Lesson 2

The purpose of this Number Talk is to elicit strategies and understandings students have for adding 2 or 3 more. These understandings help students develop fluency and will be helpful later in this lesson when students count on to add.

In this activity, students have an opportunity to notice and make use of structure (MP7). They may see patterns in the structure of the expressions by noticing that when an addend changes by one the sum changes by one.

• 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.

• ¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”

The purpose of this activity is for students to solve Put Together, Total Unknown story problems through a context they are familiar with—the game Shake and Spill. To launch the lesson, the teacher plays a round of the game with students and reminds students to draw a box around the number in the equation that answers the question.

As students find sums, they relate addition to counting on and may apply what they know about the commutative property. Some of the story problems have the smaller addend first to encourage students to consider this property (MP7). Students should make sure that the answer to each question is clear in their representations.

In the activity synthesis, use physical counters as well as students’ representations to compare the two counting on methods.

• Each group of 2 needs 10 two-color counters.
• Have one cup available to demonstrate Shake and Spill.

• Groups of 2
• Give students access to 10-frames and two-color counters.
• Juguemos juntos una ronda de ‘Revuelve y saca’” // “Let’s play a round of Shake and Spill together.”
• Demonstrate Shake and Spill.
• “¿Qué ecuación puedo escribir para representar el número total de fichas?” // “What equation can I write to represent the total number of counters?”
• 30 seconds: quiet think time
• Record responses.
• “¿Qué número en la ecuación representa el número total de fichas?” // “What number in the equation represents the total number of counters?”
• Draw a box around the total in the equation.

• Read each problem.
• 6 minutes: independent work time
• “Compartan con su pareja cómo pensaron” // “Share your thinking with your partner.”
• 4 minutes: partner discussion
• Monitor for students who find the sum of 2 and 8 by:
  • counting all
  • starting at 2 and count on 8
  • starting at 8 and count on 2

• Invite previously identified students to share in the sequence above.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?” (They are the same because they all add 3 and 6 and get 9. They all counted to get the answer. They are different because they counted different amounts. The first one counted all of the counters. The second counted 6 counters and the third counted 3 counters.)

The purpose of this activity is for students to analyze representations of the work of two students who counted on. Each student chose a different addend to count on from, which illustrates the commutative property. Methods are represented and students are asked to explain why both methods are correct using precise mathematical language (MP6). 

• Groups of 2
• Give students access to two-color counters.

• Read the task statement.
• 2 minutes: quiet think time
• 3 minutes: partner discussion

If students show that both equations are true without mentioning the 'add in any order' property, consider asking:

• “¿Cómo saben que los dos métodos son correctos?” // “How do you know that both methods are correct?”
• “¿Cómo podemos usar las mismas nueve fichas para pasar del primer método al segundo método?” // “How can we use the same nine counters to move from the first method to the second?”

• Invite 2–3 groups to share their thinking.
• “Kiran y Clare empezaron con números diferentes, pero obtuvieron el mismo valor. Con tal de que tengamos los mismos dos números, podemos sumarlos en cualquier orden. A esto lo llamamos ‘la propiedad de sumar en cualquier orden’” // “Kiran and Clare started with different numbers, but they both got the same value. As long as we add the same two numbers, we can add them in either order. This is called the add in any order property.”
• “¿Cuál método les gusta más? ¿Por qué?” // “Which method do you like best? Why?” (I like adding up from the larger number since it is faster than adding up from the smaller number.)

The purpose of this activity is for students to find the value of sums within 10. Students may apply what they learned about the commutative property and counting on. They may count on for certain equations, such as \(+1\) or \(+2\) equations as they can keep track easily, but count all for others. In the lesson synthesis, students return to the addition expressions cards they created in a previous lesson.

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

• Read the task statement.
• 5 minutes: independent work time
• 3 minutes: partner discussion

• Display answers to problems.