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Numbers as Shapes

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

How Odd

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

How many odd numbers are there between $3$ and $11$?
 
How many odd numbers are there between $4$ and $11$?
 
What do you notice?  Can you explain your observation?
 
Can you find any other pairs of numbers which have this same number of odds between them?
 
Can you find a pair of numbers which have four odd numbers between them? 
 
Can you find another pair of numbers which have four odds between them?  And another pair?
 
How would you find a pair of numbers that have five odds between them?  Six odds?
 
How would you explain to someone else how to find  a pair of numbers that have a certain number of odds between them?