• Monitor student responses during the Attribute Pictures activity (M-4-1-1_Attribute Pictures.doc) and use this information to decide if additional practice or challenge is warranted.
• Check students’ ability to accurately measure to the nearest  inch and centimeter on the Measuring Lines worksheet.
• Facilitate students’ responses to questioning and use this feedback to determine if a change in strategy is necessary.
• Use an exit ticket for a final check on students’ understanding at the end of the lesson.

“In today’s lesson we are going to explore the concept of measurement. We can measure different objects based on an object’s attributes. An attribute is a characteristic of an object. For example we can measure an object’s length, width, height, mass, capacity/volume, area, and temperature. We also can measure time. Measurement of different attributes is done using different tools like a ruler, scale, thermometer, or clock, along with different units like inches, pounds, degrees, or minutes.

“There are different units of measurement we can use based on an object’s attributes. You would not necessarily want to measure the length of a piece of notebook paper with the same unit of measurement as you would to measure the length of a football field. Just like you would not necessarily want to measure the mass of a paper clip using the same unit of measurement as you would to measure the mass of an elephant. Let’s look at a few pictures and decide what attribute of the object you can measure, and what unit of measure you could use.” (M-4-1-1_Attribute Pictures.doc) Post pictures where students can see them. Record attributes students choose and the various units of measure that can be used. Guide students to generate as many different units as possible.

Possible responses:

“In the next part of the activity we are going to actually measure some objects. We will focus on the attributes of length and width. We will use a ruler as our tool to measure. The units we will use are inches and centimeters. Remember there are two commonly used systems of measurement: the U.S. customary units of measure and the metric system of measure. Inches are a part of the U.S. customary system, while centimeters are a part of the metric system. The United States is one of very few places in the world that uses the U.S. customary units of measurement. Most of the world uses the metric system of measurement.”

Be sure each student has a ruler that has inches and centimeters. Model using a ruler and explain to students the following:

• A ruler is a tool to measure length.
• A ruler is usually 12 inches in length, or one foot.
• A ruler may also be marked in centimeters.
• A ruler has a starting point. Sometimes it is the edge of a ruler and sometimes it starts with 0. It depends on how the ruler is labeled. The starting point needs to be checked each time you use a different ruler.

Using the Inch Ruler (M-4-1-1_Inch Ruler.doc) show students how the ruler is divided into different units of length. Begin with the customary unit of measure. Show the markings for an inch, half inch, and quarter inch. To reinforce this concept you can use the Blank Ruler (M-4-1-1_Blank Ruler.doc) to review the markings without the labels. Remind students that there are other markings on the ruler that can be used to measure to the nearest eighth inch and sixteenth inch but at this time, students are only responsible for understanding the quarter-inch markings.

“Remember that an inch can be divided into halves and fourths. Let’s assume this piece of paper I am holding is 1 unit long. For now, let’s pretend the paper represents 1 inch.” (Use any sheet of blank white paper.) “If I fold the paper in half and then unfold it, the crease represents the  inch mark. The 1 (or numerator) represents the part, and the 2 (or denominator) represents the number of parts that make a whole. Now if I fold the sheet of paper back in half and then fold it in half again, this means I am dividing the inch into fourths, quarters, or 4 equal pieces. Notice when I unfold the piece of paper now, I have two new creases. The first new crease represents  inch. Notice how the  inch crease could also be labeled  inch. There is still one crease not labeled; this third crease represents   inch.”

At this point it may be beneficial for students to repeat this activity individually. Give them some time to complete the task. It does not matter what size paper students use. Just remind students that the piece they are using represents an inch, and it is not to scale. If students do use the same size paper they can put their pieces side by side to see the pattern of how a ruler is constructed.

“Each inch on a ruler has similar markings. The length of the markings on the ruler can help you to identify the measurement of an object. For a half inch, the inch is divided into two equal sections, so look for the marking in the middle of the inch markings. For a fourth inch, the inch is divided into four equal sections. So look for the shorter markings between the inch and half inch markings. Centimeters can also be divided into smaller sections, called millimeters. Each centimeter has 10 millimeters, which are shown as 10 small marks in between each centimeter on a ruler. When measuring lengths in centimeters, it is often best to give your answer to the nearest whole centimeter, plus any additional millimeters. Measuring objects takes practice.”

Give each student the Measuring Lines worksheet (M-4-1-1_Measuring Lines and KEY.doc). Remind students to measure to the nearest  inch or millimeter depending on the directions. While students are working, monitor for accuracy. Provide
on-the-spot remediation for those students who may not be correctly or accurately using a ruler. To assess understanding, ask students questions similar to the ones listed below while they are working.

