Warm-Up Change the following fractions to decimal

numbers. 1. 2/10 2. 13/17 3. 4/10 4. 397/100 5. 38/5 6. 16/5

Comparing and Ordering Comparing and Ordering DecimalsDecimals

When Will I Ever Do That???!!!When Will I Ever Do That???!!!Tuesday, February 1, 2011Tuesday, February 1, 2011

Homework Due TodayHomework Due TodayFind two equivalent ratios.Find two equivalent ratios.

1. 25/60 1. 25/60 ex: 5/12, 50/120ex: 5/12, 50/120 2.100/600 2.100/600 ex: 1/6, 2/12ex: 1/6, 2/12 3.20/80 3.20/80 ex: ¼, 2/8, 40/160ex: ¼, 2/8, 40/160

Homework Due TomorrowHomework Due Tomorrow

Monarch Type

Egg Caterpillar Pupa Butterfly

Regular 1 2 1 5Migrating 1 2 1 30

Length of Monarch’s Life Stages in Weeks

1. What fraction of a regular monarch’s life is spent as a butterfly?

2. What fraction of a migrating monarch’s life is spent as a butterfly?

2121stst Century Skills… Century Skills… Monarch ButterfliesMonarch Butterflies Some monarchs migrate as far as Some monarchs migrate as far as

2000 miles. If a 2000 mile migration 2000 miles. If a 2000 mile migration were to last for 3.5 months, what is were to last for 3.5 months, what is the average distance the monarchs the average distance the monarchs would fly in 1 day? ( Assume there would fly in 1 day? ( Assume there are 30 days in a month)are 30 days in a month)

McMcDoDonanaldld’s M’s Menenu….u….I’m Lovin It!!I’m Lovin It!!

Double Cheeseburger: $ .99Double Cheeseburger: $ .99 Big Mac Value Meal: $ 4.79Big Mac Value Meal: $ 4.79 Chicken McNuggetts Meal: $ 3.80Chicken McNuggetts Meal: $ 3.80 Small Drink: $ .99Small Drink: $ .99 McFlurry: $ 1.97McFlurry: $ 1.97 Salad: $ 4.80Salad: $ 4.80 2 Cheeseburger Meal: $ 3.702 Cheeseburger Meal: $ 3.70 Ice Cream Cone: $ .87Ice Cream Cone: $ .87

Order Up!Order Up!Least Expensive to Most Least Expensive to Most

ExpensiveExpensive Ice Cream Cone .87Ice Cream Cone .87 Double Cheeseburger: .99Double Cheeseburger: .99 Small Soft Drink: .99Small Soft Drink: .99 McFlurry: 1.97McFlurry: 1.97 2 Cheeseburger Meal: 3.702 Cheeseburger Meal: 3.70 Chicken McNuggetts Meal: 3.80Chicken McNuggetts Meal: 3.80 Big Mac Value Meal: 4.79Big Mac Value Meal: 4.79 Chicken Salad: 4.80Chicken Salad: 4.80

What Do I Mean Compare What Do I Mean Compare Decimals?Decimals?

When we compare we use terms such as:When we compare we use terms such as: Less than <Less than < Greater than >Greater than > Equal to =Equal to =

Comparing decimals is similar to Comparing decimals is similar to comparing whole numbers.comparing whole numbers. 45<4745<47 150>105150>105

When we compare decimals we use place When we compare decimals we use place value or a number line.value or a number line.

Place ValuePlace Value

1,0001,000 101000

1010 11 0.10.1 0.010.01 0.000.0011

0.0000.00011

Compare Sara’s score Compare Sara’s score with Danny’s score.with Danny’s score.

1.1. Line Up Decimal PointsLine Up Decimal Points Sara: 42.1Sara: 42.1 Danny: 42.5Danny: 42.5

2.2. Start at the left and find the Start at the left and find the first place where the digits first place where the digits differ. Compare the digitsdiffer. Compare the digits

1<5 1<5 42.1<42.542.1<42.5 This means Sara’s score was This means Sara’s score was

lower than Danny’s score.lower than Danny’s score.

