# Chunking (division)

In mathematics education at primary school level, **chunking** (sometimes also called the **partial quotients method**) is an elementary approach for solving simple division questions, by repeated subtraction. It is also known as the **hangman method** with the addition of a line separating the divisor, dividend, and partial quotients.^{[1]} It has a counterpart in the grid method for multiplication.

To calculate the result of dividing a large number by a small number, the student repeatedly takes away "chunks" of the large number, where each "chunk" is an easy multiple (for example 100×, 10×, 5× 2×, etc.) of the small number, until the large number has been reduced to zero or the remainder is less than the divisor. At the same time the student keeps a running total of what multiple of the small number has so far been taken away, which eventually becomes the final result of the sum.

So, for example, to calculate ^{132}⁄_{8}, one might successively subtract 80, 40 and 8 to leave 4,

132 80 (10 × 8) -- 52 40 ( 5 × 8) -- 12 8 ( 1 × 8) -- 4 -------- 132 = 16 × 8 + 4

to establish that ^{132}⁄_{8} is 16 (10+5+1) with 4 remaining.

In the UK, this approach for elementary division sums has come into widespread classroom use in primary schools since the late 1990s, when the National Numeracy Strategy in its "numeracy hour" brought in a new emphasis on more free-form oral and mental strategies for calculations, rather than the rote learning of standard methods.^{[2]}

Compared to the short division and long division methods that are traditionally taught, chunking may seem strange, unsystematic, and arbitrary. However, it is argued that chunking, rather than moving straight to short division, gives a better introduction to division, in part because the focus is always holistic, focusing throughout on the whole calculation and its meaning, rather than just rules for generating successive digits; and because its more free-form nature requires genuine understanding to be successful, rather than just the ability to follow a ritualised procedure.^{[3]}

## References

## Further reading

- Rob Eastaway and Mike Askew (2010),
*Maths for Mums and Dads*, Square Peg. ISBN 0-224-08635-9 - Khan Academy Arithmetic Course, Partial Quotient Method of Division: https://www.khanacademy.org/math/arithmetic/multiplication-division/partial-quotient-division/v/partial-quotient-division