# 01.01 Basic Operations Join NURSING.com to watch the full lesson now.

## Outline

### Overview

1. Opening: Faster Solutions – Concepts Before Procedures
2. Math Pro Tips
1. Mental Math for Confidence
2. Rounding and Estimating – Get Close!
3. Joining or Separating?
4. 5 Steps Problem-solving Process – Every Time!
1. Identify the Problem
2. Identify Information to Use
3. Make a Plan
4. Carry Out the Plan
3. Joining or Separating – Know the Difference
1. Joining Means Adding or Multiplying
1.  Adding Whole Numbers – Avoid Common Errors
1. Sum (total) greater than original numbers
2. Opposite of Subtracting
3. Add numbers in any order, Same result
4. Place Value – Must line up numbers
5. Key Vocabulary – Sum, Total, All, Everything, Both, etc. (Cheatsheet)
6. Worked Example
Jack scored 21 points in Monday’s basketball game, 14 points in Wednesday’s game, and only 9 in Saturday’s game. How many total points did he score last week?
2. Multiplying Whole Numbers – Avoid Common Errors
1. Product greater than original numbers
2. Opposite of Dividing
3. Just adding the same number repeatedly
4. Multiply numbers in any order, Same result
5. Key Vocabulary of Multiplication – Product, Times, Double, etc (See Cheatsheet)
6. Worked Example
Regina studies math and reading every night for her entrance exam. She studies math for 45 minutes and reading for an hour. How many minutes each week does Regina spend studying reading?
2. Separating is Subtracting or Dividing
1. Subtracting Whole Numbers – Avoid Common Errors
1. Difference (result) less than original numbers
3. Must understand order of numbers from problem; Cannot switch
4. Place Value – Must line up numbers
5. Key Vocabulary of Subtraction – Reduce, Remaining, Difference, Subtract, Less than, Fewer, Fewer/More Than, Take away, Left, Gave, How Many More (Less), etc. (See Cheatsheet)
6. Worked Example
Ron and Anita have \$1,000 to buy furniture. If they buy a couch for \$650 and a side table for \$29. How much do they have left to spend on an armchair?
2. Dividing Whole Numbers – Avoid Common Errors
1. Break whole amount into equal groups
2. How many smaller groups were possible? Left over?
3. Subtract the same amount repeatedly
4. Opposite of Multiplying
5. Must understand order of numbers from problem; Cannot switch
6. Key Vocabulary of Dividing – Quotient, Per, Ratio of, Divided by, Half (or any fraction), etc (See Cheatsheet)
7. Worked Example
Glen earns \$45,000 a year at his job. How much does he earn per week?
4. Implications of Conceptual Thinking – Word Problems Lose Mystery
1. Math on the fly with Mental Math!
2. Know how to think about any problem – Joining or Separating?
3. Problem-solving steps build confidence Join NURSING.com to watch the full lesson now.

## Transcript

Hi and welcome to course Math: Basic Operations! This is where you will learn to,  hopefully, love math!

I say this because this course does not review procedures of the four math operations of addition, subtraction, multiplication, and division.  Instead I’ll help you gain confidence with important concepts of these operations, and share some PRO Math Tips that will help you solve any word problem you come across, essentially demystifying the dreaded word problem.  So let’s get started!

Let’s start with an overview of some tips that will make you feel like a math pro. First, get into the habit of doing as much mental math as possible. The more math you confidently do in your head, the faster and more accurately you can get to solutions. Second, get really good at rounding and estimating numbers. When you estimate, you can more easily check your answer to make sure it makes sense. Third, practice thinking about the four basic operations conceptually. This can be half the battle in solving word problems, and it is the bulk of the content of this course. And last but not least, get good at the five-step process that I demonstrate here to solve word problems. This has been key to removing the stress of solving word problems for me and made me start to like the challenge.

So what do I mean by mental math? Well, when you feel confident in understanding how the basic operations affect numbers, you can actually do more to solve the word problem in your head before even putting your pencil to the paper. This makes you faster and more accurate in your math overall. I’ll show you how.

How quickly can you multiply 15  and 12? Pretty fast if you take 10 x 10, hold that hundred in your mind and then add 5 x 2.  So 110, right? The more math you do, the more shortcuts you will find to increase what you can do in your head. It’s really worth your time.

