To begin this lesson, I review ordering fractions on a number line. Using a class number line on the whiteboard, I mark zero and one at opposite ends of the number line. At the same time students are using individual whiteboards to create their own number line. For this lesson, I chose to use ordering fourths and eighths on the number line, but this could be modified to fit any classroom needs. I chose these fractions because they are used on rulers, and will give the students exposure to measuring with eighths. The Common Core standards for third grade have the students measure with halves and fourths.
I give the students fractions in random order to fill in on their number line. During this time, I use this process as a formative assessment to identify students who may still need additional assistance in ordering fractions or for students who may require enrichment and extension of this type of activity. Once all of the fractions have been given, I provide a the answers on the class number line to the students to check their work.
During guided practice the students are shown a picture of a broken ruler diagram. For example, the ruler can be broken at either end to show unit marks beginning at 3, 6, or 9. I model for the students how they can approach this type of problem by renumbering the ruler or through subtraction. I explain and connect the broken ruler to using a number line and counting jumps to find the length of an object. Each of the objects is measured using one of these different strategies and the broken ruler.
I model measuring with the broken ruler using common classroom items including a small book, a post-it note, and a small remote.
This type of problem is typically found on some standardized tests before the transition to the PARCC exam. Even though this is a skill learned in previous grades, it is something I choose to review because it does support their use of measuring and creating a line plot in future lessons.
I use strips of paper to represent "broken" rulers for the students. Students fold these strips into half repeatedly to create 16 different sections and number them from 1 to 16, or for some students they include the half marks that will be using when creating line plots in third grade.
Once the rulers are numbered, they must break off a section of the ruler to complete their measuring activities.
Students gather five objects to record and measure. I have the students work independently so that each student is actively working on measuring items and calculating the length of the objects. The items and measurements are recorded for accountability. To challenge students, I encourage them to measure something that may be longer than their ruler.
To close this activity the students record their model of a broken ruler. I create a context for their written response about how well they did with this activity, so I say the second grade teachers have asked for their help. Each one of the students in second grade needs instructions on how to use a broken ruler correctly. My students are asked to write step-by-step instructions that a second-grade student can use to measure with a broken ruler.