Lesson 12

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. For this picture, it is hard to tell how many people there are, so a wide range of responses can be considered “about right.” Students will also use this image in the cool-down, and there is an option for them to use the picture to generate ideas for story problems.

• Groups of 2
• “¿Cuántas personas hay en la imagen?” // “How many people are in the picture?”
• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time

• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “¿Cómo hicieron una estimación que fuera muy baja?” // “How did you make an estimate that was too low?” (I saw 10 to 20 kids running in front and then a whole lot of people behind them, so I made a low estimate of 50.)
• “¿Cómo hicieron una estimación que fuera muy alta?” // “How did you make an estimate that was too high?” (It is hard to tell how far back the people go, so I just said 1,000.)
• “Teniendo en cuenta esta discusión, ¿alguien quiere ajustar su estimación?” // “Based on this discussion, does anyone want to revise their estimate?”

The purpose of this activity is to write story problems for equations with an unknown value. There is a pair of addition and subtraction equations and in each pair one of them has the starting value unknown. Students may write Add To, Take From, Put Together/Take Apart, or Compare problems. When students contextualize the equations and make connections between the stories their peers share and the equations, they reason abstractly and quantitatively (MP2).

• Groups of 2
• Display list of topics for story problems from the previous lesson.

• Split the class into two groups, A and B. The students in group A will work with the equations labeled A and the students in group B will work with the equations labeled B.
• “Van a escribir historias para las 2 ecuaciones A o las 2 ecuaciones B. Consideren usar el mismo contexto para ambas historias. A los demás estudiantes les puede parecer más fácil darle sentido a sus historias si se tratan de lo mismo” //  “You will write stories for the 2 equations in A or the 2 equations in B. Consider using the same context for both of your stories. It might make it easier for others to make sense of your stories if they are about the same thing.”
• 5 minutes: independent work time
• “Compartan sus historias con su compañero” // “Share your stories with your partner.”
• 5 minutes: group work time

• Display text: “Hay 23 pelotas de béisbol en el gimnasio y 37 pelotas de béisbol en el patio de recreo” // “There are 23 baseballs in the gym and 37 baseballs on the playground.”
• “Esta es la historia de Andre. ¿La ecuación \(23 + \underline{\hspace{1 cm}} = 37\) representa la historia de Andre?” // “This is Andre’s story. Does the equation \(23 + \underline{\hspace{1 cm}} = 37\) represent Andre’s story?” (No, Andre’s story doesn’t have a question or anything happening. It might match, but it needs more information or a question.)
• “¿Cómo mejorarían la historia de Andre?” // “How would you improve Andre’s story?” (He could add a question like, “How many more baseballs are on the playground than in the gym?” He could keep it about baseballs, but add some things that happen. He might say someone took the 23 baseballs to the playground and now there are 37 baseballs on the playground and ask how many were already on the playground.)
• Record student suggestions for revising Andre’s story.
• “¿La ecuación \(23 + \underline{\hspace{1 cm}} = 37\) representa alguna de estas historias?” // “Does the equation \(23 + \underline{\hspace{1 cm}} = 37\) represent any of these stories now?” (It represents the question about how many more baseballs are on the playground.)

The purpose of this activity is for students to write math stories. Several options are available for fueling their imagination, including:

• looking at pre-selected images such as the one used in the Estimation Exploration in this lesson or those in the optional blackline master
• looking at images in magazines or newspapers
• looking around the classroom
• going for a walk around the school or community

Whichever source is used for ideas, students write a story problem that connects to mathematical ideas they have found. If students come up with a context, but are not able to count or estimate the quantities they see, display a set of numbers (such as 11, 25, 38, 56, 77, 93) that students can use to write their story problem.

When students write math stories based on images or things in their environment, and eventually answer those questions, they model with mathematics (MP4).

• Gather a see-through container with a collection of connecting cubes (or other math tool or object that might generate different math questions) to display in the launch.
• (Optional) Provide a copy of the blackline master for each group of 2 students.

• Groups of 2
• Display the see-through container with connecting cubes (or other math tool).
• “¿Qué preguntas matemáticas pueden hacer sobre los cubos encajables?” // “What are some math questions you can ask about the connecting cubes?” (How many connecting cubes are there altogether? How many green connecting cubes are there? Are there more blue connecting cubes or yellow connecting cubes? How many more?)
• 1 minute: independent think time
• 1 minute: partner share time
• Share student responses, highlighting in each case how it could be made into a story problem (for example, “How many connecting cubes are there?” could be answered if we knew how many there are of each color.)

• “Ahora vamos a buscar ideas matemáticas en _____. Su objetivo es tomar notas acerca de lo que vean. Concéntrense en cosas que se pueden contar para que puedan escribir un problema-historia sobre ellas” // “Now, we are going to look for mathematical ideas in _____. Your goal is to take notes about what you see. Focus on things that can be counted, so that you can write a story problem about it.”
• “Si les queda tiempo, pueden contar o estimar lo que ven. Si no, escriban una historia sin cantidades exactas y yo les daré algunos números que podrán usar en su historia” //  “If you have time, you can count or estimate what you see. If not, write a story without exact quantities, and I will give you numbers that you can use in your story.”
• 8 minutes: math walk
• “Escriban un problema-historia y luego compártanlo con su compañero” // “Write a story problem and then share with your partner.”
• 8 minutes: partner work time
• Monitor for students who write different types of stories: single-step, two-step, Add To, Take From, Put Together/Take Apart, and Compare.

• Invite selected students to share their stories.