Lesson 1

The purpose of this warm-up is to elicit students' personal experiences with equal sharing, which will be useful when students create equal groups of objects in the lesson activities. Although students may notice and wonder many things about the image, comments and questions about the number of children, number of objects, and ways to resolve the problem with equal shares are the important discussion points.

• 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.

• “Si estos niños están peleando por el juguete, ¿cómo podrían resolver el problema?” // “If these children are fighting over the toy, how could they resolve their problem?” (One could play with the other toy, so they both have one to play with. They could take turns playing with the dinosaur.)
• “Hoy vamos a ver formas de compartir equitativamente grupos de objetos” // “Today we are going to look at ways to share groups of objects equally.”

The purpose of this activity is for students to share a collection of objects with a partner so that both students receive the same amount and as many objects as possible. They separate groups of objects into 2 equal groups and identify numbers of objects that can be split into 2 equal groups with “no leftovers” and those that can be split into two equal groups with “some leftovers.” In the synthesis, students discuss that numbers with “some leftovers” can only have 1 leftover. Create a t-chart that lists the numbers that students find for each category. Students will add more to the t-chart in the next lesson.

When students notice that some collections of objects can be shared equally while others can not they observe an important mathematical structure (MP7) which they will name in a future lesson. 

This activity uses MLR8 Discussion Supports. Advances: speaking

• Each group of 2 needs a container of counters with 4 to 15 counters in each container. These containers will be used again in the next lesson. 
• Create a t-chart on a large piece of chart paper to display in the activity synthesis.
• Use “Two Equal Groups” as the title.
• Label the t-chart with “no leftovers” and “some leftovers” as the categories.

• Groups of 2
• Give each group 1 container of objects.

• “Compartan con su compañero los objetos que hay en su recipiente. Cada uno debe obtener la misma cantidad de objetos y tantos como sea posible” // “Share the objects in your container with your partner so that you each get the same amount and as many as possible.”
• “Anoten el número total de objetos que había en su recipiente” // “Record the total number of objects that were in your container.”
• “Luego, anoten el número de objetos que cada uno recibió en las columnas de ‘mi porción’ y ‘la porción de mi compañero’. Si sobra alguna cantidad, anótenla en la tabla” // “Then record the number of objects in your share and in your partner’s share. If there are any left over, record the number in the chart.”
• Demonstrate with the dinosaur example from the warm-up as needed.
• “Cuando terminen de compartir los objetos, guarden los objetos de nuevo en el recipiente e intercambien recipientes con otra pareja” // “When you finish sharing the objects in one container, pack up the objects and trade with another group.”
• 10 minutes: partner work time

• Display t-chart labeled “Dos grupos iguales” // “Two Equal Groups” with “no sobran” // “no leftovers” and “sobran algunos” // “some leftovers” as the categories.
• Invite students to share a total amount and whether they made 2 equal groups with no leftovers or 2 equal groups with some leftovers.
• Record the total in the appropriate column of the chart.
• Ask students to share the number in their share and in their partner’s share. Record by drawing a circle around each share. For example:

  

  

• Repeat to gather 2–3 examples of even and 2–3 examples of odd numbers.
• “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?” (I notice all the numbers show two equal groups. I notice there’s only ever one leftover. I notice some numbers have the same equal groups, like 6 has 2 groups of 3 and 7 has 2 groups of 3. I wonder why there’s only ever one leftover.)

MLR8 Discussion Supports

• Before students share, remind students to use words such as equal groups and leftovers.
• 1 minute: quiet think time
• 1–2 minutes: partner discussion
• Share responses.
• If needed, “Al hacer grupos para cada número, ¿cuánto sobró?” // “How many leftovers did each number have?”
• “Al poner objetos en 2 grupos iguales, siempre van a sobrar 0 o va a sobrar 1” // “Whenever we put objects into 2 equal groups, we will either have 0 leftovers or 1 leftover.”

The purpose of this activity is for students to determine whether the objects in a group can be separated into two equal groups. Students work with larger numbers of objects (16–20) than they did in the previous activity. They should be given access to counters (or other physical objects), but may use different ways to represent the number of objects and possible groups, including diagrams and equations.

• Groups of 2
• Give students access to connecting cubes or counters.
• “Andre tiene una colección de 17 canicas. Él quiere jugar un juego con su hermana. Para jugar, ambos deben empezar con el mismo número de canicas y quieren usar tantas canicas como puedan” // “Andre has a collection of 17 marbles. He wants to play a game with his sister. To play, they both need to start with the same number of marbles and they want to use as many as they can.”
• “Usen fichas, diagramas, símbolos u otras representaciones para mostrar de qué forma ellos podrían empezar el juego” // “Use the counters, diagrams, symbols or other representations to show how they could start the game.”
• 2 minutes: independent work time
• Monitor for different ways students group the counters or objects in the diagrams they create.
• “Comparen con su compañero cómo pensaron” // “Compare your thinking with your partner.”
• 1 minute: partner discussion
• Invite previously identified students to share their solutions. Display or record their grouping strategy.
• Display or draw:

  

  

  \(17 = 8 + 8 + 1\)

• “¿De qué manera la ecuación representa este diagrama?” // “How does the equation represent this diagram?” (17 is the total amount. Each 8 shows the group of 8 on top and the group of 8 on the bottom and his sister got the same amount. The + 1 shows the marble that is left out.)

• “Con su compañero, respondan las demás preguntas sobre las canicas de Andre” // “Work with your partner to answer the other questions about Andre’s marbles.”
• 8 minutes: partner work time

• Invite 1–2 students to share their response for 18 marbles.
• Display a student representation or draw:

• “¿Cómo usaron lo que hicieron para compartir 18 canicas para descubrir cómo compartir 20 canicas?” // “How did you use your work for sharing 18 marbles to find out how to share 20 marbles?” (20 is just 2 more than 18 so each group would get 1. There wouldn’t be any left over.)
• Display a student representation for 20 marbles or draw to show adding 1 marble to each group to the drawing of 18 marbles.
• “¿Qué ecuación podemos escribir para representar el diagrama?” // “What equation can we write to represent the diagram?” (\(10 + 10 = 20\))