• Where is the starting point on your ruler? How do you know? (depends on the ruler; either the left edge or the first marking)
• If you are measuring length in inches, which side of the ruler do you use? What about centimeters? (the inch side; the centimeter side)
• What steps do you take to measure the length of a line to the nearest  inch? (First count how many full inches the length spans. Then measure the remaining part by looking at which quarter mark () the length is closest to.)
• How do you know which is the nearest  inch? (Look at the quarter mark () that the end of the line you are measuring is closest to.)
• How do you know where  inch is located? (the middle mark between 0 and 1 inch)
• If you wanted a line that measured  inches long, where would that be on your ruler? (past the 5-inch mark, to the third-quarter mark before the 6-inch mark)
• When using centimeters, how can you measure to the nearest millimeter? (First count how many full centimeters the length spans. Then count the millimeter tick marks until you have reached the end of the line you are measuring.)
• If you wanted a line that measured 3 centimeters long, where would that be on your ruler? (at the 3-centimeter mark, halfway in between the 2- and 4-centimeter marks)

For those students who may finish early and demonstrate proficiency, ask them to find a partner. Give partners a target number like  in., 6 cm, 8 in., or 2 cm and 7 mm. Have each student try to draw a line that is approximately that length. Then have students switch with their partner and measure the lines. See how close each student estimated the length while practicing measuring to the nearest  inch or centimeter (with millimeters). By the end of the lesson be sure all students have at least been exposed to this activity so that students can begin to make reasonable estimates of length.

Students can complete an exit ticket (M-4-1-1_Exit Ticket and KEY.doc). An exit ticket is a strategy that can be used as a quick formative assessment. With about
5–10 minutes left in class, students can be given an exit ticket which they will hand in before leaving. Look over student responses for thoroughness and accuracy to determine which students have a strong understanding of the concept and which students may need additional support.

“Today we focused on measuring the length of objects to the nearest  inch and nearest centimeter (with millimeters). Using and reading your ruler correctly is important to get an accurate measurement of length.”

Extension:

Use the following strategies and activities to meet the needs of your students during the lesson and throughout the year.

• Routine:
  • Option 1: Show students a randomly drawn line on a piece of paper. Have students estimate its length to the nearest  inch or the nearest centimeter. Then have a student model the process of measuring the line to the nearest  inch or nearest centimeter with a ruler. Students can check their estimates.
  • Option 2: Have students work with partners. Have students draw a line on a piece of paper and exchange it with a partner. Students can measure each other’s lines to the nearest  inch or centimeter. Then students can switch back and check each other’s measurements. This activity provides immediate feedback.
  • Small Group: Students may need to go back and practice measuring to the nearest inch to create proficiency in this skill. Students can be asked to measure lengths of objects in the classroom or the lengths of lines drawn on a piece of paper. Once proficiency is shown in measuring to the nearest inch, students then can be asked to measure to the nearest  inch. This will allow students to become more familiar with the ruler and its markings. Once students feel comfortable measuring to the nearest inch, and then reintroduce the markings students would use to measure to the nearest  inch. Use the Inch Ruler to reinforce the different markings on a ruler.
  • Expansion: Those students who demonstrate proficiency in linear measurement can extend their learning with conversions of inches, feet, and yards. A general rule for students to understand is that when you are converting from greater to lesser units of measure, multiply or do repeated addition. When you are converting from lesser to greater units of measure, divide or do repeated subtraction. By exploring a ruler and yardstick, if available, students can determine that there are 12 inches in a foot, 36 inches in a yard, and 3 feet in a yard. Have students practice with conversions using the Conversions for Linear Measure worksheet (M-4-1-1_Linear Measure Conversions and KEY.doc). Post answers where students can check their own work for immediate feedback. The following Web site is like a Memory Game, where students match U.S. customary conversions: http://www.quia.com/cc/65838.html. Students can click on “show answers” to see conversions if they need that type of support.
    Students then can explore other types of conversions like minutes to hours and create problems that a classmate can solve. Students can record their problems on a Conversion Task Card (M-4-1-1_Conversion Task Card.doc). By folding back the answer, students can check their work after exchanging with a partner for immediate feedback.

This lesson is designed to focus on the concept of measurement. Students will demonstrate a general understanding of the appropriate units needed to measure length, mass, volume, area, and temperature. Students are not necessarily expected to do actual measurements in these different areas; rather, they are to be familiar with the various units that can be used. Linear measure will be a focus where students will be asked to measure items to the nearest  inch and centimeter using a ruler.