Lesson 2

The purpose of this Choral Count is to invite students to practice counting backward by 1 and notice patterns in the count. When students describe repeated patterns they see using the language of place value, they look for and make use of the base-ten structure of numbers and connect it to the counting sequence (MP6, MP7, MP8).

• “Cuenten hacia atrás de 1 en 1, empezando en 70” // “Count backward by 1, starting at 70.”
• Record as students count.
• Stop counting and recording at 20.

• “¿Qué patrones ven?” // “What patterns do you see?”
• 1-2 minutes: quiet think time
• Record responses.

• “¿Quién puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”

The purpose of this activity is for students to add 2 two-digit numbers within 100, without composing a ten, in a way that makes sense to them. Students may apply methods such as counting on or adding tens and tens and ones and ones. Monitor and select students with the following methods to share in the synthesis:

• counts on from 23 or 45 by tens and ones, (\(23 + 10 + 10 + 10 + 10 = 63\), \(63 + 1 + 1 + 1 + 1 +1 = 68\) or \(45 + 10 + 10 = 65\), \(65 + 1 + 1 + 1 = 68\))
• adds to 23 or 45 by adding all the tens and then all the ones (\(23 + 40 + 5\) or \(45 + 20 + 3\))
• combines tens and tens and ones and ones (\(20 + 40 = 60\), \(3 + 5 = 8\), \(60 + 8 = 68\) or \(3 + 5 = 8\), \(20 + 40 = 60\), \(60 + 8 = 68\))

During the synthesis, the teacher records each step of student thinking as equations as shown above. Students discuss connections between their classmates’ work.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

• Read the task statement.
• 5 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for students who use the methods described in the activity narrative.

If students find a value other than 68, consider asking:

• “¿Cómo encontraste el valor de 23 + 45?” // “How did you find the value of 23 + 45?”
• “¿Como puedes usar cubos encajables (o dibujos) para encontrar el valor?” // “How could you use connecting cubes (or drawings) to find the value?”
• “¿Cómo podrías usar marcas u otros dibujos para llevar la cuenta?” // “How could you use labels or other drawings to keep track of how you counted?”

• Invite previously identified student to share in the order presented above.
• As students explain their thinking, record drawings and equations.
• “¿Alguien tiene una pregunta sobre el método de _____?” // “Does anyone have a question about _____'s method?”
• “¿En qué se parecen estos métodos y estas ecuaciones? ¿En qué son diferentes?” // “How are these methods and equations the same? How are they different?” (One person started with 23 and the other started with 45. They all worked with tens and ones. The first person counted on by ten and then by one. The next person added the tens and then the ones to the first number. The last person broke apart both numbers and added the tens together and the ones together.)

The purpose of this activity is for students to analyze two different representations of addition methods and identify the equations that match each method. One of the representations shows adding tens and tens and ones and ones. The other representation shows counting on by tens and ones.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display and read the first problem.
• “Examinen el trabajo de cada estudiante y traten de descifrar lo que cada uno estaba pensando” // “Look at each student’s work and see if you can figure out what they were each thinking.”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share student responses.

• Display and read the second problem.
• “¿Cuáles ecuaciones van con cada dibujo? Prepárense para explicar cómo lo saben de una forma que los demás entiendan” // “Which equations go with each drawing? Be ready to explain how you know so that others will understand.”
• 3 minutes: partner discussion

• Display Elena’s work and the matching equations.
• “¿Cómo corresponden estas ecuaciones al dibujo?” // “How do these equations match the drawing?” (You can see she added the 60 and the 20 and then added the 3 and the 5.)
• “¿Cómo describirían la forma en la que Elena encontró la suma?” // “How would you describe how Elena found the sum?” (She added tens and tens, then ones and ones. Then she added the total number of tens and ones together.)
• Display Andre's work and the matching equations.
• “¿Cómo corresponden estas ecuaciones al dibujo?” // “How do these equations match the drawing?” (He started with the 63 then added 20 then added the 5.)
• “¿Cómo describirían la forma en la que Andre encontró la suma?” // “How would you describe how Andre found the sum?” (He started with 63 and added the tens then he added the ones.)

The purpose of this activity is for students to learn stage 5 of the Five in a Row center. Students add within 100, without composing a ten. Partner A chooses two numbers and places a paperclip on each number. They add the numbers and place a counter on the sum. Partner B moves one of the paperclips to a different number, adds the numbers, and places a counter on the sum. Students take turns moving one paper clip, finding the sum and covering it with a counter. The winner is the first one to get five counters in a row. Two gameboards are provided, one where students add a one-digit and a two-digit number and one where they add a two-digit and a two-digit number. For this activity, students work with the gameboard with one-digit numbers.

• Groups of 2
• Give each group two paper clips, a gameboard, and two-color counters.
• “Vamos a aprender una nueva forma de jugar ‘Cinco en línea’” // “We are going to learn a new way to play Five in a Row.”
• Display the gameboard. 
• “El primer jugador escoge un número de cada fila, pone un clip en cada número y los suma todos” // “The first player chooses one number from each row to add together. They place a paper clip on each number.”
• Demonstrate putting a paper clip on a one-digit number and on a two-digit number.
• “Después, ese jugador encuentra la suma de los números y ubica una ficha sobre la suma que está en el tablero” // “Then that player finds the sum of the numbers and puts a counter on the sum on the gameboard.”
• Demonstrate finding the sum of the two numbers and placing the counter on the gameboard. 
• “El siguiente jugador mueve solo un clip a un número nuevo. Después, encuentra la suma de sus dos números y la cubre con una ficha en el tablero. Por turnos, sigan moviendo un clip y cubriendo números en el tablero hasta que alguien tenga cinco fichas en línea. El ganador es esa persona” // “The next player only moves one of the paper clips to a new number. Then they find the sum of their two numbers and cover it with a counter on the gameboard. Continue taking turns moving one paper clip and covering numbers on the gameboard until someone gets five counters in a row. They are the winner.”

• 8 minutes: partner work time

• “¿Cómo decidieron cuál clip mover?” // “How did you decide which paper clip to move?”(I looked at the gameboard and saw which numbers I needed to cover. I tried to find numbers that would have that sum.)