Wake-up Place old Wake-up in the Bin Convert the following: 5.0cm to m 10.9m to mm 3.5mm to km Calculate how many seconds are in a school day (8am-3:00pm). Show your work.

Dimensional Analysis and Factor Labeling

A cat is 12 long.

Math uses numbers. Science uses quantities which are described by numbers and a unit. The unit gives meaning to the number. The cat is 46cm long. The cat is 460mm long. The cat is 18.1 in long.

Factor labeling/Dimensional Analysis a. Problem solving method used to convert the units of a number into different units

Factor Labeling/Dimensional Analysis b. Accomplished by multiplying the number by a conversion factor.

Conversion Factor Two numbers, each with different units, which are mathematically equivalent to each other.

Equivalent Values Open the bag and find equivalent values related to familiar items. Can you arrange them? Are the measurements equivalent?

English to Math Translations 1 can equivalent to 3 balls 1 can = 3 balls 1 can per 3 balls 1 can 3 balls

1 loaf equivalent to 24 slices 1 loaf = 24 slices 1 loaf per 24 slices 1 loaf 24 slices

1 carton equivalent to 12 eggs 1 carton = 12 eggs 1 carton per 12 eggs 12 eggs 1 carton

CONVERSIONS Use equivalent values to move from one measurement to another 1 dozen eggs = 12 eggs ….. 12 eggs = 1 dozen Using fractions, this can be expressed: 1 dozen OR 12 eggs 12 eggs 1 dozen

How many eggs are in 15 dozen? Let’s Practice #1…. How many eggs are in 15 dozen?

Factor Label/Dimensional Analysis Set-up and Rules 1. Draw an empty grid (initially like a plus sign); leave room for potential work

Factor Label/Dimensional Analysis Set-up and Rules 2. Start with what is given (number and unit); place desired unit after the equal sign. 15 dozen = Eggs

Factor Label/Dimensional Analysis Set-up and Rules 3. Select an equality that contains both the units of the known quantity and the desired units 1 dozen = 12 eggs

Factor Label/Dimensional Analysis Set-up and Rules 4. Create a conversion factor by writing: Desired units Known units

Practice 15 dozen 12 eggs = Eggs 1 dozen

Factor Label/Dimensional Analysis Set-up and Rules 5. Make sure that units cancel along the way

Practice 15 dozen 12 eggs = Eggs 1 dozen

Factor Label/Dimensional Analysis Set-up and Rules 6. Everything on top (side by side) on the grid is multiplied and everything on the bottom is divided

Practice 15 dozen 12 eggs = 180 Eggs 1 dozen

Factor Label/Dimensional Analysis HINT Smaller number goes with the larger unit; larger number goes with the smaller unit

Factor Label/Dimensional Analysis: Practice #2 How many wheels are there on 350 Toyota trucks? (1 pickup = 4 tires) 350 Pickups 4 Tires = 1400 Tires 1 Pickup

Calculate how many seconds are in a school day (8am-3:00pm)

Calculate how many seconds are in a school day (8am-3:00pm) 7 hours in a school day = ? seconds 60 minutes 60 seconds 7 hours = 25200 sec. 1 hour 1 minute

Practice #4 You're throwing a pizza party for 15 people. Each person will eat 4 slices. Each pizza costs $14.50 and has 12 slices per pizza. How much is the pizza going to cost you? Arrange pizza equivalences from bag.

RAILROAD: Factor-Label Method START: by writing down given 1 party 15 people party given 1 NEXT: bring down given unit NEXT: THINK and LINK NEXT: cancel and continue

How much will the pizza cost for one party of 15 people? 4 slices 1 pizza $14.50 = ? cost 1 party 1 person 12 slices 1 pizza $72.50