Chunking (division)
Encyclopedia
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
.
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 with 4 remaining.
In the U.K. 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.
Compared to the short division
and long division
methods more traditionally taught, chunking may seem unfamiliar, and also unsystematic, even 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, focussing 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.
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
at primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
questions, by repeated subtraction
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
.
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 with 4 remaining.
In the U.K. this approach for elementary division sums has come into widespread classroom use in primary schools since the late 1990s, when the National Numeracy Strategy
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 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
Short division
In arithmetic, short division is a procedure which breaks down a division problem into a series of easy steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. Short division is an abbreviated form of...
and long division
Long division
In arithmetic, long division is a standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a...
methods more traditionally taught, chunking may seem unfamiliar, and also unsystematic, even 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, focussing 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.
Further reading
- Rob Eastaway and Mike Askew (2010), Maths for Mums and Dads, Square Peg. ISBN 0224086359