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There are many problems throughout the text labeled IN YOUR OWN WORDS. Just
relax. Do not be afraid to give your opinion. For the most part, these questions
do not have "right" or "wrong" answers. You should spend about five minutes
answering each of these questions.
These problems are using the order of operations:
- Parentheses first
-
Multiplication and division, reading from left to right
- Addition and subtraction,
reading from left to right See Examples 1 and 2 for help with what we mean
by "order of operations."
For order of operations see Example 3 and, if there are parentheses,
Example 4. After looking at these examples, spend some time with Example
5, which used the order of operations agreement by giving you mixed operations.
"Mixed Operations" means that there is more than one operation in the
problem. For example, addition and subtraction, or addition and multiplications.
Problem 3 has addition and multiplication and Problem 5 has subtraction
and multiplications. If you are using a calculator in this class, then
you should also work Example 2 to make sure that you have the right type
of calculator. If you do the problem 2 + 3 x 4 and obtain the answer 20,
then you should not use that calculator. (The correct answer is 14.)
The distributive
property, which holds for all whole numbers, looks like this:
4(3 + 2)
you
identify the numbers inside the parentheses (3 and 2 for this example) and
the number outside the parentheses (4 in this example). Multiply each number
inside the parentheses by the number outside the parentheses, in turn, and
add the results:
4(3 + 2) = 43 + 42
You do not need to simplify here when illustrating the
distributive property. The distributive property changes a product to
a sum. That is,
4(3 + 2) is a product because the last operation is multiplication
43 + 42 is a sum because the last operation is addition
See Example 8
for classifying as a sum or a product, and Example 9 for the distributive
property.
One of the key steps in formulating the problem is developing skill in
translating from English into math symbolism. The term sum is
used to indicate the result obtained from addition, difference
for the result from subtraction, product for the result of multiplication,
and quotient for the result of division. See Example 7.
When a problem involves mixed operations, it is classified as a sum,
difference, product or quotient according to the last operation
performed when using the order of operations agreement. See Example 6;
this example in the text would be classified as a difference since the
last operation performed is subtraction.
Estimation can be a difficult concept to master, and it is
sort of a chicken-and-the-egg argument. You will learn how to become proficient
in estimating by practicing. But how do you practice estimating if you don't
know how to do it? The best hint I can give you here is to not be afraid to
make an attempt. Look at Example 10, and then dig it and try. You can check
your estimate by using a calculator.
These problems are designed
to make you aware of common mistakes. There are no examples for this type
of problem, so go ahead and try to determine if you think the given result
is true or false. Then, don't forget to explain your reasoning using a few
words or a few sentences. Note: Homework Hints are given only for the levels 1 and 2 problems.
You can also check some sources for homework help on the Internet (see Links,
below), or you can call the author at
(707) 829-0606 or send an e-mail to: smithkjs@mathnature.com |