/b] tool afterwards to show that these segments are indeed congruent. [/color]

I[color=#000000]n the applet below, use the limited toolbar to construct segments that are [b]triple the length[/b] of the two segments displayed.[br]Use the [b]Distance[/b] tool afterwards to show that these segments are indeed triple the length of the original segments displayed. [/color]

1.2.

1.3.

1.4.

2.

Angles

2.1.

Angle

Drag the points of angle CAB around to create an acute angle, an obtuse angle, a right angle, and a straight angle.

2.2.

2.3.

2.4.

2.5.

2.6.

3.

Properties of Quadrilaterals

1. Classifying Quadrilaterals
2. Discovering Properties of Quadrilaterals
3. Properties of a Parrallelogram
4. Trapezoid
5. Kite Properties
6. Properties of a Rectangle

3.1.

Classifying Quadrilaterals

Classify quadrilaterals A to T by coloouring. (Click a quadrilateral at the right, then click those quadrilaterals A to T in the same class.)[br]Drag and rotate (the red point) the ruler to measure lengths and right angles.

3.2.

3.3.

3.4.

3.5.

3.6.

4.

Perimeter and Area

1. Area and Perimeter of Quadrilaterals
2. Area and Perimeter of Rectangles
3. Area With Fixed Perimeter
4. Area of Circles
5. Circle Area (By Peeling!)
6. Maximizing Trapezoid Area
7. Comparing Perimeter and Area for 2D Shapes

4.1.

Area and Perimeter of Quadrilaterals

4.2.

4.3.

4.4.

4.5.

4.6.

4.7.

5.

Volume

1. Volume: Intuitive Introduction
2. Which is the Odd One Out? (3-D shapes in Geogebra)
3. Washer Action!!! (1)
4. Volume of rectangular prisms
5. Volume of cylinder
6. Surface Area: Intuitive Introduction

5.1.

Volume: Intuitive Introduction

STUDENTS:

Interact with the applet below for a few minutes. Then answer the questions that follow. [br][br][b][color=#1e84cc]To explore this resource in Augmented Reality, see the directions beneath the questions listed below. [/color][/b]

1.

In the applet above, create a rectangular prism that has its first layer measuring 3 units long by 4 units wide. Suppose this rectangular prism is 2 layers high. How many cubes make up this prism?

2.

In the applet above, create a rectangular prism that has its first layer measuring 5 units long by 3 units wide. How many cubes make up this prism if this prism is 2 layers high? 3 layers high? 10 layers high?

3.

How can we EASILY determine the number of cubes that fit inside ANY rectangular prism? Describe.

TO EXPLORE IN AUGMENTED REALITY:

1) Open up GeoGebra 3D app on your device. [br][br]2) Go to the[b] MENU (horizontal bars)[/b] in the upper left corner. Select [b]OPEN[/b]. [br] In the Search GeoGebra Resources input box, type [b]dp6ghmvv[/b][br] (Note this is the resource ID = last 8 digits of the URL for this resource.)[br][br]3) In the resource that uploads, zoom out and/or adjust the [br] LENGTH, WIDTH, & HEIGHT sliders to create a prism with dimensions you like. [br][br] Press the [b]AR[/b] button in the lower right corner of your 3D screen. Follow the directions that appear.

5.2.

5.3.

5.4.

5.5.

5.6.

6.

Rational Numbers

1. Classifying Rational Numbers
2. Rational Numbers
3. Rational numbers & Equivalent fractions

6.1.

Classifying Rational Numbers

6.2.

6.3.

7.

Add, Subtract, Multiply, and Divide Fractions

1. Adding Fractions - Visual
2. Adding fractions on a number line
3. Adding Fractions with an Area Model
4. Subtracting fractions with number lines
5. Subtracting Fractions using an Area Model
6. Fraction Addition and Subtraction
7. Multiplying fractions with area model
8. Multiply Fractions
9. Multiplying Mixed Number Fractions
10. Dividing Fractions
11. Division of fractions
12. Division of a Fraction by a Whole Number

7.1.

Adding Fractions - Visual

Enter any two fractions to see their sum. Any mixed numbers must be entered as improper fractions. The sum will not be simplified.

7.2.

7.3.

