Lesson 18

The purpose of this Number Talk is to elicit strategies and understandings students have for addition and subtraction with 3 and 5. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to create a yardstick with just the numbers 3 and 5.

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Qué otros números podemos formar con el 3 y el 5? Piensen en otros dos números que puedan formar. Pueden usar tantos treses y cincos como quieran, y pueden sumar y restar” // “What other numbers can we make with 3 and 5? Think of two other numbers you can make. You can use as many threes and fives as you like and you may subtract and add.”

The purpose of this activity is for students to create and label the tick marks on a yard stick using what they know about length units, comparing length, and adding and subtracting length. They use the sides of a 3-by-5 inch index card to mark off all inch marks from 1 to 36. Students are invited to iterate the different sides of the index card along the paper forward and backwards. They look for ways to use what they know about the structure of a measuring tool, the known lengths of the index card, and what they know about adding and subtracting lengths to mark and label new tick marks (MP1, MP7).

• Cut the chart paper into strips. Each group of 2 needs a strip of paper that is at least 36 inches long and about 3 inches wide to make their yardstick.

• Groups of 2
• Give each group a strip of paper and an index card.
• “¿Qué saben sobre las varas de una yarda?” // “What do you know about a yardstick?”
• 30 seconds: partner discussion 
• Share responses.
• Display a yardstick and highlight that:
  • a yardstick can be used to measure feet and inches
  • a yardstick shows a total of 36 inches

• “Hoy van a usar una tarjeta bibliográfica para hacer una vara de una yarda. El lado largo de la tarjeta mide 5 pulgadas y el lado corto mide 3 pulgadas” // “Today you will use an index card to make a yardstick. The long side of the card measures 5 inches and the short side measures 3 inches.”
• “¿Qué números pueden marcar en la vara de una yarda usando la tarjeta?” // “What numbers can you mark on the yardstick using the cards?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “Peguen la tira de papel en su pupitre” // “Tape the paper strip across your desk.”
• “Uno de ustedes tendrá la tarjeta bibliográfica y el otro marcará y escribirá las unidades en la vara” // “One of you will hold the index card and the other will mark and label the units on the yardstick.”
• “Intercambien roles cuando vayan por la mitad” // “Switch roles when you are about halfway done.”
• 5 minutes: partner work time
• Monitor for students with different strategies. For example:
  • students who initially use only one operation or number
  • students who look for ways to add or subtract lengths using the card
  • students who use the difference in the lengths of the short and long sides of the card
  • students who discuss and use patterns in the differences between the tick marks they have made to find and label new tick marks
• “Ahora discutan su método con otro grupo” // “Now discuss your method with another group.”
• 4 minutes: small-group discussion

• Invite students to share their methods.
• Consider asking:
  • “¿Qué números marcaron primero?” // “Which numbers did you mark first?”
  • “¿Cuáles números fueron más fáciles de encontrar?” // “Which numbers were easy to find?”
  • “¿Cuáles números fueron más difíciles de encontrar?” // “Which numbers were harder to find?”
  • “¿Se enfrentaron a algunos problemas? ¿Cómo los resolvieron?” // “Did you run into any problems? How did you solve them?”

In this activity, students use their yardstick to measure a common object, the height of their desk. They write their measurement on a sticky note and add it to a class line plot. Students analyze the line plot and discuss why some students got different answers than others when they all measured the same object. Students compare their yardstick units and revise their markings to make more accurate yardsticks.

• Create a blank line plot with a scale that includes lengths longer, shorter, and equal to the height of student desks. 

• Groups of 2
• Give each student a sticky note.
• Display the blank line plot.

• “Ahora, usemos las varas de una yarda que hicimos para medir la altura de nuestros pupitres” // “Now, let's use the yardsticks we made to measure the height of our desks.”
• “Por turnos, midan la altura de su pupitre en pulgadas. Cuando los dos estén de acuerdo, dibujen una x grande en su nota adhesiva y agreguen su medida al diagrama de puntos de la clase” // “Take turns measuring the height of your desk in inches. When you both agree, draw a big x on your sticky note and add your measurement to the class line plot.”
• 2–3 minutes: partner work time
• Invite students to add their sticky note to the line plot.
• “Ahora, respondan juntos las preguntas sobre nuestros datos de medidas” // “Now, work together to answer the questions about our measurement data.”
• 3–4 minutes: partner work time
• Monitor for students who notice the class got different measurements for the same object.
• Monitor for students who discuss reasons for the different measurements.

• Display a few student-created yardsticks next to each other for all to see.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• If it does not come up, ask “¿Cómo es posible que distintos grupos hayan encontrado respuestas diferentes si midieron el mismo objeto?” // “How is it possible that different groups found different answers when they measured the same object?”
• “¿Cuál puede ser una razón por la que ocurrió esto?” // “What could be a reason this happened?”
  • uneven markings
  • different use of yardsticks: straight, with slack, slanted
  • different location of zero
  • gaps or overlaps between inch marks
• Invite students to look at the displayed yardsticks and to see if they can see evidence for the reasons they gave.
• Highlight that it is important for a measuring tool to have equal-size units.
• If there is time, invite students to revise their yardstick markings. Alternatively, students can discuss which markings need revision.
• Invite students to explain how they revised their yardsticks with another group.

In this activity, students use the yardsticks they made to measure the length of parts of their arms. They then use the measurements to write equations and describe what information the equations give about the situation (MP2, MP4).

• Groups of 2
• “Van a usar sus varas de una yarda para medir partes de la mano y del brazo de su pareja” // “You will use your yardsticks to measure parts of your partner's hand and arm.”
• Demonstrate the two lengths they will measure.

• 10 minutes: partner work time
• Monitor for different equations using addition and subtraction.

• Invite students to share their equations and statements.
• For each student that shares, consider asking:
  • “¿Hay alguna otra manera de describir lo que nos dice la ecuación?” // “Is there another way to describe what the equation tells us?”