Transcript Decimals - Dalton State

Decimals
Children should be led to make their
own investigations, and to draw upon
their own inferences. They should be
told as little as possible which can
produce unlimited learning potential.
Herbert Spencer
Intellectual Moral and Physical
1864
McDonald’s Menu….
I’m Lovin It!!
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Double Cheeseburger: $ .99
Big Mac Value Meal: $ 4.79
Chicken McNuggetts Meal: $ 3.80
Small Drink: $ .99
McFlurry: $ 1.97
Salad: $ 4.80
2 Cheeseburger Meal: $ 3.70
Ice Cream Cone: $ .87
Order Up!
Least Expensive to Most Expensive
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Ice Cream Cone
Double Cheeseburger:
Small Soft Drink:
McFlurry:
2 Cheeseburger Meal:
Chicken McNuggetts Meal:
Big Mac Value Meal:
Chicken Salad:
.87
.99
.99
1.97
3.70
3.80
4.79
4.80
What Do I Mean Compare
Decimals?
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When we compare we use terms such as:
 Less
than <
 Greater than >
 Equal to =
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Comparing decimals is similar to comparing
whole numbers.
 45<47
 150>105
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When we compare decimals we use place value
or a number line.
Place Value
1,000
100
10
1
0.1
0.01
0.001 0.0001
Diving Results
Sara
42.1
Danny
42.5
Ross
42.0
Bethany
40.7
Jacob
46.1
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Compare Sara’s score
with Danny’s score.
1.
Line Up Decimal Points


2.
Sara:
42.1
Danny: 42.5
Start at the left and find the first
place where the digits differ.
Compare the digits
 1<5
 42.1 < 42.5
 This means Sara’s score was
lower than Danny’s score.
Let’s Try Using A Number Line
Sara
Danny
Ross
Bethany
Jacob
42.1
42.5
42.0
40.7
46.1
42
42.0 42.1
43
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 Decimals
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Decimals that name the same number
are called equivalent decimals.
 0.60 and 0.6
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Are these the same???
0.6
=
0.60
Annexing Zeros
This means placing a zero to the right of
the last digit in a decimal.
0.60
 0.6
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Although we added a zero, the value of
the decimal did not change!!
 Annexing or adding zeros is useful when
ordering a group of decimals.
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Ordering Decimals
We can order decimals from least to
greatest or we can order from greatest to
least.
 Let’s try an example:
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Order 15, 14.95, 15.8, and 15.01 from
least to greatest
15, 14.95, 15.8, 15.01
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First, line up the decimal points
15
14.95
15.8
15.01
15, 14.95, 15.8, 15.01
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Next, annex zeros so that each number has the
same number of decimal places
15.00
14.95
15.80
15.01
Finally, use place value to compare the decimals.
Always start from the left!!
14.95, 15, 15.01, 15.8
One More Example
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Order these numbers from greatest to
least
 35.06, 35.7, 35.5, 35.849
35.060
35.06
35.735.7, 35.849
35.700
35.06, 35.5,
35.5
35.500
35.849
Rounding Decimal Numbers
Sometimes close enough is good
enough!
Molly has $16 in her pocket
She buys:
3 hotdogs @ $1.89 each
3 milkshakes @ $2.19 each
3 Large French fries @ $ $1.79 each
Does she have enough money?
Gas costs $1.79 per gallon
I’m running on empty and I have a
20 gallon tank on my truck……
About how much will it cost to fill
up?
You have one hour to take a 50
question test.
About how much time can you
spend on each question?
Close enough is good enough!
The Rounding Poem
Find your number
Look right next door
4 or less, just ignore
5 or more add one more!
Rounding Whole Numbers
Round 474 to the closest
hundred.
500
474
Find your number
Look right next door
Four or less, just ignore
Five or more, add one more
Round 474 to the closest 10’s
474
Just ignore
470
Try These
4,215
394
27
127,591
638
What about decimal numbers
The same rules (and poem) apply!
