# Lesson 1

Measure in Halves of an Inch

## Warm-up: What Do You Know About Inches? (10 minutes)

### Narrative

The purpose of this warm-up is to invite students to share what they know about inches. Later in the lesson, students will explore lengths that are not a whole-number of inches.

### Launch

• Display the question.
• “What do you know about inches?”
• 1 minute: quiet think time

### Activity

• Record responses.

### Student Facing

What do you know about inches?

### Activity Synthesis

• “Inches are a unit we use to measure length. What are some lengths that we could use inches to measure?“ (The length of a shoe. The length of material for an art project. The height of a desk.)

## Activity 1: Measure Around the Room (15 minutes)

### Narrative

In grade 2, students only measured the length of objects that were whole units and sometimes described lengths as “about 4 inches.” The purpose of this activity is for students to learn that fractions of an inch can be useful for measuring the length of an object that is not exactly a whole number of inches.

Given a ruler marked with inches, students measure objects around the room. They may record measurements in whole inches even for objects whose length is not exactly a whole number inches. In the synthesis, discuss the need for fractions of an inch to describe lengths more precisely (MP6).

The rulers from this activity are used in the next activity.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Attention, Organization

### Required Materials

Materials to Copy

• Measure Around the Room

### Required Preparation

• Make copies and cut out the rulers from the blackline master (5 rulers per page).

### Launch

• Groups of 2
• Give each student a ruler.

### Activity

• “Use your ruler to measure the length of objects in the room. Work with your partner. You should each choose 3 objects.”
• 5–7 minutes: partner work time
• Monitor for students who find objects that are not exactly whole numbers of inches. Highlight the objects and their measurement in the synthesis.

### Student Facing

Use the ruler from your teacher to measure the length of objects in the room. Be prepared to discuss your reasoning.
object length (inches)

### Activity Synthesis

• Display the inch ruler and an object that wasn’t exactly a whole number of inches.
• “What is the length of this object?” (Between 3 and 4 inches. More than 3 but less than 4. Three-and-a-half inches.)
• If needed, “Could we say that the length of this object is (a whole number of) inches.” (No, It's between 3 inches and 4 inches.)
• “We need a way to make our measurements more precise. We'll think about this more in the next activity.”

## Activity 2: Partition Inches into Halves (20 minutes)

### Narrative

The purpose of this activity is for students to partition the inches on a ruler to show half inches and then use their ruler to measure lengths to the nearest half of an inch.

The unpartitioned rulers from this activity are used in the next lesson.

MLR2 Collect and Display. Circulate, listen for and collect the language and numbers students use as they measure objects. On a visible display, record numbers, words and phrases such as: seven half inches, seven halves of an inch, $$\frac{7}{2}$$, between 2 and 3 inches, six and a half inches, $$6\frac{1}{2}$$, and less than 5 inches. Invite students to borrow language from the display as needed, and update it throughout the lesson.

### Required Preparation

• Each student needs a ruler from the previous activity.

### Launch

• Groups of 2
• “How could we adjust our rulers to measure lengths that are in between whole numbers?” (We could fold each inch into smaller equal parts. We could partition each inch into halves.)

### Activity

• “Work with your partner to partition every inch on one ruler into halves of an inch. Decide whose ruler you’ll partition. Leave the other ruler in whole inches.”
• 2–3 minutes: partner work time
• “Just like in the last activity, you may have objects that don't line up with one of the marks on the ruler. How might you record those lengths? Talk to your partner about it.” (Estimate how long the object is. Record the mark that is closest.)
• 1 minute: partner discussion
• Share responses.
• “Work with your partner to choose objects to measure to the nearest half inch. You should each measure 3 objects.”
• 5–7 minutes: partner work time

### Student Facing

You will need one ruler from an earlier activity.

1. Work with your partner to partition every inch on the ruler into halves of an inch.
2. Use the ruler marked with halves of an inch to measure some lengths around the room.
object length (inches)

### Student Response

If the parts students partitioned aren’t the same size, consider asking:
• “Tell me about how you partitioned the inches into halves.”
• “How could you make sure the halves are the same size?”

### Activity Synthesis

• “How did you measure the length of objects when the length was in between the marks on your ruler?” (We recorded the mark that was closest. The length was right between 1 inch and $$1\frac{1}{2}$$ inches, so we estimated the length to be about $$1\frac{1}{4}$$ inches.)
• “Save both rulers—the one you partitioned to show halves of an inch and the one that is not partitioned—for the next lesson.”

## Lesson Synthesis

### Lesson Synthesis

“Today we used a ruler to measure length in inches.”

“How is a ruler like a number line?” (The numbers go up as we move to the right. On both a number line and a ruler, each number has a location. On both, we can partition the wholes into halves.)

Display the length of one of the objects as a fraction greater than 1 and as a mixed number (for example, $$\frac{9}{2}$$ and $$4\frac{1}{2}$$).

“How could these two numbers show the same length?” (One tells us the number of whole inches and then how many half inches. The other tells us how many halves. They would be at the same location on the ruler, so they are the same length.)

“When we record the length in fractions that are greater than 1, we can record a fraction like $$\frac{9}{2}$$, or we can use a number that combines a whole number with a fraction less than 1 like $$4\frac{1}{2}$$. Numbers like this that combine whole numbers and fractions less than 1 are called mixed numbers.”