Here’s a string I designed with a team of fifth grade teachers who were looking for creative ways to encourage a multiplicative understanding of place value. When students are reasoning additively about number, they might see 321 as equivalent to (3 x 100) + (2 x 10) + (1 x 1). And this is very common in classrooms, and is often confused as thinking multiplicatively because it does involve some multiplication. But in essence you are splitting the number into place value parts and adding those together. When students are able to reason multiplicatively about number it looks more like this: 321 = 32.1 x 10 or 3210 ÷ 10.