Maths Resource: Multiplication (Part 1)

Maths Resource: Multiplication (Part 1)Author(s): Shropshire Centre for Mathematics EducationSource: Mathematics in School, Vol. 22, No. 4 (Sep., 1993), pp. 22-27Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30215026 .

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Multiplication (part 1) by Shropshire Centre for Mathematics Education

By grouping a random arrangement of dots consistently, pupils can discover that they can calculate, rather than count the quantity. On MRes 190 pupils can investigate what sums are produced when the same collections of dots are grouped according to a different rule each time.

5 (3) +Z2 /5 2 2-/7

4L )+=/ 7 /6 - / 7

a (53 +2 I/S52z -/7

It is not uncommon to find that pupils are surprised that the different calculations produce the same answer. This idea can be further reinforced by modelling each grouping decision with Cuisenaire rods:

7(2)

4(3)+ 2

2(5) +4

MRes 191 provides an opportunity to apply this principle of grouping to discover which collection of dots is the largest.

IC3) =r 2 / 3(3) 42(4/) l -t - 1/7

/- + /o2 (5) 10~-l =

Having established that the benefit of grouping over counting is that it reduces the risk of counting errors, it becomes more appropriate to focus upon non-random groupings. Here, pupils are encouraged to make sensible decisions about how to group, by looking carefully at the spatial arrangements of dots. Attention can be focused upon the way the number of dots (or

(continued on page 27)

22 Mathematics in School, September 1993



M Res 190 @

Mathematics in School, September 1993 23



MRes 191 @




MRes 192




MRes 193




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(continued from page 22)

squares) in a rectangular array can be calculated by playing a simple dice game. Each player takes turns to throw two dice. A rectangle is drawn with the dimensions shown on the dice, and each player is asked to find a quick way of discovering how many squares are inside the rectangle that has been drawn.

s

112

On MRes 192, this principle can be reinforced in a game called "100 dots". Each player takes turns to throw two dice. A rectangular array of those dimensions is shaded in and the multiplication fact recorded underneath. When eight facts have been recorded the sub-totals are added to reveal the total number of dots out of the 100 that have been shaded.

FxOll x FBI lrumaz

M x []= 9xWk

N 1x liJ F2_1 x rs N3x = (a) axaI~a axa- -"-I

/OX3 =30

7)c3.- t /

$r3=/12.

1751

3x3. 9

/a -25 IV -2 5

S75

The challenge posed by MRes 193 is to find different ways of partition- ing dot arrays so that adding sums of the products produces the same total.

An alternative strategy is to focus on the smaller quantity of dots that are not highlighted and subtracting them from 100.

In part 2, we shall consider ways of extending these ideas and developing skills of solving "long multiplication" sums through making sensible choices.

(Multiplication tasks are included in the Teachers' Handbook "DEVELOPING A FEELING FOR NUMBER" available from the Centre 0743 232761.)




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Maths Resource: Multiplication (Part 1)