Math

Multiplying and Dividing Multi-Digit Numbers

Unit 6 of our Illustrative Mathematics resource.

Students begin the unit by using multiplication to analyze and extend patterns. They identify rules-sometimes involving addition and multiplication--or detect changes in digits to predict patterns. This process starts with growing visual patterns, progresses to repeated shape patterns, and finally transitions to numerical patterns without visuals.

Building on their prior knowledge of place value drawings and area diagrams, students multiply multi-digit numbers. They start with 2-, 3-, and 4-digit numbers multiplied by a single-digit number, using place value and rectangular diagrams to connect with the partial product algorithm. The key concept is decomposing factors by place value to calculate products (diagrams are not to scale). This approach is extended to multiplying two 2-digit numbers, emphasizing the need to decompose both factors. While students explore the relationship between partial products and the standard algorithm in lesson 11, mastery of the standard algorithm is not required until the end of grade 5.

Students begin solving 2-digit division problems by connecting division to multiplication and using place value blocks. They progress to solving up to 4-digit dividends and 1-digit divisors using the partial quotients method, building on base-10 concepts. The standard algorithm is not taught in grade 4; instead, students refine partial quotients in grade 5 and achieve fluency with the standard algorithm in grade 6. 

Unit 6 Family Support Video

Unit 6 Family Support Materials