Round 4.167 to the closest hundredths
4.167 Find your number
Look right next door
4.17
Five or more, add one more
Remember
If you are asked to round to
the nearest tenth…….your
answer
place!
stops at the tenth
Example: Round 42.73 to the
closest tenth would be 42.7
Special Case!
Rounding a 9
Round 2.197 to the
closes hundredths
Since there is a “9” in the hundredths
place consider the tenth and
hundredths together – 19 – do you
leave it at 19 or move it to 20?
Round 4.95 to the closest tenth
Since there is a “9” in the tenth
spot consider the ones and
tenths together…… should you
leave it at 49 or move it to 50?
4.95 rounded to the nearest tenth
is 5.0
Try these
Round to tenths:
Round to hundredths
4.56
4.6
18.784
18.78
5.32
5.3
9.456
9.46
0.98
1.0
9.997
10.00
Addition and Subtraction
What Does Addition Look Like?
Model using base ten blocks and an open number
line.
a) 13 + 18
b) 1.3 + 1.8
13
Show 2 different representations of the
mathematical thinking as you evaluate each
expression.
What Does Subtraction Look Like?
Model using base ten blocks and an open
number line.
a) 97 − 58
b) 9.7 − 5.08
9.7
Show 2 different representation of solutions for
each expression.
Reflect
1.
2.
3.
4.
Describe the strategies you used to
solve addition problems.
Describe the strategies you used to
solve subtraction problems.
a) How is adding whole numbers and
decimal numbers similar?
b) Different?
a) How is subtracting whole numbers
and decimal numbers similar?
b) Different?
Developing Conceptual
Understanding
The veterinarian told Camilla that the weight of her
puppy increased by 3.5 lb in the last month. If the
puppy weighs 15.6 lb now, what was its weight a
month ago?
a) Solve this problem in 2 different ways.
b) Show your work.
Compare your solutions.
How are they similar? different?
Alternative Algorithms
Traditional
Addition
1 1
348
+583
931
Partial-Sums Addition
1 1
3.48
+5.83
9.31
348
+ 583
800
120
11
931
34.8
+ 58.3
80.0
12.0
1.1
93.1
Alternative Algorithms
Adding-Up Subtraction
7.24
724
–
379 379 +
1
– 3.79
3.79 + 0.01
380 + 300
680 + 40
3.80 + 3.00
720 +
4
6.80 + 0.40
345
7.20 + 0.04
3.45
Practice
439.56
439.56
+ 88.10
417.66
+ 88.10
411.110
439.56
439.56
–
88.10
451.46
–
88.10
451.46
439.56
+ 88.10
41117.66
Sharing Strategies
1. What strategies do
you use to add and
subtract whole
numbers mentally?
257 + 39
257 − 39
2. What strategies do
you use to add and
subtract decimal
numbers mentally?
25.7 + 3.9
25.7 – 3.9
Mental Math for Addition
Adding On
Compensation
Constant Sum
136 + 143
236 + 297
153 + 598
136 + 100 = 236
236 + 40 = 276
276 + 3 = 279
236 + 300 = 536
536 – 3 = 533
Take 2 from 153
and add 2 to 598
151 + 600 = 751
So,
153 + 598 = 751
100
136
40
3
236 276 279
236
533 536
Mental Math for Subtraction
Partial
Subtraction
387 – 146
Compensation
387 – 100 = 287
287 – 40 = 247
247 – 6 = 241
547 – 300 = 247
247 + 4 = 251
So
547 – 296 = 251
6
40
241 247
547 – 296
100
287
387
247 251
547
Constant
Difference
598 – 153
Add 7 to 153 to
make it 160.
So, add 7 to 598.
605 – 160 = 445
Check:
153 + 445 = 598
Apply These Strategies
Joan is wondering whether the class’ hot lunch
sales were above or below the actual cost of the
lunches, $637.45. Here are the numbers she is
using.
Calculate using different mental math strategies:
1. 637.45 + 219.18
2. 637.45 – 219.18