mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although re ...

at the

primary school A primary school (in Ireland, the United Kingdom, Australia, Trinidad and Tobago, Jamaica, and South Africa), junior school (in Australia), elementary school or grade school (in North America and the Philippines) is a school for primary ed ...

level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple

division Division or divider may refer to: Mathematics *Division (mathematics), the inverse of multiplication *Division algorithm, a method for computing the result of mathematical division Military *Division (military), a formation typically consisting ...

questions by repeated

subtraction Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...

. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial quotients. It has a counterpart in the

grid method The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of prima ...

for multiplication as well. In general, chunking is more flexible than the traditional method in that the calculation of quotient is less dependent on the place values. As a result, it is often considered to be a more intuitive, but a less systematic approach to divisionswhere the efficiency is highly dependent upon one's

numeracy Numeracy is the ability to understand, reason with, and to apply simple numerical concepts. The charity National Numeracy states: "Numeracy means understanding how mathematics is used in the real world and being able to apply it to make the bes ...

skills. To calculate the whole number

quotient In arithmetic, a quotient (from lat, quotiens 'how many times', pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a ...

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 zeroor the

remainder In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division). In alge ...

is less than the small number itself. At the same time the student is generating a list of the multiples of the small number (i.e., partial quotients) that have so far been taken away, which when added up together would then become the whole number quotient itself. 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 Because 10 + 5 + 1 = 16, 132 8 is 16 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 The National Numeracy Strategy arose out of the National Numeracy Project in 1996, led by a Numeracy Task Force in England. The strategy included an outline of expected teaching in mathematics for all pupils from Reception to Year 6. In 2003, t ...

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. Compared to the

short division In arithmetic, short division is a division algorithm which breaks down a division problem into a series of easier steps. It is an abbreviated form of long division — whereby the products are omitted and the partial remainders are notated as sup ...

and

long division In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (Positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. ...

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. The more freeform nature of chunking also means that it requires more genuine understandingrather than just the ability to follow a ritualised procedureto be successful.Anne Campbell, Gavin Fairbairn, ''Working with support in the classroom'', SAGE, 2005; pp
59–60
via Google books An alternative way of performing chunking involves the use of the standard long division tableauexcept that the partial quotients are stacked up on the top of each other above the long division sign, and that all numbers are spelled out in full. By allowing one to subtract more chunks than what one currently has, it is also possible to expand chunking into a fully bidirectional method as well.

References

Further reading