Purpose:

Use problem solving to discover a method to estimate the number of salt grains

in a large container.

Visualize a very large number.

Here are some student methods.

Step 1 We took 1.5 grams of salt(which is one serving) and divided it into 10 sections with a credit card.

Step 2 We took one section and counted how many salt grains were there. We estimated there were 500 grains.

Step 3 We then multiplied 500 by 15 to get it back to 1.5 gram. We got 7,500 grains in 1.5 grams.

Step 4 We finally multiplied 7,500 by 491 (because 491 is the total amount of servings in the container) and got 3,682,500.

Step 1 We took 1.8 grams and piled it into a circle. Then we divided the circle into 16 seperate sections.

Step 2 We took out one section and estimated that there were 200 grains. Then we multiplied that by 16 and found out that 1.8 grams has 3,200 grains.

Step 3 Then we tried to find out how many servings of 1.8 grams were in the can. We knew that there were 491 servings of 1.5 g each, that is, 736.5 grams. We found that there were 409 1.8 gram servings by dividing 737.5 by 1.8.

Step 4 To find the final answer we multiplied 3,200(the number of grains in a serving) and 409(the number of servings) and got 1,308,800 grains.

Step 1: First we took half a teaspoon or (3 grams) of salt and put it in a paper cupcake holders.

Step 2: Next, each of us took an eraser and we counted how many grains of salt stuck to one (1 eraser = 55 grains). Then we started counting how many times it would take to get all of the salt off of the cupcake holders. Which eventually came out to 923 erasers full in half a teaspoon.

Step 3: Then, we took 1 eraser (55 grains) and multiplied it times 923 (how many erasers it took to empty out a holder) that equaled a 1/2 teaspoon.

Step 4: Finally we took the total amount of 1/4 servings in the whole container (491) then divided it by 2 and came out with 245.5. This gives the number of 1/2 tsp. Next we multiplied the amount in a half a teaspoon (50,765) by 245.5 and got 12,462,807.5.

So our conclusion was that there were 12,462,807.5 grains of salt in one container.

BUT THEN HOW DO WE VISUALIZE 200 BILLION? (There is an estimated 1 billion stars in our galaxy.)

We used one guess that there are 2,600,000 grains of salt in one container. How many containers do we need to have 200 billion salt grains. 200,000,000,000 / 2,600,000 = 76,923 containers

How big is that?

we imagined that the science demonstration counter in front of the class room was a BIG box. Using the actual salt container, we measured that we could fit 30 along the length, 8 along the side and 5.5 high, for a total 1320 containers in one demo counter.

76,923 containers in 200 billion / 1320 containers in counter = 59 demo counters

It would take 59 demonstration counters filled with salt to hold 200 billion salt grains.

WOW! AWESOME!

Conclusions:

Students were told that scientists cannot always use direct measurement (counting the grains one at a time). Therefore, methods must be used to estimate. To emphasize this, I asked the students how long would it actually take to count one million, billion or trillion if you counted one grain of salt each second.

 

(That is

one million seconds = ? time that you can visualize (min, hr,day,years)

one billion seconds = ? time that you can visualize (min, hr,day,years)

one trillion seconds = ? time that you can visualize (min, hr,day,years)

 

Using calculators they calculated that

one million seconds = 11.7 days

one billion seconds = 31.7 years

one trillion seconds = 31,700 years

 

MOST WERE VERY SURPRISED BY THESE RESULTS.

 

This activity also showed that different CORRECT methods can be discovered

by scientists (and students) - not just one right way.

Some measurements are impossible (like counting to one billion) to do directly.

Indirect methods can estimate very large numbers.

Different methods can come up with the same results.