Inequality Signs An inequality is like an equation

Inequality Signs An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to, at most, no more than > : greater than ≥ : greater than or equal to, at least

Graphing Rules Symbol Circle Direction of Arrow < > ≤ Open Closed Left Right Left ≥ Closed Right

5. 1. 1 - Volume • Key Skill: WWBAT find the volume of a three dimensional figure.

Let’s Look at Prisms • How many sides does a rectangular prism have?

Key Vocabulary • Rectangular Prism is a solid figure bounded by six faces

Key Vocabulary • Volume

Key Vocabulary • Volume is how much three-dimensional space a substance or shape occupies.

In Pairs • If I have a box that measures 1 m long by 1 m wide by 1 m tall, how many centimeter blocks can I fit inside the box?

In Pairs • If I have a box that measures 1 m long by 1 m wide by 1 m tall, how many centimeter blocks can I fit inside the box? • 100 wide by 100 long by 100 high equals: 1, 000 blocks!

Volume Formula v= l • w • h volume = length • width • height

Finding Volume • How many 1 ft by 1 ft cubes could fit in a box that measure 2 ft by 3 ft by 4 ft?

Finding Volume 2 • 3 • 4 = 24 ft 3 • Remember to label your answers properly! – Volume is cubic units

Triangular Prisms

NOT a Triangular Prism • Pyramids are NOT triangular prisms!

Volume of Triangular Prisms • Formula: volume = 1/2 • base • height • length v = (1/2)bhl

Example • Find the volume of a triangular prism with a base of 6 feet, a height of 8 feet and a length of 10 feet.

Example • Find the volume of a triangular prism with a base of 6 feet, a height of 8 feet and a length of 10 feet. • Formula is 1/2 x base x height x length, 1/2 • 6 • 8 • 10 = 240 cubic feet

Rectangular Prism Net Find Surface Area of Prism 2 cm

Rectangular Prism • Multiply 2 x 2 to get the area of one section. • Multiply your answer, 4, by the number of sides, 6, to get 24. • Answer: 24 cm 2

Units • Note that surface area is shown in square units, just like area

5. 1. 1 - Surface Area • Key Skill: WWBAT calculate the surface area of three dimensional figures.

Finding Surface Area • How much wrapping paper would it take to wrap a box that measure 2 feet by 3 feet by 4 feet? 3 4 2

Finding Surface Area • • Front: 2 x 3 = 6 sq ft Back: same = 6 sq ft Top: 2 x 4 = 8 sq ft Bottom: same = 8 sq ft Left: 3 x 4 = 12 sq ft Right: same = 12 sq ft Total = 52 sq ft 3 4 2

Surface Area Formula • Surface Area of a Rectangular Prism= 2(lw + lh + wh) • Surface Area of a Cube= 6 s 2

Word Problem Example • How much wood does it take to build a rectangular box measuring 2 m by 4 m by 6 m?

Word Problem Example • How much wood does it take to build a rectangular box measuring 2 m by 4 m by 6 m? 6 m 2 m 4 m

Word Problem Example • How much wood does it take to build a rectangular box measuring 2 m by 4 m by 6 m? • Front: 2 x 6 = 12 6 m • Back: 2 x 6 = 12 • Top: 6 x 4 = 24 2 m 4 m • Bottom: 6 x 4 = 24 • Left: 2 x 4=8 Add up the sides • Right: 2 x 4 = 8 to get 88 m 2

Rectangular Prism Formula • Surface Area = 2(lw + lh + wh) • We can do just three multiplications and then double the answer because each side has an identical twin.

Remember Units! • Volumes are measured in CUBIC units • Surface Area is measure in SQUARE units

Steps for Problem Solving 1. Draw a picture of the shape and label the measurements and units. 2. What do you need to solve ? – Surface Area - a measure of the number of square units needed to cover the outside of a figure – Volume - a measure of the number of cubic units needed to fill the space inside an object

What Kind of Question? • • • How much How much box? water to fill a pool? frosting to cover a cake? will a box hold? material to build a box? wrapping paper to cover a

What Kind of Question? • • • How much How much box? (SA) water to fill a pool? (volume) frosting to cover a cake? (SA) will a box hold? (volume) material to build a box? (SA) wrapping paper to cover a

Steps for Problem Solving 3. 4. 5. 6. 7. 8. Write the formula Rewrite the formula as an algebraic equation (Plug in the numbers) PEMDAS ? Show all work step by step Get the units right! Check all work !!

Remember Units! • Volumes are measured in CUBIC units • Surface Area is measure in SQUARE units

Remember These? • Range is the distance from the smallest to largest value in a dataset • Mode is the most popular data point • Mean is the average of the dataset – Add the data points, then divide by the number of data points • Median is the middle data point from least to greatest