Place Value

Thousands Hundreds Tens Ones Decimal Point

Tenths Hundredths

1 2 4 7 . 6 3

The place value chart below shows 1247.63

The number 1248.63 is one more than 1247.63

The number 1147.63 is one hundred less tan 1247.63

The number 1247.83 is two tenths more than 1247.63

Review Where is the decimal place?

34 $5698 508 67.89

HIDDEN DECIMAL

Review Arrange each set of numbers from greatest

to least! What strategy did you use? A) 1.8, 2.8, 1.9

B) 365.7, 358, 365.9

Review – Learn Alberta Place Valueshttp://www.learnalberta.ca/content/memg/index.html?term=Division02/Place_Value/index.html

Review – Adding and Subtracting Decimals

Review – Adding and Subtracting Decimals

2.1 Add and Subtract Decimals Pg 44 Vocabulary:

Estimate: to approximate an answer

Overestimate: Estimate that is larger than the actual answer

Underestimate: Estimate that is smaller than the actual answer

Where Does it Fit?Example #1

87.85 + 14.60 + 73.52 = 175.97Use Front-End Estimation:

Notice the leading digits 8,1 and 7 all represent tens!

***Think 80 + 10 + 70 = 160***

Using front-end estimation: 160 is a good estimation

Where Does it Fit?Example #1

87.85 + 14.60 + 73.52 = 175.97

Use Relative Size: The leading digits are all in the tens position, so

estimate each number to the nearest ten. 87.85 is between 80 and 90, and closer to 90 14.60 is between 10 and 20, and closer to 10 73.52 is between 70 and 80, and closer to 70***Think: 90 + 10 + 70 = 170***

Using relative size: 170 is a good estimation

Where Does it Fit?Example #1

87.85 + 14.60 + 73.52 = 175.97

Use Compensation: (try to round up - round down) The leading digits are all in the tens position, so

estimate each number to the nearest ten. 87.85 is closer to 90 (round up) 14.60 is closer to 10 (round down) 73.52 is closer to 70 (round down)***Think: 90 + 10 + 70 = 170***

Using compensation: 170 is a good estimation

Where Does it Fit?Example #1

87.85 + 14.60 + 73.52 = 175.97

Use Compatible numbers: (5’s, 10’s 50’s 100’s 1000’s)

87.85 is closer to 90 14.60 is closer to 10 73.52 is closer to 70 ***Think: 90 + 10 + 70 = 170***

Using compatible numbers: 170 is a good estimation

Try Another OneExample #2

4956.2 – 1542.1 = 3414.1Use Front-End Estimation:

Notice the leading digits 4,1 all represent thousands!

***Think 4000 – 1000 = 3000***

Using front-end estimation: 3000 is an OK estimation

Could we make a better estimation?

Try Another One?Example #2

4956.2 – 1542.1 = 3414.1

Use Relative Size: The leading digits are all in the thousands position, so

estimate each number to the nearest thousand. 4956.2 is between 5000 and 4000, and closer to 5000 1542.1 is between 2000 and 1000, and closer to 2000

***Think: 5000 – 2000 = 3000***

Using relative size: 3000 is a OK estimation

Try Another One?Example #2

4956.2 – 1542.1 = 3414.1

Use Compensation: (try to round up - round down) The leading digits are all in the thousands

position, so estimate each number to the nearest thousands.

4956.2 is closer to 5000 (round up) 1542.1 is closer to 2000 (round up)***Think: 5000 – 2000 = 3000***

Using compensation: 3000 is a OK estimation

Where Does it Fit?Example #1

4956.2 – 1542.1 = 3414.1

Use Compatible numbers: (5’s, 10’s 50’s 100’s 1000’s)

4956.2 is closer to 5000 1542.1 is closer to 1500

***Think: 5000 – 1500 = 3500***

Using compatible numbers: 3500 is the BEST estimation

Try It On Your Own! Rewrite each question using front-end

estimation. Then estimate each answer. A) 45 + 33 + 92

____ + ____ + ____ = ____

B) $475.12 - $210.38 _________ - ________ = ________

Is your estimate higher or lower than the calculated answer? _____________

Try It On Your Own!

Use any strategy to estimate the answers. A) 45 + 33 + 92

____ + ____ + ____ = ____

B) $475.12 - $210.38________ - ________ = _______

Try It On Your Own!

Using estimation, where would you put the decimal point in the answer? A) 631.5 + 902.4 + 217.83 = 175173

______ + ______+ ______ = _______

B) $475.12 - $210.38= $26474 _______ - _______ = _______

Try These On Your Own! For Homework Due Tomorrow! Pg 48. #4, 7, 8ac, 10ac, 14, 20, 21 Extend 22, 24, 25

Page 2.1 worksheet

Multiplying Decimal Numbers Problem: Page 52

Ashley and Marshall’s family keep busy travelling across the country by solving sudoku puzzles! During a stop, they look in a convenience store for more puzzles.

Marshall finds sudoku books on sale for $1.69. he wants to buy five books and has $9.00.

Help him estimate the total cost of the five puzzle books!

$1.69 x 5 = ______?

