Measurement projects

I have a feeling blogging might slow down over the summer...

I've been dealing with math daily, though (of course). I'm writing a collection of worksheets for a company, and teaching too.

The last few days have been spent with writing an answer key. I thought I'd post a few problems here for your enjoyment - sort of measuring projects. Maybe you can involve your kids in some hands-on splish splosh splash water experiments and learn geometry too. :)


1. You need: an empty cylinder (for example from inside a toilet paper roll), a small ball, and a tennis ball.
The small ball should fit inside the cylinder fairly snugly, and the tennis ball shouldn't.

a. What should you measure from the ball and the cylinder to know whether a ball fits, without actually trying it out?

b. Find how many balls you could stack inside the cylinder, if you had more. Think what measurements and calculations you should do to find that out.

c. How many of the small balls would fit inside a cylinder that is 1 m 34 cm tall?

d. How many tennis balls would fit inside a cylinder that is 1 m 34 cm tall?



2. You need: a measuring cup that measures in milliliters, water, a small ball, a tennis ball, a drinking glass.

Figure out a method to find out the volume of the balls. After all, you cannot pour water inside them.

The volumes are:
the small ball _______ml,
the tennis ball _______ml,
the drinking glass _______ml.

The volume of the small ball is about ____________of the volume of the drinking glass.
The volume of the tennis ball is about ____________of the volume of the drinking glass.




3. How could you find out the volume of the toilet paper roll cylinder? Is it more than a glass of water?



4. You need: some baby blocks, some dice, a small cardboard box.

Experiment, measure, and find a method so you can find the answers.

a. How many baby blocks would fit inside the box?

b. How many dice would fit inside the box?


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Comments

Anonymous said…
hey can you give me the answers for exercise number 1? i really need them, actually, to know how many balls would fit inside a cylinder, i have been thinking, to only calculate both volumes, and make, Vcylinder/Vball, wouldnt give me the correct answer, i think we would need to use some 3rd grade math, to calculate the space beetween the balls when they are perfectly set inside the cylinder, and figure it out a way to discover the way they get perfectly set, am I just causing problems, or it is complicated as i am thinking to make the things exactly, without having to take fake assumptions to easy stuff?

ty a lot, sorry for the trouble
9:17 PM, October 30, 2007
Maria Miller said…
Here goes:

1. a. You should measure the diameter of the ball and of the cylinder.

b. Once you know that a ball fits snugly, then to find how many fit, measure the height of the cylinder. You already know the diameter of the ball. Divide the height of the cylinder by the diameter, and round down to the nearest whole number.

c. Well this depends on the diameter of your ball - and of the cylinder. You were supposed to have a ball that fits snugly inside the cylinder, so that means their diameters are the same.
Divide the height of the cylinder by the diameter, and round down to the nearest whole number.

d. Well the tennis balls won't fit. : )
6:35 AM, October 31, 2007
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