BBC Maths: Numbers - Problem solving

Problem solving

1. Money problems

• Read the words of the problem carefully to decide whether
  to use adding, subtracting, multiplying or dividing.
• If some of the prices in the problem are in pence and some
  are in pounds, change some of them so they are either ALL
  in pounds or ALL in pence.
• Treat money problems just like normal number
  calculations, but remember to put the decimal point and
  pound symbol in the right place.
• Example: You buy a talking robot for £9.87 and a magazine
  for 73p. How much will you spend altogether?
  a) First make sure both amounts are in the same units.
  73p = £0.73.
  b) Then add the two amounts by lining up the decimal
  points.
  
  c) So the total you will spend is £10.60. (If you had
  worked this out on a calculator, you would have got 10.6.
  Remember to write this as £10.60.)
• Read the words of a money problem carefully to work out
  which calculations you need to do.
• Example: You can buy a 4-can pack of lemonade for £1.00
  or individual cans for 28p.
  Which is better value for money?
  a) Work out how much one can in the 4-can pack costs by
  dividing the price by the number of cans. £1.00 ÷ 4 = £0.25 or 25p.
  b) So the 4-can pack is better value because each can costs
  25p, that is 3p cheaper than individual cans.

2. Measures problems

• Read the words of the problem carefully to decide whether
  to use adding, subtracting, multiplying or dividing.
• It's really important to change the units of quantities so
  that ALL are in the same units before you start working out
  the answer.
• Example: Sophie is 1.29 m tall. Her little brother, Josh, is
  32 cm shorter. How tall is Josh?
  a) This is a subtraction problem. You need to take away 32 cm from Sophie's height.
  But you shouldn't work out 1.29 - 32 because the 1.29 is
  in metres and the 32 is in centimetres.
  Change so both are in the same units. 1.29 m = 129 cm.
  b) Then carry out the subtraction. 129 - 32 = 97 cm.
  c) So Josh is 97 cm tall.

3. Time problems

• Read the words of the problem carefully to decide whether
  to use adding, subtracting, multiplying or dividing.
• If some of the times in the problem are in seconds, some in
  minutes and some in hours, change some of them so they
  are either ALL in seconds, ALL in minutes or ALL in hours.
• When reading timetables, make sure you know what type
  of information is in each column and row.
• Example: How long does it take the 11.55 train from
  Normington to get to Kirfield?
  
  The empty space in the table means the 10:39 train from Normington doesn't stop at Baskwell.
  
  a) Look along the Normington row until you reach the
  column that starts with the 11.55.
  b) Look down that column until you get to Kirfield and
  read off the time, 12.44.
  Now you need to find the difference between 11.55 and
  12.44. A good way to do this is to break up the time into
  smaller steps.
  
  c) 5 + 44 = 49 minutes. So the 11.55 train from
  Normington takes 49 minutes to get to Kirfield.

QUIZ

• BBC Maths: Numbers - Using a calculator
• BBC Maths: Numbers - The number system
• BBC Maths: Numbers - Subtraction
• BBC Maths: Numbers - Problem solving
• BBC Maths: Numbers - Percentages
• BBC Maths: Numbers - Number patterns
• BBC Maths: Numbers - Multiplication
• BBC Maths: Numbers - Mental maths
• BBC Maths: Numbers - Fractions
• BBC Maths: Numbers - Division
• BBC Maths: Numbers - Decimals
• BBC Maths: Numbers - Addition