Lesson 4

This warm-up prompts students to compare four images. It gives students a reason to use language about measurement precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the measurement tools, measurement units, and objects in the images. During the synthesis, ask students to explain the meaning of any terminology they use to describe the tools, objects, and lengths.

• Groups of 2
• Display image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “Si la unidad de longitud de las herramientas fuera centímetros, ¿cuáles imágenes muestran figuras que tienen una longitud de 4 centímetros? Expliquen” // “If the length unit on the tools should be centimeters, which images show shapes that have a length of 4 centimeters? Explain.” (A shows a length of 4 centimeters because the side starts at 0 and ends at 4. B shows 4 cm because I can count 4 cm lengths starting at the beginning of the ruler or counting back from the 4. C does not show 4 cm because each length between the numbers is not a cm. D shows 4 cm because I can count 4 cm lengths from 1 to 5.) 
• “Las herramientas para medir pueden ser diferentes. No en todas las herramientas se marca el 0. La primera unidad en algunas herramientas empieza justo al principio de la herramienta. En todas las herramientas para medir debe haber la misma longitud entre un número y el siguiente” // “Measuring tools can look different. Not all tools label 0. The first unit on some tools start right at the beginning of the tool. All measuring tools should have the same length between each number.”

The purpose of this activity is for students to practice the skill of estimating a reasonable length in centimeters based on their experiences and known information. When students compare and explain their estimates in pairs and in the full class discussion they make, interpret, and defend mathematical claims (MP3).

This activity uses the Estimation Exploration routine in the launch. This gives students the opportunity to revisit the meaning of estimation and estimate before making estimations on their own. The launch can be completed with the images provided or with an object that is more interesting to your students.

If needed, review all the objects that students will estimate as a class and record the names of each object (or length) so that all students can see.

• Each group of 2 needs access to several objects between 5–30 cm long and at least one object between 50–90 cm long.

• Groups of 2
• Give objects to each group.
• Display the image or a real notebook.

  

  

• “Andre quería medir la longitud de su cuaderno, pero no tenía ninguna herramienta para medirla. Él hizo una estimación que le pareció razonable” // “Andre wanted to measure the length of his notebook, but he didn’t have any tools to measure it. He made a guess that he thought would be close.”
• “Observen el cuaderno y piensen en qué tan largo creen que es en centímetros” // “Look at the notebook and think about how long you think it is in centimeters.”
• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.
• “Observemos otra imagen del mismo objeto” // “Let’s look at another image of the object.”
• Display the image or hold a folder next to a 10-centimeter tool.

  

  

• “Teniendo en cuenta la segunda imagen, ¿quieren ajustar o cambiar sus estimaciones?” // “Based on the second image, do you want to revise, or change, your estimates?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.
• “¿Cómo cambió su estimación?” // “How did your estimation change?”
• 30 seconds: quiet think time
• Share responses.

• As needed, display the names of the objects that students will estimate.
• “Ahora, observen los objetos que le entregué a cada grupo y piensen en qué tan largos son. Solos, escriban sus estimaciones en la hoja de registro” // “Now look at the objects I gave each group and think about how long they are. Record your estimates on the recording sheet on your own.”
• “Cuando ustedes y su compañero terminen, comparen sus estimaciones y expliquen por qué piensan que son ‘razonables’” // “When you and your partner finish, compare your estimates and explain why you think they are ‘about right’.”
• 5 minutes: independent work time
• 2 minutes: partner discussion

If students make estimates without justifying their thinking, consider asking:

• “Cuéntame más sobre cómo decidiste que el objeto medía aproximadamente ___ cm” // “Tell me more about how you decided that the object was about ___ cm.”
• “¿En qué objetos puedes pensar que midan aproximadamente 1 cm? ¿10 cm?” // “What objects can you think of that are about 1 cm? 10 cm?”
• “¿Cómo podrían las longitudes de los objetos que conoces ayudarte a explicar la longitud estimada de otro objeto?” // “How could the lengths of objects that you know help you explain the estimated length of another object?”

• Share and record estimates for each of the classroom objects.
• “¿Cómo hicieron sus estimaciones? ¿En qué pensaron?” // “How did you make your estimates? What did you think about?” (I thought about the size of a 10-centimeter tool and imagined measuring with it. I thought about the length of the ruler we made.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “¿Pueden imaginar una situación en la que tengan que estimar la longitud de un objeto?” // “Can you think of a time when you might need to estimate the length of an object?”

The purpose of this activity is for students to measure the lengths they estimated in the previous activity with a centimeter ruler to find the actual lengths. As needed, encourage students to use base-ten blocks to check their measurements to help them assess their accuracy and deepen their understanding of how length is represented on the ruler (MP2, MP6).

• Groups of 2
• Give students centimeter rulers and access to base-ten blocks.
• “¿Qué observan acerca de esta regla? ¿En qué se parece y en qué se diferencia de las reglas que ustedes hicieron?” // “What do you notice about this ruler? How is it the same and different from the rulers you created?”
• 30 seconds: quiet think time
• Share responses.
• Depending on your rulers, say one of the following:
  • “Miren el borde de su regla. Nuestras reglas tienen el 0 marcado, pero tienen un espacio antes del 0. Nuestras mediciones no serán correctas si empezamos desde el borde de la regla en vez de empezar en el 0. Así que necesitamos alinear nuestros objetos con el 0, no con el borde de nuestra regla” // “Look at the edge of your ruler. Our rulers have 0 labeled, but they have some space before the 0. Our measurements won’t be accurate if we start at the edge of the ruler instead of 0. So, we need to line up our objects with the 0, not the edge of our ruler.”
  • “Miren el borde de su regla. Parece que nuestras reglas empiezan en el 1 porque ese es el primer número. De todas maneras, hay un espacio antes del 1. Este espacio mide 1 centímetro de largo. El borde de nuestra regla es el 0, pero no había espacio para marcarlo. Así que, para medir correctamente, tenemos que alinear nuestros objetos con el borde de la regla de manera que empecemos desde el 0” // “Look at the edge of your ruler. It looks like our rulers start at 1, because that is the first number. There is some space before the 1, though. This space is 1 centimeter long. The edge of our ruler is 0, but there was no room to label it. So, in order to measure accurately, we must line up our objects with the edge of the ruler, so we are beginning at 0.”

• “Ahora vamos a usar nuestras reglas para medir los objetos y para encontrar sus longitudes reales” // “Now we will use our rulers to measure the objects to find their actual length.”
• 10 minutes: partner work time
• Monitor for a few students to share their chosen object in the synthesis.

• Invite previously identified students to share the chosen object.
• “¿Qué estimación de ____ sería razonable? Expliquen” // “What is an estimate for the ____ that is about right? Explain.”
• 1 min: quiet think time
• Share and record responses.
• Ask the student to demonstrate how they used the ruler to find the actual measurement, or, if possible, ask all students to find and share the actual measurement.
• Repeat with other objects, if time permits.