Sunday, 25 May 2014

Learning Basic Facts

Thinking Strategies for Learning Basic Facts

When students have a solid conceptual base of multiplication and division, they can then be presented with an array with all the addition/multiplication facts, OR build the array with the students, fact by fact.

First discuss the reasons and importance of committing the basic facts to memory.
  • Multiplication Tables are a quick way of adding, ONLY if you have memorised the facts
  • They are needed in all levels of mathematics learning and make maths EASY
  • They are needed in everyday life; 4 Big Macs at $3.95

Then use the array to:
  • help them organise the information in a way that is natural to them
  • help them to see and understand the mathematical connections (commutative, Family of Facts)
  • show them that there is a way to reason: (if I want 9 x 8; I could do 10 times 8 and take off 8; 5     times table is half of the ten times table)
The emphasis in helping the students learn the basic facts should be on aiding them in organising their thinking and seeing the relationships among the facts prior to memorising them.
Present the students with a blank grid on which they can systematically complete as they learn the facts (a record of their progress)
Using the completed grid to teach strategies and eliminate what they know.  ALTERNATIVELY, build an array using the following rules
  •  adding added does not change the number
  •  adding one.... we get one more
  •  doubles... both addends the same
  •  doubles plus one or doubles minus one
  •  order of addends .... 3 + 4  and 4 + 3  (what is the same? different?)
  •  adding to ten
  •  families of facts    
  • etc
Similarly with the ‘times’ tables:
  • Multiplying by zero…. we get zero
  • Multiplying by one …..we get the number we started with
  • Square numbers …… often the facts kids love to learn:  2x2, 3x3
  • Multiplying by ten …… the digits in the number move one place to the left (please DO NOT teach them to add a zero it is mathematically incorrect)

When using these thinking strategies talk to the students about
  • ‘how come? 
  • Why?’ 
 and aim at generalisations in their language.  Show them that there is a way to reason.  As they eliminate what they know they will see what is left to learn.There is still a place for:
            Chanting,    Singing,    Flash cards.   if the emphasis is on memorising KNOWN Facts   
  • after the children understand the facts
  • if they help children memorise basic facts!!