1.2 Modeling Quantities

Today’s Target: I will be able to use rate, ratios and

proportions to create scale drawings and models, convert measurements and

determine lengths.

How much would 1 can of apple juice cost?

Once you know how much one costs, you can find the cost of any number of items.

What would you need to do to figure out how much 7 eggs cost?

How much would 3 bottles of blackberry

soda cost?

Unit Rate• A rate in which the denominator of the fraction is 1 unit.

Ex: Miles per hourCost per ounceTickets per dollar

Find the unit rate.• 1.

• 2.

• 3.

Vocabulary

Ratio: a comparison of two numbers by division

Proportion: an equation that states that two ratios are equal

Page 15• A totem pole that is 90 feet tall casts a

shadow that is 45 feet long. At the same time, a 6-foot tall man casts a shadow that is x feet long.

• The man and the totem pole are both perpendicular to the ground, so they form right angles with the ground. The sun shines at the same angle on both, so similar triangles are formed.

Complete page 15 with your table.

Using scale drawings and models

to solve problems...

• Scale: a ratio of any length in a scale drawing or scale model to corresponding actual lengths

• Scale drawing: a drawing that uses a scale to represent an object as smaller or larger than the original object

• Scale model: a three-dimensional model that uses a scale to represent an obect as smaller or larger than the actual object.

Page 16

• The actual distance from Chicago to Evanston is 11.25 miles. What is the distance on the map?

• Complete page 16 with your table.

1 in: 18 mi

Using Dimensional Analysis to Convert Measurements

• Convert 14 ft/sec to miles per hour

=∙1𝑚𝑖5280 𝑓𝑡

∙60 𝑠𝑒𝑐1𝑚𝑖𝑛

Pages 17 - 18

• Use dimensional analysis to convert measurements: Complete page 17 with your table.

• Use dimensional analysis to convert and compare rates: Complete page 18 with your table.

Page 19

• Graphing a proportional relationship: compete page 19 with your table.

• When done be able form a conclusion about unit rates.

Homework

• Due• Page 21 #1– 26 skip 25 (Be sure to show the units of your proportion)