7.4.

7.5.

7.6.

7.7.

7.8.

7.9.

7.10.

7.11.

7.12.

8.

Equivalent Fractions, Simplifying, and Denseness

1. Equivalent Fractions
2. Equivalent Fractions Task
3. Equivalent ftraction
4. Simplifying Fractions
5. Fractions on a numberline

8.1.

Equivalent Fractions

8.2.

8.3.

8.4.

8.5.

9.

Types of Graphs

1. Table View
2. Dot Plot Tool
3. dotplot
4. Scatter Plot and Best Fit Line
5. Comparing Histogram, Dot and Stem & Leaf Diagrams
6. Stem and Leaf Plot Template
7. Bar Charts and Pie Charts
8. Pie Chart
9. AQR Section 17: Creating a Box and Whisker Plot
10. Graph the Linear Equation
11. Graph the Line
12. Graph the Line (v.2)

9.1.

Table View

What is the Table View?

Create a table of values for a function using the [img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img] [i]Table View of[/i] [url=https://www.geogebra.org/graphing]GeoGebra Graphing Calculator[/url]![br][br]With [img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img] [i]Table View [/i]you can...[br][list][*]generate a table of values in a specified range[/*][*]show / hide the generated points in [i]Graphics View[/i][/*][*]edit the function[/*][*]edit the range of values[br][/*][/list]Explore the table of values for functions by opening the [img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img] [i]Table View[/i]. [br]Then follow the instructions to learn how to use the [img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img] [i]Table View [/i]step by step.

Explore the construction...

Instructions

[table][tr][td]1.[br][br][/td][td][img]https://wiki.geogebra.org/uploads/thumb/9/98/AlgebraBlack.svg/24px-AlgebraBlack.svg.png[/img][/td][td]Type [math]x+2[/math] into the [i]Input Bar[/i] and press [i]Enter[/i]. The function will be automatically labeled [i]f(x)[/i] and displayed in the [i]Graphics View[/i]. [/td][/tr][tr][td]2.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/4/41/Icon-menu.svg/16px-Icon-menu.svg.png[/img][br][/td][td]Open the context menu by pressing the [i]More [/i]button on the right side of the row containing [i]f(x)[/i].[/td][/tr][tr][td]3.[/td][td][/td][td]Select [i]Table of values[/i].[/td][/tr][tr][td]4.[br][br][/td][td][/td][td]A dialog opens where you can define [i]Start value for x[/i], [i]End value for x[/i] and [i]Step[/i]. Press [i]OK[/i] to confirm your settings.[/td][/tr][tr][td]5.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img][/td][td]The [i]Table View [/i]opens automatically so you can see the values immediately.[/td][/tr][tr][td]6.[br][br][/td][td][img]https://wiki.geogebra.org/uploads/thumb/9/98/AlgebraBlack.svg/24px-AlgebraBlack.svg.png[/img][/td][td]Go back to [i]Algebra View[/i], type [math]x^3+2x^2[/math] into the [i]Input Bar[/i] and press [i]Enter[/i]. The function will be automatically labeled [i]g(x)[/i] and displayed in the [i]Graphics View[/i]. [/td][/tr][tr][td]7.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/4/41/Icon-menu.svg/16px-Icon-menu.svg.png[/img][/td][td]Open the context menu by pressing the [i]More [/i]button on the right side of the row containing [i]g(x)[/i].[/td][/tr][tr][td]8.[/td][td][/td][td]Select [i]Table of values[/i].[/td][/tr][tr][td][br][br][/td][td][/td][td][b]Note:[/b] This time the dialog for defining start and end values will not show, because you already set those values in step 4. You can change the values later.[/td][/tr][tr][td]10.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img][/td][td]The [i]Table View [/i]opens automatically so you can see the values immediately.[br][/td][/tr][/table]

Try it yourself...

