CKMath Unit 6: Multiplying and Dividing Multi-digit Numbers
Focus:
In this unit, students extend their knowledge of multiplication and division to find products and quotients of multi-digit numbers. In grade 3, students learned that they could find the value of a product by decomposing one factor into smaller parts, finding partial products, and then combining them. To support this reasoning, they used base-ten diagrams (decomposing two-digit factors into tens and ones) and area diagrams (decomposing one side length into smaller numbers). Here, students use those understandings to multiply up to four digits by single-digit numbers, and to multiply a pair of two-digit numbers. Students begin by describing features of geometric and numerical patterns using ideas and language related to multiplication and multiplicative relationships (such as factors, multiples, double, and triple). Next, students reason about products of multi-digit numbers. They transition from using diagrams to using algorithms to record partial products. Students learn that they can multiply the factors by place value, one digit at a time, and then organize the partial products vertically. Later, students divide dividends up to four-digit by single-digit divisors. Students see that it helps to decompose a dividend into smaller numbers and find partial quotients, just as it helped to decompose factors and find partial products. They also recognize that sometimes it is most productive to decompose a dividend by place value. For instance, to find 465÷5, we can divide each 400, 60, and 5 by 5. Students encounter various ways to record the division process, including an algorithm that records partial quotients in a vertical arrangement. At the end of the unit, students apply their expanded knowledge of operations to solve multistep problems about measurement in various contexts—calendar days, distance, and population.
Number of Lessons: 24 and 1 optional
Instruction Time:
Approximately 60 minutes
(Please note that each lesson is designed for one instructional block, and may be divided into shorter or longer segments based on teacher pacing and student needs.)
