• Mastery PD Materials

Structures: quotitive and partitive division

Spine 2: Multiplication and Division – Topic 2.6

Introduction

Introduce the quotitive and partitive structures of division; skip count using the divisor, or use known multiplication facts, to find the quotient; generalise about the quotient when dividend = 0, dividend = divisor, or divisor = 1.

Teaching points

  • Teaching point 1: Objects can be grouped equally, sometimes with a remainder.
     
  • Teaching point 2: Division equations can be used to represent ‘grouping’ problems, where the total quantity (dividend) and the group size (divisor) are known; the number of groups (quotient) can be calculated by skip counting in the divisor. (quotitive division)
     
  • Teaching point 3: Division equations can be used to represent ‘sharing’ problems, where the total quantity (dividend) and the number we are sharing between (divisor) are known; the size of the shares (quotient) can be calculated by skip counting in the divisor. (partitive division)
     
  • Teaching point 4: Strategies for finding the quotient, that are more efficient than skip counting, include using known multiplication facts and, when the divisor is two, using known halving facts.
     
  • Teaching point 5: When the dividend is zero, the quotient is zero; when the dividend is equal to the divisor, the quotient is one; when the divisor is equal to one, the quotient is equal to the dividend.

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