Lesson 4

Comparemos y ordenemos decimales

Warm-up: Exploración de estimación (10 minutes)


The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. In this case, the given decimal pushes students to think in terms of increments of tenths (0.1) and to relate the fractional measurement to nearby whole numbers.


  • 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.

Student Facing

La persona de la imagen mide 1.7 metros de alto.

Estima la envergadura del águila (la distancia entre las puntas de las alas cuando están extendidas), en metros.

Image of person next to eagle wingspan. Wingspan is about one and half times the height of the person.

Escribe una estimación que sea:

muy baja razonable muy alta
\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)

Student Response

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Activity Synthesis

  • “¿Por qué puede que 1.8 metros sea un estimación muy baja?” // “Why might 1.8 meters be too low of an estimate?”
  • “¿En qué parte de la imagen de la persona podríamos marcar una altura de 1 metro? ¿Y en la imagen del águila?” // “Where might a height of 1 meter be on the image of the person? On the image of the eagle?”
  • Consider asking:
    • “¿Alguien hizo una estimación menor que 2? ¿Alguien hizo una estimación mayor que 3?” // “Is anyone’s estimate less than 2? Is anyone’s estimate greater than 3?”
    • “Teniendo en cuenta esta discusión, ¿alguien quiere ajustar sus estimaciones?” // “Based on this discussion does anyone want to revise their estimate?”

Activity 1: Todos en orden (15 minutes)


This activity prompts students to apply what they know about tenths and hundredths and decimal notation to arrange two sets of numbers in order, first from least to greatest, and then the other way around.

A number line is given here, but students are likely to start seeing its limits as a tool for comparing and ordering decimals. It takes time to plot each value on the number line, the scale of the number line accommodates only a small range of numbers (numbers like 1.25 and 12.05 would go beyond the line), and there are other ways to discern how two decimals compare—by reasoning about the name of the decimals in tenths and hundredths, and by relating to benchmarks such as whole numbers and 5 tenths (0.5, 1.5, 2.5, and so on).


  • Groups of 2
  • Display the six decimals in the first problem.
  • “¿Cómo podemos describir estos decimales en términos de décimas y centésimas? Leamos cada uno en voz alta” // “How do we name these decimals in terms of tenths and hundredths? Let’s read each one aloud.”
  • Display the six decimals in the second problem.
  • “Con su compañero, tomen turnos para leer cada decimal. Descríbanlos en términos de décimas y centésimas” // “Take turns reading each decimal with your partner. Name them in terms of tenths and hundredths.”
  • 1 minute: partner work time


  • “Tómense unos minutos para completar la actividad en silencio. Luego, compartan sus respuestas con su compañero” // “Take a few quiet minutes to complete the activity. Then, share your responses with your partner.”
  • 5 minutes: independent work time
  • 2–3 minutes: partner work time
  • Monitor for students who order the decimals by:
    • plotting the decimals on the number line
    • using and comparing the word names of the decimals
    • relating each decimal to benchmarks such as 0, 0.5, and 1
  • Ask them to share their strategies during the synthesis, in the order as shown.

Student Facing

  1. Ordena los números de menor a mayor. Si te ayuda, usa la recta numérica.







    Number line. 13 evenly spaced tick marks. First tick mark, 0. Eleventh tick mark, 1.

  2. Ordena los números de mayor a menor. Si te ayuda, usa la recta numérica.







Student Response

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Advancing Student Thinking

Students may arrange the numbers by looking only at the digits in the numbers, without attending to the relative sizes of each decimal. (For example, they may say that 0.45 is greater than 0.9 because 45 is greater than 9.) Consider asking them to name the numbers and think about them in terms of tenths and hundredths, or to express them in fraction notation.

Activity Synthesis

  • Select previously identified students to share their responses and reasoning.
  • “Después de observar estas estrategias, ¿cuál o cuáles prefieren usar para ordenar decimales? ¿Por qué?” // “After seeing these strategies, which one(s) do you prefer to use for ordering decimals? Why?”

Activity 2: Carrera de 400 metros a toda velocidad (20 minutes)


In this activity, students compare and order decimals in the context of running times. Unlike in preceding activities, in which most decimals they encountered were less than one or were in the low ones, here the numbers all have two-digit whole numbers, prompting students to be more attentive to the place value of the digits. The context of track and field may be unfamiliar, so time is built into the launch for orienting students and for supporting them in making sense of the problem.

