# Lesson 8

Clasifiquemos triángulos

## Warm-up: Exploración de estimación: La medida de un ángulo (10 minutes)

### Narrative

This warm-up prompts students to estimate the measure of an angle in a triangle. This will be important as they classify triangles in this lesson so will need to distinguish acute, right, and obtuse angles. They will not need to measure angles explicitly but recalling angle measure will help them distinguish the different types of triangles.

### Launch

• Groups of 2
• Display the image.
• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

### Student Facing

¿Cuál es la medida del ángulo?

Escribe una estimación que sea:

muy baja razonable muy alta
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### Activity Synthesis

• “¿Cómo sabemos que el ángulo mide más de 90 grados?” // “How do we know the angle is more than 90 degrees?” (90 degrees is a right angle and this angle is obtuse. It's more than a right angle.)
• “¿Cómo sabemos que el ángulo mide menos de 180 grados?” // “How do we know the angle is less than 180 degrees?” (180 degrees is a straight line and this bends inward so it’s less than 180 degrees.)

## Activity 1: ¿Cuáles lo cumplen? (20 minutes)

### Narrative

The purpose of this activity is to sort triangles according to their angle measures and side lengths. When they finish sorting, students will notice that two of the possible categories will not have any matching triangles, namely if all 3 sides of a triangle have the same length then the triangle will not have a right angle or an obtuse angle. Students think about whether or not such a triangle could exist and present informal arguments to explain their reasoning (MP3). The activity synthesis formally introduces the category of right triangles.

Engagement: Internalize Self-Regulation. Provide students an opportunity to self-assess and reflect on their own progress. For example, ask students to compare grids and discuss whether or not their choices for whether a triangle fits a certain criteria are the same and why.
Supports accessibility for: Language, Social-Emotional Functioning

### Required Materials

Materials to Copy

• Card Sort Triangles (Grade 5)

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Give each pair of students a set of triangle cards from the blackline master.

### Activity

• 5 minutes: independent work time
• 5 minutes: partner work time

### Student Facing

1. Para cada espacio de la tabla, encuentra tarjetas de triángulo que cumplan con las características dadas.
2. Si crees que no es posible encontrar un triángulo que cumpla con ciertas características, explica por qué no.
los tres lados tienen longitudes distintas exactamente dos lados tienen la misma longitud los tres lados tienen la misma longitud
tiene un ángulo de 90 grados
tiene un ángulo que mide más de 90 grados
los tres ángulos miden menos de 90 grados

Explicaciones:

### Student Response

If a student needs an entry point into the task, cover the criteria listed in the top row of the table prompt them to find triangles that fit in the criteria listed in the first column. Then, reveal one criteria at a time from the top view and ask, “¿Cuál otro triángulo también cumple con esta descripción?” // “Which triangle also fits this description?”

### Activity Synthesis

• Display a set of triangle cards and a blank table from the workbook. Place the cards in the correct location in the table as you discuss the questions in the synthesis.
• “¿Cómo decidieron cuáles triángulos tienen ángulos de 90 grados?” // “How did you determine which triangles have 90 degree angles?” (I used the corner of a sheet of paper, measured it using a protractor, or used the grids.)
• “Los triángulos que tienen un ángulo de 90 grados se llaman triángulos rectángulos” // “Triangles with a 90 degree angle are called right triangles.”
• “¿Cómo podemos estar seguros de que un triángulo es un triángulo rectángulo?” // “How can we be certain that a triangle is a right triangle?” (We can measure the angles or use the grid.)
• Display shape F.
• “¿Qué observan acerca de los ángulos de este triángulo?” // “What do you notice about the angles of this triangle?” (One is a 90 degree angle and the other two are equal to each other. The other two are half of a 90 degree angle.)
• “¿Qué observan acerca de los lados de este triángulo?” // “What do you notice about the sides of this triangle?” (Two of them are the same length.)

## Activity 2: Todos, algunos, ninguno (15 minutes)

### Narrative

The purpose of this activity is for students to sort triangles in a way that makes sense to them and then make observations about right triangles. Students make statements about the right triangle shape cards using the quantifiers all, some, or none. The main shape characteristics students will likely use in their statements are the angle measures, particularly for the two angles that are not right angles, and the side lengths. Students might also choose other characteristics like the orientation of the triangles.

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

### Required Preparation

• Gather materials from previous activity:
• Triangle Cards

### Launch

• Groups of 2 or 4 (if doing a gallery walk)

### Activity

• 5 minutes: independent work time
• 5 minutes: small-group work time

MLR7 Compare and Connect

• “Creen una presentación visual que muestre cómo pensaron en los problemas. Incluyan detalles, como notas, diagramas o dibujos, para ayudar a los demás a entender sus ideas” // “Create a visual display that shows your thinking about the problems. You may want to include details such as notes, diagrams, or drawings to help others understand your thinking.”
• 2–5 minutes: independent or group work
• 5–7 minutes: gallery walk

### Student Facing

1. Clasifica las tarjetas de triángulo de la actividad anterior de una manera que tenga sentido para ti.
2. Ahora, agrupa los triángulos que tienen un ángulo de 90 grados. Teniendo en cuenta estos triángulos, escribe afirmaciones para cada categoría.

• Todos los triángulos que tienen un ángulo de 90 grados...
• Algunos de los triángulos que tienen un ángulo de 90 grados...
• Ninguno de los triángulos que tienen un ángulo de 90 grados...

### Activity Synthesis

• Invite students to share how they sorted the cards, including
• triangles with a right angle
• triangles with an obtuse angle
• triangles with acute angles
• triangles with no sides equal
• triangles with 2 or more sides equal
• “¿Cómo supieron cuáles tarjetas tienen triángulos rectángulos?” // “How did you know which triangle cards have right triangles?” (I used the grid lines. I measured with a protractor. I used the corner of a card.)
• Invite students to share their responses for properties all of the right triangles share.
• Record their responses.

## Lesson Synthesis

### Lesson Synthesis

“Hoy clasificamos triángulos” // “Today we sorted and classified triangles.”

“Mencionen varias maneras en las que podemos clasificar triángulos” // “What are some different ways you can sort triangles?” (We can sort them by angle size and side lengths. We can look for a right angle. We can look for 2 or 3 sides that are the same length.)

“¿En qué se parecen la clasificación de triángulos y la clasificación de cuadriláteros?” // “How is classifying triangles the same as classifying quadrilaterals?” (We looked at side lengths and angles in both cases. Right angles were important for both and so were equal side lengths.)

“¿En qué son diferentes la clasificación de triángulos y la clasificación de cuadriláteros?” // “How is classifying triangles different from classifying quadrilaterals?” (There are fewer sides for triangles and so there are not as many possibilities. A triangle can only have one right angle while a quadrilateral can have as many as 4.)