Lesson 16

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.

• 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

• Record responses.

• “¿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.”

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 and then the 2 remaining tens can be broken into ones to complete the division.

• Each group of 3–4 students needs a set of base-ten blocks that includes 4 hundreds blocks, 10 ten blocks, and 25 ones blocks.

• 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.”
• 5–6 minutes: group work time

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.”

Students may show their reasoning and computation only by writing expressions or equations. Consider asking: 

• “¿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?”
• “¿Qué significa la respuesta que encontraste en términos de los bloques?” // “What does the answer you found mean in terms of the blocks?”

• “¿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

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.

• 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.”

• 5–6 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for students who draw base-ten representations using small and large squares and rectangles labeled with numbers, to share in the lesson synthesis.

Students may use mental math to solve problems. Consider asking: “¿Cómo podrías usar los bloques para verificar tus cálculos mentales?” // “How might your use the blocks to check your mental math?”

• See lesson synthesis.