Lesson 26

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting a teen number from another teen number. The expressions are sequenced to encourage students to break the subtrahend into a ten and some ones. Students can then subtract the ten and ones in two different steps. Based on the previous lesson students may decompose the subtrahend into \(10 + n\) and subtract 10 first and then n.

• 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.

• “Si nos sabemos \(15 - 10\), ¿cómo nos ayuda con \(15 - 12\)?” // “How can \(15 - 10\) help with \(15 - 12\)?” (We know 12 is 10 and 2 so we can use \(15 - 10\) and subtract 2 more.)

The purpose of this activity is for students to solve two story problems that highlight the relationship between addition and subtraction. Both are Change Unknown stories that use the same numbers. Although one story sounds like addition and the other subtraction, both stories can be solved using either operation. The same equations can be used to solve both problems.

Students write equations to represent each problem and there are many equations students could write. The important thing is for students to be able to explain how the equation they wrote matches the story problem. Some students may write each of their steps as equations.

For example, for \( 6 + \boxed{\phantom{3}} = 18\) students may write:

• \(6 + 4 = 10\)
• \(10 + 8 =18\)
• \(4 + 8 = \boxed{12}\)

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.

• Read the task statement.
• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who write and can explain a variety of equations such as:
  • \(6 + \boxed{12} = 18\)
  • \(18 - 6 = \boxed{12}\)
  • \(18 - \boxed{12} = 6\)

• Invite previously identified students to share their equation for each problem.
• If needed, ask, “¿Cómo corresponde su ecuación a la forma como resolvieron el problema?” // “How does your equation match how you solved the problem?”
• “¿Qué observan sobre la ecuación que se usó para resolver cada problema?” // “What do you notice about the equation used to solve each problem?” (They could be the same. You can add \(6 + 12\) or subtract \(18 - 6\) for both problems to solve it.)
• “¿Por qué el número desconocido es el mismo en todas las ecuaciones?” // “Why is the missing number the same in each of these equations?” (Because \(6 + 12 = 18\) and \(18 - 6 = 12\). The difference is the same whether I add or subtract.)

The purpose of this activity is for students to solve related addition and subtraction story problems with the unknown in different positions. Students work with a partner to solve a story problem and create a poster of their work. They share their work with groups who solved a different problem and compare their representations and methods.

• Groups of 2
• Give each group tools to create a visual display and access to double 10-frames and connecting cubes or two-color counters.
• Assign each group a story problem to solve.
• “Resuelvan el problema-historia con su pareja y hagan un póster para mostrar cómo lo resolvieron. Asegúrense de incluir las ecuaciones que usaron. Si pueden resolver el problema de más de una forma, muestren las distintas formas y las ecuaciones” // “Work with your partner to solve the story problem and create a poster showing how you solved. Be sure to include any equations you used. If you can solve the problem in more than one way, show the different ways and equations.”

• 8 minutes: partner work time
• Arrange groups together so each larger group has students who have solved each of the four problems.
• “Compartan el póster con su grupo. Expliquen de qué manera las ecuaciones que escribieron corresponden a la historia. Mientras comparten, discutan en qué se parecen y en qué se diferencian los problemas. Hagan una lista de las ecuaciones que usaron en cada problema” // “Share your poster with your group. Explain how the equations you wrote match the story. As each group shares, discuss how the problems are the same and different. Make a list of equations you used for each problem.”
• 10 minutes: group work time

• Display a list of equations one group made for each problem.
• “¿Qué observan sobre las ecuaciones que este grupo usó en los distintos problemas?” // “What do you notice about the equations this group used for each problem?” (They used the same equations for each problem. All the problems have more than one equation. All the problems have addition and subtraction equations.)