Polygon Types and Circle Properties

• Polygons get their names from the number of line segments they have

Polygon Names and Sides

• Triangle: 3 sides
• Quadrilateral: 4 sides
• Pentagon: 5 sides
• Hexagon: 6 sides
• Heptagon: 7 sides
• Octagon: 8 sides
• Nonagon: 9 sides
• Decagon: 10 sides
• Hendecagon: 11 sides

Regular vs Irregular Polygons

• Regular polygons have equal sides and equal angles
• Regular polygons are both equilateral and equiangular
• Equilateral means all sides are the same length
• Equiangular means all corresponding angles are equal
• Irregular polygons are polygons that are not regular

Circles

• Circle: A set of points at the same distance from a fixed point, called the center
• The circle is named after its center point
• Chord: A segment joining any two points on the circle
• Diameter: A chord connecting two points on the circle and passing through the center
• Radius: A line segment from the center to a point on the circle
  • Radius is one-half the diameter

Finding Diameter from Radius

• If the radius is 8 cm, the diameter is 16 cm (2 x 8 cm)
• If the radius is 10 inches, the diameter is 20 inches (2 x 10 in)
• If the radius is 16 m, the diameter is 32 m (2 x 16 m)

Finding Radius from Diameter

• If the diameter is 26 mm, the radius is 13 mm (26 mm ÷ 2)
• If the diameter is 18 inches, the radius is 9 inches (18 in ÷ 2)
• If the diameter is 46 m, the radius is 23 m (46 m ÷ 2)

Circumference of a Circle

• Circumference refers to the distance around the circle and is its perimeter
• Formula: C = πd, where π (pi) is approximately 3.14, and d is the diameter

Example Circumference Calculation

• Using π = 3.14, a circle with a 9-inch diameter has a circumference of 28.26 inches (3.14 x 9 in)
• Mike is painting the edges of a round clock with a diameter of 7 inches, needing 21.98 inches of trim (3.14 x 7 in)

Area of a Circle

• Area of a circle is the measure of interior space enclosed by the circle
• Formula: A = πr², where π (pi) is approximately 3.14 and r is the radius

Example Area Calculation

• A circle with a 4 cm radius has an area of 50.24 cm² (3.14 x 4 cm x 4 cm = 3.14 x 16 cm²)
• Jai is designing a round flower bed with a radius of 7 meters and needs 153.86 m² of space (3.14 x 7 m x 7 m = 3.14 x 49 m²)

Solid Figures

• Solid figures have length, width, and height

Types of Solid Figures

• Cube: Symmetrical with all faces made of squares
• Prism: Has two identical bases and side faces are polygons
• Cylinder: Has two circular bases and a curved body face
• Cone: Has one circular base and one vertex opposite the base

Volume of a cube

• The volume refers to the space occupied by a solid figure measured in cubic units
• Examples include cubic centimeters (cm³) and cubic meters (m³)
• Volume can be found by multiplying its three sides
• Formula: V = s x s x s = s³, where s is the length of a side

Volume of a cube - example

• If a cube has sides of 8 cm, the volume is 512 cm³ (8 cm x 8 cm x 8 cm)
• What is the volume of a block of cheese if each side measures 4 iches
  • Volume = 4 x 4 x 4 = 64 𝑖𝑛³

Volume of a Rectangular Prism

• Volume V of a rectangular prism = length(l) x width(w) x height(h) or V = l x w x h

Volume of a Rectangular Prism - Examples

• A prism with length=7cm, width=2cm, height=8cm, volume would be calculated, V = 7cm x 2cm x 8cm = 112 cm³
• A farmer uses a wooden crate to store freshly harvested apples
• The crate has a length of 14 inches, a width of 15inches and a height of 12inches -To find volume, use the formula:
• V = 14 in x 15 in x 12 in = 2520 in³

Understanding Time

• 1 hour is 60 minutes
• 1 minute is 60 seconds

Converting 12-Hour Time to 24-Hour Time

• Within the 1st hour of the day: Subtract 12 from the given time
  • 12:46 a.m. is 00:46 in 24-hour format
• 2nd hour and other hours before noon: Retain the given time
  • 7:17 a.m. remains 07:17
• Any hour after noon: Add 12 to the given time
  • 7:23 p.m. becomes 19:23

Converting 24-Hour Time to 12-Hour Time

• Within the 1st hour of the day (00:00 to 00:59): Add 12 to the given time and affix a.m.
  • 00:19 is 12:19 a.m.
• 2nd hour and other hours before 13:00 (01:00 to 12:59): Retain the given time and affix a.m. or p.m
  • 08:32 is 8:32 a.m.
• Any hour after 12:59 (13:00 to 23:59): Subtract 12 to the given time and affix p.m.
  • 16:29 is 4:29 p.m.

Calculating Elapsed Time

• To find the time elapsed, subtract the beginning time from the ending time
• Directly subtract minutes if the ending time has more minutes than the beginning time
• If the ending time has fewer minutes: Borrow 1 hour (60 minutes) and add it to the ending minutes, then do subtraction
• Mark started playing baseball ad 3:18pm - stopped at 5:49pm - Mark spent 2 hours and 31 minutes playing baseball
• The school meeting lasted from 8:35 a.m. and at 9:15 a.m - Meeting lasted for 40 minutes

Arithmetic Sequences

• Arithmetic Sequence: Is a list of numbers following a specific pattern in which terms are obtained by adding or subtracting the same value from the previous number
• 1, 4, 7, 10, 13, 16,
• 94, 86, 78, 70, 62

Geometric Sequence:

• Geometric Sequence: Is a set of numbers where each number is found by multiplying or dividing the previous number by the same value known as the common ratio

Common Ratio

• Common Ratio: Fixed number that is multiplied or divided to each sequence term

Examples of Geometric Sequence:

• 6, 18, 54,162 is multiplied by x3
• 1600, 400, 100, 25 is divided by ÷4

Interpreting data & frequency

• 30 students were asked about their favorite fruit
  • Apple -7, Banana - 9, Orange - 8, Grape - 6
  • How many students prefer Oranges? - 8 students
  • How many more students like bananas compared to apples? - 9-7= 2 students
  • Which is the least favourite fruit among students? - Grape
  • What is the total frequency? -7+9+8+6 =30

Analysing data sold per day

• 30 pens were sold on Friday
• Highest number of pens were sold on Thursday
• 60 pens were sold on Monday and Tuesday

Probability

• Probability: Is a mathematical way of describing that something will/will not happen
• Sample space: List of possible outcome of an activity/experiment
• Example: Rolling a six-sided dice - sample space is {1, 2, 3, 4, 5, 6}
• To calculate probability, it involves knowing the things that can happen
• Experimental Probability: Probability based on an experiment

Experimental Probability Formula:

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟𝑠 P 𝐸 = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠/𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠

Applying The Experimental Probability formula:

• Bobbie rolled a six-sided die 50 times

• 6 times dice lands on 4

• 6÷2 / 50÷2 = 3/25

• 10 times dice lands on 1

• 10÷10 / 50÷10 = 1/5

• Jake flipped a coin 50 times

  • Got heads 32 times and tails 18 times Experimental probability of flipping heads = 32/50 or 16/25