Exploring Double-Digit Multiplication

-Poonguzhali and SandhiyaBala

Exploring Double-Digit Multiplication with Number Tiles and Base-10 Blocks.

After building a strong foundation with single-digit multiplication, we moved on to the double-digit multiplication as the area of a rectangle with the two numbers representing the length and breath. We continued using Dienes blocks, and Polypad’s interactive tools.

Making Sense of Double-Digit Multiplication

We started by revisiting the structure of two-digit numbers:

“The number 23 is made of 2 tens and 3 ones.”

Using Dienes blocks:

• Unit cubes represented single units
• Tens rods represented groups of 10
• Hundreds plates represented groups of 100
• Students physically built multiplication rectangles like 23 × 13 and 26 × 14

We then explored multiplication using area models and arrays.

Students Built This on Polypad:

• Used number tiles and cubes to represent each of the 4 areas (product of 10s as 100, product of ones and tens (2) as tens and product of ones as ones)
• Counted and added up all the products

In this example, students created a 23 × 13 array using colored number tiles on Polypad. This allowed them to observe:

• Visualize the product as a rectangular area
• Break the numbers into tens and ones
• Count smaller sections to understand how multiplication builds up
• See how rows and columns represent the factors
• They understood that multiplication is not just a number sentence, but a pattern in space

Children explored

Double-digit multiplication is easier when numbers are broken into parts.

The area model helps organize thinking.

Visual tools help them see and understand how multiplication works.

Counting tile blocks helped with mental math and estimation.

They felt confident trying new problems independently.

Impact on Learning

Helped children better understand place value

Helped children feel that big multiplication problems are easier to do

Made children feel more confident when working with bigger numbers

Children saw that multiplication has a clear pattern and can be shown with pictures.