Four Operations

Process and Steps Have this text onscreen as sort of a pop-up so it stands out. Maybe a person holding money, grocery items, cake, etc. and then this pops up in a speech bubble? The goal isn’t only to get the correct answer. Understanding the process and steps taken to calculate an answer helps you gain a better understanding of basic math concepts. These basic concepts are then used even when doing more complex operations. “Four operations” might sound like a highly technical term, but you probably perform calculations using the four operations every day. You might subtract money from your checking or debit account, add the cost of items while in line at a store, multiply to determine your student loan interest amount, or divide a birthday cake into equal portions for your party guests. Being able to do all four operations is a valuable skill.

Addition Show the same problem—3+2—using the pencils and the number line. Addition means putting things together. One easy way to solve simple addition problems such as 3 + 2 is to picture objects being added together. Picture 2 pencils being added to 3 pencils. If you count up all the pencils, you get 5, so 3 + 2 = 5. Another way to look at addition involves using the number line. Draw your line, look at the first number (addend), and then count up on the number line to add. The number you end up on is your answer.

Base 10 Might want to make your own graphic—these are pretty blurry Base 10 blocks can be useful when trying to understand addition problems, especially when those problems involve larger numbers into the hundreds, thousands, and beyond. Using blocks is an easy way to create ones, tens, hundreds and so on. Building the quantities you need for a math problem makes it possible for you to add values and count the physical objects to get your answer. Borrow your child’s blocks to create these if you want a concrete representation of numbers!

Subtraction Create pencils like addition slide to show 15-8 15 - 8 15 - 8 32 - 15 32 - 15 When you take something away, you are subtracting. Again, visualizing or using objects can help you solve subtraction problems. A problem like 15 - 8 is relatively easy to visualize and solve, but what about a problem like 32 - 15? You could try to envision and count 15 items being taken away from 32, or you could simplify by subtracting units from units and tens from tens by using a technique called borrowing.

Borrowing Create graphic similar to picture (with Legos) to illustrate 32 – 15. Show three tens and 2 ones. Next picture shows one ten broken up and placed with the ones. 32 - 15 When you borrow, you take a group from one place value to another. For example, in this problem, it might appear that you can’t subtract 5 from 2. However, you can “borrow” from the tens column. Building bricks are a very good way to help you understand borrowing. You can create tens and hundreds, and actually remove bricks from them to show the number you’re borrowing. When you borrow, you’re adding units from a higher place value to a lower one. In this problem, you can’t subtract 2 from 5, so you borrow a 10 and add it to the 2 in the ones place. Now you’re subtracting 5 from 12 and can solve the problem.

Multiplication Insert image showing three groups of 7 items (Legos? Three people with 7 apples?) Multiplication is similar to addition except that you’re adding groups of items rather than individual items. One way to think of it is that you’re adding sets of things. In the problem 7 x 3, you have three groups of 7. This is the same as 7 + 7 + 7. You can count all these up, or if you know your multiplication facts, you can figure out that the answer is 21.

Multiplication Facts RULE EXAMPLE Order of numbers doesn’t matter in multiplication, so 8 x 5 is the same as 5 x 8. 5 x 8 = 40 8 x 5 = 40 When multiplying by five, your answer should always end with five or zero. 3 x 5 = 15 4 x 5 = 20 When multiplying by two, add the number to itself 2 x 9 = 9 + 9 If you multiply by nine, the digits of your answer should equal nine. 3 x 9 = 27 2 + 7 = 9 7 x 9 = 63 6 + 3 = 9 To multiply by ten, add a zero to the number you’re multiplying. 7 x 10 = 70 15 x 10 = 150 To multiply, it helps to know your “times table” or multiplication facts. Knowing it means practicing multiplication problems often. There are some tricks you can use to help you learn these. Redo the table however it looks good…

Division Show 27 dollars, and then divide between three people Division is in some ways the opposite of multiplication. When you divide, you split items into groups. Setting up the problem correctly helps you calculate the correct answer. Consider 27/3. You could put this into real-life terms. Imagine you have 27 dollars to split between three people. How much would each person get? You could also use the building bricks. Put 27 bricks into three groups and count how many are in each group.

Remainders Image to show remainder—you can reuse the pencils. Maybe 16/3 or something simple? Put the problem and image onscreen Write out problem 253 divided by 6 and show how it’s solved. I can’t find the right symbols but like this: 6 253 Division problems often have remainders. When dividing a number into equal groups, if there are some left over, it is called a remainder. Remainders are designated by the letter R. Long division always involves remainders. In a problem such as 253/6, you would use the remainder of each step to complete the calculation. Using objects or pictures, or coming up with real-life ways to think of long division problems can help you figure out these types of problems.

Summary The four operations form the basis for all mathematics. Practice as much as you can until you are comfortable with them all. Once you’ve learned them, almost any other math can be simplified into parts consisting of the four operations.