Lesson 5

The purpose of this Number Talk is to elicit strategies students have for counting by 2 and 5. These understandings help students develop fluency and will be used later in this lesson when students will need to be able to scale bar graphs.

When students notice the number of equal addends are doubled in the second expression, they are looking for and making sense of structure (MP7). When they notice the pattern repeats in the second pair of expressions and use the pattern to find the value of the sum, they are also looking for and expressing regularity in repeated reasoning (MP8).

• 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.

• “¿Cómo les ayudaron las primeras dos expresiones a hallar el valor de la tercera y la cuarta expresión?” // “How did the first two expressions help you solve the third and fourth expressions?” (If you notice there are double the number of twos or fives you can just double your sum.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
  • “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
  • “¿Alguien quiere agregar algo a la estrategia de _____?” // “Does anyone want to add on to _____’s strategy?”

The purpose of this activity is to introduce students to a scaled bar graph. Students consider a single-unit scale bar graph next to a bar graph with a scale of 2, both representing the same set of categorical data. They discuss similarities and differences between a single-unit scale bar graph and a bar graph with a scale of 2.

• Groups of 2

• Display the images.
• “¿En qué se parecen estas gráficas de barras? ¿En qué son diferentes?” // “How are these bar graphs alike? How are they different?”
• 1 minute: quiet think time
• 4 minutes: partner discussion

• “¿Qué fue parecido en las gráficas? ¿Qué fue diferente?” // “What was the same? What was different?”
• Share and record responses.
• If it doesn't come up, elicit the idea that the scale on the second graph counts by 2.
• “Cuando cada salto en la escala es un número diferente de 1, decimos que es una gráfica de barras con escala” // “When each jump on the scale is some number other than 1, we say that it’s a scaled bar graph.”
• “¿Para qué sirve hacer una gráfica de barras con escala?” // “Why would it be helpful to make a scaled bar graph?” (If you didn't want to count one by one. If you wanted to show larger numbers on your graph.)

The purpose of this activity is for students to create a scaled bar graph. Students decide on a scale of 2 or 5, so it will be important to ask students why they chose their scale and how accurately they can tell the exact number the bar represents (MP6). In the activity synthesis, students discuss how they represented an odd number of students with a scale of 2 and a number of students that was not a multiple of 5 on a scale of 5. This question should be adjusted based on the data your class collects.

• Each student needs the picture graph they creaed in the previous lesson.

• Groups of 2
• Make sure each student has their scaled picture graph from the previous lesson.

• “Ayer recolectamos datos sobre las formas en las que nos gustaría viajar. Hoy los vamos a representar en una gráfica de barras con escala” // “Today, we will represent the data we collected yesterday about ways we would like to travel in a scaled bar graph.”
• “Decidan con su pareja si quieren usar una escala de 2 o de 5. Prepárense para explicar su decisión. Si tienen tiempo, hagan una gráfica con una escala de 2 y otra con una escala de 5” // “Decide with your partner whether you want to use a scale of 2 or 5. Be prepared to explain your choice. If you have time, try making one graph with a scale of 2 and one with a scale of 5.”
• 12 minutes: partner work time
• Consider asking, “¿Cómo les ayudó su gráfica de dibujos con escala a hacer su gráfica de barras con escala?” // “How did your scaled picture graph help you to make your scaled bar graph?”

If students draw the top of the bar in a location that doesn’t correspond with the ways we would like to travel data, consider asking:

• “¿Cómo decidiste hasta dónde debía llegar la parte más alta de la barra?” // “How did you decide where the top of the bar would end?”
• “¿Cómo te ayudaría contar de 2 en 2 (o de 5 en 5) para decidir hasta dónde debe llegar la parte más alta de la barra?” // “How could you use counting by 2 (or 5) to help you decide where the top of the bar should end?”

• “¿Qué escala escogieron con su pareja? ¿Por qué?” // “What scale did you and your partner choose? Why?”
• Display student work with both scales.
• “¿Cómo hicieron para representar una forma viajar que no correspondía exactamente a un número de la escala?” // “How did you represent a way of travel that didn’t land right on the numbers in the scale?” (It was between the 2 numbers, so I had to make a guess about where the bar should stop.)
• “¿Qué diferencias observan entre la gráfica con una escala de 2 y la gráfica con una escala de 5?” // “What differences do you notice when the graph is with a scale of 2 and when the graph is with a scale of 5?" (Sample responses: The bars look taller when the scale is 2. It's hard to tell what number some bars represent when the scale is 5. It was easier to count up to larger amounts when the scale was 5.)