Lesson 15

Resolvamos problemas-historia con tres números

Warm-up: Cuántos ves: Tableros de 10 (10 minutes)

Narrative

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. Two-color counters are arranged on 10-frames so that students might notice there are three addends in the problem.

Launch

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Flash the image.
• 30 seconds: quiet think time

Activity

• Display the image.
• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

Student Facing

¿Cuántos ves?
¿Cómo lo sabes?, ¿qué ves?

Activity Synthesis

• “¿Qué ecuación podría escribir para cada imagen?” // “What equation could I write for each image?”
• If needed, “¿Cómo puedo escribir una ecuación que muestre el número de fichas de cada color?” // “How can I write an equation that shows the number of each color of counters?” ($$10 + 5 = 15$$, $$5 + 5 + 5 = 15$$)

Activity 1: Los pájaros de Louis Agassiz Fuertes (20 minutes)

Narrative

The purpose of this activity is for students to solve a story problem with three addends in which two of the addends make 10. The addends that make a ten are not next to each other to encourage students to use the commutative and associative properties to make 10. Students are given access to double 10-frames and connecting cubes or two-color counters. Students read the prompt carefully to identify quantities before they start to work on the problem. They have an opportunity to think strategically about which numbers of birds to combine first since 3 and 7 make 10. They also may choose to use appropriate tools such as counters and a double 10-frame strategically to help them solve the problem (MP1, MP5).

Monitor and select students with the following methods to share in the synthesis:

• Represent addends in the order presented, counting all.
Teacher records: $$3 + 8 + 7 = \boxed{18}$$
• Use the associative property to make a ten by adding 3 and 7 and then adds on 8 more. Teacher records:
• $$3 + 7 + 8 = \boxed{18}$$
•  $$3 + 7 = 10$$
• $$10 + 8 = \boxed{18}$$
• Use the associative property to make a ten by adding 3 and 7 and recognizes that the answer is 18. Teacher records:
• $$3 + 7 + 8 = \boxed{18}$$
• $$3 + 7 = 10$$
• $$10 + 8 = \boxed{18}$$

During the activity synthesis, the teacher records student thinking as drawings and equations so it is visible to all students. Teachers should consider having several blank copies of 10-frames available and three different colored markers to represent the three addends so that students can see how making a ten can make solving more efficient.

MLR6 Three Reads. Keep books or devices closed. To launch this activity, display only the problem stem, without revealing the question. “Vamos a leer este problema-historia tres veces” // “We are going to read this story problem three times.” After the 1st Read: “Cuéntenle a su compañero lo que ocurrió en la historia” // “Tell your partner what happened in the story.” After the 2nd Read: “¿Cuáles son todas las cosas de esta historia que podemos contar?” // “What are all the things we can count in this story?” Reveal the question. After the 3rd Read: “¿De qué formas diferentes podemos resolver este problema?” // “What are different ways we can solve this problem?”

Required Materials

Materials to Gather

Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “¿Qué tipos de pájaros ven en el lugar en el que viven? ¿En dónde ven estos pájaros?” // “What kind of birds do you see where you live? Where do you see the birds?” (I see pigeons on wires. I see a big bird in the park. I see red birds at the bird feeder. I hear loud birds in the morning.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses. Write the authentic language students use to describe the birds they see and where they see them.
• “Louis Fuertes era un pintor de pájaros. Cuando era niño, le encantaba pintar los pájaros que veía” // “Louis Fuertes was a bird artist. When he was a child, he loved to paint the birds he saw.”
• Consider reading the book The Sky Painter by Margarita Engle.
• “Vamos a resolver algunos problemas sobre pájaros” // “We are going to solve some problems about birds.”

Activity

• 3 minutes: independent work time
• 2 minutes: partner discussion
• As students work, consider asking:
• “¿Qué están haciendo para encontrar el número total de pájaros?” // “How are you finding the total number of birds?”
• “¿Cómo decidieron en qué orden sumar los números?” // “How did you decide the order to add the numbers?”
• “¿Hay otra forma en la que pueden sumar los números?” // “Is there another way you can add the numbers?”
• Monitor for students who use the methods described in the narrative.