SaraSara 42.142.1

DannyDanny 42.542.5

RossRoss 42.042.0

BethanBethanyy

40.740.7

JacobJacob 46.146.1

Half pipe Results

Let’s Try Using A Number Let’s Try Using A Number LineLine

SaraSara 42.142.1DannyDanny 42.542.5RossRoss 42.042.0BethanyBethany 40.740.7JacobJacob 46.146.1

42.0 42.1 42.5

Numbers to the right are greater than numbers to the left. Since 42.5 is to the right of 42.1 we have: 42.5>42.1

Equivalent DecimalsEquivalent Decimals Decimals that name the same Decimals that name the same

number are called equivalent number are called equivalent decimals.decimals.

0.60 and 0.6 0.60 and 0.6

Are these the same???Are these the same???

0.60

0.6=

AnnexingAnnexing Zeros Zeros This means placing a zero to the This means placing a zero to the

right of the last digit in a decimal.right of the last digit in a decimal. 0.6 0.600.6 0.60 Although we added a zero, the value Although we added a zero, the value

of the decimal did not change!!of the decimal did not change!! AnnexingAnnexing or adding zeros is useful or adding zeros is useful

when ordering a group of decimals.when ordering a group of decimals.

Ordering DecimalsOrdering Decimals We can order decimals from least to We can order decimals from least to

greatest or we can order from greatest or we can order from greatest to least.greatest to least.

Let’s try an example:Let’s try an example:

Order 15, 14.95, 15.8, and 15.01 Order 15, 14.95, 15.8, and 15.01 from least to greatestfrom least to greatest

First, line up the decimal pointsFirst, line up the decimal points 1515 14.9514.95 15.815.8 15.0115.01

15, 14.95, 15.8, 15.0115, 14.95, 15.8, 15.01

15, 14.95, 15.8, 15.0115, 14.95, 15.8, 15.01 Next, Next, annexannex zeros so that each zeros so that each

number has the same number of number has the same number of decimal placesdecimal places

15.0015.00 14.9514.95 15.8015.80 15.0115.01

15, 14.95, 15.8, 15.0115, 14.95, 15.8, 15.01 Finally, use place value to compare the Finally, use place value to compare the

decimals. Always start from the left!!decimals. Always start from the left!! 15.0015.00 14.9514.95 15.8015.80 15.0115.01 14.95, 15, 15.01, 15.814.95, 15, 15.01, 15.8

One More ExampleOne More Example Order these numbers from greatest Order these numbers from greatest

to leastto least 35.06, 35.7, 35.5, 35.84935.06, 35.7, 35.5, 35.849

Ordering Negative numbers…

You can also order negative numbers. The more negative a number, the

smaller it’s value. EXAMPLE: -10 is smaller than -5 EXAMPLE: -0.6 is smaller than -0.4

Lets try one: Order the following negative numbers: -5.4, -7, -4, -1.5 -6, and -5.5

MINI-LESSON: Square roots Cube Roots

Ordering Radicals… You can also order radicals:

Example: is greater than 1.25 Example: is less than 1.85

Lets try one: Order the following numbers:

-2, , 3, 2.5, -0.5

2

33

6

Ordering fractions… To order fractions it is best to

practice estimating, drawing pictures sometimes helps: Example: 5/7 is greater than 1/2 Example 1/3 is less than 1/2

Lets try: 13/7, 1/2, 3/4, 3/8, 11/10

Ordering Activity Each group will be given several

pieces of paper with fractions, decimals, percents, and radicals on them.

Each group will construct a number line and place the numbers in their correct locations on the number line.

Exit Ticket:Place the following numbers in order

from greatest to least.1. 0.75, 0.615, 0.58, 0.1952. -1, 1/2, -0.32, 3/4Place the following numbers in order

from least to greatest.3. -5, - , 0, 3.3, 0.06, 4. -3/4, , 0.5, 2/5, -1/8

5

13

83