Problem Solving
Lesson Overview
This lesson helps students build confidence as they tackle more challenging mathematical situations by identifying the important parts of a problem and thinking through each step carefully. Students practise choosing the right math skills for each task and learn that complex problems become more manageable when they are broken down into smaller, clearer parts.
Through guided problem solving, students strengthen their reasoning, decision-making, and mathematical understanding as they work toward accurate solutions. The lesson encourages them to think critically, explain their thinking, and apply familiar skills in new ways so they become more independent and effective problem solvers.
Key Objectives
- Students develop problem-solving skills by breaking complex mathematical tasks into smaller, manageable parts and identifying the information needed to solve each part. They apply appropriate math skills accurately, use logical thinking, and check their work for reasonableness. Students also follow classroom safety and learning routines, handle materials carefully, and prepare to work independently or with support as needed.
- Whiteboard and marker
- Paper or exercise books
- Pencils and erasers
- Number cards or manipulatives
- Printed problem-solving worksheets
- Rulers
- Counting objects or counters
Introduce the Problem
Students listen carefully, spot the numbers, and notice what the question asks.
🌟 Today’s problem
There are 3 red apples and 2 green apples in a basket.
How many apples are there altogether?
| Important numbers | 3 and 2 |
|---|---|
| What is being asked? | How many apples are altogether |
| Helpful clue word | Altogether |
🗣️ Teacher prompts
- 1 Listen to the whole problem before answering.
- 2 Point to the numbers you hear.
- 3 Tell what the problem wants you to find.
- 4 Say whether the clue suggests counting or adding.
🧩 Quick visual
Break Down the Problem
Find the smaller parts first
Students look closely at the problem, name the important parts, and decide what they need to find first before solving.
Guided sequence
-
1
Listen again. Students hear the problem one more time and notice the key numbers, words, and what is being asked.
-
2
Say it in smaller parts. Students explain the problem in their own words and separate it into easy pieces.
-
3
Spot the first job. Students decide what they need to find first before any counting or calculating happens.
| Look for | Ask |
|---|---|
| Numbers | Which numbers matter? |
| Clue words | What words tell us what is happening? |
| The question | What do we need to find out? |
| First step | What should we do first? |
Thinking map
Teacher prompts
- What is this problem asking us to find?
- Which part do we understand first?
- Can you say the problem in your own words?
- What information do we need before we solve it?
Choose a Strategy
Students look at each small part of the problem and decide which math skill helps them move forward. The focus is on matching the strategy to the task, then saying why it fits.
Think Like a Solver
The teacher guides students to name the clue, choose a method, and explain their thinking in a simple sentence.
- Students choose counting when they need to find how many there are altogether.
- Students choose addition when they join groups or add more.
- Students choose subtraction when they take away or find what is left.
- Students choose another familiar method when it matches the problem best.
Strategy Match Table
| What students notice | Helpful strategy |
|---|---|
| More items are being added | ➕ Addition |
| Some items are being taken away | ➖ Subtraction |
| Students need to find the total by one-by-one counting | 🔢 Counting |
| The problem feels familiar in another way | ✅ A known strategy |
Teacher Prompts
- “What do you think this part of the problem is asking?”
- “Which math skill helps you solve this part?”
- “Why does counting, addition, or subtraction fit here?”
- “Can you say your strategy in your own words?”
Solve Together
Students work through the problem step by step, using the strategy they choose and showing their thinking as they go.
What the teacher does
- Leads the class through each step of the solution.
- Models clear thinking with simple, child-friendly language.
- Asks students to say what they notice before each move.
- Pauses to check whether the answer still matches the problem.
What students do
- Use the chosen strategy to solve one part at a time.
- Count, add, subtract, or group objects as needed.
- Point, say, or write each step of their thinking.
- Notice mistakes and make small corrections.
Step-by-step problem-solving flow
Helpful teacher prompts
- “What do we know first?”
- “Which part do we solve now?”
- “How does your strategy help?”
- “Does your answer match the problem?”
Check and Explain
Students review their answer, describe their thinking, and decide whether the result makes sense.
Teacher prompts
- “Show me how you solved it.”
- “Which step helped you most?”
- “Can you explain your answer in your own words?”
- “Does your answer match the story problem?”
- Read the problem again.
- Point to the numbers and answer.
- Explain each step using math words.
- Check if the answer is reasonable.
Quick visual check
Solve → Read again → Explain → Check ↑ ↓ └──── Does it make sense? ┘
Compare solution paths
| What students do | What they say | What the teacher notices |
|---|---|---|
| Explain the steps | “First I counted, then I added.” | Students can describe the order of their thinking. |
| Compare answers | “My friend used subtraction, and I used counting.” | Students notice different strategies can work. |
| Check reasonableness | “My answer is close, so it makes sense.” | Students connect the answer back to the problem. |
- Students say how they solved the problem.
- Students use simple math language to explain their ideas.
- Students notice when an answer is correct or needs fixing.