Lesson 7

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting numbers within 1,000. These understandings help students develop fluency and will be helpful as students relate subtraction algorithms to strategies they have used to subtract within 1,000.

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿En qué les ayudó el valor posicional mientras restaban estos números?” // “How was place value helpful as you subtracted these numbers?” (When we were subtracting 10, only the tens place changed. For the last expression we were able to subtract the tens, then the ones.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____'s reasoning in a different way?”
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
  • “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
  • “¿Alguien quiere agregar algo a la estrategia de _____?” // “Does anyone want to add on to _____’s strategy?”

The purpose of this activity is for students to subtract numbers within 1,000 using any strategy that makes sense to them to find the difference of two numbers within 1,000. The expressions in this activity give students a chance to use different strategies, such as subtracting hundreds from hundreds, tens from tens, and ones from ones, or adding up. Students may also use a variety of representations, which will be the focus of the activity synthesis. Students who choose to use base-ten blocks or number lines to represent their thinking use tools strategically (MP5).

This activity uses MLR7 Compare and Connect.
Advances: Representing, Conversing

• Groups of 2
• Give students access to base-ten blocks.
• “Por un momento, piensen cómo pueden restar estos números” // “Take a minute to think about how you could subtract these numbers.”
• 1 minute: quiet think time
• Share responses.

• “Con su pareja, resten estos números de cualquier forma que tenga sentido para ustedes. Expliquen o muestren su razonamiento” // “Work with your partner to subtract these numbers in any way that makes sense to you. Explain or show your reasoning.”
• 5–7 minutes: partner work time
• Monitor for an expression for which students use a variety of representations, such as:
  • using base-ten blocks
  • drawing a number line
  • writing their reasoning in words
  • writing equations
• During the synthesis, students will create a visual display that shows how they found the value of the selected expression.
• Give each group tools for creating a visual display.

MLR7 Compare and Connect

• “Creen una presentación visual que muestre cómo encontraron el valor de ______. Incluyan detalles, como notas, diagramas, dibujos, etc., para ayudar a los demás a entender cómo pensaron” // “Create a visual display that shows how you found the value of ______. You may want to include details such as notes, diagrams, drawings, and so on, to help others understand your thinking.”
• 2–5 minutes: partner work time
• 5–7 minutes: gallery walk
• “¿En qué se parecen y en qué son diferentes las maneras en las que los grupos representaron la resta?” // “What is the same and what is different about the ways that groups represented the subtraction?” (Some groups used equations. Some groups used base-ten blocks. They all used the same numbers. They all got the same answer.)
• Display one example of 2–3 different representations side-by-side for all to see.

• “¿Cuáles representaciones muestran la misma idea o nos ayudan a encontrar la diferencia de la misma forma?” // “Which representations show the same idea or help us find the difference the same way?” (The number line and equations show the same idea of adding up. The base-ten blocks are different because they show a ten or a hundred decomposed into smaller units before some of the blocks are taken away.)

The purpose of this activity is for students to make sense of drawings of base-ten blocks. Students compare two base-ten drawings. The first drawing is the same as what they saw in grade 2, where the tens block is decomposed into 10 individual ones and moved over to the ones place before subtracting the ones. In the second drawing, the tens block is moved over and partitioned into 10 parts but not decomposed into individual ones. The subtraction of ones is shown directly on the ten that was moved over. Students then match base-ten diagrams to subtraction expressions and subtract to find the value of each expression. This will be helpful in later lessons when students relate base-ten diagrams to written algorithms.

• Groups of 2
• “Por un minuto, miren los dibujos que muestran cómo Jada y Han usaron bloques en base diez para restar” // “Take a minute to look at the drawings of how Jada and Han used base-ten blocks to subtract.”
• 1 minute: quiet think time
• “Discutan con su pareja en qué se parecen y en qué son diferentes los dibujos de Jada y de Han” // “Discuss with your partner how Jada and Han’s drawings are alike and how they are different.”
• 1 minute: partner discussion
• Share responses.

• “Juntos, emparejen cada expresión con un diagrama que la represente. Después, encuentren el valor de cada expresión” // “Work together to match each expression with a diagram that represents it. Then, find the value of each expression.”
• 3–5 minutes: partner work time

• Invite students to share the expression that matches each diagram.
• “¿A qué tuvieron que prestarle atención mientras emparejaban cada diagrama con una expresión?” // “What did you have to pay attention to as you matched each diagram to an expression?” (I had to look for the numbers that were being subtracted. I had to look for tens over by the ones and hundreds over by the tens if there weren’t enough tens or ones.)