2 Step Word Problems 5th Grade

Tackling Two-Step Word Problems: A 5th Grader's Guide to Success

Fifth grade marks a significant leap in math, introducing students to the complexities of two-step word problems. These problems require more than just one operation; they demand a sequential approach, involving two distinct steps to arrive at the solution. While challenging, mastering two-step word problems builds crucial analytical and problem-solving skills essential for future mathematical endeavors. This comprehensive guide provides strategies, examples, and practice problems to help 5th graders conquer these mathematical puzzles.

Understanding the Structure of Two-Step Word Problems

Two-step word problems present a scenario requiring two mathematical operations—addition, subtraction, multiplication, or division—to find the answer. The key is to deconstruct the problem into its constituent parts. Each part represents a single step. Let's break down a typical structure:

• Step 1: Identifying the First Step: This involves carefully reading the problem to identify the initial question or piece of information needed to solve the problem. This often requires understanding the context and relationships between the numbers and quantities mentioned.

• Step 2: Identifying the Second Step: Once the first step is completed, the result is usually used to solve the second step. This step leads directly to the final answer.

• Step 3: Performing the Calculations: After identifying both steps, perform the calculations accurately and methodically. Always double-check your work!

• Step 4: Writing the Answer: Express your final answer clearly and concisely, ensuring it addresses the original question posed in the word problem.

Keywords and Clues: Deciphering the Problem

Success with two-step word problems often hinges on identifying key words and clues embedded within the problem's text. These words signal the mathematical operation required.

Keywords for Addition:

• Increased by: Indicates adding a value to an existing quantity.
• More than: Implies adding a value to a base amount.
• Total: Suggests the sum of multiple values.
• Combined: Indicates the addition of two or more quantities.
• Sum: Refers to the result of adding numbers.
• In all: Indicates a total amount.

Keywords for Subtraction:

• Decreased by: Implies subtracting a value from an existing quantity.
• Less than: Suggests subtracting a value from a base amount.
• Difference: Refers to the result of subtracting two numbers.
• Remainder: Indicates the amount left after subtraction.
• Reduced by: Implies subtracting a value.
• Left: Often indicates the result after subtraction.

Keywords for Multiplication:

• Times: Indicates multiplying a value by another.
• Product: Refers to the result of multiplying numbers.
• Each: Often used when distributing a quantity among multiple items.
• Twice: Implies multiplying by two.
• Triple: Implies multiplying by three.
• Groups of: Suggests multiplication.

Keywords for Division:

• Divided by: Implies dividing a value by another.
• Shared equally: Often used when dividing a quantity equally among multiple recipients.
• Quotient: Refers to the result of division.
• Each: Used when distributing a quantity equally.
• Split equally: Implies equal division.
• Per: Indicates division, such as "price per item".

Strategies for Solving Two-Step Word Problems

Several proven strategies can simplify the process of solving two-step word problems.

1. The "Read, Understand, Plan, Solve, Check" (RUPSC) Method:

• Read: Carefully read the entire problem at least twice to comprehend the scenario.
• Understand: Identify the key information, including the numbers and the questions being asked.
• Plan: Determine the steps required to solve the problem. Identify the operations needed (addition, subtraction, multiplication, division). Write down a small equation or plan for each step.
• Solve: Perform the calculations step-by-step.
• Check: Review your work for accuracy. Does your answer make sense in the context of the problem?

2. Draw a Diagram or Picture: Visual aids can significantly improve comprehension, particularly for word problems involving quantities or spatial relationships.

3. Use a Table or Chart: Organizing information into a table or chart can clarify the relationships between different quantities.

4. Work Backwards: In some cases, working backwards from the final result can help determine the intermediate steps.

5. Break It Down: Decompose complex problems into smaller, more manageable steps.

Examples of Two-Step Word Problems and Their Solutions

Let's work through some examples to solidify your understanding:

Example 1:

Sarah bought 3 boxes of pencils. Each box contains 12 pencils. She then gave 5 pencils to her friend. How many pencils does Sarah have left?

Solution:

• Step 1: Find the total number of pencils: 3 boxes * 12 pencils/box = 36 pencils
• Step 2: Find the number of pencils remaining: 36 pencils - 5 pencils = 31 pencils
• Answer: Sarah has 31 pencils left.

Example 2:

A farmer has 25 sheep. He buys 15 more sheep. He then divides his sheep equally into 5 pens. How many sheep are in each pen?

Solution:

• Step 1: Find the total number of sheep: 25 sheep + 15 sheep = 40 sheep
• Step 2: Find the number of sheep per pen: 40 sheep / 5 pens = 8 sheep/pen
• Answer: There are 8 sheep in each pen.

Example 3:

John earns $10 per hour. He works for 6 hours on Monday and 4 hours on Tuesday. How much money did John earn in total?

Solution:

• Step 1: Calculate total hours worked: 6 hours + 4 hours = 10 hours
• Step 2: Calculate total earnings: 10 hours * $10/hour = $100
• Answer: John earned $100 in total.

Example 4:

Maria has 48 cookies. She wants to divide them equally among 6 friends. After giving cookies to her friends, she eats 3 cookies herself. How many cookies does she have left?

Solution:

• Step 1: Find the number of cookies each friend receives: 48 cookies / 6 friends = 8 cookies/friend
• Step 2: Find the number of cookies Maria has left: 48 cookies - (6 friends * 8 cookies/friend) - 3 cookies = 0 cookies
• Answer: Maria has 0 cookies left.

Practice Problems

Here are some practice problems for you to try:

1. A bakery made 75 cupcakes. They sold 48 cupcakes in the morning and 15 in the afternoon. How many cupcakes are left?

2. David has 25 marbles. He buys 15 more. He then divides his marbles equally among 4 friends. How many marbles does each friend receive?

3. A school bus holds 36 students. If 2 buses are full, and 12 students walk, how many students are there in total?

4. A train travels 60 miles per hour. How far will it travel in 3 hours?

5. Sarah has $50. She buys a book for $15 and a pen for $5. How much money does she have left?

Remember to use the strategies discussed above to tackle these problems. Break them down into steps, identify the key words, and always check your work! Practice makes perfect, so the more you work through two-step word problems, the easier they will become. By consistently applying these strategies, 5th graders can build confidence and mastery in solving these essential mathematical problems. Remember to always re-read and check your work. Accuracy is key!