Transcript Rounding and Estimation PowerPoint

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
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.
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
 Clustering: numbers “cluster” around a value
 Compatible numbers: numbers grouped together
to make computation easy
Guess vs. Estimate
 If a local building contractor presented you with a
“guess” at how much it was going to cost you to build
your new house, you'd still be in the dark on what the
actual cost would be. If the builder guessed wrong,
he/she would likely go broke through either accepting
jobs for which the guess was far too low or lose jobs
that the guess was too high. Contractors “bid” on jobs,
so a close estimate is important.
 An actuary (a mathematician who looks at statistical
information) guessing how much his company would pay
in claims that year, then using that guess to set his
company's insurance rates, could in the same (sinking)
boat.
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.
Questions You Should Ask
"How did you get that
answer?"
"Why do you think it's a
reasonable answer?"
Estimation
Strategies
Front-End
Estimation
Front-End Estimation
8857
+
4758
8857
8000
4000
4758
7045
7000
7045
2110
+ + 2110
2000
Draw the line after the
first number
In each addend.
8000
A. Between 11,000 and 15,000
4000
B. Between 16,000 and 20,000
7000
C. Between 20,000 and 25,000
+2000
D. Between 28,000 and 33,000
21,000
Front-end Estimation
+
62,899
62899
60,000
10,236
10,000
10236
75,000
70,000
75000
37,596
+ + 37596
30,000
Draw the line after the
first number
In each addend.
60,000
A. Between 150,000 and 159,000
70,000
B. Between 160,000 and 169,000
10,000
C. Between 170,000 and 179,000
+ 30,000
170,000
D. Between 180,000 and 189,000
Use Front-end Estimation
 Estimate the sum:
500,000
357,289 + 238,499 = _________
A. 500,000
B. 580,000
C. 595,000
D. 600,000
Is the front-end estimation reasonable? No, it is low.
What could you do to improve the front-end
estimate? Estimate with compensation.
What is the best estimate and why? 600,000 is a closer.
Use compatible numbers since 60,000 + 40,000 would be about 100,000 more.
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? 4,000,000
 Is the error acceptable? No, 2,000,000 is too low.
Learn multiple estimation strategies.
Always ask the question:
Is the answer reasonable?
http://www.aaamath.com/grade3.html
Rounding
8857
+
4758
8857
9000
5000
4758
7045
7000
7045
2110
+ + 2110
2000
9000
A. Between 11,000 and 15,000
5000
B. Between 16,000 and 20,000
7000
+ 2000
23,000
Exact: 22,770
C. Between 20,000 and 25,000
D. Between 28,000 and 33,000
+
247
247
200
6542
6500
6542
489
489
500
92
++ 100
92
200
6500
500
+
100
7300
Exact: 7,370
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 8,000
5028
5028
5000
6732
6732
7000
1285
1285
1000
+ 835
835
++ 1000
Exact: 13,880
14,000
5028
5028
5000
6732
6732
6700
1285
1285
1300
+ 835
++ 800
835
Exact: 13,880
13,800
Identify the
estimation strategy
Front-End
Rounding
3,876
4,000
3,000
5,814
6,000
5,000
3,176
3,000
3,000
+ 7,895
20,761
+ 8,000
21,000
+ 7,000
18,000
Closer estimate
9,876
9,000
10,000
8,514
8,000
9,000
6,092
6,000
6,000
+ 3,895
+ 3,000
+ 4,000
28,377
26,000
29,000
Closer estimate
Estimate
Front-End
vs.
Rounding
5000
A. Between 13,000 and 14,000
6700
B. Between 12,000 and 13,000
1200
C. Between 11,000 and 12,000
+ 800
Exact:13700
D. Between 10,000 and 11,000
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
Real World Problems
Can I buy four for $100?
Yes
a) 4 x $25 = $100 and $23 is less than $25
b) $23 rounds to $20 and 4 x $20 = $80
c) $23 rounds to $25 and 4 x $25 = $100 (high estimate)
Can I buy three for $100?
$37
No
a) 3 x $33 is $99, so 3 x $37 would be more than $100.
b) 3 x $40 is $120
Can I buy five for $60?
No
a) 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.
The soccer ball would have to cost ______
$12.00 or less for me to purchase five of
them for $60.
Can I buy three for $20?
Yes
a) 3 x $5 = $15
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.
Yes, 3 x $5 = $15 (high estimate)
 If you buy 2 items for $6.29 and 1 item for
$3.55 will $15.00 be enough? Explain.
No, 2 x $6 + 1 x $4 = $16
 If you buy items for $4.32, $6.90, and $7.86, will
$18.00 be enough? Explain.
No, $4 + $7 + $8 = $19
0.01
0.001
or
or
100
1000
0.0001
or
0.1 or 10
10,000
1 digit
2 digits