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The purpose of an Estimation Exploration is for students to practice the skill of estimating a reasonable answer, based on experience and known information. It gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3). Asking: “Does this make sense?” is a component of making sense of problems (MP1), and making an estimate or a range of reasonable answers with incomplete information is a part of modeling with mathematics (MP4).
In this activity, students are given information about a parking garage along with pictures of its interior and exterior. Invite students to share their estimates and the assumptions they used to make them. For example, students may share how they used the photos to estimate how many floors there were and how many cars could fit on each floor. They may share the assumptions they made that, based on the pictures, there are 10 floors and each floor holds the same amount of cars.
En estas imágenes se muestran el exterior y el interior de una torre de estacionamientos en Wolfsburg, Alemania. El estacionamiento es automatizado: cada automóvil se sube en un ascensor y se ubica en un estacionamiento.
¿Cuántos automóviles caben en la torre?
Escribe una estimación que sea:
| muy baja | razonable | muy alta |
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In this activity, students use given descriptions and their knowledge of multiplication to make some estimates of the cost and the time associated with brushing teeth. To complete the estimation, students need to make some assumptions about what constitutes “a lifetime” and the cost of a single toothbrush. The activity gives students another example before they write their own Estimation Exploration.
Jada cepilla sus dientes durante 2 minutos, dos veces al día. Ella cambia su cepillo de dientes cada 3 meses.
Usa esta información para hacer algunas estimaciones. Explica o muestra cómo razonaste.
Aproximadamente, durante toda su vida:
Averigua aproximadamente cuántos minutos pasará cepillándose sus dientes:
In this activity, students create an Estimation Exploration that focuses on multi-digit multiplication. Students may choose to present a situation (as in the toothbrush example), something observed in the classroom (such as a large shelf filled with books), or an image (as in the Warm-up). They need to anticipate the reasoning strategies others might use to make an estimate.
Es su turno de crear un problema de estimación.
| muy baja | razonable | muy alta |
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In this activity, students facilitate the Estimation Exploration they created for another group in the class. If time allows, encourage students to run the activity for multiple groups.
Sigan estos pasos para dirigir su actividad tipo “Exploración de estimación” y presentársela a otro grupo:
Invite students to reflect on their process. Discuss questions such as:
“¿Qué diferencia hubo entre el proceso de crear una actividad tipo ‘Exploración de estimación’ y responder una?” // “How was the process of creating an Estimation Exploration different from answering one?” (Creating the activity is more involved. It requires researching, thinking of possible ways to estimate, actually making estimates, and maybe revising the question. Doing the activity only involves finding a way to estimate and explaining it.)
“¿Qué aprendieron mientras dirigían su actividad tipo ‘Exploración de estimación’?” // “What did you learn as you facilitated your Estimation Exploration?” (The estimates that others find could be close or far from our estimates or the actual number. Others might use other strategies that we did not think of or make assumptions that are very different than ours.)
“Si tuvieran la oportunidad de ajustar su actividad, ¿cambiarían algo? ¿Qué cambiarían?” // “If you had a chance to revise your activity, would you change anything? What would you change?”