Introduction to Two-Step Word Problems - First Grade Mathematics

Welcome to the ultimate challenge of first grade problem solving: Two-Step Word Problems! In everyday life, things rarely happen in just one simple step. Imagine you collect three shells on the beach, find four more shells by the water, and then accidentally drop two shells back into the ocean. That is a two-step story! To solve a two-step problem, you cannot rush straight to the end; you must solve Step 1 first, get an intermediate answer, and then use that answer to solve Step 2. In this chapter, you will learn how to navigate two-step adventures step by step.

The Architecture of a Two-Step Problem

A two-step problem is really two friendly one-step problems linked together like cars on a train.

The Two-Step Bridge:
[ STORY PART 1 ] -> Solve Step 1 -> [ HIDDEN ANSWER ]
                                            |
                                            v
[ STORY PART 2 ] -> Solve Step 2 -> [ FINAL ANSWER! ]

The "Hidden Question"

In every two-step problem, there is a question you must ask and answer yourself before you can solve the main question! That secret question is called the hidden question.

Example 1: Add Then Subtract

Let us follow a two-step story where you join first, then take away.

The Story:
Maya picked 6 red apples and 5 yellow apples from the orchard.
On the walk home, she gave 3 apples to her neighbor.
How many apples does Maya have now?

Step 1: The Hidden Question: "How many apples did Maya pick in total?"
        Equation: 6 + 5 = 11 apples picked.

Step 2: The Main Question: "How many apples does she have after giving 3 away?"
        Equation: 11 - 3 = 8 apples.

Final Answer: Maya has 8 apples now!

Tracking the Hidden Answer

Notice that the number 11 was not mentioned anywhere in the story! You had to calculate 11 yourself in Step 1 so you could use it to subtract in Step 2.

Example 2: Add Then Add Again

Sometimes both steps involve addition.

The Story:
Leo has 4 toy cars.
His sister gives him 3 toy cars.
Then his grandmother gives him 5 more toy cars.
How many toy cars does Leo have in all?

Step 1: 4 + 3 = 7 cars.
Step 2: 7 + 5 = 12 cars!
Final Answer: Leo has 12 toy cars in all!

Writing as One Big Expression

You can also write this entire journey as a single three-number addition sentence: 4 + 3 + 5 = 12!

Practice Exercises

Exercise 1: Read and solve this two-step problem: "Oliver had 10 pennies in his bank. He earned 5 more pennies doing chores. Then he spent 4 pennies on a piece of bubblegum. How many pennies does Oliver have now?" State Step 1, Step 2, and the final answer.

Exercise 2: Read and solve: "There were 8 birds on a branch. 4 more birds landed on the branch. Then 2 birds flew away. How many birds are on the branch now?"

Exercise 3: In the problem: "Emma baked 7 chocolate cookies and 6 vanilla cookies. Her brother ate 4 cookies. How many cookies are left?", what is the hidden question that you must answer first?

Exercise 4: Explain why you cannot solve Step 2 of a two-step word problem without completing Step 1 first.

Solutions and Explanations

Solution to Exercise 1: Step 1: Find total pennies earned: 10 + 5 = 15 pennies. Step 2: Subtract the pennies spent: 15 - 4 = 11 pennies. Final Answer: Oliver has 11 pennies now.

Solution to Exercise 2: Step 1: Add the birds that joined: 8 + 4 = 12 birds. Step 2: Subtract the birds that flew away: 12 - 2 = 10 birds. Final Answer: There are 10 birds on the branch now.

Solution to Exercise 3: The hidden question is: "How many cookies did Emma bake in all?" (7 + 6 = 13 cookies).

Solution to Exercise 4: You cannot solve Step 2 first because Step 2 requires the result from Step 1. In Emma's cookie problem, you cannot subtract the 4 cookies eaten until you first know the total number of cookies available to eat from!