Lesson Plan: Teaching Math for Understanding, Not Memorization

Grade Level: 3–5

Subject: Mathematics

Time: 60 minutes

Focus Concept: Multiplication as Equal Groups (can be adapted to other topics)

Learning Objectives

Students will:

• Understand multiplication as equal groups, not just a memorized fact

• Represent multiplication using models (arrays, drawings, repeated addition)

• Explain their thinking using words, numbers, and visuals

• Solve problems using more than one strategy

Materials

• Counters or small objects (e.g., cubes, beans)

• Grid paper

• Whiteboard/markers

• Chart paper

• Math journals

• Printable Worksheet

Lesson Sequence

1. Warm-Up (10 minutes) – Number Talk

Write on the board:

4 × 6 = ?

Ask students:

• “How can you solve this without memorizing?”

• “What does 4 × 6 mean?”

Record different strategies:

• 6 + 6 + 6 + 6

• 4 + 4 + 4 + 4 + 4 + 4

• (4 × 3) + (4 × 3)

Goal: Activate prior knowledge and show multiple ways to think.

2. Mini-Lesson (15 minutes) – Build Understanding

Step 1: Concrete Model

Give students counters:

• “Show me 4 groups of 6.”

Discuss:

• What do you notice?

• How many total?

Step 2: Visual Model (Array)

Draw an array:

● ● ● ● ● ●  
● ● ● ● ● ●  
● ● ● ● ● ●  
● ● ● ● ● ●   

Ask:

• “How does this show 4 × 6?”

• “What else could it represent?” (6 × 4)

Step 3: Connect to Equation

Write:

• 4 × 6 = 24

• 6 × 4 = 24

Emphasize meaning, not just answer.

3. Guided Practice (15 minutes)

Give students a problem:

“There are 3 bags with 8 apples in each. How many apples are there?”

Students must:

• Draw a model

• Write an equation

• Explain their thinking

Use Think-Pair-Share:

• Think independently

• Discuss with partner

• Share with class

Teacher prompts:

• “Why does your model make sense?”

• “Can you solve it another way?”

4. Independent Practice (10 minutes)

Students complete in journals:

Solve and show 2 different strategies:

1. 5 × 7

2. 6 × 3

They must include:

• A drawing or array

• An equation

• A written explanation

5. Closure (10 minutes) – Reflection

Ask:

• “Why is understanding multiplication better than just memorizing it?”

• “What strategy helped you the most today?”

Exit Ticket:
“Solve 4 × 5 and explain how you know your answer is correct.”

Assessment

• Observation during discussion

• Student models and explanations

• Exit ticket responses

Look for:

• Conceptual understanding
• Use of multiple strategies
• Ability to explain reasoning

Differentiation

Support (Struggling Students)

• Use smaller numbers

• Provide pre-drawn arrays

• Work in guided small groups

Extension (Advanced Students)

• Explore:

  • “What is 12 × 4 using what you know?”

  • Break apart strategy (10 × 4 + 2 × 4)

• Create their own word problems

Best Practice Strategies Embedded

• Multiple representations (concrete → visual → abstract)

• Student discourse and explanation

• Open-ended problem solving

• Emphasis on reasoning over speed

• Productive struggle

Teacher Reflection (After Lesson)

• Did students explain why, not just what?

• Were multiple strategies visible?

• Which students relied on memorization vs understanding?

Optional Extension Activity

“Multiplication Gallery Walk”
Students post their strategies around the room and walk around to analyze others’ thinking.

Read related Best Practice article: Teaching Math for Understanding, Not Memorization

Posted: 3-27-26

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