Lesson 2

Los compañeros hacen parejas

Warm-up: Cuál es diferente: Día de lavar (10 minutes)

Narrative

This warm-up prompts students to compare four images. It gives the teacher an opportunity to hear how students use terminology and talk about an equal group of 2 objects as a pair. This language will be important as students pair objects during the lesson and reason about even and odd throughout the section.

Launch

• Groups of 2
• Display image.
• “Escojan uno 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

Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 23 minutes: partner discussion
• Record responses.

Student Facing

¿Cuál es diferente?

Activity Synthesis

• “¿Cómo muestra cada imagen parejas de calcetines?” // “How does each image show pairs of socks?” (Sample responses: A shows 4 pairs side-by-side, but they don’t match. B shows 3 pairs of socks that are the same color and right next to each other. C shows socks in 2 rows. The matching pairs are above and below each other. D shows matching pairs side-by-side.)

Activity 1: Hagamos parejas (20 minutes)

Narrative

The purpose of this activity is for students to separate objects into groups of 2 and identify numbers of objects that can be split into pairs with “no leftovers” and numbers of objects that can be split into pairs with “one leftover.” In the synthesis, create a t-chart with students that lists the numbers that belong to each category. Students share what they notice and wonder about each group of numbers. Save the t-chart for use in the lesson synthesis.

When recording student responses in the synthesis, record how students counted to find the total number of counters by drawing pairs in rows (see activity synthesis). This helps students see the groups of 2 and prepares them for analyzing arrays in future lessons.

This activity uses MLR8 Discussion Supports. Advances: speaking.

Required Materials

Materials to Gather

Required Preparation

• Each group of 2 needs a container of 4 to 15 counters.
• Create a t-chart on a large piece of chart paper to display in the activity synthesis.
• Use “Making Pairs” as the title.
• Label the t-chart with “no leftovers” and “one leftover” as the categories.

Launch

• Groups of 2
• Give each group a bag of counters.

Activity

• “Con su compañero, hagan todas las parejas que puedan que tengan 1 ficha roja y 1 ficha amarilla. Representen sus fichas en la primera columna con un dibujo o con símbolos” // “Work with your partner to make as many pairs of 1 red and 1 yellow counter that you can. Represent your counters with a drawing or symbols in the first column.”
• “Anoten la cantidad total de fichas y el número de fichas que sobran después de haber hecho parejas” // “Record the total amount of counters and the number of counters left over, after you have made pairs.”
• “Cuando terminen de hacer parejas con las fichas, guarden las fichas en la bolsa e intercámbienla con otro grupo” // “When you finish pairing the counters in one bag, pack up the counters and trade with another group.”
• 10 minutes: partner work time

Student Facing

Haz parejas con 1 ficha amarilla y 1 ficha roja.

mis fichas

total de fichas

fichas que sobran

Student Response

If students make 2 equal groups of counters and the arrangement does not clearly show pairs of red and yellow counters. Consider asking:

• “En tu organización, ¿cómo se ve una pareja de fichas que tiene 1 roja y 1 amarilla?” // “How does your arrangement show a pair of counters that has 1 red and 1 yellow?”
• “¿Cómo podrías reorganizar tus fichas para mostrar parejas?” // “How could you rearrange your counters to show pairs?”

Activity Synthesis

• Display t-chart labeled “Hagamos parejas” // “Making Pairs” with “no sobran” // “no leftovers” and “sobra uno” // “one leftover” as the categories.
• Invite students to share a total amount and whether they made pairs with no leftovers or pairs with a leftover.
• Record the total on the chart.
• “¿Cómo contaron las fichas para encontrar el total?” // “How did you count the counters to find the total?” (I counted each pair by 2.)
• Represent how the student counted by drawing dots in rows. If students count by 2, represent this by drawing two dots at a time and count by 2.
• For example:

• “Observen los números de cada columna. ¿Qué observan? ¿Qué se preguntan?” // “Look at the numbers in each group. What do you notice? What do you wonder?” (All of the numbers show pairs. The numbers in the leftover group have only 1 leftover, the rest make pairs. I wonder what other numbers go in these groups. I wonder if these are the same numbers we found had 1 leftover yesterday.)
MLR8 Discussion Supports
• Before students share, remind students to use words such as pairs, equal groups, and leftovers.
• 1 minute: quiet think time
• 1-2 minutes: partner discussion
• Share responses.
• If needed, “Al hacer parejas para cada número, ¿cuánto sobró?” // “How many leftovers did each number have?”

