estimation
DESCRIPTION
Clothing. Estimation. Groceries. Travel Costs. Construction. Computation Estimation. Simplified mental calculation. Computation estimation is : using some computation using easy mental strategies using number sense using a variety of strategies - PowerPoint PPT PresentationTRANSCRIPT
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Estimation
Clothing
Groceries
Travel Costs
Construction
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Computation Estimation
Computation estimation is: using some computation using easy mental strategies using number sense using a variety of strategies getting close to the exact answer
It is not: just a guess doing hand calculations using a calculator exact
Quickly and easily get a
number that is close
enough to the exact
answer to be useful
Simplifi
ed
mental
calcu
lation
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When do we estimate?
When there is no need to have an exact answer and an estimate is good enough: for example "Do I have enough money?"
When there is not enough information to get an exact answer: for example, "About how many times will my heart beat in an hour?"
To check if the answer from a calculation is reasonable.
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Estimation Vocabulary
Front-end: take only the first number, cut-off (truncate) the other numbers Adjusting with front-end: compensate for the values
that were truncated Compensation: adjust, amend, improve, revise, modify
your estimate, make it bigger, make it smaller
Rounding: round to the nearest to the desired place value
Compatible numbers: numbers grouped together to make computation easy
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Use a variety of strategies
There is not really any such thing as a "wrong" estimate... some estimates are less useful than others... any estimate made using the original problem is a
valid estimate.
The goal is not to find the one correct "estimate" but to have the skill to reason about the numbers being used, to be able to come up with a range that is suitable for using to predict the answer, and to have a quick and easy-to-do method for checking to see what a reasonable answer would be.
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Questions You Should Ask
"How did you get that answer?"
"Why do you think it's a reasonable answer?"
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Estimation Strategies
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Front-End Estimation
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8857
4758
7045
+ 2110
8857
4758
7045
+ 2110
8000
4000
7000
+ 2000
Draw the line after the first number
In each addend.
Front-End Estimation
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A. Between 11,000 and 15,000
B. Between 16,000 and 20,000
C. Between 20,000 and 25,000
D. Between 28,000 and 33,000
8000
4000
7000
+2000
21,000
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62,899
10,236
75,000
+ 37,596
62899
10236
75000
+ 37596
60,000
10,000
70,000
+ 30,000
Draw the line after the first number
In each addend.
Front-end Estimation
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A. Between 150,000 and 159,000
B. Between 160,000 and 169,000
C. Between 170,000 and 179,000
D. Between 180,000 and 189,000
60,000
70,000
10,000
+ 30,000170,000
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Use Front-end Estimation
Estimate the sum: 357,289 + 238,499 = _________
A.500,000 B.580,000 C.595,000 D.600,000
Is the front-end estimation reasonable? What could you do to improve the front-end
estimate?What is the best estimate and why?
No, it is low.
Estimate with compensation.
600,000 is a closer.
Use compatible numbers since 60,000 + 40,000 would be about 100,000 more.
500,000
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What error is acceptable?
The numbers: “59”, “54”, “55” are all “50” using front-end estimation.
1,999,999 + 1,999,999 = 2,000,000 What is a better estimate? Is the error acceptable?
Learn multiple estimation strategies. Always ask the question: Is the answer reasonable?
4,000,000No, 2,000,000 is too low.
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Rounding
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8857
4758
7045
+ 2110
8857
4758
7045
+ 2110
9000
5000
7000
+ 2000
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A. Between 11,000 and 15,000
B. Between 16,000 and 20,000
C. Between 20,000 and 25,000
D. Between 28,000 and 33,000
9000
5000
7000
+ 200023,000
Exact: 22,770
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247
6542
489
+ 92
247
6542
489
+ 92
200
6500
500
+ 100
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200
6500
500
+ 100
A. A little less than 7,000
B. A little more than 7,000
C. A little less than 8,000
D. A little more than 8,0007300
Exact: 7,370
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5028
6732
1285
+ 835
5000
7000
1000
+ 1000
5028
6732
1285
+ 835
14,000Exact: 13,880
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5028
6732
1285
+ 835
5000
6700
1300
+ 800
5028
6732
1285
+ 835
13,800Exact: 13,880
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Identify the estimation strategy
Front-End Rounding
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3,876
5,814
3,176
+ 7,895
4,000
6,000
3,000
+ 8,000
3,000
5,000
3,000
+ 7,000
Closer estimate
20,761 18,00021,000
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9,876
8,514
6,092
+ 3,895
9,000
8,000
6,000
+ 3,000
10,000
9,000
6,000
+ 4,000
Closer estimate
28,377 26,000 29,000
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Estimate
Front-End Roundingvs.
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A.Between 13,000 and 14,000
B.Between 12,000 and 13,000
C.Between 11,000 and 12,000
D.Between 10,000 and 11,000
5000
6700
1200
+ 800Exact:13700
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290
6840
481
+ 94
Exact: 7705
A. Between 6,500 and 7,000
B. Between 7,000 and 7,500
C. Between 7,500 and 8,000
D. Between 8,000 and 8,500
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Real World Problems
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23
Can I buy four for $100?
Yesa)4 x $25 = $100 and $23 is less than $25b)$23 rounds to $20 and 4 x $20 = $80c)$23 rounds to $25 and 4 x $25 = $100 (high estimate)
Explai
n
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$37
Can I buy three for $100?
Noa)3 x $33 is $99, so 3 x $37 would be more than $100.b)3 x $40 is $120
Explai
n
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The soccer ball would have to cost ______ or less for me to purchase five of them for $60.
Can I buy five for $60?
Noa)5 x $15 = $75 which is more than $60.b)5 x $14 = $70 which is more than $60.c)$60 divided by 5 = $12, and $13.87 is more than $12.00.
$12.00
Explai
n
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$4.95
Can I buy three for $20?
Yesa)3 x $5 = $15
Explain
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Would you have enough money?
Estimate to find your answer.
If you buy 3 items that cost $4.93 each, will $15.00 be enough to buy all 3 items? Explain.
If you buy 2 items for $6.29 and 1 item for $3.55 will $15.00 be enough? Explain.
If you buy items for $4.32, $6.90, and $7.86, will $18.00 be enough? Explain.
Yes, 3 x $5 = $15 (high estimate)
No, $4 + $7 + $8 = $19
No, 2 x $6 + 1 x $4 = $16
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0.1 or 10
0.01
or
100
0.001
or
1000
0.0001
or
10,000
1 digit 2 digits