Lesson 6

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. Students will work with this problem in the next activity.

• 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.

• If needed ask, “¿Han tendrá más fichas o menos fichas en su vaso? ¿Cómo lo saben?” // “Will Han have more counters or fewer counters in his cup? How do you know?”

In this activity students solve a new type of story problem—Add To, Start Unknown. Students represent and solve it in any way that makes sense to them. 

Monitor for students who:

• show three counters and count on to 10 or know the sum (\(3 + \boxed{7} = 10\))
• show the total number of counters and subtract three to find the difference (\(10 - 3 = \boxed{7}\))
• think about the story problem as \(\boxed{7} + 3 = 10\) and use a known fact.

• Groups of 2
• Give students access to 10-frames and connecting cubes and two-color counters.
• Display and read the story.
• “¿En qué es diferente la historia ahora comparada con la que vieron en el calentamiento?” // “How is the story different now than when you saw it in the warm up?” (There are numbers to show how many counters Han has in the cup and how many he puts in his cup.)
• 30 seconds: quiet think time
• Share responses.

• “Ahora tienen tiempo para resolver el problema solos” // “Now you have time to solve the problem on your own.”
• 5 minutes: independent work time
• “Compartan con su pareja cómo pensaron. Si cada uno encontró una respuesta diferente para el problema, pónganse de acuerdo en una respuesta” // “Share your thinking with your partner. If you each found a different answer to the problem, work together to agree on an answer.”
• 3 minutes: partner discussion
• Monitor and select students who use the methods described in the narrative.

If students use three counters and then ten more counters and get thirteen, consider asking:

• “¿Como decidiste cuántas fichas usar?” // “How did you decide how many counters to use?”
• “La historia dice: ‘Después, él puso 3 fichas más en su vaso. Ahora tiene 10 fichas’. ¿Cómo puedes usar fichas para mostrar las 10 fichas que Han tiene al final? ¿Dónde están las tres fichas que agregó al vaso?” // “The story says, ‘Then he put three more counters in his cup. Now he has ten counters.’ How can you use counters to show the ten counters Han has at the end? Where are the three he added to the cup?”

• Invite previously identified students to share in the order above.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?” (Two use the add in any order property. The difference is 7. I can subtract or add to find the answer.)
• If needed, “En cada una de estas ecuaciones se ve que la respuesta a la pregunta es 7” // “In each of these equations, it shows that the answer to the question is 7.”

The purpose of this activity is for students to solve various Add To/Take From and Put Together problems with the unknown in all positions. Problems are presented through the familiar Shake and Spill context and all sums are within 10 so students can attend to making sense of each problem. Students use the commutative property, count on, take away or use known sums. When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2). During the synthesis, students focus on sharing equations and comparing the start and change unknown problems, as well as how the commutative property can help them solve story problems with an unknown start. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

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

• Read the task statement.
• 7 minutes: independent work time
• “Discutan con su pareja cómo pensaron” // “Share your thinking with your partner.”
• 3 minutes: partner discussion
• Monitor for students who write equations and can explain their thinking for Kiran’s and Clare’s problems.

• Invite previously identified students to share.
• “¿En qué se parece el problema sobre Kiran y el problema sobre Clare? ¿En qué son diferentes?” // “How are the problems about Kiran and Clare the same? How are they different?” (They are the same because they both have a number of counters missing, not the total number. You can use addition or subtraction to find the answer to both. They are different because I know how many Kiran starts with and then he adds more. I don’t know how many counters are in Clare’s cup to start with, but I know that three are added to make nine.)
• If needed ask, “¿Qué ecuaciones representan estos problemas-historia?” // “What equations represent these story problems?”
• “¿Qué ecuaciones representan el problema de Noah? ¿Y el problema de Priya?” // “What equations represent Noah’s problem? Priya’s problem?”