Math 205 Book: Fractions
Table of Contents
- Modeling Rational Numbers
- Fractions on a number line
- Fraction Models
- Overview of + ; - ; / ; x
- Operations between fractions: formative assessment
- Adding & Subtracting Fractions
- Instructions for diagram Activity
- Adding Fractions
- Subtracting Fractions
- Adding and Subtracting Fractions with Diagrams
- Adding & Subtracting Proper Fractions
- Multiplying and Dividing Fractions
- Multipling Fractions
- Multiplying Proper Fractions
- Dividing Proper Fractions
- Division of Fractions Process
- Fraction Equivalence, Ordering, and Simplifying
- Simplifying Fractions
- Ordering/Comparing Fractions
- Ordering Fractions
- Ordering Fractions Number Line
- Equivalent fractions
- Equivalent Fractions 2
- Writing Fractions with Common Denominators
- Fraction Density
- Denseness of Fractions
- Arranging Fractions
- Geometry: Lines, Rays, Segments, Points, Parallel/Perpendicular
- Parallel & Perpendicular Lines
- Difference between a point, a line segment, a ray and a line
- Geometry: Angles and Triangles
- Types of Angles
- Types of Triangles
- Geometry: Quadrilaterals
- Naming Shapes
- Properties of Quadrilaterals
- Geometry: Perimeter & Area
- Perimeter and Area
- Practice: Finding triangle Area and Perimeter
- Trapezoid
- Area of Circle
Fractions on a number line
Play with the numbers and build your own fraction using the [i]+ [/i]and - buttons in the upper left. [br][br]Notice the relationship between the numerator (top number), denominator (bottom number) and where the arrow points on the number line. [br][br]Additionally, look at how as you adjust the numbers, the number line itself also changes.
Operations between fractions: formative assessment
Operations between fractions
The following file contains some slides with the definition of the operations between fractions and some examples which illustrate them.
Instructions for diagram Activity
[size=150][color=#e06666][b]1.[/b] Select Addition or Subtractions using the box on the top of the screen. [/color][br][br][color=#b45f06][b]2. [/b]Shift numerators and denominators to desired numbers on each side. (Notice how changing these numbers changes the circles: number of sections, number of shaded regions, etc)[/color][br][br][color=#38761d][b]3.[/b] Try and solve the problem you created. (Move the right circle so it lays over the left circle using the slider on the left and try and find relationships between the two fractions)[/color][br][br][color=#741b47][b]4.[/b] Check your answer by selecting the [i]EquivalentFraction[/i] box on the left side of the screen.[/color][/size]
Multipling Fractions
Multipling Fractions
Simplifying Fractions
How to use the sliders to help simplify a fraction.
1. Click and drag the blue sliders on the left to the numerator and denominator of the (non-simplified) fraction you are given.[br]2. Find the GCF (greatest common factor of this numerator and denominator. If the GCF is 1, you are done. 3. If the GCF is greater than 1, divide the numerator by the GCF - the result is the "new" numerator. [br]4. Divide the denominator by the GCF - the result is the "new" denominator. [br]5. Click and drag the purple sliders on the right to the new numerator and new denominator.[br]6. Finally, click and drag the handle (the red point) to overlap the two squares to see if they match.
Definition: A fraction is simplified if the numerator and denominator have no common factors
1. Simplify [math]\frac{9}{15}[/math][br]a) The square on the left illustrates [math]\frac{9}{15}[/math] (9 sections out of 15 are shaded blue).[br]b) Find the GCF of 9 and 15 to simplify [math]\frac{9}{15}[/math]. [br]c) Adjust the purple sliders for the numerator and denominator to create the simplified fraction for [math]\frac{9}{15}[/math].[br]d) Use the handle (red point) to drag the purple square on top of the blue square. If the shaded portions completely overlap, then you have simplified the fraction correctly.
Denseness of Fractions
What is fraction density?