Student Facing

7 pájaros azules vuelan en el cielo.
8 pájaros marrones están parados en un árbol.
3 pájaros bebé están en un nido.
¿Cuántos pájaros hay en total?
Muestra cómo pensaste. Usa objetos, dibujos, números o palabras.

Ecuación: ________________________________

Activity Synthesis

• Invite previously identified students to share in the given order.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?” (They are the same because they all got 18. The last two methods use the “add in any order” property to move addends to make $$3 + 7$$. Then they added $$10 + 8$$. There was a lot of counting in the first method, some counting in the second, and no counting in the last method.)
• If needed, ask, “¿Dónde ven 10 en el problema-historia?” // “Where is 10 in the story problem?” ($$3 + 7$$, the number of blue birds in the sky and baby birds in a nest.)
• “¿Hay algún método diferente al suyo que les gustaría probar?” // “Is there a method that is different than yours, that you would like to try?” (I want to make ten because I know my facts to ten.)

Activity 2: Las tarjetas de pájaros de Fuertes (20 minutes)

Narrative

The purpose of this activity is for students to solve more story problems with three addends, in which two of the addends make 10. Students are encouraged to look for addends that have a sum of 10 and think about how that helps when adding (MP7). Students should have access to double 10-frames and connecting cubes or two-color counters to use if they choose.

When recording student thinking, it is important that the teacher write each part of the equation on a separate line. For example, when representing student thinking for $$5 + 9 + 5 = \boxed{\phantom{3}}$$ record:

• $$5 + 9 + 5 = \boxed{\phantom{3}}$$
• $$5 + 5 = 10$$
• $$10 + 9 = \boxed{19}$$
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Attention, Organization

Required Materials

Materials to Gather

Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “Muchas de las obras que Louis Fuertes pintó quedaron impresas en tarjetas que a la gente le gustaba coleccionar. La gente sacaba sus tarjetas al aire libre para nombrar los pájaros que veía. Resolvamos algunos problemas-historia sobre las tarjetas de pájaros” // “Many pictures of birds that Louis Fuertes painted were printed on cards that people liked to collect. They would bring their cards outside and try to name the birds they saw. Let’s answer some story problems about the bird cards.”

Activity

• 10 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who use different methods to solve $$10 + 6 + 4 = \boxed{\phantom{3}}$$.

Student Facing

1. Noah consiguió 3 tarjetas de imágenes de pájaros.
Clare consiguió 4 tarjetas.
¿Cuántas tarjetas consiguieron entre todos?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

2. Jada usó sus tarjetas para nombrar los pájaros que vio.
Vio 4 orioles.
Vio 2 jilgueros.
Vio 8 gorriones.
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

3. Escribe tu propio problema.
Vimos algunos pájaros.
Vimos 9 ________________________________.
Vimos 8 ________________________________.
Vimos 1 ________________________________.
¿Cuántos pájaros vimos en total?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

4. $$10 + 6 + 4 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

Muestra cómo pensaste. Usa dibujos, números o palabras.

5. $$5 + 9 + 5 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

Muestra cómo pensaste. Usa dibujos, números o palabras.

Activity Synthesis

• Invite previously identified students to share their work.
• “¿Alguien puede explicar el método de _____ con otras palabras?” // “Who can restate _____’s method?”
• Repeat for each student’s work.
• “¿Qué conexiones ven entre los distintos métodos?” // “What connections do you see between the different methods?” (There are two tens in each method. Each method is addition.)

Lesson Synthesis

Lesson Synthesis

“Hoy aprendimos sobre un hombre que fue un muy buen pintor. Él quiso pintar pájaros mientras estaban vivos y por esto aprendió a pintar rápido. También encontramos la suma de tres números. ¿Qué hizo hoy cada uno de ustedes que les haya ayudado a resolver un problema con tres números?” // “Today, we learned about a man who was a very good painter. He wanted to paint birds while they were alive so he learned how to paint quickly. We also found the sum of three numbers. What did each of you do today that helped you solve a problem with three numbers?”