Multiplication and Division

Multiplication and Division

1. Multiplication

   • Terminology
     • multiplicand is the number being multiplied.
     • multiplier is the number by which something is multiplied.
     • product is the result/answer
     • per means 'for each'
   • Laws
     • associative law is the idea that it does'nt matter how you group numbers when you add.
     • distributive law means that you get the same answer when you multiply a number by a group of numbers added together as when you do each multiplication separately
     • commutative law means that for additon and multiplication, it does not matter on the order to the sum.
   • Methods
     • Mental
       • repeated aggregation is repeated addition to multiply.
       • doubling
       • partitioning to separate via place value to make multiplication smaller
       • counting in steps up to a number allows children to break-down multiplication
       • recalling number facts
         • also, using known facts and then adjusting to get children near to an answer
       • using place value/distributivity
       • using factors allows children to access difficult multiplication
     • Written
       • the grid method involves partitioning of the numbers and then working through individual multiplications
       • expanded written method involves detailed written multiplication
       • compact method involves mental calculation with a simple written structure

2. Division

   • Different situations:
     • equal-sharing
       • quantity is shared evenly between a set number of portions.
         • sharing toys, sharing sweets etc.
     • inverse-of-multiplication
       • how many group of 4 are in 20?
         • how many classes do we need?
     • ratio structure
       • using division to compare quantities
         • money or measurments
     • inverse of multiplication
   • Terminology
     • Quotient is the result of a division
     • the dividend is the number to be divided
     • divisor is the number by which something is divided.
   • Laws
     • distributive law is that you can distribute a division across a subtraction or addition
   • methods
     • written
       • chunking is the breaking-down of a division into multiples
       • short division is a simplified version of long division that relies more on mental calculation
       • long division is an expanded method which requires written division in a complex and detailed form.
     • mental
       • repeated subtraction works by repeating minus operations until the answer is found.
       • sharing works by allocating a set number of groups a value of the total
       • grouping works by establishing groups within the total
       • counting in steps involves counting up to an answer in set stages
       • recalling facts
       • factorising the second number allows children to make smaller division steps

3. the relationship between division and multiplication...

   • inverse operations
     • They act in opposite of each other. This is often called BOGOF. For example if 7x3=21 then 21 divided by 3 is 7

4. Common misconceptions

   • multiplication is not repeated addition
   • dividing is taking away
   • 0 is not a place holder

5. Useful resources...

   • dienes
   • whiteboards and pens
   • objects to share/group