Lesson 9

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. 

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

• “Si quisieran saber el perímetro de la base en forma de estrella, ¿cómo lo encontrarían?” // “If you wanted to know the perimeter of the star-shaped base, how would you find it?” (We’d need to know the length of each side and add the lengths together. If the lengths were the same we could count them and multiply the length by number of sides.)
• Consider asking:
  • “Teniendo en cuenta esta discusión, ¿alguien quiere ajustar su estimación?” // “Based on this discussion does anyone want to revise their estimate?”

The purpose of this activity is for students to find the length of a missing side of a shape when the perimeter is given, using any strategy that makes sense to them. The synthesis highlights the variety of methods students used to solve the problem.

• Groups of 2
• “En una lección anterior, encontramos el perímetro de figuras en las que no estaban marcadas todas las longitudes de los lados. Ahora encontremos longitudes de lado desconocidas cuando conocemos el perímetro” // “In an earlier lesson, we found the perimeter of shapes when not all the side lengths were labeled. Now, let’s find some missing side lengths when we know the perimeter.”

• 5–7 minutes: partner work time
• Monitor for students who:
  • subtract each side length from the perimeter
  • double a given side length, subtract the result from the perimeter, and divide to find the other two sides
  • divide the perimeter when the side lengths are all equal

• Select previously identified students to share their strategies. Be sure to share at least one method (more if possible) for each problem.
• Consider asking:
  • “¿Cuándo sería más útil esta estrategia?” // “When would this strategy be most useful?”
  • “¿Alguien pensó sobre esto de otra manera?” // “Did anyone think about it in a different way?”

The purpose of this activity is for students to solve problems in situations that involve perimeter (MP2). Students may draw diagrams with length labels or simply reason arithmetically. They also explain how each problem does or does not involve perimeter. The activity synthesis provides an opportunity to begin discussing the difference between area and perimeter, which will be fully explored in upcoming lessons.

• Groups of 2

• “Tómense un momento para resolver individualmente estos problemas” // “Take some time to solve these problems on your own.”
• 5 minutes: independent work time
• “Compartan con su compañero su razonamiento sobre su problema favorito” // “Share with your partner your reasoning on your favorite problem.”
• 2 minutes: partner discussion
• Monitor for a variety of ways students solve these problems, such as by drawing a diagram or writing expressions or equations. Identify one student to share for each problem, with a variety of ways shown across the problems.

If students say they aren’t sure how to get started on a problem, consider asking:

• “¿De qué se trata este problema?” // “What is the problem about?”
• “¿Cómo puedes representar el problema?” // “How could you represent the problem?”

• Select previously identified students to share their reasoning for each problem. After each problem, consider asking: “¿Alguien resolvió este problema de otra forma?” // “Did anyone solve this problem in a different way?”
• If possible, keep the student work displayed for the lesson synthesis.