Activity 2: ¿Sienten que sobran? (15 minutes)

Narrative

The purpose of this activity is for students to determine whether a group of people (1620) can be organized into groups of 2 without any person left alone or any groups of 3. They begin to reason about whether a group of objects is even or odd by using what they know about counting or adding by 2 (MP7, MP8). Students should be given access to counters, but may use other representations, including equations.

Engagement: Internalize Self-Regulation. Provide students an opportunity to self-assess and reflect on their own progress. For example, ask them if there is a pattern they notice or something they see that relates to pairing. Another option is to have students explain what happens in their own classroom when pairing up for group work. “¿Qué ocurre si alguien no tiene un compañero?” // “What if someone does not have a partner?”
Supports accessibility for: Conceptual Processing, Social-Emotional Functioning

Required Materials

Materials to Gather

Launch

• Groups of 2
• Have students pair up to find a new partner or line up in pairs.
• “¿Todos tienen un compañero?” // “Does everyone have a partner?”
• “Cuando necesitamos un compañero para una actividad, ¿siempre hemos podido hacer solo grupos de 2?” // “When we need a partner for an activity, are we always able to have only groups of 2?” (No. When ___ was absent, we had to make a group of 3.)

Activity

• “Pensemos en clases de distintos tamaños. En cada una, mostremos si todos los estudiantes se pueden emparejar para hacer solo grupos de 2” // “Let’s show whether all students in different class sizes can be paired up to make only groups of 2.”
• “Respondan individualmente la primera pregunta” // “Do the first question on your own.”
• 3 minutes: independent work time
• “Comparen con su compañero cómo pensaron. Luego, respondan juntos las preguntas 2 y 3” // “Compare your thinking with your partner. Then answer numbers 2 and 3 together.”
• 8 minutes: partner work time
• Monitor for different ways students show pairs for 19 students to share in the synthesis.

Student Facing

Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones. Si te ayuda, usa cubos o fichas.

1. Hoy hay 18 estudiantes en la clase de Clare. Van a trabajar en parejas. ¿Estarán todos en algún grupo de 2?
2. Hay 20 estudiantes en la clase de Priya. ¿Estarán todos en algún grupo de 2?
3. Hay 19 estudiantes en la clase de Noah. ¿Estarán todos en algún grupo de 2?

Activity Synthesis

• Draw or display:

• “¿Cómo podemos mostrar con esta representación que todos los estudiantes de la clase de Noah tendrán un compañero?” // “How could we use this representation to show whether everyone in Noah’s class will have a partner?” (There are 18 circles and you can see they are in pairs. 19 is one more than 18. So, one circle would be left out).
• Share responses. Include reasoning from previously selected students.

Lesson Synthesis

Lesson Synthesis

Display t-chart from the last activity and the t-chart created in the previous lesson.

“¿Qué observan sobre los números de cada tabla? ¿Qué se preguntan?” // “What do you notice about the numbers in each chart? What do you wonder?” (I notice the numbers in the “no leftovers” group are the same on both charts. Both charts have a group that has numbers with one leftover and the numbers are the same on both charts. What other numbers go in these groups? Why are the same numbers split up in different categories on both charts? Do these numbers have a special name?)

“Cuando el número de objetos se puede separar en dos grupos iguales o cuando se pueden formar parejas sin que sobre ningún objeto, decimos que el número es par” // “When the number of objects can be split into two equal groups or made into pairs without any objects left over, we say the number is even.”

“Los números que no son pares se llaman impares. Cuando intentamos hacer dos grupos iguales de objetos, pero hay un objeto que sobra, hay un número impar de objetos. Si intentamos poner objetos en parejas, pero tenemos uno que sobra, hay un número impar de objetos” // “Numbers that are not even are called odd. When we try to make two equal groups of objects but there’s one left over, there is an odd number of objects. If we try to put objects into pairs but we have one left over, there is an odd number of objects.”

Add the words even and odd to each chart above the appropriate category.