Which is Longer?

Task

Materials

• Blackline Master
• Pencil or Crayons
• Long, skinny objects to compare; for example:
  • a pair of scissors
  • a crayon
  • a glue stick
  • a long, skinny wooden block from the classroom block set
  • a marker

Actions

The teacher will pre-select a group of classroom objects (8-12) for the students to use. Each student will choose two objects to compare and they will lay them next to each other and compare which is longer. The teacher may need to show students that they need to make sure the starting ends are correctly lined up, like this: Not like this this: The teacher can have the students record their findings in one of two ways: * Students can trace both objects on a black piece of white paper. The students can label their drawings depending on their literacy skills and then circle the longer object. * Students can use the attached blackline master. This requires higher level skills as students must decide which object is the longer and shorter object, conserve that information in their brain and then write the word/draw pictures (not trace) of the item in the correct box. This also asks students to work with both the concepts longer and shorter instead of simply determining which is longer. Students should repeat the activity with multiple pairs of objects.

IM Commentary

The purpose of this task is for students to compare two objects to determine which object is longer and which object is shorter. This task asks students to work at the most basic level of measuring for kindergarteners, comparing one object to another without the use of a measuring tool (such as unifix cubes). Once students can easily compare objects and competently discuss their findings they can move on to 1.MD How Long?

Technically, length is a property of one-dimensional objects such as line segments. However, students need opportunities to think about how to measure objects in their world. The objects suggested above are purposefully chosen so that one dimension is clearly much bigger than the other two dimensions. If available, Cuisenaire rods would be ideal for this. When students get older, they will measure the lengths of the two dimensions of two-dimensional objects (like the base and height of a piece of paper) and the lengths of the three dimensions of three-dimensional objects (like the base, height, and width of a box).

The word "length" gets used with two different meanings. In everyday usage, people talk about the length of a 3-D object when they mean the largest dimension. For example, they might look at a book and say the length is the longest side. Especially at later grades, this usage can make it harder for students to distinguish between the longest side of a rectangle and the length of a chosen side of a rectangle. So taking care with students' first experiences measuring length will help them avoid pitfalls later in their mathematical careers.

1.MD How Long? is grouped with the first grade tasks because in that task, students measure each object with unifix cubes, count the unifix cubes and record their answer on paper. Only after students have mastered comparing the length of two object should students move on to something like 1.MD How Long?. The kindergarten standards do not specify that students must measure using nonstandard units such as unifix cubes, however this skill is a natural extension and something that is appropriate for kindergarteners who have mastered comparing objects. It is within the scope of the standards and the quote from the K-5 Geometric Progression document speaks to the importance of kindergarteners measuring with a non-standard measuring tool if they are ready.

Students who have these competencies can engage in experiences that lay the groundwork for later learning. Many can begin to learn to compare the lengths of two objects using a third object, order lengths, and connect number to length. For example, informal experiences such as making a road “10 blocks long” help students build a foundation for measuring length in the elementary grades.

Additionally measuring with the non-standard object supports students’ emerging counting and number-writing skills.

The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.

This particular task helps illustrate Mathematical Practice Standard 6, Attend to precision. Kindergartners will be working with the most fundamental ideas of measurement during this activity, directly comparing two objects to determine which object is shorter and which is longer. Since this may be a new experience for kindergartners, there will be learning involved as to how to position the two objects to accurately and precisely compare their lengths. The necessity of aligning endpoints can be explicitly addressed and reinforced throughout this task (MP.6). The opportunity for conversation often occurs in comparison situations (“This crayon is shorter than my new pencil!”) and provides an opportunity for students to explain which objects are longer or shorter using their new vocabulary (MP.3, MP.6).

Solution

The blue block is longer than the red block. The red block is shorter than the blue block.