Using Mental Math to Solve Two-Step Problems

Instructor: Cassandra Cook

Cassandra Cook has taught grades K-8 and has a Specialist degree in Curriculum and Instruction

For this lesson you will learn how to solve two step word problems using addition and subtraction. We will explore ways to solve simple problems by identifying key information in the word problem.

Using Mental Math to Solve Two-Step Problems

Have you ever needed to figure something mathematically out quickly? Maybe you have had these thoughts: do I have enough money for a pretzel and a drink?, or If I eat four slices of pizza tonight, will I have enough for lunch tomorrow? Using mental math to solve two-step word problems can be easy and very useful in everyday life, and you might not even know it.

What is Mental Math?

Mental math is solving math problems in your head, without the use of your fingers, paper and pencil, or a calculator. Mental math helps you solve problems faster, without having to rely on anything to help you count.

What are the four operations in math?

Mental math works great for four of the six operations of math: addition (4+4=8), subtraction (8-4=4), multiplication (4x2=8), and division (8/4=2). These four operations can be used to solve any math problem. Now let's take a trip and see how it all works!

Road Trip

Addition and Subtraction

Let's imagine you and your best friend are heading on a road trip. You have your bags packed and are ready to go. While on the highway, there are a total of seven cars in your lane. Soon three cars leave but seven more join. How many cars are in your lane now?

To solve this problem first we identify all the numbers and the operations that will be used. We know that we start with seven cars and three leave. The key word leave tells us that we subtract. Our problem is this:

7 cars in the lane - 3 cars that leave= 4 cars left in the lane

Now we have to add the seven cars to our lane, because they joined us. The word joined indicates addition:

4 cars in the lane + 7 cars that joined= 11 cars in total

To solve this problem, first we subtracted the cars that left and then added the cars that joined. We can also solve the problem this way:

7 cars in the lane + 7 cars that joined= 14 cars

14 cars - 3 cars that left= 11 cars in total

The answer is the same even though we solved the problem two different ways. Having to add and subtract were the two-steps used to solve the problem.

Now on your road trip you and your friend stop for food. As you are placing your order a soccer team of 26 players enter and five guests leave. How many guests are now in the restaurant?

You and your friend make 2 people + 26 soccer players= 28 guests

28 guests - 5 that leave= 23 guests left.

You can solve this problem using subtraction first like this:

26 soccer players - 5 that leave= 21 guests

21 guests + 2 people (you and your friend)= 23 guests

The answer is the same no matter which operation you use first to solve the problem.

Multiplication and Division

At the counter you and your friend decide to order a pizza and soda. But what size pizza should you order? A small has six slices, a medium has eight, and a large has ten. The two of you both want four slices of pizza to eat.

2 people (you and your friend) x 4 slices of pizza each= 8 slices of pizza (medium pizza)

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