Lesson 11

This warm-up prompts students to compare four strings of numbers. To identify a string that doesn’t belong, students may use what they know about properties and kinds of numbers—factors and multiples, odd and even numbers, numbers in base ten, and so on. 

This warm-up also prepares students for a series of design activities that prepare students to create their own Which One Doesn’t Belong activity.

• Groups of 2
• Display the image.

• “Escojan una 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
• 2–3 minutes: partner discussion
• Record responses.

• “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”
• “¿En qué se fijaron para decidir cuál era diferente o para encontrar una razón por la que cada una era diferente?” // “What did you look for when deciding which one doesn’t belong, or when finding a reason why each one doesn’t belong?”
• “¿Qué tuvo que tener en cuenta el autor de esta actividad cuando la diseñó?” // “What did the writer of this activity have to consider when designing this activity?” (Sample responses: All items must have something in common, but each item must have a feature that the other three don’t have.)

In this activity, students use their knowledge of numbers in base ten and of geometric figures to complete two Which One Doesn’t Belong sets. Students first study the attributes of the given items. They articulate why the items all belong to a set and why each one has a reason not to belong. Next, they propose a new item that shares a feature with others in the set but also has a unique feature that excludes it from the set.

• Groups of 3–4
• 7–8 minutes: small-group work time on the first set

• Pause for a whole-class discussion. Select a group to share their reasoning and new item. Record their responses.
• After their explanation, ask if others:
  • reasoned the same way but created a different fourth item. Invite them to share their addition.
  • saw other reasons why the given items belong in a set and why each one doesn’t.
• 4 minutes: independent work time on the second set
• 4 minutes: small-group discussion on the second set

• Select another group to share their responses, reasoning, and new item for the second set. Record their responses.
• Ask others in the class if they reasoned about the properties of the given figures the same way as the presenting group but produced a different item to complete the set. Invite them to share their thinking and creation.

In the second round of analysis and design, students use their knowledge of operations and expressions to complete a Which One Doesn’t Belong set with two missing items. Students first study the attributes of the given items. They articulate why the items all belong to a set and why each one has a reason not to belong. Next, they propose a new item that shares a feature with others in the set but also has a unique feature that excludes it from the set.

• Groups of 2
• 5 minutes: independent work time

• “Con su compañero, asegúrense de que para cada nuevo elemento que agreguen al grupo haya una razón por la que se parece y una por la que es diferente de los otros” // “Work with your partner to make sure each new item added to the set has a reason to belong and not to belong.”
• 5 minutes: partner work time

• Invite students to share their analyses and new items.
• “¿Por qué A y B se parecen?” // “Why do both A and B belong to the set?”
• “¿Qué características de las expresiones examinaron o con cuáles experimentaron para completar su grupo?” // “What were some features of the expressions that you looked at or experimented with to complete your set?” (The kind of numbers used, how many numbers are used, the order of the numbers, the symbols, the value of the expression.)
• If no students considered the value of the expression, ask them about it.
• “Después de agregar C y D, ¿había todavía una razón por la que A y B eran diferentes en su grupo? ¿Tuvieron que cambiar sus elementos?” // “After adding C and D, did A and B still have a reason not to belong in your set? Did you have to revise your items?”

In this optional third round of analysis and design activity, students are given only one item showing multi-digit multiplication using an algorithm with partial products. Students apply their understanding of operations on multi-digit numbers and algorithms to add three new items that would complete a Which One Doesn’t Belong set.

As before, students begin by examining what’s given, but because only one item is shown, they now have considerably more freedom to define the attributes of other items in the set. Expect the increased openness to be a greater cognitive lift for students and to yield more varied sets. For instance, students might add to the set an area diagram, a calculation in standard algorithm, and a division algorithm.

For the activity synthesis, ask each group to test their set by presenting it to another group, and then to make note of one or more ways to improve their set based on their peers’ feedback.

• Groups of 3–4
• “Miren el único elemento dado del grupo para una actividad tipo ‘Cuál es diferente’. ¿Qué observan? ¿Qué se preguntan?” // “Look at the only item in the given Which One Doesn’t Belong set. What do you notice? What do you wonder?”

• 1 minute: quiet think time
• 2 minutes: Invite students to share as many observations as they can. Record their responses.
• “Con su grupo, agreguen tres elementos más para completar un grupo para una actividad tipo ‘Cuál es diferente’. Al igual que antes, para cada elemento debe haber al menos una razón por la que se parece a los otros y una por la que es diferente” // “Work with your group to add three more items to make a Which One Doesn’t Belong set. Just like before, each item has to have at least one reason to belong and one reason not to.”
• 12–15 minutes: group work time
• 2–3 minutes: Record the completed set on poster paper.

• “Reúnanse con otro grupo. Por turnos, presenten su grupo de elementos. Denle a sus compañeros 1 minuto para pensar en silencio y 2 minutos para que discutan sus observaciones. Anoten las respuestas de sus compañeros” // “Partner with another group and take turns presenting your set. Give your audience 1 minute of quiet think time and 2 minutes to discuss their observations. Record their responses.”
• “Teniendo en cuenta los comentarios de sus compañeros, anoten los cambios que ustedes podrían hacer para mejorar el grupo de elementos” // “Based on your peers’ feedback, make a note of changes your group could make to improve the set.”
• “¿A qué características matemáticas les prestaron atención cuando crearon y revisaron los nuevos elementos?” // “What were some mathematical features you paid attention to when creating and checking the new items?” (Sample responses: the operation, number of digits, algorithm used, odd- or even-numbered result, whether carrying was involved, whether the numbers represent certain quantities)