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:  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  to one significant figure  32,800,000,000 to three significant figures

Upper and lower bounds OOO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 which is 24cm.  Maximum perimeter is which is 28cm.

A rectangle is measured as 5cm by 8cm to the nearest cm  Minimum area is 4.5 X 7.5 =  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 £ £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?