The purpose of this activity is for students to use their knowledge of base-ten diagrams and place value to make sense of a written method. They describe how numbers, words, and equations can be used to represent the steps they have shown with other representations (MP2). Students will explore other ways to use equations, including the standard algorithm, in future grades. Although some grade 2 students may begin to use recording methods, such as the standard algorithm, it is important to encourage students to use the methods that make the most sense to them.

If students rely on one way to show subtracting by place with numbers or equations, consider asking:

• “¿Cómo representó Elena el valor de cada dígito de 726 y 558?” // “How did Elena represent the value of each digit in 726 and 558?”
• “¿De qué otra forma podrías representar los valores de los dígitos y mostrar cómo restar usando el valor posicional?” // “What is another way you could represent the values of the digits and show subtracting by place?”

• Display a student representation of Elena’s steps with a base-ten diagram and 1 or 2 other representations that use numbers and equations.
• “¿En qué se parecen estas representaciones? ¿En qué son diferentes?” // “How are these representations the same? How are they different?” (All show decomposing a hundred and a ten to subtract. They all show subtracting hundreds from hundreds, tens from tens, and ones from ones. Each representation is different, including a base-ten diagram, numbers and words, and subtracting by place value.)

The purpose of this activity is for students to practice subtracting within 1,000. Each student starts with a card that has a three-digit number on it. Students walk around the room and find a student with a different number. They find the difference between their numbers and write an equation to represent the difference. As time allows, students find a new partner. The numbers on the cards were chosen so any pair of numbers would require decomposing a hundred and a ten when subtracting by place. In addition to monitoring for ways students use written methods for subtracting by place, monitor for the ways students use what they know about the relationships between the numbers to choose a method. For example, if students are finding the value of , they may choose to add on 2 to 198 and count on by place, instead of decomposing a hundred and a ten.

• Invite previously identified students to describe the steps they used to find the difference for one of their expressions.
• Consider asking:
  • “¿Qué preguntas le quieren hacer a _____ sobre sus pasos o su representación?” // “What questions do you have for _____ about their steps or their representation?”
  • “¿En qué se parecía su representación? ¿En qué se parecían sus pasos? ¿En que eran diferentes?” // “How was your representation the same? How were your steps the same? How were they different?”