20771_Problem_solving_Year_6_Background_information_resources

A NOTE ON CALCULATOR USE
Many of the problems in this series demand the use of a number of consecutive calculations, often adding, subtracting,
multiplying or dividing the same amount in order to complete entries in a table or see a pattern. This demands (or
will build) a certain amount of sophisticated use of the memory and constant functions of a simple calculator.
1. To add a number such as 9 repeatedly, it is sufficient
on most calculators to enter an initial number (e.g.
30) then press + 9 = = = = to add 9 over and over.
• 30, 39, 48, 57, 66, …
• To add 9 to a range of numbers, enter the first number
(e.g. 30) then press + 9 = 30 + 9 = 39, 7 = gives 16, 3 =
gives 12, 21 = gives 30, …
• These are the answers when 9 is added to each
number.
2. To subtract a number such as 5 repeatedly, it is
sufficient on most calculators to enter an initial
number (e.g. 92) then press – 5 = = = = to subtract 5
over and over.
• 92, 87, 82, 77, 62, …
• To subtract 5 from a range of numbers, enter the first
number (e.g. 92) then press – 5 = 95 – 5 = 37, 68 =
gives 63, 43 = gives 38, 72 = gives 67, …
• These are the answers when 5 is subtracted from each
number.
3. To multiply a number such as 10 repeatedly, most
calculators now reverse the order in which the
numbers are entered. Enter 10 x, then press an initial
number (e.g. 15) = = = = to multiply by 10 over and
over.
• 10, 150, 1500, 15 000, 150 000, …
• These are the answers when the given number is
divided by 8.
• This also allows squaring of numbers: 4 x = gives 16 or
42.
• Continuing to press = gives more powers:
• 4 x = = gives 43 or 64, 4 x = = = gives 44; 4 x = = = =
gives 45 and so on.
• To multiply a range of
numbers by 10, enter 10 x
then the first number (e.g. 90)
and =
• 10 x 90 = 900, 45 = gives 450,
21 = gives 210, 162 = gives
1620, …
• These are the answers when
each number is multiplied by
10.
CALCULATOR BSCX56
AC %
900
ON
OFF
MRC M– M+ CE
7 8 9 ÷
4 5 6 x
1 2 3 –
0 . = +
4. To divide by a number such as 8 repeatedly, enter a
number (e.g. 128).
• Then press ÷ 4 = = = = to divide each result by 4.
• 32, 16, 8 , 2, 0.5, …
• These are the answers when the given number is
divided by 8.
• To divide a range of numbers by 8, enter the first
number (e.g. 90) and ÷ 4 = 128 ÷ 4 = 32, 64 = gives 4,
32 = gives 8, 12 = gives 1.5, …
• These are the answers when each number is divided
by 8.
5. Using the memory keys M+, M– and MR will also
simplify calculations. A result can be calculated and
added to memory (M+). Then a second result can be
calculated and added to (M+) or subtracted from (M–)
the result in the memory. Pressing MR will display
the result. Often this will need to be performed for
several examples as they are entered onto a table or
patterns are explored directly. Clearing the memory
after each completed calculation is essential!
A number of calculations may also need to be
made before addition, subtraction, multiplication
or division with a given number. That number can
be placed in memory and used each time without
needing to be re-keyed.
6. The % key can be used to find percentage increases
and decreases directly.
• To increase or decrease a number by a certain per cent
(e.g. 20%), simply key the number press = 20% or –
20% to get the answer:
• 80 + 20% gives 96 (not 100) – 20% of 80 is 16, 80 + 16
is 96.
• 90 – 20% gives 72 (not 70) – 20% of 90 is 18, 90 – 18
is 72.
7. While the square root key can be used directly,
finding other roots is best done by a ‘try and
adjust’ approach using the multiplication constant
described above (in point 3).
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