When students look carefully at the meaning of each digit in the numbers and interpret them in terms of the running context they are reasoning abstractly and quantitatively and observing place value structure (MP2, MP7).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

Representation: Access for Perception. Begin by showing a video of an Olympic Women’s 400-Meter final event to support both engagement and understanding of the context. To emphasize the relative magnitude of decimals in this context, invite students to attend to the running clock, the moment when the athletes cross the finish line, and the table of final results. Ask, “¿Por qué los decimales son importantes aquí?” // “Why are decimals important here?”
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing


  • Groups of 2
  • Display a picture of a standard 400-meter running track.
  • “¿Cuánto tiempo creen que tardarían en correr una vuelta de aproximadamente 400 metros? Piénsenlo por un momento. Luego, compartan su estimación con su compañero” // “How long do you think it would take you to run a lap, about 400 meters? Think about it for a moment, and then share your estimate with your partner.”
  • 1 minute: partner discussion
  • Explain that in track and field, runners compete to run different distances: 100 meters, 200, 400, 800, and more. The United States, Jamaica, and the Bahamas have produced some of the fastest track runners in the world.
MLR6 Three Reads
  • Display only the opening paragraph, the eight running times, and the table, without revealing the questions.
  • “Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
  • 1st Read: “La tabla muestra a ocho de las mejores corredoras de la prueba de 400 metros para mujeres. Abajo se muestran sus mejores tiempos de carrera, que las ubican entre las 25 mejores del mundo en esta prueba” // “The table shows eight of the top runners in the Women’s 400-Meter event. Their best running times, listed here, put the runners in the world’s top 25 in this event.”
  • “¿De qué se trata la historia?” // “What is this story about?”
  • 1 minute: partner discussion
  • Listen for and clarify any questions about the context.
  • 2nd Read: Read the opening paragraph a second time.
  • “Nombren las cantidades. ¿Qué cosas podemos contar o medir en esta situación?” // “Name the quantities. What can we count or measure in this situation?” (times in seconds, years)
  • 30 seconds: quiet think time
  • Share and record all quantities.
  • Reveal the questions.
  • 3rd Read: Read the entire problem aloud, including the questions.
  • “¿Cómo podríamos identificar correctamente cuál es el tiempo de cada corredora?” // “How might we go about matching the times to the right runners?” (Arrange the times in order, from shortest to longest.)


  • “Completen la actividad con su compañero” // “Work with your partner to complete the activity.”
  • 6–8 minutes: partner work time

Student Facing

La tabla muestra a ocho de las mejores corredoras de la prueba de 400 metros para mujeres. Abajo se muestran sus mejores tiempos de carrera, que las ubican entre las 25 mejores del mundo en esta prueba.






photograph of Allyson Felix running

Los nombres de la tabla están ordenados de acuerdo al mejor tiempo de las corredoras. La corredora más rápida aparece en la parte de arriba.

corredora mejor tiempo (segundos) año
Shaunea Miller-Uibo (Bahamas) 2019
Sanya Richards (Estados Unidos) 2006
Valerie Brisco-Hooks (Estados Unidos) 1984
Chandra Cheesborough (Estados Unidos) 1984
Tonique Williams-Darling (Bahamas) 2004
Allyson Felix (Estados Unidos) 2015
Pauline Davis (Bahamas) 1996
Lorraine Fenton (Jamaica) 2002
  1. Ordena los tiempos, de menor a mayor, para que correspondan con las corredoras.
  2. ¿Cuántos segundos tardó Sanya Richards en correr los 400 metros?
  3. ¿Cuál es el mejor tiempo de Allyson Felix?

Student Response

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Activity Synthesis

  • Display the table from the activity.
  • Invite students to share their ordered list and discuss how they went about arranging the numbers.
  • Highlight explanations that are based on place-value reasoning or on understanding of tenths and hundredths.

Lesson Synthesis

Lesson Synthesis

“Hoy comparamos decimales y los ordenamos de acuerdo a su tamaño” // “Today we compared decimals and put them in order by their size.”

Display these decimals with missing digits:

\( \boxed{0} \ . \boxed{\phantom{0}} \)

\(\boxed{0} \ . \ \boxed{1} \ \boxed{\phantom{0}}\)

\(\boxed{1} \ \boxed{\phantom{0}} \ . \ \boxed{\phantom{0}} \ \boxed{\phantom{0}}\)

\(\boxed{2} \ . \ \boxed{\phantom{0}}\)

\(\boxed{\phantom{0}} \ . \ \boxed{2}\)

“Aunque a todos los números les faltan dígitos, ¿hay algunos que ya podamos comparar?” // “Are there numbers that we can compare, even though they are all missing digits?” (Yes, we know 1__.__ __ is greater than all the others and 2. __ is greater than 0.__ and 0.1__.)

“¿Hay números que todavía no podamos comparar?” // “Are there numbers that we can’t compare?” (0.__, 0.1__, and __.2)

“¿Qué hace que ya podamos comparar algunos decimales, pero otros todavía no?” // “What makes it possible for us to compare some decimals but not others?” (Sample responses:

  • We know that a number with tens is greater than numbers with only ones.
  • We can compare numbers that are greater than 1 and those less than 1.
  • We can’t compare numbers when the digit in the place with the largest value is not known.)

Cool-down: De menor a mayor (5 minutes)


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