Geometry - Area Divisibility Rules

the outline of a shape , boundary, “the fence” Foldable - Vocabulary Sides: Height: Perpendicular: Diagonals: the outline of a shape , boundary, “the fence” the distance between the bases or between the top and bottom of the shape; a line or dotted line that is perpendicular with the base two lines that form a 90° angle a line that connects vertices across from one another

Foldable - Characteristics Rectangles: 4 sides, 4 right angles, opposite sides are equal (Congruent), 2 sets of parallel lines 4 sides, 4 angles - but zero right angles, opposite sides are congruent (equal), 2 sets of parallel lines Parallelograms: Trapezoids: 4 sides, 4 angles - might have 2 right angles or Zero, opposite sides may NOT be equal, 1 set of parallel lines

Sometimes a right angle - called a right triangle Triangle: Characteristics Continued: 4 sides, 2 sets of parallel lines, all sides are equal, no right angles Rhombus: 3 sides, 3 types - Isosceles, 2 equal sides; Equilateral, 3 equal sides; Scalene, no equal sides; Sometimes a right angle - called a right triangle Triangle:

Triangles Name: 3 # of sides: Side + Side + Side Perimeter:

Name: Rectangles 4 # of Sides: Side + Side + Side + Side Perimeter:

Rectangles Square 4 Side + Side + Side + Side Name: # of Sides: Perimeter:

Parallelogram Name: 4 # of Sides: Side + Side + Side + Side Perimeter:

Trapezoid Name: 4 # of Sides: Side + Side + Side + Side Perimeter:

Rhombus Name: 4 # of Sides: Side + Side + Side + Side Perimeter:

How would I find the Perimeter? Area = Base x Height divided by 2 Formula A = bh/2 How do I find the height? So we are going to say that the top triangle is an Isosceles Triangle what does mean? Ok...so two sides are going to be 10 inches, one side is going to be 8 inches and the height is 14 inches. What is the Area? A = bh/2 A = 8 x 10 / 2 ??? A = 8 x 14 / 2 How would I find the Perimeter? A = 112 / 2 A = 56 P = 10 + 10 + 8 P = 28

Area = Base x Height divided by 2 A = bh/2 Formula Area = Base x Height divided by 2 A = bh/2 What kind of triangle is the bottom triangle? Can it also be an Isosceles Triangle? Ok...so 2 sides 10 inches, one side is going to be 12 inches What is the Area? A = bh/2 How do I know what the height is going to be? A = 10 x 10 / 2 perimeter??? A = 100 / 2 P = 10 + 10 + 12 A = 50 P = 32

Area = Base x Height A = bh Perimeter??? A = bh A = 12 x 5 Formula: Area = Base x Height A = bh Top rectangle - base is 12 cm and the height is 5 cm. What is the area? Perimeter??? A = bh A = 12 x 5 P = 12 + 12 + 5 + 5 A = 60 P = 34

′ ′ ′ ′ Area = Base x Height A = bh Side = 8, What is the area? A = bh Formula: Area = Base x Height ′ A = bh Side = 8, What is the area? ′ ′ A = bh Perimeter??? ′ A = 8 x 8 P = 8 + 8 + 8 + 8 A = 64 P = 32

Area = Base x Height A = bh A = bh Perimeter ??? A = 13 x 5 Formula: Area = Base x Height A = bh How do I find the height? OK….so a side is 6 meters, the base is 13 meters, and the height is 5 meters. What is the area? A = bh Perimeter ??? A = 13 x 5 P = 6 + 6 + 13 + 13 A = 65 P = 38

Area = (Base one + Base two) x Height divided by 2 Formula: Area = (Base one + Base two) x Height divided by 2 A = (b₁ + b₂)h / 2 Top trapezoid - how do I find the height? Ok, so bases are 5 yards and 12 yards, sides are 10 yards, and height is 7 yards. What is the area? A = (b₁ + b₂)h / 2 Perimeter ??? A = (5 + 12) x 7 / 2 P = 10 + 10 + 5 + 12 A = 17 x 7 / 2 P = 37 A = 119 / 2 A = 59.5

′ ′ ′ ′ Area = Diagonal₁ x Diagonal₂ divided by 2 A = d₁d₂ / 2 Formula: Area = Diagonal₁ x Diagonal₂ divided by 2 ′ A = d₁d₂ / 2 Ok, one diagonal is 22 inches and one is 18 inches. The side is 12 inches. What is the area? ′ Diagonals - ??? ′ A = d₁d₂ / 2 ′ A = 22 x 18 / 2 Perimeter??? P = 12 + 12 + 12 + 12 A = 396 / 2 P = 48 A = 198

Divisibility Rules Interactive Notebook

Examine the numbers and find rules to determine in which group the number belongs just by looking at it.

Can we say that 36 is divisible by 2 and 4 but is Looking back at the last slide - 36 had factors of 2 and 4 but not 5, 8, and 10 Can we say that 36 is divisible by 2 and 4 but is NOT divisible by 5,8, and 10? WHY? How about 24, 80, and 975? What can we say about them? Divisibility - When a number can be evenly divided by another number, with no remainder

What do the numbers 12, 18, 30, 66, and 93 all have in common? What if you calculate the sum of the digits for each number? What do the sums of each number have in common? 12: 1 + 2 = 3 18: 1+8 = 9 30: 3 + 0 = 3 66: 6+6 = 12 93: 9 + 3 = 12 Can I divide the ‘sum’ of each number by 3 with NO remainder? Then all of those numbers are divisible by 3 Are the following numbers divisible by 3? 219: ___, 432: ____, 2754:___, 9043281: ____

Now look at the numbers 27, 36, 54,72, and 99 What do they have in common? What if you calculate the sum of the digits for each number? What do the sums of each number have in common? 27: 2+7 = 9 36: 3+6 = 9 54: 5+4=9 72: 7+2=9 99: 9+9=18 Can I divide the ‘sum’ of each number by 9 with NO remainder? Are the following numbers divisible by 9? 108: ___, 234: ____, 5247:___, 3904182: ____ Are these numbers also divisible by 3?

Write yes or no if it is divisible 2 3 6 12 20 21 32 33 54 2 3 6 12 20 21 32 33 54 Yes yes yes Yes no no No yes no Yes no no Whats the rule???? If 2 and 3 works – 6 works

**If a number is divisible by 9, it is also divisible by 3; but if a number is divisible by 3, it is not necessarily divisible by 9. Divisibility rule for 6: If the number is divisible by 2 AND 3, then it is divisible by 6 6

Circle ALL the numbers that are divisible of the given number Circle ALL the numbers that are divisible of the given number. Explain your answers! 2,838 is divisible by 3 9 4 6 2. 34,515 is divisible by 5 10 3. 10,534,347 is divisible by 2 4. 4,376 is divisible by 9 4 8 6 5. 6,140 is divisible by 10 6. 9,430,620 is divisible by 2 5 9 3 6 10 4 8

Write a 3 digit number that is divisible by 3 and 4. 420 624 216 2. Write a 4 digit number that is divisible by 5 and 6. 6030 5250 9810 3. Can you write a number that is divisible by 2,3,4,5,6,9, and 10 36720 98640