The purpose of this What Do You Know About _____? is to invite students to share what they know about base-ten blocks in the context of division. Some students may choose to reflect on base-ten blocks and division, while others may simply describe what they know about base-ten blocks. Any reflection offered by students is useful for activating prior knowledge for the lesson.
Launch
Display a pile of base-ten blocks.
“¿Qué saben sobre los bloques en base diez?” // “What do you know about base-ten blocks?”
1 minute: quiet think time
Activity
Record responses.
¿Qué sabes sobre los bloques en base diez?
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Cuáles bloques usarían para representar el número 324?” // “Which blocks would we use to represent the number 324?”
“Ustedes han usado bloques en base diez para representar números grandes. Hoy van a entender cómo los bloques nos pueden ayudar a dividir números más grandes” // “You have used base-ten blocks to represent large numbers. Today you are going to see how they can be helpful to divide larger numbers.”
Activity 1
Standards Alignment
Building On
Addressing
4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
The purpose of this activity is for students to find quotients using base-ten blocks and represent their methods. Students solve two problems, one where decomposing a hundred or ten is not necessary and one where it is. Students use base-ten blocks to represent the problem and find the quotient, then they work in small groups to create a visual display of how they used the base-ten blocks. This builds on work students have done in previous grades representing operations with base-ten representations.
The base-ten blocks help highlight the important role place value plays in division (MP7). There are not enough hundreds in 104 to divide into 8 equal groups but there are enough tens to put 1 ten in 8 equal groups. Then the 2 remaining tens can be broken into ones to complete the division.
Launch
Groups of 3–4
Give each group at least 4 hundreds blocks, 10 tens blocks, and 25 ones blocks.
“Con su grupo, representen cada expresión con bloques en base diez. Después, encuentren el cociente” // “Work with your group to represent each expression with base-ten blocks, then find the quotient.”
Activity
5–6 minutes: group work time
“¿En qué se pareció encontrar el primer cociente a encontrar el segundo? ¿En qué fue diferente?” // “How was finding each quotient the same? How was it different?” (With the first one, you could just split the blocks into 4 groups. With the second one, you had to trade in some blocks to make 8 groups.)
MLR7 Compare and Connect
Give each group tools for making a visual display.
“Creen una presentación visual que muestre cómo usaron los bloques en base diez para encontrar el cociente. Incluyan detalles, como notas, diagramas, dibujos, etc., para ayudar a los demás a entender cómo pensaron” // “Create a visual display that shows how you used the base-ten blocks to find the quotient, including details such as notes, diagrams, drawings, and so on, to help others understand your thinking.”
2–5 minutes: group work
5–7 minutes: gallery walk
“Mientras ven las presentaciones de otros grupos, anoten cosas que sean parecidas y cosas que sean diferentes” // “As you look at the displays from other groups, record things that are the same and things that are different.”
Usa los bloques en base diez para representar cada expresión. Después, encuentra el valor de cada expresión.
Activity Synthesis
“¿En qué se parecen y en qué son diferentes las representaciones?” // “What is the same and what is different between the representations?”
30 seconds quiet think time
1 minute: partner discussion
Activity 2
Standards Alignment
Building On
Addressing
4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
The purpose of this activity is for students to find quotients and represent their thinking with base-ten blocks. The numbers in the expressions are designed to encourage students to think about when the base-ten blocks may be helpful and when they become cumbersome. In future lessons, students will be asked to interpret base-ten representations but may use any method or representation that makes sense to them.
Representation: Develop Language and Symbols. Synthesis: Use gestures or annotations such as labels or arrows to make connections between representations on displayed student work. Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Launch
Groups of 2
Give students access to base-ten blocks.
“Van a resolver algunos problemas individualmente. Usen bloques en base diez y representen sus ideas en su libro” // “You are going to solve some problems on your own. Use base-ten blocks and represent your thinking in your book.”
Activity
5–6 minutes: independent work time
2 minutes: partner discussion
Monitor for and select students who draw base-ten representations using small and large squares and rectangles labeled with numbers.
Encuentra el valor de cada expresión. Explica o muestra cómo pensaste. Si te ayuda, usa bloques en base diez.
Student Response
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Advancing Student Thinking
If students use mental math to solve problems, consider asking:
“¿Me explicas cómo encontraste el valor de ______?” // “Tell me more about how you found the value of ______.“
“¿Cómo podrías usar los bloques para verificar tus cálculos mentales?” // “How might your use the blocks to check your mental math?”
Activity Synthesis
“En la síntesis de la actividad, vamos a comparar distintas representaciones de un problema de división” // “In the Lesson Synthesis, let’s compare some different representations for a division problem.”
Lesson Synthesis
Display student work showing base-ten representations for the last expression ().
“¿Cómo representó este estudiante su razonamiento?” // “How did this student represent their reasoning?” (They drew 10 tens and then crossed out 2 tens and drew 20.)
“¿Tienen preguntas o sugerencias que puedan ayudarles a ellos a que su trabajo sea más claro?” // “Do you have any questions or suggestions that could help them make their work clearer?” (They could add numbers to label the parts.)
Repeat with other student’s work, as time allows.
“Tómense un minuto y, si quieren, ajusten su trabajo para que otros lo entiendan más fácilmente” // “Take a minute, and if you’d like, revise your work to make it easier for someone else to understand.”
Standards Alignment
Building On
Addressing
Building Toward
4.NBT.A
Generalize place value understanding for multi-digit whole numbers.
If students find the value of each expression using only numbers and symbols, consider asking:
“¿Cómo encontraste el valor de esta expresión?” // “How did you find the value of this expression?”
“¿Cómo puedes usar bloques en base diez para representar la división y mostrar cómo pensaste en ella?” // “How can you use base-ten blocks to represent the division and show your way of thinking about it?”