Transcript Estimate - Notre Dame Academy

Place Value
 The place value chart below shows 1247.63
Thousands
1
Hundreds Tens
2
4
Ones
7
Decimal
Point
Tenths
.
6
Hundredths
3
 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 Values
http://www.learnalberta.ca/content/memg/index.html?term=Division02/Place_Value/index.html
Review – Adding and Subtracting Decimals
What do you need to do?
2.
Line up the decimals
Add zeros into place values that are empty (if you wish)
3.
Ex: 12.3 + 2. 4 =
1.
12.3
+ 2.4
14.7
12.3
+ 02.4
14.7
Review – Adding and Subtracting Decimals
What do you need to do?
2.
Line up the decimals
Add zeros into place values that are empty (if you wish)
3.
Ex: 187.415 + 34.6 =
1.
187.415
187.415
1.
+ 34.6
+ 034.600
2.1 Add and Subtract Decimals

Pg 44 Vocabulary:
 Estimate:


Overestimate:


to approximate an answer
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 = 175.97
Use 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 One
Example #2

4956.2 – 1542.1 = 3414.1
Use 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
DID YOU
KNOW!!!!
 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 row
Each column
Each 3 x 3 square.
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

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
25 x 1 = 25
25 x 2 = 50
HINT: The answer lies between 25 and 50.
Multiplying Decimals



Using paper and pencil
Multiply without decimals add decimals to
product
Ex: 2.6 x 3.7=
26
x 37
962
Multiplying Decimals Learn Alberta
http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10
Slides 1-5
Practice Makes Perfect

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
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
16 ÷ 4 = 4 So
1.6 ÷ 4 = 0.4
12 ÷ 4 = 3 So
1.2 ÷ 4 = 0.3
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)
2)
3)
Estimate
Calculate- by hand and with calculator
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
(2 + 3)
The “E” stands for Exponents
Do anything that has a exponent (power)
2
8
The “DM”


Represents divide and multiply
Do which ever one of these comes first
in the problem
Work these two operations
from 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
3) 39 ÷ (9 + 4)
39 ÷ 13
3
2) 8 – 3 x 2 + 7
8 - 6 +7
2 + 7
9
4)
6)
10 + 8 ÷ 2 – 6
10 + 4 - 6
14 - 6
8
36 ÷ (1 + 2)2
36 ÷ 32
36 ÷ 9
4
5)
15 x 103
15 x 1,000
15 000
7) 3 x 104
3 x 10 000
30 000
8)
(5 – 1)3 ÷ 4
43 ÷ 4
64 ÷ 4
16
9)
14 + 3(7 -2) – 2 x 5
14 + 3 x 5 - 2 • 5
14 + 15 - 2 x 5
14 + 15 – 10
29 – 10
19
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