Lesson 12

The purpose of this warm-up is for students to think mathematically about a context they will be working with in the next activity. Students may generate a variety of mathematical questions related to the story problem types they solved in previous lessons. This warm-up prompts students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved (MP1).

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

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

• “¿Qué preguntas matemáticas pueden hacer acerca de esta imagen?” // "What math questions can you ask about this picture?"
• “Vamos a trabajar en muchos problemas-historia sobre útiles escolares” // "We are going to work on lots of story problems about school supplies."

The purpose of this activity is for students to solve a Compare, Difference Unknown story problem using modified language. Students begin the activity by looking at the problem displayed, rather than in their books. They identify the important quantities before working on the problem, giving them an entry point for addressing the question, phrased negatively, of how many students will not have a pencil (MP1). When students open their books and work on the problem, they have access to connecting cubes or two-color counters. In the lesson synthesis, students connect equations to different ways of solving the problem.

This activity uses MLR6 Three Reads. Advances: reading, listening, representing.

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

MLR6 Three Reads

• Display only the problem stem, without revealing the question(s). 
• “Vamos a leer este problema tres veces” // “We are going to read this problem three times.”
• 1st Read: “Hay 10 estudiantes en la mesa. Hay 6 lápices” // “There are 10 students at the table. There are 6 pencils.”
• “¿De qué se trata esta historia?” // “What is this story about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “Hay 10 estudiantes en la mesa. Hay 6 lápices” // “There are 10 students at the table. There are 6 pencils.”
• “¿Cuáles son todas las cosas de esta historia que podemos contar?” // “What are all the things we can count in this story?” (the number of students, the number of pencils)
• 30 seconds: quiet think time
• 1 minutes: partner discussion 
• Share and record all quantities.
• Reveal the question(s).
• 3rd Read: Read the entire problem, including question(s) aloud.
• “¿De qué formas diferentes podemos resolver este problema?” // “What are different ways we can solve this problem?” (I can use red connecting cubes for the students and blue for the pencils. I can draw circles for the students and lines for the pencils.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “Resuelvan el problema” // "Solve the problem."
• 3 minutes: independent work time
• “Compartan con su pareja cómo pensaron” // “Share your thinking with your partner.”
• 2 minutes: partner discussion
• Monitor for a student who represents counting up from 6 to 10 and one who represents subtracting 6 from 10.

• Display previously identified student work.
• “¿Cómo resolvieron ellos el problema?” // “How did they solve the problem?”
• Write an equation to match each method of solving.

The purpose of this activity is for students to represent and solve Compare, Difference Unknown story problems. Students may use one of the following methods to find the difference or may come up with their own method.

Add on to the smaller set to make them equivalent.
(\(5 + \boxed{3} = 8\))

Match the sets and then count how many don’t have a partner. (\(8 - 5 =\boxed{3}\))

Show the total (8), color in the known amount (5), count the difference. (\(8 = 5 + \boxed{3}\) or \(8 - 5 =\boxed{3}\)) 

In the activity synthesis, students consider methods related to counting up and counting back.

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

• “Van a resolver más problemas-historia sobre útiles escolares. Muestren cómo piensan. Usen dibujos, números o palabras. Escriban una ecuación para cada problema-historia” // “You will solve more story problems about school supplies. Show your thinking using drawings, numbers, or words. Write an equation for each story problem.”
• 6 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for a student who counted up and one who counted back for the problem about folders.

• Invite previously identified students to share.
• “¿En qué se parece el trabajo de ellos? ¿En qué es diferente?” // “How is their work the same? How is it different?” (They both use 2, 7 and 9. One uses addition and one uses subtraction. The answer is in a different place in each equation.)
• “En cada representación, ¿dónde está la respuesta a la pregunta?” // “Where is the answer to the question in each representation?” (When they added the answer was in the middle. When they subtracted it was at the end.)
• Add a box around the answer in each equation.