# Lesson 10

Algoritmos de resta (parte 3)

## Warm-up: Observa y pregúntate: Dígitos que desaparecen (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the observation that a hundred that has been decomposed into more tens can be recorded using a condensed notation, which will be useful later in the lesson when students decompose hundreds and tens to facilitate subtraction. While students may notice and wonder many things about these numbers, how the decomposition is recorded is the important discussion point. Base-ten blocks or diagrams can be used during the discussion if students need additional support in making sense of the condensed notation.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

¿Qué observas? ¿Qué te preguntas?

### Activity Synthesis

• “La expresión en forma desarrollada y el número muestran ambas una unidad en base diez que se está descomponiendo en unidades en base diez más pequeñas. ¿Dónde ven esto en cada caso?” // “Both the expression in expanded form and the number show a unit being decomposed into smaller units. Where do you see this happening in each case?” (The 300 has been turned into 200 in both examples. The 200 is shown with 200 in the first example, but just a 2 in the second example. The 2 tens has been turned into 12 tens in both examples. The 12 tens is shown as 120 in the first example, but just a 12 in the tens place in the second example.)

## Activity 1: Un nuevo algoritmo de resta (20 minutes)

### Narrative

The purpose of this activity is for students to learn a subtraction algorithm that records the difference in each place value position as a single digit. The algorithm also records a decomposed hundred as a single digit in the hundreds place and as two digits in the tens place. Students carefully analyze and discuss two different ways to subtract, highlighting similarities and differences and explaining how and why they work (MP6).

### Launch

• Groups of 2
• Display Andre and Clare’s work.
• “¿En qué se parecen los algoritmos?” // “How are the two algorithms alike?” (They are both stacked vertically. They show the same two numbers, 528 and 271. They both show a hundred decomposed into 10 tens.)
• “¿En qué son diferentes?” // “How are they different?” (One pair of numbers is written in expanded form, but the other pair is not. In Andre’s case, the decomposing of a hundred is recorded as 400 and 120. In Clare’s case, it is written as 4 in the hundreds place and 12 in the tens place.)
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Share and record responses. Emphasize the different ways of recording the decompositions.
• “Observamos que este nuevo algoritmo usa menos dígitos porque no se escribe el valor de cada dígito. Simplemente registramos hasta 2 dígitos en cada posición para saber cuántas centenas, decenas o unidades hay” // “We noticed that this new algorithm uses fewer digits by not writing out the value of each digit. We just record up to 2 digits in each place to tell how many hundreds, tens, or ones there are.”

### Activity

• “Tómense unos minutos en silencio para trabajar en la actividad. Después, discutan sus respuestas con su pareja // “Take a few quiet minutes to work on the activity. Afterward, discuss your responses with your partner.”
• 3–5 minutes: independent work time
• 2–3 minutes: partner discussion

### Student Facing

Andre y Clare encontraron el valor de $$528 - 271$$. Así empezaron su trabajo.

Algoritmo de Andre

Algoritmo de Clare

1. Completa los dos algoritmos para encontrar la diferencia.
2. Andre y Clare empezaron a restar de formas distintas. ¿Cómo influyó cada forma de empezar en los pasos que siguieron para encontrar la diferencia?

### Activity Synthesis

• Invite students to share their work for completing each algorithm.
• “¿Qué hicieron de una forma diferente al completar cada uno de estos problemas?” // “What did you do differently as you completed each of these problems?” (With Andre’s work I subtracted all the place values, then I had to add up all the parts of the difference. With Clare’s work once I subtracted the digits in each place value, the answer was complete.)

## Activity 2: Prueba el algoritmo de Clare (15 minutes)

### Narrative

The purpose of this activity is for students to practice using the algorithm they learned in the previous activity, in which the difference in each place value position is recorded with one digit and the decomposition of a place value unit is recorded using one or two digits.

MLR8 Discussion Supports. Display sentence frames to support partner discussion: “Primero, yo ____ porque . . .” // “First, I _____ because . . . .”, and “Después, yo _____ porque . . .” // “Then, I _____ because . . . .”
Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were most important/needed to solve the problems. Display the sentence frame: “La próxima vez que reste usando el algoritmo de Clare, voy a buscar . . .” // “The next time I subtract using Clare’s algorithm, I will look for . . . .”
Supports accessibility for: Conceptual Processing

### Launch

• Groups of 2
• “Ahora intentemos usar el algoritmo para restar números que aprendieron en la actividad anterior. Pueden usar los pasos que registraron en la actividad anterior o usar el trabajo de Clare como ejemplo” // “Now let's try using the algorithm you learned in the last activity to subtract some numbers. You can use the steps you recorded from our last activity or use Clare’s work as an example.”

### Activity

• 3–5 minutes: independent work time
• “Compartan su trabajo y sus soluciones con su pareja” // “Share your work and solutions with your partner.”
• 2–3 minutes: partner discussion

### Student Facing

Clare usó un algoritmo para encontrar el valor de $$538-156$$.

Intenta usar su algoritmo para encontrar el valor de cada diferencia.

1. $$691 - 358$$

2. $$926 - 584$$

3. $$317-182$$

4. $$492-325$$

### Activity Synthesis

• Display student work on the first expression.
• “¿En dónde vemos el 91 después de tachar el 9 y el 1?” // “Where do we see the 91 after the 9 and the 1 have been crossed out?” (The 8 and the 11 represents 80 and 11, which is 91.)

## Lesson Synthesis

### Lesson Synthesis

Display Andre and Clare’s work from the first activity.

“¿Cómo nos ayudó el valor posicional a usar menos dígitos cuando registrábamos las centenas o decenas nuevas que se componían?” // “How did place value allow us to use fewer digits when recording newly decomposed hundreds or tens?” (We knew what place each digit is in and what value each digit has. We knew the 4 stood for 400, and the 12 stood for 12 tens or 120.)