Understanding the concept of place value, and the names for each relative to the decimal point, is important for avoiding common pitfalls in all four operations. It also helps you estimate faster.  I know you estimate numbers regularly in your daily life. For example, if you owe your friend \$47, you’re likely to just pay her fifty, right?. In order to estimate that number correctly, you first had to know how to round 47 to the nearest ten. and how did you know it was 50 and not 40? Well, if rounding sometimes trips you up, here’s a helpful rhyme. “5 and above, give it a shove. 4 and below, stay low.”  Try it yourself! Round 1,375 to the nearest hundred…did you say “1,400”? Which number was your guide? The 7, because it’s one digit to the right of the place value you were asked to round to. If you feel unsure of rounding, it is worth your time to practice to build your confidence.

And here’s a general concept to keep in mind with any math problem. Ask yourself,  “Am I joining values, like when I add or multiply whole numbers?” or “Am I separating values, like when I subtract or divide whole numbers?”. This is important to consider because if you got a much higher or lower answer than you were expecting, maybe you performed the wrong operation. Think – Joining = Bigger (Add or Multiply) and Separate = Smaller (Subtract or Divide) This type of thinking feels like half the battle when to me when I’m solving word problems.

Now I want to share with you a five-step problem-solving plan that has entirely changed my vision of myself as a math person. It’s no magic formula, but a systematic way to break down word problems so you reduce anxiety around solving word problems. Here is a major pitfall that happens folks don’t use a systematic plan to solve word problems – they read it once and then begin taking a stab at the computation. But hold on – take a few minutes to identify the problem, to discover what numbers are important and what operation to use (hint: KEY WORDS), then you make the plan for how to solve it.  Guess what? There is no actual math until the 4th step. None! Only planning. So the first 3 steps are about being a good reader! After you actually DO the math in step 4, then you check it!

Step 1 – Identify the problem. Have you ever noticed how the question is always at the end of a word problem? Knowing this, I only pay attention to the numbers in the question on my first reading. I get a general idea of the context and then focus on the question. If I can restate that problem in my own words, noticing the unit,, then I know exactly what I need to do.. Additional tip – I always write the problem with the correct unit. So in this case, I’m being asked to find how much sugar needed, and the sugar is in ounces.

In step 2, identify just the information needed to solve the problem.  To do that, I have to read the problem again, but this time paying close attention to all the numbers because there’s often unnecessary information meant to distract. So if you know you need the amount of brown sugar, you notice you can ignore the amount of granulated sugar and vanilla. All you need is 8 oz. but you’re not done in Phase 2 yet. Look for language that signals whether you need to join or separate amounts. Here I see the word doubling, and that tells me my numbers need to get bigger – which is joining. So I’ll need to either add or multiply.

For step 3, you read that you have to DOUBLE the amount of brown sugar you and that you started with 8oz. Now I have all the information I need to write my number sentence. Doubling can mean I either add the amount of brown sugar twice or I can multiply it by 2. So I can use either  8 * 2 equals…or 8+8=… The next step is actually “Do the Math!”, so you see why earlier I said you don’t do any math until step 4? I was serious!

Now step 4. We have our number sentence 8 * 2 equals, so let’s just do the math. The number answer is 16, but the answer isn’t done until you can name the unit. So look back at the problem –  since brown sugar is listed in ounces, your complete answer must be 16 oz.

Additional Tip: If the math is complicated it’s recommended you always write all your work, that way if you have to make a correction you can look back to see exactly where the mistake happened and you don’t have to start over.

Step 5 of the 5-step plan is really only to check your answers. Does 16 oz make sense in this context? Sure it does. In this step always check both your number and the unit. if I accidentally said that Susan needed 16 pounds of brown sugar, based on what I know about baking, I need to trust my instinct and go back and check that pounds is the right unit. Discovering that the right unit was actually ounces can save you from a wrong answer. This final check of both number and unit is super important and shouldn’t be skipped.

So now let’s move forward into thinking about the four basic operations very conceptually. I’m not going to teach you how to add, subtract, multiply or divide, but I am going to point out some ways to think about them so that you can avoid some common pitfalls when working with them. 