Lesson 1

Exploremos estimaciones con fracciones

Warm-up: Cuál es diferente: Fracciones (10 minutes)

Narrative

This warm-up prompts students to compare four images. It gives students a reason to use language precisely. It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as parts, pieces, whole, shapes, triangle, quadrilateral, or halves.

Launch

• 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

Activity

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

Student Facing

¿Cuál es diferente?

Activity Synthesis

• “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.”

Activity 1: Exploración de estimación: Diagrama (15 minutes)

Narrative

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. In this activity, students estimate what fraction of a square is shaded to revisit area diagrams.

MLR2 Collect and Display: Circulate, listen for and collect the language students use as they estimate the fraction of the square that is shaded. On a visible display, record words and phrases such as: area, partition, larger area, between one-half and three-fourths, and more than one-half. Invite students to borrow language from the display as needed, and update it throughout the lesson.

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 pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

Student Facing

Escribe una estimación que sea:

muy baja razonable muy alta
$$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$ $$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$ $$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$

Activity Synthesis

• “¿Alguien hizo una estimación menor que ______? ¿Alguien hizo una estimación mayor que _______?” // “Is anyone’s estimate less than _____? Is anyone’s estimate greater than _____?”
• “Teniendo en cuenta esta discusión, ¿alguien quiere ajustar su estimación?” // “Based on this discussion does anyone want to revise their estimate?”
• “Si quisieran encontrar exactamente qué fracción del cuadrado está sombreada, ¿cómo lo harían?” // “If you wanted to find out exactly what fraction of the square is shaded, how would you go about doing that?” (Try to partition the square into equal parts and see how many of the parts are shaded.)
• 2 minutes: partner discussion
• Share and record responses.
• Optional: Have students find the exact fraction shaded. ($$\frac{5}{8}$$)

Activity 2: Exploración de estimación: Tira de fracciones (10 minutes)

Narrative

The purpose of this activity is for students to use their experience with fraction strips and tape diagrams to estimate what fraction of a strip is shaded.

Engagement: Internalize Self-Regulation. Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, their progress with estimation exploration.
Supports accessibility for: Social-Emotional Functioning

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 pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

Student Facing

¿Qué fracción de la tira está sombreada?

Escribe una estimación que sea:

muy baja razonable muy alta
$$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$ $$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$ $$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$

Activity Synthesis

• “Si quisieran encontrar exactamente qué fracción de la tira está sombreada, ¿cómo lo harían?” // “If you wanted to find out exactly what fraction of the strip is shaded, how would you go about doing that?” (See how many copies of the shaded part can fit into the whole strip. Partition the strip into fractions we know and see what fraction the end of the shaded part lines up with.)
• 2 minutes: partner discussion
• Share and record responses.
• Optional: Have students find the exact fraction shaded. ($$\frac{1}{3}$$)

Activity 3: Exploración de estimación: Recta numérica (10 minutes)

Narrative

The purpose of this activity is for students to use their experience locating and labeling fractions to estimate the location of the point on a number line.

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 pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

Student Facing

¿Qué número está representado por el punto?

Escribe una estimación que sea:

muy baja razonable muy alta
$$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$ $$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$ $$\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}$$

Activity Synthesis

• “Si quisieran encontrar exactamente qué fracción está en ese punto en la recta numérica, ¿cómo lo harían?” // “If you wanted to find out exactly what fraction is at that point on the number line, how would you go about doing that?” (Partition the number line into fractions we know and see what fraction the point lines up with.)
• 2 minutes: partner discussion
• Share and record responses.
• Optional: Have students find the exact location marked on the number line. ($$\frac{4}{3}$$)

Lesson Synthesis

Lesson Synthesis

Display the number line from the last activity.

“Hoy practicamos nuestras habilidades para estimar con fracciones que estaban presentadas de distintas formas. Cuando estimaron la ubicación de este punto en la recta numérica, ¿qué cosas supieron inmediatamente?” // “Today we practiced our estimation skills with fractions shown in different ways. When you were estimating the location of this point on the number line, what were some things you knew right away?” (The fraction would be greater than 1 and less than 2. The numerator had to be larger than the denominator. I could write it as 1 and a fraction. It would be closer to 1 than 2.)

“¿En qué cosas tuvieron que esforzarse un poco más?” // “What did you have to work a little harder to think about?” (What denominator to use in my estimate because no parts are marked on the number line. What fraction would be greater than 1 but less than $$1\frac{1}{2}$$.)