A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. ... When rates are expressed as a quantity

of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

Example #1: Convert each ratio to a unit rate.1)60 miles per 3 hours

2) $4.50 per 12 oz

3) 50 push-ups in 4 minutes

4)Kyle charges $260 to clean 8 class rooms. How much does he charge to clean one class room?

You Try….1) Convert $3.99 per 5 pounds to a unit rate.

2) Cherelle traveled 657 miles in 9.5 hours. How many miles did she travel in 1 hour?

Example #2: Application of Unit Rates.1) Mario can do 150 push-ups in 5 minutes.

At this rate, how many push-ups can he do one hour (assuming he doesn’t stop)?

2) Stacey heart rate was 155 beats/minute after performing jumping jacks. How long would it take her heart to beat 900000 times?

3) Cartier can run 5 miles in one hour. If he continues at this pace, how many minutes will it take Cartier to run 5 miles?

4) Which is cheaper, a 14 ounce box of Cheerios costing $3.99 or a 12 ounce box of Sugar Smacks costing $3.25?

5) Carl Lew can run 800 yards in 3 minutes. James Lew can run 750 yards in 2.5 minutes. Who can run the fastest?

You Try…..Cydney can do 78 sit-ups in 2 minutes. At this rate, how long will it take her do 800 sit-ups?Unit 3A Lesson 2: Number Sense & Ratios

Example #1: Conversions in U.S System1) 1 yd = 3 ft. 5 yards = ? ft

2) 1lb = 16 oz. 108 oz = ? lb

3) 42 ft/sec to meters/sec

You Try….

1) 1 ton = 2000 lb. 8500 lb = ? tons

2) 3600 sec = 1 hour. 6 cm/sec to cm/h

3) 1 mile = .62 km and 3600 sec = 1 hour. 290 km/sec to mile per hour

4) 1 mile = .62 km and 1 g = 1.06 liters. 85 miles per gallon to kilometers per liter

More Examples1) 1 inch = 3 miles. If Susie traveled 32 miles, how many inches

is that?

You Try……1)Which is greater, 83 feet or 786 inches?

2)Which will save you more gas, a compact car that gets 38 miles per 3 gallons or a hybrid that gets 54 miles per 2 gallons?

Unit 3A Lesson 3: Number Sense Scale Drawings & Proportions

Don’t Forget….Solve Proportions

1) x5=127

2) y+38 = y4

Example #1: Real World Connections

1)Photography: A photo that is 8 inches wide and 513 inches high is enlarged to a poster that is 2 feet wide and 113 feet high. What is the ratio of the width of the photo to the width of the poster?

2)Drafting: The scale: 1 inch = 16 feeta) If the scale drawing of the bedroom below is 78∈by

58∈¿, find the actual dimensions of the bedroom.

3) Geography: Students at the University of Minnesota in Minneapolis built a model globe 42 ft in diameter using a scale of 1: 100000 feet. Mount Everest is about 29,000 feet tall. How tall is Mount Everest on the model?

You Try…Selly’s Sandwich shop is 40 feet tall. The shop is an enlargement of an actual milk bottle. The scale used was 5 ft = 2 cm. Find the height of the scale model milk bottle.

Unit 3B Lesson 1: Area & PerimeterExample #1: Find the area and perimeter of each figure below:

Area: _________________ Area:_________________________

Perimeter:_______________________ Perimeter:__________________________

Example #2: Find the area & perimeter of each irregular shape.

Area: _________________ Area:_________________________

Perimeter:_______________________ Perimeter:__________________________

Example #3: Calculate the length and perimeter.

1) A rectangle has an area of 195 square feet and a width of 13 feet. Find the length and perimeter.

2) A rectangle has an area of 1248 feet and a length of 24 feet find the width and perimeter.

You Try…Question #1: Area: _______________ Perimeter: ______________________

Question #2: If the area of a rectangle is 3120 square feet and the width is 65 feet, find the perimeter and the length.

Unit 3B Lesson 2: Maximize Area & Minimize PerimeterFacts:

1) Maximum Area for a rectangular shape for a given perimeter is ALWAYS a square.

2) The least amount perimeter comes from sum of the sides of a square.

Maximize Area = ( Perimeter4)2

Minimize Perimeter = 4 (√Area)

Example: Maximizing Area1) Find the largest possible rectangular area you can enclose

with 96 meters of fencing.

2) Find the largest possible rectangular area you can enclose with 324 meters of fencing.

Example #2: Minimizing Perimeter1) If you are given an area 625 square yards. Find the least

amount of perimeter that will needed to have this area.

2) If you are given an area 289 square meters. Find the least amount of perimeter that will needed to have this area.

Unit 3B Lesson 2: Coordinate ConnectionsFormulas you not forget…..

Proving a Quadrilater is a Parallelogram – show ONE pair of sides is BOTH parallel AND congruent

Example #1:

Proving a Quadrilateral is a Rectangle Show CONSECUTIVE sides are Perpendicular (Slope) Show OPPOSITE sides are congruent (distance)

Example #2:

You Try…

Unit 3B Lesson 4: Area & Surface Area

Formulas to know…

Example #1: Find the area

Example #2: Find the surface area

Example #3: Area Word Problems

Example 4: Surface Area word problems

Unit 3B Lesson 4: Volume

Example #1: Find the volume.

Example #2: Volume Word problems