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 2 equal groups with “some leftovers.” In the Synthesis, students discuss the fact 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 cannot, they observe an important mathematical structure (MP7) which they will name in a future lesson.

This activity uses MLR8 Discussion Supports. Advances: speaking.

• Display the “Dos grupos iguales” // “Two Equal Groups” t-chart with “no sobran” // “no leftovers” and “sobran algunos” // “some leftovers” labeled 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 categoría. ¿Qué observan? ¿Qué se preguntan?” // “Look at the numbers in each category. What do you notice? What do you wonder?” (I notice all the numbers show 2 equal groups. I notice there’s only ever 1 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 1 leftover.)

MLR8 Discussion Supports

• Before students share, remind them to use words, such as “grupos iguales” // “equal groups” and “que sobran” // “leftovers.”
• 1 minute: quiet think time
• 1–2 minutes: partner discussion
• Share responses.
• If needed, ask “Al hacer grupos para cada número, ¿cuánto sobró?” // “How many leftovers did each number have?”
• “Al poner objetos en 2 grupos iguales, siempre va 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 2 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 students may use different ways to represent the number of objects and possible groups, including diagrams and equations.

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

• “¿Cómo lo que hicieron para compartir 18 canicas les sirvió 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?” ()