Making Sticks
Kimie and Sebastian were making sticks from interlocking cubes. Kimie made blue sticks two cubes long. Sebastian made red sticks three cubes long. They both made a lot of sticks.
Kimie put her blue sticks end to end in a long line. Sebastian put his red sticks end to end in a line underneath Kimie's.
- What are the different lengths that Kimie can make using only her blue sticks? What do you notice?
2, 4, 6, 8, 10, 12 etc.( all even no.s/ multiples of 2 because the blue sticks have 2 cubes).
- What are the different lengths that Sebastian can make using only his red sticks? What do you notice?
3, 6, 9, 12 etc.( all multiples of three because the red sticks have three cubes).
- Can they make their lines the same length? How many sticks could Kimie use? How many would Sebastian put down? How long is the line altogether?
3 Kimie, 2 Sebastian - 6
6 Kimie, 4 Sebastian - 12
9 Kimie, 6 Sebastian - 18 etc.
( all common no.s in tables of 3 and 2 ).
- Can they make any other same lines using only blue sticks or only red sticks ? What do you notice?
Yes. Every 5 no.s there is a common multiple as per as picture 1
- What lengths can we make using 2 and 3 together?
Every length except 1
- Explain your findings.
We can make every no. except 1 because-
even+odd= odd
even+even= even.
If your not convinced, 2x any no. is an even no.. Like this, we have all the possible even no.s. Then, we replace any one of the 2s with 3 (2+1) which makes it possible to make every no. except 1.
So, we can make every no. except 1.
You will see the pattern in picture 2.