Problem Teachers' Notes Solution

Four Goodness Sake

$1 = (4/4) * (4/4)$
$2 = (4/4) + (4/4) $
$3 = (4 + 4 +4 ) / 4$
$4 = (4/4) * \sqrt{4*4}$ or $4! - [(4+4)/.4]$
$5 = (4/4) + \sqrt{4*4}$
$6 = 4 + [(4 + 4) / 4]$
$7 = 4 + (4/4) + \sqrt{4}$
$8 = [(4+4)/4] * 4$
$9 = [4* \sqrt{4] + (4/4)}$
$10 = [4* \sqrt{4} + [4/ \sqrt{4}]$
$11 = [4! / \sqrt{4}] - (4/4)$
$12 = (4*4) - [ \sqrt{4*4}]$ or$(4 + 4) + [ \sqrt{4*4}]$
$13 = (4*4) - [ \sqrt{4*4}]$
$14 = (4 * 4) - [4/\sqrt{4}]$
$15 = (4 * 4) - (4/4)$
$16 = (4*4) * (4/4)$ or $[(4*4)/.4] - 4!$
$17 = (4 * 4) + (4 /4)4$
$18 = (4*4) + [4/ \sqrt{4}] $or $4! + 4 - (4/.4)$
$19 = 4! - [4 + (4/4)]$
$20 = 4! - [4* (4/4)]$

This was quite a challenge and lots of you obviously had a really good go at it. These are from pupils at Moorfield Juniors.

Adam, Abbey and Gemma arrived at $12$ like this:
$4/4=1$ $4-1=3$ $3$x$4=12$

Jimbo and Matt P worked out ways to get $15, 16$ and $17$:
$4/4=1$ $4$x$4-1=15$
$4+4+4+4=16$
$4/4=1$ $4$x$4+1=17$

Numbers $1-9$ were a little harder but you coped very well! Among the correct solutions were these from Emma, Amy, Matthew, Hannah, Steven and Jenny:

    $4-4=0+4=4-4=0$
    $4-4=0+4=4/4=1$
    $4/4=1+1=2$
    $4*4=16-4=12/4=3$
    $4-4=0$x$4=0+4=4$
    $4*4=16+4=20/4=5$
    $4+4=8/4=2+4=6$
    $4+4=8-4/4=1 8-1=7$
    $4+4=8$x$4=32/4=8$
    $4+4=8 ; 4/4=1+8=9$

Well done for getting these, but could they have been written down in a slightly better way do you think?

Getting $10$ was rather tricky. Pupils at Ysgol Gynradd found a solution but using square roots:

Square root of $4$ + square root of $4+$square root of $4 +4 =10$ .