4th Grade - Math

LESSON PROBLEM: Estimation: You are in a store, without a calculator or pen and paper. If you have to quickly decide whether you have enough money to buy 23 packets of rice cookies @$1.69 or not, how would you go about it?


STUDY GUIDE

Peter is standing in front of a rack of rice snacks. He looks at the temptingly packaged rice cookies, and then he raises his eyes toward another shelf. Wow! There are his favorite rice crackers, and a whole lot of other rice treats. He wants to buy as many as possible with the money he has.

Now the problem of calculating comes up. How to find how much to buy of each item? He has $100 with him. He wants to buy treats for a party he is hosting for his six best friends. Keeping 35 dollars for the juice and ice cream, he decides to buy rice snacks with the rest.

Now he looks at their prices. With $65, he has to buy a variety of rice snacks. The prices for the snacks, per box or package, read as follows:

Rice cakes: $1.75
Rice cookies: $1.99
Rice chips: $0.89
Rice noodles: $0.15

He wants to have 8 of each item. How can he solve his problem?

In this situation, estimation is helpful. You do not need to calculate the exact amount. The purpose is to make a rough estimate of the money needed to pay the bill, as you would not like to run short at the checkout counter.

In estimation, we ignore amounts that are less than half, and count half and more than half as one. If we do this in our present situation, we shall get our amounts as follows:

Rice cakes: $2.00 (rounded to the nearest dollar)
Rice cookies: $2.00 (rounded to the nearest dollar)
Rice chips: $1.00 (rounded to the nearest dollar)
Rice noodles: $0.00 (rounded to the nearest dollar)

The price for the rice noodles comes to $0.00. It does not mean that Peter will get them free. But it means that this small amount of 15 cents would get adjusted in the price of other items that have been rounded to the next higher dollar amount.

This makes the calculation very simple. He is to get 8 of every item. It would be easier to first add the amount required to buy one of each item. That comes to 5 dollars. So for 8 of every item he would require 5 x 8 = 40 dollars. Peter has enough money to buy eight boxes or packages of everything.

Now you try to estimate the money required for the following:

a) 7 bags of long grain rice @ $24.69
b) 15 bags of rice flour @ $15.99
c) 5 bags of brown rice @ $10.35
d) 20 bags of parboiled rice @ $ 9.77
e) 10 bags of medium grain rice @ $18.79

Your number need not be in a dollar amount to qualify for estimating. Any amount, or for that matter any number, can be rounded off to the nearest 10, 100, 1,000, etc. for estimation purposes. Rather, you can round off both the multiplier and the multiplicand (the number that multiplies, and the number that is to be multiplied). For example, if you have to multiply 739 and 987, you should round off both the numbers to the nearest 100 and then multiply.

When rounded off to the nearest 100, 739 becomes 700, and 987 becomes 1,000. Our estimated product would be 700 x 1,000 = 700,000. How simple!

Now you calculate the estimated value of the following, rounding to the nearest 100. ( Don't bother about the price of the bag. A bag you buy for your family, and the bag a rice trader buys, vary greatly in size. Bags can be as small as 0.5 kg (kilograms), and large as 100 kg, or even bigger.)

a) 345 bags of rice flour @ $795
b) 567 bags of medium grain white rice @ $213
c) 234 bags of basmati rice @ $2,095
d) 89 bags of precooked rice @ $995
e) 397 bags of long grain brown rice @ $2,591

When you round off to the nearest 1,000, the method is the same. If the yield from a farmer's field is 5,820 pounds/acre, his estimated total production from a field measuring 489 acres would come to:

6,000 x 500 = 3,000,000 pounds

(We have simply rounded off 5,820 to the nearest thousand which is 6,000 and also rounded off 489 to 500.)

Now you try the following, rounding to the nearest 1,000 pounds:

a) Rice produced in a field in Mississippi measuring 789 acres @ 5,650 pounds /acre
b) Rice produced in a field in Arkansas measuring 543 acres @ 5,850 pounds /acre
c) Rice produced in a field in Louisiana measuring 905 acres @ 4,980 pounds /acre
d) Rice produced in a field Missouri measuring 1,625 acres @ 5,400 pounds /acre
e) Rice produced in a field in Texas measuring 1,239 acres @ 5,900 pounds /acre




ACTIVITIES

Visit a supermarket, and try to estimate the money you would require to buy each of the following:

13 boxes of rice cookies
29 bags of rice flour
17 boxes of rice crispies
8 bags of long grain rice
11 bags of parboiled rice

You do not need to estimate the total amount you would need. Calculate only for individual items, e.g., for rice cookies only, for rice flour alone, and so on.




EXTENDED LEARNING

If you were to estimate the products of decimal numbers, how would you go about it? You can review multiplication of decimals at this site.




VOCABULARY
  • product
  • multiplicand
  • multiplier
  • cwt
  • yield
  • adjust
  • ignore
  • calculate


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