Module 3 opens in Topic A by extending students’ kindergarten experiences with direct length measurement to indirect measurement whereby the length of one object is used to compare that of two other objects (1.MD.1). Students explore direct comparison in Lesson 1, comparing the length of two objects paying close attention to the endpoints of each to ensure accurate comparisons. Students draw on their kindergarten experiences as they use longer than and shorter than as they compare. In Lesson 2, students begin to use indirect comparison (or transitivity) as they compare each item to one consistent item, such as a piece of string or a strip of construction paper of a specific length. Items are then compared to each other through indirect comparison. For instance, if the crayon is shorter than the paper strip and the pencil is longer than the paper strip, we can say that the crayon is also shorter than the pencil. As a way to prove their conclusions from indirect comparisons, students use direct comparison to verify their claims. Lesson 3 extends the use of indirect comparison to compare distances between objects that cannot be moved next to each other for direct comparison. Students use the same transitive process to compare short distances within the classroom in order to see what the shortest path to their classroom door is, which is helpful to know for lining up and emergencies. After measuring each path from their desks to the door with the same piece of string, students are able to make statements such as, “Maya’s path is shorter than the string. Bailey’s path is longer than the string. That means Bailey’s path to the door is longer than Maya’s path.”
Module 3, Topic B adds a new level of precision to measurement by introducing the idea of a length unit. In Lesson 4, centimeter cubes are laid alongside the length of objects as students learn that the total number of cubes laid end to end with no gaps or overlaps is the length measure of that object. The objects being measured by students include many of the same objects measured in Topic A so that students can add greater precision to their measurements as they specify the number of units equal to the length of the objects being compared. For example, the length of the crayon can now be described not only as shorter than the paper strip but more precisely as 9 centimeter cubes (1.MD.2). In Lesson 5, students lay those same centimeter cubes alongside a ruler, recognizing the meaning of the numbers on the ruler as describing the number of centimeter length units up to that number. The centimeter then connects students to their world, as they come to realize that the centimeter unit is used by first-grade students in Brazil, by the restaurant owner across the street, and even by their families. Students explore the question, “Why would we use a standard unit to measure?” As the use of rulers to measure is a Grade 2 standard, students in Grade 1 simply rename their centimeter cube as a centimeter, as they continue to use the cubes to measure objects. The progressions document suggests that students engage in standard unit measurement in order to develop a solid understanding of why and how to measure, rather than measuring using a plethora of nonstandard measurement units. The topic closes with Lesson 6, where students measure and compare sets of three items with centimeter cubes, returning to the transitive statements of Topic A but with more sophisticated insights: “The pencil measures 10 centimeters. The crayon measures 6 centimeters. The book measures 20 centimeters. In order from shortest to longest is the crayon, the pencil, the book. The book is longer than the pencil, and the pencil is longer than the crayon, so the book is longer than the crayon” (1.MD.1). Students finally solve compare with difference unknown word problems, determining how much longer a given object is than another.