Lesson objective: Using place value and array models can make it easier for us to multiply two multi-digit numbers.

Students bring prior knowledge of multiplication arrays from 3.OA.A.1. This prior knowledge is extended to multi-digit arrays as students decompose both factors by place value in the array. A conceptual challenge students may encounter is connecting place value to each digit in the array using the base ten blocks.

The concept is developed through work with base ten blocks and place value, which allow for multiplication using two-digit arrays.

This work helps students deepen their understanding of operations because using place value and the distributive property to decompose numbers helps to solve multiplication problems with two multi-digit numbers.

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them) as they apply the base ten array concept to help them determine what is the best way to complete the array with two sets of double-digit numbers.

**Key vocabulary:**

- array
- base ten block
- cube
- decomposition
- flat
- place value
- rod

**Special materials needed:**