Options

Switch to the [img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img] [i]Table View [/i]to change the following options.[br][br][b]Change the range of values[/b][br][table][tr][td]1.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/4/41/Icon-menu.svg/16px-Icon-menu.svg.png[/img][/td][td]Open the context menu by pressing the [i]More [/i]button next to [i]x.[/i][/td][/tr][tr][td]2.[/td][td][img]https://wiki.geogebra.org/uploads/5/56/Editgray24.png[/img][/td][td]Select [i]Edit[/i].[/td][/tr][tr][td]3.[br][/td][td][/td][td]The dialog opens where you can change [i]Start value for x[/i], [i]End value for x[/i] and [i]Step[/i]. Press [i]OK[/i] to confirm your settings.[/td][/tr][/table][br][b]Show / hide points in [/b][i][b]Graphics View[/b][br][/i][table][tr][td]1.[/td][td][i][img]https://wiki.geogebra.org/uploads/thumb/4/41/Icon-menu.svg/16px-Icon-menu.svg.png[/img][/i][/td][td]Open the context menu by pressing the [i]More [/i]button next to the function you want to hide the points for, e.g. [i]f(x)[/i].[i][/i][/td][/tr][tr][td]2.[/td][td][i][/i][/td][td][i][/i]Select [i]Hide points[/i][i].[/i][/td][/tr][tr][td][i][/i]3.[br][/td][td][i][img]https://wiki.geogebra.org/uploads/thumb/4/41/Icon-menu.svg/16px-Icon-menu.svg.png[/img][/i][/td][td][i][/i]The points are now not shown in [i]Graphics View[/i][i]. [/i]To show them again, open the context menu by pressing the [i]More [/i]button and select [i]Show points.[/i][/td][/tr][/table][br][b]Edit a function[/b][br][table][tr][td]1.[/td][td][i][img]https://wiki.geogebra.org/uploads/thumb/4/41/Icon-menu.svg/16px-Icon-menu.svg.png[/img][/i][/td][td]Open the context menu by pressing the [i]More [/i]button next to the function you want to edit, e.g. [i]f(x)[/i].[i][/i][/td][/tr][tr][td]2.[/td][td][img]https://wiki.geogebra.org/uploads/5/56/Editgray24.png[/img][/td][td]Select [i]Edit[/i].[/td][/tr][tr][td]3.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/9/98/AlgebraBlack.svg/24px-AlgebraBlack.svg.png[/img][/td][td]The [i]Algebra View [/i]opens automatically. Now you can edit the function.[br][/td][/tr][/table][br][b]Remove a column[/b][br][table][tr][td]1.[/td][td][i][img]https://wiki.geogebra.org/uploads/thumb/4/41/Icon-menu.svg/16px-Icon-menu.svg.png[/img][/i][/td][td]Open the context menu by pressing the [i]More [/i]button next to the function you want to remove from the [i]Table View[/i], e.g. [i]f(x)[/i]. [i][/i][/td][/tr][tr][td]2.[/td][td][img]https://wiki.geogebra.org/uploads/0/0f/Deletegray24.png[/img][/td][td]Select [i]Remove column[/i].[/td][/tr][tr][td]3.[br][br][/td][td][img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img][/td][td]Now the column is removed from [i]Table View[/i].[br][b]Note:[/b] The function itself is not removed from [i]Algebra View[/i]. You can generate the table of values again by following the instructions above.[br][/td][/tr][/table]

Extend the Table View

If you don't need the [i]Graphics View [/i]you can extend the [img]https://wiki.geogebra.org/uploads/thumb/1/11/TableBlack.svg/24px-TableBlack.svg.png[/img] [i]Table View [/i]to full screen so you have more space for your input and explorations.

9.2.

9.3.

9.4.

9.5.

9.6.

9.7.

9.8.

9.9.

9.10.

9.11.

9.12.

10.

Mean, Median, and Mode

1. AQR Section 17: Where's the Mean?
2. Comparing Mean, Median, and Mode
3. 05.1 Measures of Central Tendency
4. Exploring Mean and Median
5. Mean Median Mode Game
6. AQR Section 6: Weighted Average Exploration
7. Lotto Tickets Simulation
8. AQR Section 17: Calculating Summary Statistics

10.1.

AQR Section 17: Where's the Mean?

This applet is designed for use with AQR Section 17.[br][br]For each box-and-whisker plot below, drag the red point to where you think the mean of the data set is located. Click on the "Check the Means" button to confirm. Click on the "New Box Plots" button to create two new box-and-whisker plots.

Is there any way to tell which side of the median the mean will be located on?

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