[color=#38761d]The important idea that between any two fractions there are an [i]infinite[/i] number of other fractions. [br](Ex. between 2/10 and 9/10, there 3/10, 4/10, 5/10 and an unlimited number of other fractions)[/color]
How to find a fraction between two fractions:
[color=#900000]1. Make sure the denominators of the two fractions are the same, if they're not convert them to their LCD. [br]2. Find numbers that are in between the numerators of the fractions. (Ex. 3, 4, and 5 are between 2 and 9. Therefore; 3/10, 4/10, and 5/10 are between 2/10 and 9/10)[br][br][br][/color]Using the diagram below, practice finding a common denominator between two fractions
Parallel & Perpendicular Lines
PARALLEL LINES
[color=#000000]The following applet demonstrates a property that parallel lines have when they're drawn in the coordinate plane. [br] [i] [br]Be sure to move the [color=#1e84cc][b]blue points[/b][/color] around quite a bit![/i] [/color]
QUESTION 1
If you move the blue points to make the lines vertical, are the lines consider parallel?
[color=#000000]What can you conclude about parallel lines drawn in the coordinate plane? [/color]
PERPENDICULAR LINES
[color=#000000]This applet demonstrates a property that perpendicular lines have when they're drawn in the coordinate plane. [br][br][i]Be sure to move the points around quite a bit and observe carefully as you do! [/i][/color]
[color=#000000]What can you conclude about perpendicular lines that are drawn in the coordinate plane? [br](Assume the lines are not aligned horizontally and vertically). [/color]
Types of Angles
[size=200][size=150]Different types of angles have their own names.[br]Use the diagram to find the names of the five angle types.[br][u][b]IN YOUR NOTES[/b][/u] write a definition and drawing of each.[/size][/size]
Does line length affect the angle?
Try it:
An angle measures [math]\angle83^\circ[/math]. What type of angle is it?
An angle measures [math]\angle197^\circ[/math]. What type of angle is it?
An angle measures [math]\angle90^\circ[/math]. What type of angle is it?
An angle measures [math]\angle149^\circ[/math]. What type of angle is it?
Identify the types of angles below.
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What type of angle?
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What type of angle?
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What type of angle?
Naming Shapes
Naming Shapes![br]What shapes do you see? Can you name them using their points? What makes a shape a shape?
Name 3 squares using their points.[br][br]1.[br]2.[br]3.[br]• How do you know these are squares? Explain.[br][br][br][br]Name one right triangle using its points.[br][br]1.[br]• How do you know this is a right triangle? Explain.[br][br][br][br][br]Name one equilateral triangle using its points.[br][br]1.[br]• How do you know this is an equilateral triangle? Explain.[br][br][br][br][br]Name 3 rectangles using their points.[br][br]1.[br]2.[br]3.[br]• How do you know these are rectangles? Explain.[br][br][br][br]Name one line using two points. [br][br]1.[br]• How do you know this is a line? Explain.
Perimeter and Area
10.1 Perimeter
[b][color=#ff0000]10.1 Perimeter[/color][color=#0000ff][br][br]How do you determine the perimeter?[/color][/b][br][i][color=#0000ff][size=85]Bagaimana anda menentukan perimeter?[/size][/color][/i]
[b][color=#0000ff]Perimeter is the total length around an enclosed area.[/color][/b][br][color=#0000ff][size=85]Perimeter ialah jumlah ukuran panjang sisi yang mengelilingi suatu kawasan tertutup.[/size][/color]
[b][color=#0000ff]Which Object has the largest perimeter.[/color][/b][br][br]A) I[br]B) II[br]C) III[br]D) IV
Largest perimeter is Object:[br]Perimeter terbesar adalah Objek:[br][br][br]Reason:
Select the distance or length [icon]/images/ggb/toolbar/mode_distance.png[/icon]tool. Find the perimeter of each of the following shapes.
[b][color=#ff0000]Which Object has the largest perimeter?[/color][/b]
[b][color=#ff0000]Draw an quadrilateral with perimeter 18 cm[br][/color][/b]Lukiskan rajah Sisi Empat yang berperimeter 18 cm
Draw an quadrilateral with perimeter 18 cm
[b][color=#ff0000]Draw a triangle with perimeter 18 cm[br][/color][/b]Lukiskan rajah segitiga yang berperimeter 18 cm
Draw a Triangle with Perimeter 18 cm
Circle
Use the Polygon [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool and estimate the perimeter of circle given
Perimeter (Circumference) of Circle
Perimeter of Circle is