Copyright © University of Cambridge. All rights reserved.
'Making Shapes' printed from http://nrich.maths.org/
Sydney worked hard at this problem. He
I tried various combinations of numbers of dots to make rectangles.
I discovered by factoring each number of dots I could figure out
how many rectangles I could make out of each number of dots.
That is very well expressed. In other
words, by finding pairs of numbers that multiply together to make
each number of dots, you can find out how many rectangles there
are. Sydney continued:
So, all numbers make a skinny rectangle.
$6$ also makes a $2\times3$
$12$ dots make three rectangles: $1\times12$, $2\times6$, and
$8$ a $2\times4$
$10$ a $5\times2$
$12$ a $2\times6$ and $3\times4$
$14$ a $2\times7$
$16$ a $2\times8$
$18$ a $2\times9$ and $3\times6$.
Well done. I think by a "skinny rectangle" you
mean a rectangle which is just one row of counters?
Cong of St Peter's RC Primary School,
Aberdeen, points out that:
If a square can be thought as a special rectangle, then square
numbers $1$, $4$, $9$, $16$ can also make special rectangles as $1
= 1 \times 1$; $4 = 2 \times 2$; $9 = 3 \times 3$; $16 =
4 \times 4$
He also spotted that
$15$ counters can make a rectangle as $15 = 3 \times 5$
(three rows of $5$ counters).