Lesson 1

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.

• 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

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

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.

• 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

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

• Consider asking:
  • “¿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. (\(\frac{5}{8}\))

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.

• 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

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

• “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. (\(\frac{1}{3}\))

• 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

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

• “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. (\(\frac{4}{3}\))