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).
Launch
Groups of 2
Display the expression.
“¿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
Activity
“Discutan con su compañero cómo pensaron“ // “Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Monitor for students who estimate by using .
Escribe una estimación que sea:
muy baja
razonable
muy alta
Student Response
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Advancing Student Thinking
Activity Synthesis
Invite students to share estimates.
“¿Por qué es una buena estimación del producto?” // “Why is a good estimate for the product?” (10,000 is just 1 more than 9,999 and 896 is close to 900.)
“¿Cuál es el valor de ? ¿Cómo lo saben?” // “What is the value of ? How do you know?” (9,000,000, because the two numbers have 6 factors of 10 combined.)
Activity 1
Standards Alignment
Building On
Addressing
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
The purpose of this activity is for students to consider possible mistakes when multiplying greater numbers. Monitor for students who:
Revise their answer after examining Kiran’s mistake.
Recognize that so must be greater than 5,850.
Can explain why Kiran should be multiplying .
Recognize that , so there should be three zeros in the second partial product.
When students determine Kiran's error and make sense of his work, they interpret and critique the work of others (MP3).
MLR1 Stronger and Clearer Each Time. Synthesis: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their responses to “¿Con qué partes del trabajo de Kiran están de acuerdo? ¿Con qué partes están en desacuerdo?” // “What parts of the work [Kiran’s] do you agree with? What parts of the work do you disagree with?” Invite listeners to ask questions and give feedback that will help their partner clarify and strengthen their ideas and writing. Give students 3–5 minutes to revise their written explanation based on the feedback they receive. Advances: Writing, Speaking, Listening
Launch
Groups of 2
Display or write for all to see:
Display each number in a different corner of the room:
14,000
18,000
13,000
19,000
“Cuando yo diga ‘ya’, párense en la esquina que tenga el número que crean que es la estimación más razonable de . Prepárense para explicar cómo razonaron” // “When I say go, stand in the corner with the number that you think is the most reasonable estimate for . Be prepared to explain your reasoning.”
1 minute: quiet think time
Ask a student in each corner to explain their reasoning.
“¿Alguien quiere cambiar de esquina?” // “Does anyone want to switch corners?”
Ask a student who switched corners to explain their reasoning.
“Ahora van a encontrar este producto y a analizar un trabajo” // “Now you are going to find this product and analyze some work.”
Activity Synthesis
Ask previously identified students, as described in the Activity Narrative, to share their thinking.
Display Kiran's work.
“¿Por qué 5,850 no tiene sentido?” // “Why doesn’t 5,850 make sense?” ( so should be greater than 6,500.)
“¿Qué tiene sentido en el trabajo de Kiran?” // “What makes sense about Kiran’s work?” (. , but he needs to multiply .)
Display a student's correct solution or the image from Student Responses.
“¿Cómo sabemos que 17,550 es un valor razonable del producto?” // “How do we know that 17,550 is a reasonable value for the product?” (because )
Activity 2
Standards Alignment
Building On
Addressing
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
The purpose of this activity is for students to practice multiplying multi-digit numbers that have one or more digits of 0 at the end. Monitor for students who:
Use the standard algorithm to find the value of .
Multiply the product by 10 to find the value of the product .
Multiply the product of by 10 to find the value of the product .
Students who observe that and and use these relationships to find the values of the products are observing regularity in repeated reasoning and using their knowledge of how to multiply a whole number by 10 (MP7, MP8).
Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were important to find products of multi-digit numbers that have zero digits. Display the sentence frame, “La próxima vez que multiplique un número que contenga dígitos que son cero, prestaré atención a . . .” // “The next time I multiply a number that contains zero digits, I will pay attention to . . . .“ Supports accessibility for: Conceptual Processing, Memory
Launch
Groups of 2
If needed, remind students that they can estimate the product first to help them know if their calculated product is reasonable.
Activity
5–7 minutes: independent work time
5–7 minutes: partner discussion
Encuentra el valor de cada producto.
1.
2.
3.
4.
Activity Synthesis
Display the product .
Ask previously identified students to share their solutions.
Display correct student work or the image from Student Responses:
“¿Qué relación hay entre y ?” // “What is the relationship between and ?” (The product is 10 times as great as because one of the factors is 10 times greater.)
“¿Qué relación hay entre y ?” // “What is the relationship between and ?” (The product is 100 times as great as since 6,700 is .)
Lesson Synthesis
“Hoy multiplicamos números de varios dígitos usando el algoritmo estándar. ¿Qué fue retador en los problemas que resolvimos hoy?” // “Today we multiplied multi-digit numbers using the standard algorithm. What was challenging about the problems we solved today?” (It was hard to keep track of the numbers as we multiplied. I wasn’t sure how many zeroes to write in the second partial product.)
“¿Qué es importante recordar al usar un algoritmo estándar para multiplicar ?” // “What is important to remember when using a standard algorithm to multiply ?” (Estimate first so you know if your answer is reasonable. Pay attention to which place each digit is in.)
Display:
“¿Cuál sería una estimación razonable del valor de ?” // “What is a reasonable estimate for ?” (21,000, 24,000, 28,000.)
Ask students to describe to a partner how they would use the standard algorithm to find the value of the product.
Standards Alignment
Building On
Addressing
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.