Transcript Upper and lower bounds - Middle School Mathematics

Upper and lower bounds
starter
28 has been rounded to the nearest
whole number. What is the minimum
and maximum value?
Upper and lower bounds
 The lower bound is 27.5 and the upper
bound is 28.5
 To find the upper and lower bounds we
added and subtracted 0.5 because this is
half of one whole number
Upper and lower bounds
 240 has been rounded to the nearest ten.
 What are the minimum and maximum
values?
 What is the quick way of working out the
answer?
Upper and lower bounds
 The lower bound is 235 and the upper
bound is 245
 The quick way to work out the answer is to
add and subtract 5 because 5 is half of ten.
Upper and lower bound
 If a number is rounded to the nearest 100 what do
we add and subtract to find the minimum and
maximum values?
 If a number has been rounded to the nearest one
tenth what do we add and subtract to find the
minimum and maximum values?
 If the number has been rounded to the nearest ten
thousand what do we add and subtract this time?
Upper and lower bound
 When rounded to the nearest 100 we add
and subtract 50
 When rounded to the nearest one tenth we
add and subtract 0.05
 When rounded to the nearest ten thousand
we add and subtract 5,000
Write down the upper and lower
bounds with the following:
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56 to the nearest whole number
7.8 to the nearest tenth
3,400 to the nearest thousand
5.17 to the nearest hundredth
8,000,000 to the nearest million
570,000 to two significant figures
0.00006 to one significant figure
32,800,000,000 to three significant figures
Upper and lower bounds
 Objective: To do calculations involving
maximum and minimum using the four
arithmetic operations
A rectangle is measured as 5 cm by
8cm to the nearest cm.
 Write down the minimum and maximum
values for the lengths.
 Calculate the minimum and maximum
values for the perimeter of the rectangle.
 Calculate the minimum and maximum
values for the area of the rectangle.
 Minimum and maximum lengths are:
 4.5cm and 5.5cm
7.5cm and 8.5cm
A rectangle is measured as 5cm by
8cm to the nearest cm
 The perimeter is found by adding all four
sides together:
 Minimum perimeter is 4.5 + 7.5 + 4.5 + 7.5
which is 24cm.
 Maximum perimeter is 5.5 + 8.5 + 5.5+ 8.5
which is 28cm.
A rectangle is measured as 5cm by
8cm to the nearest cm
 Minimum area is 4.5 X 7.5 = 33.75
 Maximum area is 5.5 X 8.5 = 46.75
Addition and multiplication
 When adding numbers together the
minimum value is found by adding the lower
bounds together and the maximum value is
found by adding the upper bounds.
 When multiplying the minimum is found by
multiplying the lower bounds and the
maximum is found by multiplying the upper
bounds
In a month Fred earns £1200 to the
nearest hundred pounds and Mary
earns £1500 to nearest hundred
 What is the minimum and maximum
values?
 What is the minimum and maximum
difference in their earnings?
 Minimum and maximum values are:
 Fred: £1150 and £1250
 Mary: £1450 and £1550
Fred earns £1200 and Mary earns
£1500 to nearest hundred pounds
 Minimum difference in earnings will be found
as £1450 - £1250 = £200.
 Maximum difference in earning will be found
as £1550 -£1150 = £400.
Subtraction
 To find the minimum difference subtract an
upper bound from a lower bound.
 To find the maximum difference subtract a
lower bound from an upper bound.
Billy travelled 700 miles to nearest
hundred miles in 20 hours rounded
to nearest hour.
 Write down the upper and lower bounds for
the mileage and the number of hours.
 Calculate the minimum and maximum
average speed.
 Minimum and maximum values are:
 650 miles and 750 miles
 19.5 hrs and 20.5 hrs
Billy travelled 700 miles in 20 hours
 Minimum average speed is found by dividing
650 by 20.5 which is 31.7 mph
 Maximum average speed is found by
dividing 750 by 19.5 which is 38.5 mph
Division
 To calculate the minimum value divide the
lower bound by upper bound
 To calculate the maximum value divide the
upper bound by lower bound
Advice
 If you can not work out whether to use upper
or lower bounds in a question work out all
the possibilities!!!!
Plenary
 Volume of a cuboid 6cm by 4cm by 7cm
when lengths rounded to nearest whole
number.
 Three people earn £3,000 £5,000 and
£7,000 rounded to nearest thousand. What
is the total and average earnings?
 The distance between Sheerness and
Canterbury is 30 miles to nearest mile. What
is the distance between the places?