### Standards Unit N6: Developing Proportional

```Suitable for any students at Level 5 or 6.
Much quicker with Level 7 or 8 students, but still worthwhile to introduce ‘max’ and
‘min’ concept. Or could easily go straight to ‘plenary’ task to do same investigations,
but with compound rectangular shapes. In that case could also get students to input
into Excel etc.
Standards Unit SS2:
Understanding Perimeter and Area
>30 mins. Paired activity.
Mini-whiteboards for final plenary, and possibly to collect
info mid-session.
Simply investigates the non-uniform dependency between
area and perimeter.
Consumable Resources Needed:
Several sheets of centimetre squared paper
Pencil and ruler
Re-usable Resources Needed:
Mini-whiteboards
1 calculator / pair
Notes to start.
Perimeters and Areas
6
6
Think of a square 6 × 6 bar where each piece is 1cm by 1cm.
What is meant by the perimeter and area of the bar?
What is its perimeter? What is its area?
In this lesson we will study area and perimeter in more detail.
If the area goes up, does the perimeter always increase too?
If the perimeter of a shape increases, does the area go up too?
Pair Activity 1
Use squared paper to draw
the different rectangles.
4
6
9
6
Perim = 24cm
Perim = ?
Re-arrange the chocolate squares to make different shaped
rectangles. But always keep the same number of squares.
Work out the perimeter of each rectangle, and find which rectangle
has the:
i) largest perimeter
ii) smallest perimeter
Which bar would you prefer? Why?!
How many different shaped bars of chocolate did you find?
What were their sizes?
Height × Length
Perimeter
6×6
24cm
4×9
26cm
3 × 12
30cm
2 × 18
40cm
1 × 36
74cm
What about if we could create rectangular bars but without being
whole numbers of centimetres?
Could we make the perimeter even larger, or smaller?
See:
SS2_PerimeterArea.xlxs
Tab 1
Use squared paper to draw
the different rectangles.
Pair Activity 2
14
13
6
7
Perim = 40cm
Area = 40cm2
Perim = 40cm
Area = ? cm2
Again, re-arrange the chocolate squares to make different
shaped rectangles. But this time the PERIMETER must remain the
same.
Work out the AREA of each of your rectangles, and find which
rectangle has the:
i) largest area
ii) smallest area
Height × Width
Perimeter (cm)
Area (cm2)
3 × 17
2(3+17)= 40
51
4 × 16
2(4+16)= 40
64
5 × 15
2(5+15)= 40
75
6 × 14
2(6+14)= 40
84
7 × 13
2(7+13)= 40
91
8 × 12
2(8+12)= 40
96
9 × 11
2(9+11)= 40
99
10 × 10
2(10+10)= 40
100
Could we make the area even larger, or smaller?
See:
SS2_PerimeterArea.xlxs
Tab 2
Mini-Whiteboard Questions
Draw a rectangle with:
1. An area of 50cm2
2. An area of 50cm2 and a perimeter of 45cm
3. A perimeter of 40cm
4. A perimeter of 40cm and an area of 75cm2
Extension investigation:
Repeat previous investigations but allowing compound rectangles
```