Lesson objective: Understand that place value can be used to multiply one-digit numbers by multiples of 10.

Students bring prior knowledge of representing and solving problems involving multiplication and division. This prior knowledge is extended to applying knowledge of place value as students multiply one-digit numbers by multiples of 10. A conceptual challenge students may encounter is thinking that multiplying one by the digit and "adding a zero" is a correct strategy.

The concept is developed through arrays, which illustrate the Commutative Property of Multiplication by showing that orientation of the picture and order of factors does not affect the product.

This work helps students deepen their understanding of numbers because understanding place value helps us multiply a one-digit number by any number that is a multiple of 10 (that has 10 as a factor).

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they explore patterns in place value and construct two-digit numbers to multiply with one-digit numbers. Examining patterns in arithmetic is rooted in the structure of a number system. Strategies move from skip-counting and repeated addition to multiplication, and the representations are arrays.

**Key vocabulary:**

- array
- factor
- place value
- product