Lesson 3

This warm-up prompts students to carefully analyze and compare different representations of numbers. In making comparisons, they solidify their understanding of the connections across representations.

• 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 compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Cómo podríamos ajustar una o más opciones para que todas representen el mismo valor?” // “How might we revise one or more of the options so that they all represent the same value?” (Sample responses:
  • Change the \(\frac{80}{10}\) to \(\frac{8}{10}\) or \(\frac{80}{100}\).
  • Change option A to say “eight,” option C to say “8” or “8.0,” and the label for the first tick mark in option D to say “1.”)

In this activity, students reason about the relative size of decimals by locating them on a number line. As in a previous activity, they rely on their experience of locating fractions on a number line and the relationship of the decimal values relative to 0 and 1.

If desired and logistically feasible, consider carrying out the activity on a giant number line rather than on paper.

• Stretch a long strip of tape across a wall, at least 8 or 10 feet long. Partition the tape into 12 equal intervals, using shorter pieces of tape as tick marks. Label the locations of 0 and 1.
• Give each group of students 2–3 dot stickers, 4–5 sticky notes, and a thick marker.
• Ask each group to write (on sticky notes) labels for two of the tick marks, with one sticky note for each label.
• Assign each group one or two of the eight decimals in the second problem. Ask them to locate their assigned decimals on the number line, using dot stickers to mark the location and sticky notes to label them.

• Groups of 3–4

• If creating a giant number line, lead the activity as outlined in the Activity Narrative. Otherwise, ask students to work with their group on the first two problems.
• Pause and discuss:
  • how students knew where to put each decimal
  • how the number line could help us see the least and greatest
• “Tómense unos minutos para completar en silencio el resto de la actividad” // “Take a few quiet minutes to complete the rest of the activity.”
• 5–6 minutes: independent work time

Students may be unsure whether to label the tick marks between 0 and 1 in terms of tenths or hundredths, or whether to use fraction or decimal notation. Consider asking: “¿Qué marcas podemos poner para ayudarnos a ubicar los decimales de la actividad?” // “What labels might be helpful for locating the decimals in the activity?”

• Select students to display their completed number lines (showing the locations of five additional decimals).
• Invite the class to agree or disagree with the locations of the point and discuss any disagreements.
• Select other students to share their comparison statements and how they know each statement is true.

In this activity, students continue to compare decimals to hundredths. They begin by reasoning with a number line and work toward generalizing their observations. Some students may compare two numbers by analyzing the value of the digits in the same place (for example, the tenths in one number and the tenths in the other), but comparing decimals by place value is a standard for grade 5 and thus not expected at this point.

• Groups of 2

• “En silencio, trabajen unos minutos en la actividad. Luego, compartan con su compañero cómo pensaron” // “Take a few quiet minutes to work on the activity. Then, share your thinking with your partner.”
• 7–8 minutes: independent work time
• 3–4 minutes: partner discussion
• For the comparisons in the second problem, monitor for students who:
  • name the decimal in words and compare the number of hundredths (for instance, 62 hundredths and 26 hundredths)
  • relate the decimals to benchmarks such as 0, 0.5, and 1

• See lesson synthesis.