Area Model Multiply

Overview

In this lesson 10 of 12, students learn to multiply a 2-digit number by a 1-digit number using an area model. They will connect partial products to the distributive property and practice explaining the total number of objects represented by the model.

Learning intentions

• Students will be able to represent a 2-digit number as tens and ones in an area model.
• Students will be able to multiply tens and ones separately by a 1-digit number.
• Students will be able to add partial products to find the total product.
• Students will be able to explain how multiplication relates to repeated groups in a real context.

Success criteria

• I can draw an area model for (tens + ones) × 1-digit and label each region.
• I can find the products for the tens part and the ones part correctly.
• I can add the partial products to get the total product.
• I can explain why my answer makes sense using the model.

Curriculum links

• Operations and Algebraic Thinking: interpret products as totals of groups.
• Operations and Algebraic Thinking: use properties of operations and distributive property to find products.
• Operations and Algebraic Thinking: fluently multiply within 100 using strategies and properties; recall basic facts.

Lesson structure (60 minutes)

1. 0–8 min · Warm-up: “Groups in pictures.” Teacher displays a simple array picture (e.g., 4 groups of 7) and asks students to state the total as 4 × 7, then explain what each factor means. Students answer with a short verbal explanation and a number sentence.

2. 8–20 min · Mini-lesson: Build the area model. Teacher models (34 × 6) by drawing a rectangle partitioned into tens and ones columns, labeling 30 and 4 along the top (or side) and labeling 6 rows. Students help label each region and predict two partial products before multiplying.

3. 20–32 min · Guided practice: Tens and ones partial products. Teacher completes the example with students:

• 30 × 6 (tens region)
• 4 × 6 (ones region)
• Add totals to get 34 × 6 Students copy the area model, calculate each region, and write the final equation using addition of partial products.

4. 32–45 min · Partner-style practice (teacher-led since 1 student). Teacher gives two problems on the board: (42 × 3) and (57 × 4). Teacher draws the area model outline for the first problem and students fill in products for each region; for the second problem, students draw the partition lines independently while the teacher checks labels. Students produce correct region products and totals.

5. 45–52 min · “Match the story to the model.” Teacher reads a word problem: “A craft table has 5 bags of 23 beads each. How many beads are there?” Teacher asks: What does 23 represent, and what do we do with the tens and ones? Students connect the factors to an area model interpretation and write a multiplication sentence and partial products.

6. 52–58 min · Formative check: Quick area model exit response. Teacher projects a partially blank area model for (63 × 2). Students complete the labels and compute the total, then explain one sentence: “I multiplied ___ because it represents ___ groups of ___.”

7. 58–60 min · Wrap-up: Strategy reflection. Teacher asks: “How does the area model show the distributive property?” Student shares a brief explanation connecting (tens + ones) × 1-digit to tens×digit plus ones×digit.

Resources

• Grid paper or blank area model templates
• Base-ten blocks or two-color counters (tens and ones)
• Whiteboard/markers and student notebook
• Colored pencils (or one-color + pencil for tens/ones)
• Word problem cards (printed)
• Small set of multiplication fact cards (for quick recall)
• Projector or interactive board (optional)

Assessment

• During warm-up, listen for correct interpretation of factors as groups and totals.
• During guided and independent practice, check that students:
• correctly split the 2-digit number into tens and ones in the model
• multiply each region accurately
• add partial products to get the total
• Exit response: accuracy of region products, total, and one-sentence reasoning from the model.

Differentiation

• Support: Provide sentence starters for explanations, such as “The tens part is ___ and the ones part is ___, so I multiply ___ and ___. Then I add ___. ” Offer a pre-drawn area model for the first problem.
• Support for computation: Encourage using known facts (e.g., 3 × 30 as 3 × 3 then add a zero based on place value).
• Extension: If ready, ask an additional question: “What would the area model look like for (63 × 5)?” Students can sketch without full computation, focusing on correct region labeling.
• EAL/SEN considerations: Keep language consistent: “tens,” “ones,” “rows,” “regions,” “partial product,” and “total.” Use gestures to point to regions while computing. Provide extra wait time for explanations.