Rod Area

This task challenges you to create symmetrical U shapes out of rods and find their areas.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

For this task, imagine using a number of rods, each with a length of 1 unit.

You will use the rods to create a letter U shape which is symmetrical.

Example 1:

 

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Rod Area
      
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Rod Area
        
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Rod Area
 

   28 rods                      U shape                 Area of 39 square units

Example 2:

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Rod Area
          
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Rod Area
           
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Rod Area

   34 rods                        U shape                      Area of 57 square units



The following are not allowed as they are not U-shaped:

Image
Rod Area

 

 

Challenge 1

 

Using 20 rods each time, find one U shape which has an area that is an even number of square units and one which has an area that is an odd number of square units.

 

 

Challenge 2

 
Using any whole number of rods find a U shape with an area of 14 square units.

Can you find all the U shapes with an area of 14 square units?

How do you know you've got them all?

Here is a printable sheet of the activity.