MathIsimple

Multi-Step Operation Applications

Master the art of solving complex word problems that require multiple steps and different operations. Become a problem-solving detective!

Learning Scenario

Meet the Problem-Solving Squad! Maya, Alex, and Sarah are organizing a school fundraiser. They need to figure out how much money they'll raise if they sell 15 cookies at $2 each, then buy supplies for $8, and finally donate half of the remaining money to charity. This is a multi-step problem that requires addition, multiplication, subtraction, and division! Let's help them solve it step by step.

What are Multi-Step Problems?

Definition

Multi-step problems are word problems that require you to perform more than one mathematical operation to find the answer. You need to think through the problem carefully and decide which operations to use and in what order.

Think of it like this: Multi-step problems are like following a recipe - you need to do each step in the right order to get the final result!

Why Multi-Step Problems Matter

  • They help you practice multiple math skills at once
  • They prepare you for real-world problem solving
  • They improve your logical thinking and planning skills
  • They make you a stronger mathematician overall

Problem-Solving Strategy

The 4-Step Method

1

Read and understand the problem

What are you trying to find? What information do you have?

2

Plan your solution

What operations will you use? In what order?

3

Solve step by step

Work through each operation carefully

4

Check your answer

Does your answer make sense? Can you verify it?

Key Words to Look For

Addition Words

  • • total, sum, altogether
  • • more than, increased by
  • • combined, together

Subtraction Words

  • • difference, less than
  • • decreased by, remaining
  • • left over, take away

Multiplication Words

  • • times, multiplied by
  • • each, per, every
  • • groups of, sets of

Division Words

  • • divided by, split
  • • shared equally, per
  • • half, third, quarter

Example Problems

Example 1: Fundraiser Problem

Maya, Alex, and Sarah are organizing a fundraiser. They sell 15 cookies at $2 each, then spend $8 on supplies. They want to donate half of the remaining money to charity. How much will they donate?

Step 1: Read and understand

We need to find how much money they'll donate to charity.

Step 2: Plan

1) Find total money from cookies 2) Subtract supplies cost 3) Find half for donation

Step 3: Solve

Money from cookies:15 × $2 = $30
After buying supplies:$30 - $8 = $22
Half for donation:$22 ÷ 2 = $11

Answer: They will donate $11 to charity

Example 2: School Supplies

A teacher buys 4 boxes of pencils. Each box has 12 pencils. She gives 8 pencils to students and puts the rest in the supply closet. How many pencils are in the supply closet?

Step 1: Read and understand

We need to find how many pencils are left in the supply closet.

Step 2: Plan

1) Find total pencils 2) Subtract pencils given to students

Step 3: Solve

Total pencils:4 × 12 = 48
Pencils in closet:48 - 8 = 40

Answer: There are 40 pencils in the supply closet

Interactive Activities

Activity 1: Plan Your Solution

For this problem, plan the steps you would take:

Problem: A store has 50 apples. They sell 3 bags with 8 apples each, then receive a delivery of 25 more apples. How many apples do they have now?

Step 1:
Step 2:
Step 3:

Activity 2: Create Your Own

Create a multi-step problem using these numbers: 20, 4, 5, 12

Make sure your problem:

  • Uses at least 2 operations
  • Makes sense in real life
  • Has a clear question to answer

Common Mistakes to Avoid

❌ Not reading the problem carefully

Take time to understand what the problem is asking before you start solving.

❌ Doing operations in the wrong order

Think about what needs to happen first, second, and so on. Plan before you solve!

❌ Forgetting to check your answer

Always ask: "Does this answer make sense?" and try to verify it.

❌ Rushing through the problem

Multi-step problems require patience. Work through each step carefully.

Practice Problems

Problem 1

A bakery makes 24 cupcakes. They sell 3 boxes with 6 cupcakes each, then make 15 more cupcakes. How many cupcakes do they have now?

Problem 2

A class has 30 students. They form 5 equal groups for a project, then 3 students join the class. How many students are in each group now?

Key Takeaways

What You Learned

  • Multi-step problems require multiple operations to solve
  • Always read, plan, solve, and check your work
  • Key words help identify which operations to use
  • Take your time and work through each step carefully

Next Steps

  • Practice with more complex multi-step problems
  • Learn to identify patterns in word problems
  • Apply these skills to real-world situations