Again Chapter one Stuff...
Discuss how the notion of symmetry could be used to estimate the number of marbles in a one-liter jar.
I'm lost I'm thinkthing somewer along the lines of counting them up nice and simple but I have no idea
The only relevance of symmetry I can think of is the following, basically subdividing the litre jar into 8 smaller pieces, a little easier to calculate.
A litre jar has a capacity of 1000 cm3.
If we look at symmetry in the x-y, y-z and z-x planes, we basically cut up the volume into 8 parts, each of which has 125 cm3, or the equivalent of a 5 cm. cube.
If we think of a marble as a sphere of 1 cm diameter, we can squeeze in 5*5*5=125 marbles in each of the subdivided cubes. Hence for the litre jar, we can probably squeeze in 1000 marbles.
Tell us what you think.
(sorry I probably won't be here to answer you tomorrow morning, but other teachers can help you out)
To estimate the number of marbles in a one-liter jar using the notion of symmetry, you can follow these steps:
1. Start by taking a smaller, representative sample from the jar. For example, you could randomly select 10 marbles.
2. Count how many of those selected marbles have a certain property. This could be something like color or size. Let's say 6 out of the 10 marbles are blue.
3. Now, examine the remaining marbles in the jar. Look for symmetry in the sample you've taken. This means assuming that the ratio of blue to non-blue marbles in the sample is representative of the ratio in the entire jar.
4. Using the assumption of symmetry, estimate the number of marbles in the jar. If 6 out of 10 marbles are blue in the sample, you can estimate that roughly 60% of the marbles in the jar are blue.
5. Finally, use the estimated proportion to calculate the number of marbles in the jar. If you assume that 60% of the marbles are blue, and you know the sample size (10 marbles), you can estimate the total population size using the formula:
Estimated number of marbles = (Number of blue marbles / Proportion of blue marbles) * Sample size
In this case, if you assume 60% of the marbles are blue, and the sample size is 10, the estimated number of marbles would be:
Estimated number of marbles = (6 / 0.6) * 10 = 100 marbles
Remember that this is just an estimate based on the assumption of symmetry and the properties observed in the smaller sample. The actual number of marbles could be different.