Stage Four
Bricks &
Boxes
Three bricks measure 18cm by 9cm by 6cm. Using all three bricks at once, how many different heights can you build with them?
Investigate different sized containers which would hold 60 bricks. (Note: the bricks are to remain whole.)
The bricks are used to cover an area 1.8m by 1.8m. Work out several different paving patterns which:
- use whole bricks only.- use half bricks as well as whole bricks.
Three bricks measure 18cm by 9cm by 6cm. Using all three bricks at once, how many different heights can you build with them?
Lets work through the possibilities:
18 + 18 + 18 = 54cm
18 + 18 + 9 = 45cm
18 + 18 + 6 = 42cm
18 + 9 + 9 = 36cm
18 + 9 + 6 = 33cm
18 + 6 + 6 = 30cm
9 + 9 + 9 = 27cm
9 + 9 + 6 = 24cm
9 + 6 + 6 = 21cm
6 + 6 + 6 = 18 cm
That's about all the combinations that I can
find... Giving 10 different possible heights. Can you see any
more?
Investigate different sized containers which would hold 60 bricks. (Note: the bricks are to remain whole.)
There are lots of possibilities here. I'm going to look at some that are regular prisms.
Such as:
A box, 5 bricks by 2 bricks by 6 bricks.
Ant set of 3 factors of 60 will do the job: 1x1x60, 1x2x30, 2x3x10 and so on.
But who said it had to be a prism? Explore the
other possibilities!
The bricks are used to cover an area 1.8m by 1.8m. Work out several different paving patterns which:
- use whole bricks only.- use half bricks as well as whole bricks.
Here's one possibility:
And there are lots more for you to find. Using half bricks adds many more possibilities as well.
