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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). The task intentionally uses a simpler problem type to encourage students to focus on the act of estimating, using their understanding of place value. Students independently solve story problems with numbers beyond 100 in grade 3.
En la escuela de Mai, hay 358 estudiantes en segundo grado y 465 estudiantes en tercer grado.
¿Aproximadamente cuántos estudiantes hay en segundo grado y tercer grado en total?
Escribe una estimación que sea:
| muy baja | razonable | muy alta |
|---|---|---|
The purpose of this activity is for students to decide if different estimates for a problem make sense, based on what they know about the problem type and place value. If they do not think an estimate makes sense, they are asked to show or explain a way to improve it. In the Activity Synthesis, they are encouraged to reflect on the strengths and weaknesses of each estimation strategy. As in the previous activity, a simple problem type is used to encourage students to focus on estimating rather than problem solving outside of 100.
En la escuela de Mai, hay 227 estudiantes en kínder y 378 estudiantes en primer grado.
Sus compañeros hicieron algunas estimaciones del número total de estudiantes que hay en kínder y primer grado.
Con tu compañero, decide cuáles estimaciones tienen sentido. Sugiere una forma en la que cada persona podría mejorar su estimación.
Jada: 500 estudiantes, porque 2 centenas y 3 centenas es 5 centenas.
Lin: 100 estudiantes, porque si tengo 3 centenas y quito 2 centenas, queda 1 centena.
Andre: 600 estudiantes, porque 227 está cerca de 225 y 378 está cerca de 375. , y .
If students find the actual sum first and use that when making their suggestions, consider asking:
The purpose of this activity is for students to use estimation strategies to reason about whether their computations make sense when adding and subtracting within 1,000. Monitor for the different ways students use what they know about place value and compatible numbers to reason about which estimates are too high, too low, or about right and their discussions with their partners about whether their answers make sense. Each problem includes at least one estimate that can be found using front-end estimation, without adjusting for the tens and the ones. Students are not incorrect when sorting these into the “about right” column, but consider looking for ways to pair them with students who place the estimates in other columns to compare their reasoning.
En cada caso, decide si el valor exacto de la expresión es mayor o menor que la estimación.
Con tu compañero, encuentra el valor exacto.
Encuentra el valor de una de las expresiones. Explica o muestra tu razonamiento.
Intercambia tu trabajo con el de un compañero. Decide si el valor de la expresión de tu compañero tiene sentido. Explica tu razonamiento.
“Hoy hablamos sobre lo que significa que las respuestas tengan sentido. También usamos distintas estrategias de estimación para pensar si una respuesta tiene sentido cuando sumamos o restamos números de tres dígitos” // “Today we talked about what it means for answers to make sense and used different estimation strategies to think about whether an answer makes sense when we are adding or subtracting three-digit numbers.”
“¿Cómo supieron cuándo una estimación o una respuesta no tenía sentido? Den un ejemplo si les ayuda a explicar” // “What are some ways you knew when an estimate or an answer did not make sense? Give an example if it is helpful.” (The size of the number didn’t make sense with the other numbers. The answer gets larger when it should get smaller. The answer made sense with the hundreds place, but not with the tens or ones place.)
Display .
“Si estuvieran estimando esta suma, ¿sumarían solo los valores que están en la posición mayor o estimarían de otra manera? Expliquen” // “If you were estimating this sum, would you just add the greatest place, or would you estimate in another way? Explain.” (I wouldn’t just add the greatest place, because there’s still at least 50 and 40 to add. I would add the greatest place first, and then add 100 more to it. I would just use friendly numbers, because 552 is close to 550 and 348 is close to 350.)