Teacher Guide: Multi-Step Word Problems

🎯 Learning Objective 10-15 min lesson

Students will: Solve one- and two-step real-world problems using addition, subtraction, multiplication, and division. Students will understand the context of problems, identify the operations needed, and determine the reasonableness of answers.

Important: The standard includes ALL FOUR operations. Multiplication is limited to factors within 12 and their related division facts. Focus on understanding context, not just keyword hunting.

📦 Materials Needed

Counters or base-ten blocks (for modeling)
Chart paper for problem-solving steps
Student worksheets
Number lines (optional)

⚠️ Common Misconceptions to Address

Misconception #1: Keyword Dependency

Students rely on keywords like "altogether" = add, "left" = subtract. But keywords can be misleading! "Maria has 3 times as many as her brother" uses "times" but isn't always straightforward multiplication.

How to Address:

Teach students to visualize the story first. Ask: "What's happening? What do we know? What do we need to find?" Draw pictures or act it out before choosing an operation.

Misconception #2: Solving in the Wrong Order

In two-step problems, students may perform operations in the wrong order (e.g., adding before multiplying when they should multiply first).

How to Address:

Break the problem into parts. Ask: "What do we need to find FIRST before we can answer the final question?" Use step numbers: Step 1, Step 2.

Misconception #3: Not Checking Reasonableness

Students calculate without checking if the answer makes sense. They might say "I have 500 cookies left" when the problem started with only 24 cookies.

How to Address:

Always ask: "Does this answer make sense? Is it too big? Too small?" Estimate first, then solve. Compare the answer to the estimate.

📝 Lesson Steps

1

Introduce the Problem-Solving Process (3 min)

Teach the CUBES strategy or similar framework: Circle the numbers, Underline the question, Box key words, Evaluate what steps to take, Solve and check.

SAY THIS:

"When we solve word problems, we're like detectives. We need to understand the story first, THEN figure out the math. Let's learn a process to help us."

2

Model a One-Step Problem (3 min)

Problem: The library has 8 shelves. Each shelf holds 9 books. How many books are on the shelves?

Think Aloud: "What's happening? The library has shelves with books. What do I know? 8 shelves, 9 books each. This is equal groups! I need to multiply: 8 × 9 = 72 books. Does it make sense? Yes—72 is more than 9 (one shelf) but not hundreds."

3

Model a Two-Step Problem (4 min)

Problem: Jake has 5 boxes of crayons with 8 crayons in each box. He gives 12 crayons to his friend. How many crayons does Jake have now?

Think Aloud: "First, I need to find how many crayons Jake has total. That's 5 × 8 = 40 crayons. Then he gives some away. That's subtraction: 40 - 12 = 28 crayons left. I did two steps: multiply, then subtract."

SAY THIS:

"Notice how I had to find something FIRST (total crayons) before I could answer the question. Two-step problems are like that—you need to figure out a piece before you can solve the whole puzzle."

4

Guided Practice: Different Operations (3 min)

Work through problems that use different combinations of operations:

Addition + Subtraction: "Sam had 45 stickers. He got 23 more, then gave away 15. How many now?" (45 + 23 = 68; 68 - 15 = 53)
Multiplication + Addition: "3 bags of 6 apples, plus 4 loose apples. How many total?" (3 × 6 = 18; 18 + 4 = 22)
Division + Subtraction: "36 pencils shared among 6 students. Maria uses 2. How many does she have left?" (36 ÷ 6 = 6; 6 - 2 = 4)

5

Independent Practice

Distribute worksheets. Remind students to: (1) read the whole problem first, (2) identify what they need to find, (3) break it into steps, (4) check if the answer makes sense.

🧠 Problem-Solving Strategies to Teach

Draw a Picture

Sketch the situation. Draw groups, arrays, or a simple diagram to visualize what's happening.

Act It Out

Use counters or students to model the problem physically. Great for "sharing" and "grouping" problems.

Write an Equation

Translate the story into numbers and symbols. Use a box or question mark for the unknown.

Work Backwards

Start from what you need to find. Ask: "What do I need to know to find this?"

💻 IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Two-step word problems Multiplication word problems Division word problems Addition and subtraction word problems Choose the operation Multi-step problems with all operations

🏠 Differentiation

For struggling students: Start with one-step problems only. Provide manipulatives. Use simpler numbers (single digits). Read problems aloud together.

For advanced students: Add a third step. Introduce problems with extraneous information. Ask students to write their own multi-step problems.

For home: Encourage parents to create word problems from real life: shopping (prices, quantities), cooking (recipes, servings), organizing (items, containers).