Lesson 6

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

• “¿Cómo saben que 15 es una estimación muy baja?” // “How do you know that 15 is an estimate that is too low?” (If we add two more towers of 5, it still won't reach the end of the desk.)

The purpose of this activity is for students to measure length by physically lining up length units that do not connect. Students discuss how measuring with paper clips is the same and different as measuring with connecting cube towers.

• Each group of 2 needs about 30 1-inch paper clips.

• Groups of 2
• Give each student a copy of the blackline master and a handful of 1-inch paper clips.

• “Hemos medido longitudes con cubos encajables. Ahora vamos a usar un objeto diferente para medir. Midan la longitud de este rectángulo usando clips. Cuando cada uno haya medido, comparen con su pareja cómo pensaron” // “We have been measuring length with connecting cubes. Now we are going to use a different object to measure. Measure the length of this rectangle using paper clips. When each partner has measured, compare your thinking with your partner.”
• 4 minutes: partner work time
• Monitor for a student who measures without gaps or overlaps.

If both partners agree on a measurement other than 9 paper clips, have them compare their thinking with another group and consider asking:

• “¿Por qué crees que tu número de clips es diferente?” // “Why do you think your number of paper clips is different?”
• “¿En qué es diferente la forma en que usaste los clips para medir?” // “What is different about the way you used the paper clips to measure?”

• Invite previously identified students to share.
• “¿En qué se parece medir con clips a medir con cubos encajables? ¿En qué es diferente?” // “How is measuring with paper clips the same and different as measuring with connecting cubes?” (Paper clips don’t connect. You need to be careful about laying paper clips down, they move easily. You still start at one endpoint and end at the other endpoint.)

The purpose of this activity is for students to analyze representations of length measurements. Students determine that two of the measurements are inaccurate because there are gaps between length units or some length units overlap. Students identify that in order to measure accurately, they need to lay the length units directly next to each other, touching, but not overlapping (MP6).

• Groups of 2

• Read the task statement.
• 5 minutes: partner work time
• Monitor for students who disagree with Andre’s and Clare’s measurement and can explain why they are inaccurate.

• “¿Qué consejos les darían a Andre y a Clare la próxima vez que ellos midan?” // “What advice would you give Andre and Clare the next time they measure?” (Place each paper clip end to end. Make sure they do not overlap and that there are no gaps between them.)

The purpose of this activity is for students to measure the length of tape strips using paper clips as the length unit. Students apply what they have learned in the previous two activities to measure accurately.

Set up tape strips of the designated lengths around the classroom, labeled with letters (A-F). Assign each group a tape to start with and then have them rotate to a new tape, as time allows.

• Put strips of tape of the designated lengths on the floor. Label each strip. There should be one strip of tape per group.
  • Tape A: 18 inches
  • Tape B: 16 inches
  • Tape C: 12 inches
  • Tape D: 20 inches
  • Tape E: 22 inches
  • Tape F: 25 inches

• Groups of 2–4
• Give each group paper clips.

• “Hay cintas alrededor del salón. Con su pareja, midan la longitud de cada cinta usando clips. Completen cada afirmación con el número de clips que hace que sea verdadera” // “There are strips of tape around the classroom. Work with your partner to measure the length of each strip using paper clips. Complete each statement with the number of paper clips that make it true.”
• 10 minutes: partner work
• Monitor for groups who measure Tape C without gaps or overlaps.

If students find measurements other than the precise measurement for each tape, consider asking:

• “¿Puedes mostrarme cómo usaste los clips para medir esta cinta?” // “Can you show me how you used the paper clips to measure this tape strip?”
• “¿Cómo usaste los consejos que les dimos a Andre y a Clare cuando estabas midiendo?” // “How did you use the advice we gave Andre and Clare when you were measuring?”

• Invite previously identified students to share.
• “¿Cómo saben que midieron la cinta C de manera precisa?” // “How do you know that you measured Tape C precisely?” (The paper clips had no gaps and no overlaps, the paper clips started at the beginning of the tape and went to the end of the tape.)

• “Los dos grupos se aseguraron de que no hubiera espacios ni sobreposiciones en sus clips. Los dos grupos dijeron que la cinta C mide 12 clips de largo” // “Both groups made sure there were no gaps or overlaps with their paper clips. Both groups said Tape C is 12 paper clips long.”