Research-based guidance and classroom activities for teachers of mathematics

# Division

 Division is a theme within ratio and proportional reasoning. Links to relevant activities and resources are on the right hand side of this page.

To get a full understanding of ratio, proportionality and the multiplicative relationship, learners’ early ideas of division as ‘sharing out’ or ‘grouping’ have to be put aside and more complex meanings developed instead.

Division arises in many ways:

• as a component of the multiplicative relationship
• as the inverse of multiplication achieved by reversing multiplication facts, usually associated with integers
• as algorithms that combine chunking numbers, reversing multiplication facts, and repeated subtraction until zero, a remainder, or a decimal representation is achieved
• in fraction notation where fractions are a meaningful outcome and representation of division, and cancelling by common factors simplifies the division
• with non-integer answers and hence leading to fractional answers
• as the result of partitioning continuous or discrete quantities, or unit quantities, or numbers, into n parts, expressed as fractions or decimals
• as the number of parts achieved for a given portion size (as fractions or decimals)
• as the ‘undoing’ of enlargement using a reciprocal scale factor

Oh! Harry!