#### FD 8 – MULTIPLICATIVE RELATIONSHIPS BETWEEN FRACTIONS

Children develop deep understanding of multiplicative relationships by building their own fraction wall.
They explain that fractions are named after their relationship to one.
They fold / divide a half in half to make a quarter, explaining that a quarter is half of a half.
They fold / divide a quarter in half to make an eighth, explaining that an eighth is half of a quarter. They fold / divide a half in quarters to make an eighth, explaining that an eighth is quarter of a half.
They fold / divide a fifth in half to make a tenth, explaining that a tenth is half of a fifth.
They fold / divide a third in half to make a sixth, explaining that a sixth is half of a third.
They fold / divide a sixth in half to make a twelfth, explaining that a twelfth is half of a sixth. They fold / divide a half in sixths to make a twelfth, explaining that a half is a sixth of a twelfth. They fold / divide a quarter in thirds to make a twelfth, explaining that a twelfth is a third of a quarter. They fold / divide a third in quarters to make a twelfth, explaining that a twelfth is quarter of a third.

As children create fractions, they identify that the denominator tells us the number we divided by.
This concept is intrinsically linked to division by single-digit numbers, because when we divide we are finding a fraction of the number – integrated Multiplication and Division 10, Multiplication and Division 11, Multiplication and Division 12, Multiplication and Division 13, Multiplication and Division 14, Multiplication and Division 15, Multiplication and Division 16, Multiplication and Division 17.