Lesson 3

The purpose of this warm-up is to elicit the idea that a ruler can be marked with halves and fourths of an inch, which will be useful when students use a ruler like this in a later activity. While students may notice and wonder many things about these rulers, focus the conversation on how the quarter-inch marks are distinguished from the half-inch and whole-inch marks. 

• Each group of 2 needs the rulers from the previous lesson.
• Cut out a ruler from the blackline master for each student.

• Groups of 2
• Make sure each group has rulers from the previous lesson.
• Give each student a ruler from the blackline master.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “How is this ruler like the rulers you used in earlier lessons?” (They all have marks showing whole inches and are partitioned into smaller parts.)
• “How is it different than those rulers?” (We had one ruler showing fourth inches and one showing half inches. On this ruler, both halves and fourths are shown. The marks for whole inches and half inches are different from those for fourth inches.)
• “On these rulers, the location of 0 is shown with a label. On some other rulers, there’s no gap between the edge of the ruler and the 0, so the edge itself is the 0. Before you use a ruler to measure, it’s good to look at the ruler and check where the 0 is located.”
• Consider showing students a ruler where one edge of the ruler marks the location of 0, if available.

The purpose of this activity is for students to measure lengths using a ruler that is marked with half inches and quarter inches. Building on their understanding of equivalent fractions, students recognize that lengths that line up with a half-inch mark can be read as one-half of an inch or two-fourths of an inch. They also recognize that lengths that are whole numbers of inches can be expressed as fractions.

• Each student needs a ruler marked with half inches and quarter inches from the warm-up.

• Groups of 2
• Display the problem.
• “Think about how Kiran and Jada record the length of the worm. Use the ruler to explain how both of their measurements make sense.”
• 1 minute: quiet think time
• 2–3 minutes: partner discussion
• Monitor for students that say they both make sense because \(4\frac{1}{2}\) is equivalent to \(4\frac{2}{4}\) and select them to share their responses.
• Make sure each student has a ruler marked with half inches and quarter inches from the previous activity.

• “Now, work with your partner to measure the length of some worms. Some lengths can be recorded in more than one way. Be ready to explain how you recorded each length.”
• 3–5 minutes: partner work time

If students start measuring from the edge of their ruler instead of from 0, consider asking:

• “In the image for the first problem, how is the ruler lined up to the worm?”
• “Why does it make sense to not line up the left end of the ruler with the left end of the worm?”

• Invite students to share how they recorded their measurements and why they chose to record them in the way they did.
• “Let’s think more about the first worm you measured. What are all the ways that we could record its length?” (4 inches. \(\frac{8}{2}\) inches. \(\frac{16}{4}\) inches.)
• “What are all the ways that we could record the length of the last worm?” (\(3\frac{1}{2}\) inches. \(3\frac{2}{4}\) inches. \(\frac{7}{2}\) inches. \(\frac{14}{4}\) inches.)
• “We can use different numbers to describe the same length because the numbers are equivalent.”

The purpose of this activity is for students to practice measuring with a ruler that is marked with halves and fourths of an inch, as well as to identify lengths that can be described in different ways because they are equivalent. This activity gives students an opportunity to attend to the details of each measurement and to use language precisely (MP6). Students are prompted to find objects with whole-number lengths and those with fractional lengths. The work here allows students to reinforce earlier work on expressing whole numbers as fractions and naming equivalent fractions.     

• Each student needs a ruler marked with half inches and quarter inches from the previous activity.

• Groups of 2
• Make sure each student has a ruler marked with half inches and quarter inches from the previous activity.
• “We are going to practice measuring some objects around the room with the same ruler you used earlier.”
• “Take a minute and think about some things you could measure. Write down the objects as you think of them.”
• 1 minute: independent work time
• Share student responses. Encourage students to add objects to their list that they didn’t have.

• “Work with your partner to measure these objects and record the length of each object.”
• 5–7 minutes: partner work time
• “Now, trade lists with another group. Find an object whose length could be recorded a different way. Record the object, its length, and an equivalent length.”
• 2 minutes: group work time
• Repeat as many rounds of trading lists and recording equivalent lengths as time allows.
• Monitor for students who write fractions that are equivalent to whole-number measurements.

• “Discuss with your partner how you used equivalent fractions as you measured lengths today.” (The ruler is marked with half inches and quarter inches. I knew that the mark for \(\frac{2}{4}\) was also the mark for \(\frac{1}{2}\).)
• “Since some of the marks on the ruler can be described with halves or fourths, how did you decide which way to describe the lengths you measured?” (If the end of the object landed right on one of the half marks, we described it as a half. If it landed in between the half marks, we used fourths to describe the length.)
• Select previously identified students to share the equivalent lengths they wrote.
• If no students express whole numbers as fractions, ask: “Could 7 inches be expressed in another way? How many half inches is that? How many quarter inches?”