Lesson 20

This warm-up prompts students to compare four images of letters made with sticky notes and attend to the ways the sticky-note units are composed to make the letters. To identify reasons that one or more of them don't belong, students need to pay attention to the length and width of the overall designs as well as the orientation of the sticky notes. 

• Groups of 2
• Display image.
• “Cada rectángulo representa una nota adhesiva” // “Each rectangle represents a sticky note.”
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Qué hace que se vean diferentes las tres ‘H’ de las opciones B, C y D?” // “What makes the three 'H's in options B, C, and D look different?”
• “¿Pueden pensar en otra manera de hacer una letra H que sea diferente a estas tres? ¿Qué podrían cambiar?” // “Can you think of another way to make a letter H that is different than these three? What might you change?” (Sample responses: the number of sticky notes to use for the vertical segments or for the horizontal segment, the orientation of the sticky notes)
• Consider asking: “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. It gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it. In this activity, students estimate how many sticky notes are needed to make a row or column along a piece of paper. There are 4 possible ways to interpret the question: the two orientations of the paper and two orientations of the sticky notes. Students use their understanding of multiplication of a fraction by a whole number to make and represent their estimate (MP2).

• Gather rectangular sticky notes with fractional lengths. If this is not possible then cut rectangles from card stock with fractional lengths.

• Groups of 2
• Distribute one sticky note and paper to each student.
• “¿Cuántas notas adhesivas caben a lo ancho o a lo largo de la hoja? ¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “How many sticky notes will fit across the top or the side of the page? 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.
• “¿Qué información necesitarían para hacer una mejor estimación?” // “What information do you need to help you make a better estimate?” (measurement of the paper, measurement of the sticky note, orientation of the note and/or paper)
• Provide measurements. If students mention orientation, have them consider one based on their choice.
• 5 minutes: partner work time
• Monitor that student that consider the different orientations of the sticky note.

• Invite previously selected students to share.
• If it doesn’t come up, highlight the different orientations of the sticky note.
• Consider asking:
  • “¿De qué otras maneras podrían haber organizado las notas adhesivas?” // “What are some other ways you could have arranged the sticky notes?”
• Invite a few students to share their expressions.
• “¿Cómo se conecta esta expresión con la estimación?” // “How does this expression connect to the estimate?” (The whole number represents the number of sticky notes.)
• “¿Cómo podemos usar la expresión para mostrar si la estimación es muy alta, muy baja o razonable?” // “How can we use the expression to show if the estimate is too high, low, or about right?” (We can compare the product of the expressions to the side lengths of the paper.)

In this activity, students use their understanding of multiplication of fractions to make an original design with sticky notes. They may choose:

• the letter to make
• the orientation of the letter
• the orientation of the page
• the arrangement of the sticky notes next to each other

Before making their design, students determine if their design will fit on the given paper. While not a part of the task, students can be asked to estimate how many sticky notes they need before they make a calculation.

Alternatively, instead of asking students to choose their own letter, the class can choose a joint project, such as making the name of the school or a club. In that case, groups should each get one letter of the project to design and work together.

• Groups of 2
• “En esta actividad van a hacer un plan para diseñar la inicial de su nombre con notas adhesivas. Antes de recibir los materiales, descifren si su diseño cabe en la hoja y cuántas notas adhesivas necesitan” // “In this activity you will make a plan to design your initial with sticky notes. Before you get the supplies, figure out if your design will fit on the paper and how many sticky notes you need.”

• 10 minutes: independent work time
• 5 minutes: partner share
• As students work, monitor for designs that use different orientations and arrangements.

• “Si organizáramos todos nuestros diseños alrededor del salón, ¿cuánto espacio necesitaríamos?” // “If we arranged all your designs around the classroom, how much space would we need?”