Mathematics

: Billy Goat's Pen

Approach: Station
Resources: Video, model fence (12 flexible linked 'gates'), marker pen, ruler, graph answer sheet (wall ruled in).
Questions / instructions:
		% responses
		y4	y8
Watch the video about a farmer who wants to make a pen for the family's billy goat. The farmer drew a plan that looked like the one on the squared paper. Look at it now.
1. Draw plans to show all of the different ways that the pen could be made. The pen: must use all of the 12 pieces of fence. must have 3 sides of fencing and use the wall for the fourth side. must be a square or an oblong. Draw your plans on the answer sheet.	number of correct shapes: 4		9
	3		23
	2		30
	1		21
	0		17
	number of incorrect shapes: 0		58
	1		25
	2		7
	<2		10
2. Each piece of the real fence is 2 metres long. If the farmer built the pen shown on the plan, what would the area of the pen be? Write your answer inside the pen.	64		9
	32		9
	16		10
3. Put a big tick inside the pen that has the largest area.	largest valid pen		43
	largest pen (not valid)		8
Commentary: Few year 8 students managed all components of this task well. Some components were handled poorly by most students.