The purpose of this activity is for students to determine whether a group of objects is even or odd. The context and the structure of the images allow students to look for ways to make 2 equal groups (1 yellow group and 1 blue group) or to make pairs (1 yellow and 1 blue). Students are given access to yellow and blue crayons or colored pencils, but are not required to color the designs. Some students might be able to answer all of the questions without coloring.

Monitor for and select students with the following approaches to share in the synthesis:

• Look for a way to make 2 equal groups (1 yellow group and 1 blue group).
• Look for a way to make pairs (1 yellow with 1 blue).
• Count by 2.

The approaches are sequenced from more concrete to more abstract ways of representing the context in order to make connections between the ways students solve the problem and the ways they have learned to determine whether a group of objects has an even or odd number. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently.

Students who color the images or pair them in an organized fashion are determining whether there are an even or odd number by finding a visual structure in the collection of images (MP7).

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “Piensa en las estrategias para descubrir qué diseños podría usar Han. En estas estrategias, ¿cómo ves distintas maneras de pensar sobre un número igual de figuras amarillas y azules?” // “How does each way of figuring out which designs Han could use show thinking about an equal number of yellow and blue shapes?” (One way was looking for 2 equal groups. One way was looking for pairs of yellow and blue. One way was counting by 2s because there are 2 colors that Han wants to use.)
• Connect students’ approaches to the learning goal by asking:
  • “¿Qué diseños tienen un número par de figuras? Expliquen cómo lo saben” // “Which designs have an even number of shapes? Explain how you know.” (A and D because there is an equal number of yellow and blue. A and D because every yellow circle can be paired with a blue circle.)

The purpose of this activity is for students to determine and justify why a representation shows an even or odd number of objects. They connect equations to visual representations and use them to reason about even and odd numbers (MP2). Although some images may be designed to elicit reasoning about 2 equal groups or pairs of objects, students should be encouraged to explain their thinking using the method that makes the most sense to them, including skip-counting by 2.

This activity uses MLR8 Discussion Supports. Advances: speaking, listening, conversing.

• Invite previously selected students to share the 3 cards that show 12 objects.
• “¿Cómo muestran estas tarjetas que el número de objetos es par?” // “How do these cards show that the number of objects is even?”
• Invite previously selected students to share the 3 cards that show 11 objects.
• “¿Cómo muestran estas tarjetas que el número de objetos es impar?” // “How do these cards show that the number of objects is odd?”