Lesson 4

The purpose of this Number Talk is to elicit strategies and understandings students have for finding sums when both addends are the same and sums when one addend is one less or one more than the other. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to decompose numbers into two equal addends or two addends that are as close as possible as they reason about even and odd numbers.

• 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 se parecen estas expresiones? ¿En qué son diferentes?” // “How are the expressions the same? How are they different?”

The purpose of this activity is for students to recognize that even numbers can be represented as the sum of two equal addends. The activity is designed to elicit student curiosity about which types of decompositions are possible and which are not. Students may notice many patterns in the ways even and odd numbers can be decomposed which will be useful in future lessons. However, the synthesis should be focused on representing even numbers as sums of equal addends.

• Groups of 2
• Give students access to counters.

• “Descubran varias maneras en las que los estudiantes podrían repartir sus galletas” // “Figure out different ways the students could share their cookies.”
• “Muestren cómo pensaron en cada caso. Usen ecuaciones para mostrar los grupos” // “Show your thinking for each way. Use equations to show the groups.”
• “Puede que algunas maneras de repartir no sean posibles. Prepárate para mostrar y explicar por qué” // “Some ways may not be possible. Be ready to show and explain why.”
• 5 minutes: independent work time
• “Compartan con su compañero cómo pensaron. ¿En qué se parecen sus ecuaciones? ¿En qué son diferentes?” // “Share your thinking with your partner. How are your equations the same? How are they different?”
• 10 minute: partner discussion

• “¿Qué observaron sobre las distintas formas en las que los estudiantes pudieron repartir sus galletas?” // “What did you notice about the possible ways the students could share their cookies?” (Kiran and Lin could share their cookies in the most ways. Noah could only share with one bag of even and one bag of odd.)
• Display:
  • \(12 = 6 + 6\)
  • \(14 = 7 + 7\)
  • \(15 = 7 + 8\)
• “¿De qué manera estas ecuaciones representan las galletas de los estudiantes?” // “How do these equations represent the student’s cookies?”
• “¿Cuáles estudiantes hornearon un número par de galletas? Usen las ecuaciones para explicar cómo lo saben” // “Which students baked an even number of cookies? Use the equations to explain how you know.” (Kiran and Lin because the equations show you can split their cookies into two equal groups.)

The purpose of this activity is for students to represent even numbers as a sum of two equal addends. They sort all numbers between 0 and 20 into even and odd and notice that all even numbers can be represented as sums of two equal addends while odd numbers cannot (MP8). Students may also use the sorting activity to understand and explain why 0 is an even number.

• Groups of 2
• Give students access to counters.

• “Intentemos descomponer más números en dos sumandos iguales” // “Let’s try to decompose more numbers into two equal addends.”
• “Por turnos, escojan un número que esté entre 0 y 20. Decidan juntos si el número es par o impar y anoten esto en la tabla” // “Take turns picking a number between 0 and 20. Decide together whether the number is even or odd and record it in the table.”
• “Luego, intenten descomponer el número en dos sumandos iguales. Si lo logran, anoten la suma en la tabla” // “Then try to decompose the number into two equal addends. If you can, record it on the table.”
• “Si no pueden descomponer el número en dos sumandos iguales, encuentren dos sumandos que formen su número y que estén lo más cerca posible el uno del otro” // “If you cannot find a way to decompose the number into two equal addends, find two addends that are as close together as possible that make your number.”
• Demonstrate with Kiran (12) and Noah’s (15) cookies as needed.
• “Sigan hasta que hayan clasificado todos los números del 0 al 20” // “Keep going until you have sorted all the numbers from 0 to 20.”
• 10 minutes: partner work time

If students place an odd number in the even group or an even number in the odd group,  consider asking: 

• “¿Cómo podrías usar fichas o un dibujo para mostrar si este número es impar o par?” // “How could you use counters or a drawing to show if this number is odd or even?”

• Display the completed table.
• “¿Qué observan sobre los números pares y los números impares?” // “What do you notice about even and odd numbers?” (All the even numbers have the same addends. All the even numbers are “doubles.” The odd numbers have one addend that is one more than the other.)
• “Expliquen por qué los números pares se pueden descomponer en dos sumandos iguales” // “Explain why even numbers can be decomposed into two equal addends.”