Lesson 2

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 100. These understandings help students develop fluency and will be helpful later in the unit when students add two-digit numbers within 100. When students share methods based on adding tens and tens and ones and ones, they show they are looking for and making use of the base-ten structure of two-digit numbers (MP7).

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Alguien usó el mismo método, pero lo explicaría de otra forma?” // “Did anyone have the same method but would explain it differently?”
• “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”

The purpose of this activity is for students to identify objects that are longer or shorter than a given object. Students find two objects that are longer and two objects that are shorter than an unsharpened pencil. The students use the language of “longer than” and “shorter than” and record their findings in complete sentences so that indirect comparison can be discussed during the activity synthesis.

• Each group of 4 students needs access to the materials from the previous lesson and one unsharpened pencil.
• Create a two-column chart with the headings “longer” and “shorter” for the synthesis.

• Groups of 4
• Give each group an unsharpened pencil and access to the objects from the previous lesson.
• Display two objects that are not the same length (for example, a crayon and a marker).
• “Comparen las longitudes de estos objetos. ¿Qué pueden decir?” // “How do the lengths of these objects compare?” (The crayon is shorter than the marker. The marker is longer than the crayon.)
• 30 seconds: quiet think time
• Share responses.

• “Van a comparar la longitud de varios objetos con la longitud del lápiz sin tajar. Encuentren dos objetos que sean más largos que el lápiz y dos objetos que sean más cortos que el lápiz. Escriban una oración para cada comparación” // “You are going to compare the length of objects to the length of the unsharpened pencil. Find two objects that are longer than the pencil and two that are shorter than the pencil. Write a sentence for each comparison.”
• 8 minutes: independent work time
• Monitor for two objects that are close in length but one is found to be longer than the unsharpened pencil and one is found to be shorter.

• Display the T-chart with headings “longer” and “shorter.”
• “¿Qué objetos son más largos que un lápiz sin tajar?” // “What objects are longer than an unsharpened pencil?” (a book, the ruler, the height of the desk)
• Record responses.
• “¿Qué objetos son más cortos que un lápiz sin tajar?” // What objects are shorter than an unsharpened pencil?” (a marker cap, a crayon, a toothpick)
• Record responses.
• Display previously identified objects that are close in length.
• “Compara las longitudes de los dos objetos, ¿qué puedes decir?” // “How do the lengths of the two objects compare?” (The book that is shorter than the pencil is also shorter than the block because the block is longer than the pencil.)
• “Sabemos que algunos objetos son más largos o más cortos que otros sin tener que alinearlos porque comparamos la longitud de los objetos con la longitud del lápiz” // “Because we compared the length of objects to the pencil, we know that some objects are longer or shorter than others without lining them up.”

The purpose of this activity is for students to use a third object to compare two lengths that can't be lined up by endpoints. Students compare the length of a side of their desk to the length of one of the legs of their desk indirectly using a string. This lesson helps students use a familiar object in their classroom and encourages them to mathematize their environment (MP4).

Since the side of the desk can not be easily compared to the leg of a desk directly, students need to determine how to use the string to compare. For example, they may mark where the length of the side reaches on the string and then compare that to the length of the leg. They may cut the string to be the length of the leg and then lay the string on the side of the desk to compare. Throughout the activity, when students reflect on the language they use and revise it to describe the attributes of objects, the lengths they measure, and how they use tools, they attend to precision (MP6).

If students sit at furniture that is significantly different than the desk pictured in the task, the teacher can adjust what students measure. For example, if students sit a table, identify one side of the table that is near the same length as one of the table legs for students to measure.

• Each group of 2 needs a piece of string longer than the length of the side of the students’ desks shown in the activity.

• Groups of 2
• Give each group a piece of string and scissors.
• “Vimos que algunas veces podemos comparar la longitud sin alinear los objetos. Ahora van a comparar la longitud de un lado de su pupitre con la longitud de una de las patas de su pupitre” // “We saw that sometimes we can compare length without lining up the objects. Now, you are going to compare the length of a side of your desk to the length of one of the legs of your desk.”
• Display the image.
• “Esta imagen muestra cuál lado vamos a medir. Tracen con su dedo el lado que van a medir” // “This image shows which side we will be measuring. Trace the length of the side you will measure with your finger.”
• “¿Por qué es importante que todos sepan cuál lado del pupitre debemos medir? ¿Importa cuál pata del pupitre miden?” // “Why is it important that everybody knows which side of the desk we should measure? Does it matter which leg of the desk you measure?” (One side is longer than the other, so we need to make sure we are measuring the same thing. All the legs are the same length, so it shouldn’t matter which one we measure.)

• “Usen una cuerda para comparar la longitud del lado de su pupitre con la longitud de una de las patas de su pupitre. Luego, muestren cómo saben cuál es más largo. Usen palabras o dibujos” // “Compare the length of the side and the length of one of the legs of your desk using the string. Then, show how you know which is longer using words or drawings.”
• 10 minutes: partner work time
• Monitor for students who compare indirectly by marking or cutting the string to match one length and then comparing the string to the other length.

If students say that both the side and the leg of the desk are shorter than the string, but do not say which part is longer, consider asking:

• “¿Cómo usaste la cuerda para comparar la longitud del lado del pupitre con la longitud de la pata?” // “How did you use the string to compare the length of the side of the desk and the length of the leg?”
• “¿Cómo puedes usar la cuerda para saber si es más largo el lado o es más larga la pata?” // “How could you use the string to tell whether the side or the leg is longer?”

• Invite previously identified students to share.
• “¿Cómo les ayudó la cuerda a comparar las longitudes?” // “How was the string useful in comparing the lengths?” (You could put the string next to each part of the desk to see which one is longer.)