Lesson 8

The purpose of this warm-up is to elicit the idea that there is a unit of measure that is longer than a centimeter but is still small—an inch. This will be useful when students are introduced to customary units beginning with the inch tile and the inch ruler. While students may notice and wonder many things about these images, the difference in the length between tick marks on the rulers (the length-unit) is an important discussion point.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “¿En qué se parecen estas imágenes? ¿En qué son diferentes?” // “How are these images the same? How are they different?” (They both look like rulers. They both start with 0 and count up. One of the rulers lines up with the square from 0–1, but the other ruler does not show the same length unit.)
• “Hemos aprendido que hay diferentes unidades de longitud que podemos usar para medir. Hemos medido con unidades estándar del sistema métrico, como los centímetros y los metros. En la siguiente actividad, vamos a aprender más sobre una nueva unidad estándar que es más larga que un centímetro, pero mucho más corta que un metro” // “We have learned that there are different length units we can use to measure. We have measured with standard units from the metric system like centimeters and meters. In the next activity, we will learn more about a new standard unit that is longer than a centimeter, but much shorter than a meter.”

The purpose of this activity is to introduce the inch as a length unit in the U.S. customary system. In the launch, students use inch tiles and classroom objects that are “about an inch” to help them develop a benchmark for an inch. They may continue to use the inch tile to measure lengths in inches or as a tool for checking their measurements with a ruler throughout the lesson.

Although students have measured objects that are not a whole number of length units long in previous lessons, it will be more likely that students will measure lengths that are clearly not a whole number of inches long. Students should not record measurements to the half inch, but should instead discuss the reasoning they use to decide which whole number to use and the language they use to express that their measurement is not exactly that number of inches long (MP3, MP6).

• Each group of 4 needs access to several objects between 1–11 inches long. Consider using classroom objects such as markers, colored pencils, 11 connecting cubes, books, or any other object with a length shorter than 12 inches.

• Groups of 4
• Give students access to inch tiles and 12-inch rulers.
• Display image of an inch tile and a ruler.

  

  

• “¿Qué observan acerca de esta imagen? ¿Qué se preguntan?” // “What do you notice about this image? What do you wonder?” (The square fits between the 0 and the 1 on the ruler. The length of the side is the same as the length from 0 to 1 on the ruler. What is the name of the length unit? Does the square have a special name like the centimeter cube did?)
• 1 minute: partner discussion
• Monitor for students who say the units don’t look like centimeters or who wonder if it’s an inch.
• Share responses.
• “Han aprendido lo importante que es tener unidades estándar de medida” // “You have learned how important it is to have standard units of measure.”
• “Hemos trabajado con unidades métricas —centímetros y metros— que se usan en todo el mundo” // “We have been working with metric units—centimeters and meters—that are used around the world.”
• “En los Estados Unidos, nuestro sistema de medidas se llama 'sistema tradicional'. Una pulgada es la unidad más pequeña para medir longitud en nuestro sistema” // “In the U.S., our measurement system is called the customary system. An inch is the smallest unit for measuring length in our system.”
• Hold up an inch tile.
• “Esta es una ficha de pulgada. La longitud de cada lado de la cara cuadrada mide 1 pulgada” // “This is an inch tile. The length of each side of the square face is 1 inch.”
• As needed, invite students to use their rulers to verify that each side of the square face of the tile is 1 inch long.
• “¿En qué cosas pueden pensar que midan aproximadamente una pulgada?” // "What are some things you can think of that are about an inch?”
• 1 minute: quiet think time

• “Usen su ficha de pulgada para encontrar 2 cosas en el salón que midan aproximadamente una pulgada de largo. Anótenlas” // “Use your tile to find 2 things around the classroom that are about an inch long and write them down.”
• 3 minutes: independent work time
• Share and record responses.
• “Ahora van a medir algunos objetos en el salón usando una regla de pulgadas. Anoten la longitud de cada objeto en pulgadas” // “Now you are going to measure a few objects around the room using an inch ruler. For each item, record the length in inches.”
• 5 minutes: small-group work time
• Monitor for a student who measures an object that is not a whole number of inches.

Students may measure the correct number of length units, but record the length in centimeters or meters. Consider asking:

• “¿Cuál es la longitud de ___? ¿Cómo lo sabes?” // “How long is the ___? How do you know?”
• “Si usara las fichas de pulgada para medir __, ¿encontraría la misma medida?” // “If I used the inch tiles to measure the __, would I find the same measurement?”
• “Si usara cubos de un centímetro para medir __, ¿encontraría la misma medida?” // “If I used centimeter cubes to measure the __, would I find the same measurement?”
• “¿Cómo puedes ajustar tu medida para mostrar la longitud precisa?” // “How could you revise your measurement to show the accurate length?”

• Share a student’s object that is not a whole number of inches long.
• “¿Cómo podemos describir la longitud de _____ cuando su extremo no queda alineado con una de las marcas de pulgada de la regla?” // “How can we describe the length of the _____ when its end doesn’t line up with one of the inch marks on the ruler?” (If it is close to 3 inches, I can write “about 3 inches.”)
• 1 minute: quiet think time
• Share responses.

The purpose of this activity is for students to estimate and measure in inches. Students first estimate the length of given sides of shapes and then measure the sides using inch rulers. In the activity synthesis, students share how they measured the different sides and continue to discuss how to communicate the measurement of lengths that are not clearly a whole number of units long (MP6). They also make sure to indicate that their measurements are in inches since students now have both centimeters and inches they can use to measure lengths.

In the lesson synthesis, students discuss how they might measure longer lengths in inches. The discussion is designed to elicit their experiences with centimeters and meters and build curiosity for the next lesson in which students measure in feet.

• Groups of 2
• Give students access to inch tiles and 12-inch rulers.

• “Ahora podrán practicar la medición de los lados de figuras” // “Now you will get a chance to practice measuring the sides of shapes.”
• “Primero, estimen la longitud del lado y anoten su estimación. Luego, midan cada lado y anoten sus respuestas. No olviden las unidades: pulgadas” // “First, estimate the length of the side and record your estimate. Then, measure each side, and record your responses. Don’t forget to include the unit, inches.”
• 6 minutes: independent work time
• “Ahora comparen sus medidas con las de su compañero” // “Now compare your measurements with your partner’s.”
• 2 minutes: partner discussion
• Monitor for students who recognize that the third problem has a measurement that is more than 5, but not quite 6 inches.

• “Yo observé que algunos estudiantes tenían medidas diferente para el lado más largo del triángulo. ¿Por qué piensan que pasa eso?” // “I noticed that some students had different measurements for the longest side of the triangle. Why do you think that is?” (It was less than 6, but more than 5. It was in between 5 and 6 inches.)
• Invite previously identified students to share their reasoning for 6 inches.
• “Algunas veces, el objeto que estemos midiendo tendrá una longitud que esté entre 2 medidas de la regla. Escojan el número que está más cerca del extremo del objeto. Algunas veces, la longitud del objeto en pulgadas puede ser mayor o menor que la longitud real” // “Sometimes, the object we are measuring will have a length that falls between 2 measurements on the ruler. Choose the number that is closest to the end of the object. Sometimes the length of the object in inches may be longer or shorter than the actual length.”