Finding perimeters

1. Set up a scenario involving perimeter. You might use the Rooster Race on the PowerPoint as an example. Alternatively, you might propose a new scenario that makes more relevant links to students' interests, cultural backgrounds, and learning from other curriculum areas.
   Roosters love to show off. Often, they will race each other around the farmyard to see who is fastest. Imagine each rooster runs around the outside of their run. Show the roost images from the PowerPoint.
   Is the race fair?
   
   
    
2. Let students discuss the distances that Flame and Speckles run.
   How far does Flame run? Is there an easy way to work that distance out?
   Animate the slide to see how Flame covers both lengths 11 metres and 14 metres twice.
   How many straight sides does Flame run along? (four).
   What are the lengths of the sides? (Two of them are 11 metres and two of them are 14 metres).
   How can we work out the total distance?
    
3. Record ways to work out the total distance.

• 11 + 14 + 11 + 14 = 50 metres                   
• 2 x 11 + 2 x 14 = 50 metres 
• 2 x (11 + 14) = 50 metres.
   

4. Similarly animate the slide to follow Speckle’s run and record the calculations.

• 18 + 8 + 18 + 8 = 52 metres                       
• 2 x 18 + 2 x 8 = 52 metres       
• 2 x (18 + 8) = 52 metres
   

5. The distance around the outside of a shape is called the perimeter. Which rooster had the greatest perimeter to run?
   Does that mean that the area of Speckle’s run is greater than the area of Flame’s run?
   Let students investigate the area of each run.
   Flame’s run has an area of 11m x 14m = 154m².
   Speckle’s run has an area of 18m x 8m = 144m².
   So even if one rectangle has a greater perimeter than another, you cannot predict it will also have a greater area.
   Did you notice the different measurement units, m and cm²? What do these units mean?
   As relevant, introduce te reo Māori kupu, such as paenga (perimeter), mita (metre), roa (length), and tapawhā hāngai (rectangle).
    
6. Use a metre ruler to mark a length of 1 metre and 1 square metre. You might draw them with chalk on the pavement or carpet of your classroom.
    
7. Use the same scenario to pose similar comparison problems. You might change the animals, as is done in slides 2 and 3 of the PowerPoint. Alternatively turn the problems into a measurement challenge by marking out the rectangular runs outside using a ruler or tape measure, chalk, and cones.
   Which rectangle has the greatest perimeter?
   Which rectangle has the greatest area?
    

Next steps

1. Give students open-ended challenges like this:

• Design five rectangles with an area of 24 square units.
  Can you tell before measuring which rectangle has the largest perimeter?
  (Generally, if area is fixed the rectangle that is most oblong and least square has the longest perimeter)
• Design five rectangles with a perimeter of 48 units.
  Can you tell before measuring which rectangle has the largest area?
  (Generally, if perimeter is fixed the rectangle that is most square and least oblong has the largest area).
   

2. Have students write open-ended questions and then swap to solve each other's questions.