Multiplying Decimal Numbers 1. Marshall estimates the total bill as $5.00

a) How do you think Marshall got his estimate? b) Is Marshall’s estimate over or under the total?

How do you know?

2. Ashley estimates the total bill as $10.00 a) How do you think Ashley got her estimate? b) Is Ashley’s estimate over or under the total?

How do you know?

Sudoku

Sudoku was invented hundreds of years ago, and traded around the world by ancient mathematicians.Each digit from 1 to 9 must occur in:

Each rowEach columnEach 3 x 3 square.

DID YOU KNOW!!!!

Multiplying Decimals Use front-end estimation and relative size to

estimate: 2.65 x 3.72

Front-End Estimation:

Relative Size:

Multiplying Decimals

Estimate to make sure your answer is reasonable! Multiply 1.54 x 25

What strategy will you use?

Multiplying Decimals

Use a calculator to solve the equation:Multiply 1.54 x 25

25 x 1 = 25 25 x 2 = 50 HINT: The answer lies between 25 and 50.

Multiplying Decimals

Multiplying Decimals Learn Alberta

Practice Makes Perfect Page 57 3, 6ab, 9, 13, 14,17 Extend 20, 21

Dividing Decimal Numbers Example 1:

A) 15.4 ÷ 3.6 = 4.27778

Front-End Estimation: Think: 15 ÷ 3 = 5

The answer closest to 5 is 4.27778

Dividing Decimal Numbers Using a Number Line

Ex: 10 ÷ 2 =

Use Estimation to Place the Decimal Point.

Example #2:Four friends buy 1.36L of pure orange juice and

divide it equally. A) Estimate each person’s share. B) Calculate each person’s share.

Use Estimation to Place the Decimal Point.

Solution: A) To estimate, round 1.36L to a number that is

easier to work with. Try 1.2

1.2 ÷ 4 = 0.3 Underestimate Try 1.

1.6 ÷ 4 = 0.4 Overestimate

12 ÷ 4 = 3 So 1.2 ÷ 4 = 0.3

16 ÷ 4 = 4 So1.6 ÷ 4 = 0.4

Dividing Decimals Problem Questions:

1. How many pens do you think you can buy with $6.00 if one pen costs $0.40

Use both front-end estimation and relative size estimation to find your educated guess.

2. How many pens can you purchase! Calculate your answer.

Working Together!!

Pg 66 #10 A package of 7 fish hooks costs $17.99 How much will one fish hook cost?

1) Estimate

2) Calculate- by hand and with calculator

3) Did you over/under estimate?

ANSWER: $17.99 ÷ 7 = $2.57

Working Together! Pg 66 #11

Ashley wants to find how many 355 mL cans of juice are in a 2-L bottle.

A) Show Ashley how to estimate the answer

B) Show Ashley how to calculate the answers

Dividing Decimals Learn Alberta

http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10

Slides 6-10

Assignment Page 65 – 67 #4, 8, 12, 13, 14, 17, 19 Extend #21, 22

BEDMAS

Remember the order by the phrase

B - BRACKETS E - EXPONENTS D/M – DIVIDE OR MULTIPLY A/S – ADD OR SUBTRACT

The “B” and “E” The “B” stands for items in brackets Do all items in the brackets first

The “E” stands for ExponentsDo anything that has a exponent

(power)82

(2 + 3)

The “DM”

Represents divide and multiply Do which ever one of these comes first

in the problem

Work these two operationsfrom left to right

The “AS” Represents Add and Subtract Do which ever one of these comes first Work left to right You can only work with 2 numbers at a

time.

1) 5 + (12 – 3)

5 + 9

14

2) 8 – 3 x 2 + 72) 8 – 3 x 2 + 7

8 - 6 + 78 - 6 + 7

2 + 72 + 7

993) 39 ÷ (9 + 4)3) 39 ÷ (9 + 4)

39 ÷ 1339 ÷ 13

33

4) 10 + 8 ÷ 2 – 6 10 + 4 - 6 14 - 6 8

5)5) 15 x 1015 x 1033 15 x 15 x

1,0001,000 15 00015 000

6)6) 36 ÷ (1 + 2)36 ÷ (1 + 2)22

36 ÷ 336 ÷ 322

36 ÷ 936 ÷ 9 44

7) 3 x 107) 3 x 1044

3 x 10 3 x 10 000000

30 00030 000

8) (5 – 1)3 ÷ 4

43 ÷ 4

64 ÷ 4

16

9)9) 14 + 3(7 -2) – 2 x 514 + 3(7 -2) – 2 x 5

14 + 3 x 5 - 2 • 514 + 3 x 5 - 2 • 5

14 + 15 - 2 x 514 + 15 - 2 x 5

14 + 15 – 1014 + 15 – 10

29 – 1029 – 10

1919

Let’s Practice Place the operations shown in square

brackets to make each statement true. 9__ 5__5 = 50 (+, x)

15 __ 3 __2 = 24 (x,-)

Let’s Practice What are the missing numbers?

A) _____ + 5 x 6 = 32

B) _____ - 3.2 ÷ 0.5 = 5

Assignment Page 71-73 # 5, 6ab, 7ab, 9ab, 11, 14, 17, 18a, 19 Extend #22, 23, 24