Lesson 6

The purpose of this warm-up is to elicit the idea that adjusting the scale changes the size of the bars in a bar graph and can make it easier or more difficult to interpret. While students may notice and wonder many things about these graphs, the different scales in the bar graphs are the most important discussion points.

• Groups of 2
• Display the graphs.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “¿En qué son diferentes las tres gráficas?” // “How are the three graphs different?” (They show the same data, but the bars are different heights. They have different scales.)

The purpose of this activity is for students to analyze a scale and create a scaled bar graph. Students consider a large collection of pattern blocks and decide which scale will work best to represent the categorical data. They consider three students’ ideas, choose a scale of 2, 5, or 10, and create a scaled bar graph to represent the categorical data. Students must justify why they agree that a particular scale would be best. During the activity and whole-class discussion, students share their thinking and have opportunities to listen to and critique the reasoning of their peers (MP3). Providing a variety of scales for students to choose from allows for discussion about the benefits of using larger scales for larger groups of objects and the effect of a scale on how easy it may be to read and interpret data in a graph.

• Groups of 2
• Display the image.
• “Observen estas fichas geométricas un momento y piensen en cómo las representarían en una gráfica de barras con escala” // “Take a minute to consider these pattern blocks and think about how you could represent them in a scaled bar graph.”
• 30 seconds: quiet think time

• “Ahora, en parejas, respondan las preguntas sobre organizar y representar las fichas geométricas en una gráfica de barras. Prepárense para justificar su elección de la escala” // “Now answer the questions about organizing and representing the pattern blocks in a bar graph with your partner. Be prepared to justify your choice of scale.”
• 12 minutes: partner work
• Monitor for students who used each of the scales to create their bar graph.

If students use a scale of 2, consider asking:

• “¿Cómo decidiste qué escala usar en tu gráfica?” // “How did you decide on the scale to use in your graph?”
• “¿Cómo cambiaría la gráfica si usaras una escala de 5 o de 10?” // “How would using a scale of 5 or 10 affect your graph?”

• Display selected student work showing each of the scales.
• “¿Qué escala usaron en su gráfica de barras? ¿Por qué escogieron esa escala?” // “What scale did you use for your bar graph? Why did you choose that scale?” (I used a scale of 5 because each amount can be counted by 5. I used a scale of 10 so I don’t have to make as many marks on the scale.)

The purpose of this activity is for students to represent data in a scaled bar graph. In this activity, the categorical data is presented in a table. Students choose a scale and make a scaled bar graph of the categorical data. Students have prior experience with scales of 2, 5, and 10, and are not directed to a specific scale in this activity. However, due to the larger numbers, it is likely that students choose a scale of 5 or 10. If students struggle to get started, you could suggest a scale of 5 or 10. In the whole-class discussion, students share how their choice of scale affected their graph.

Students will use their scaled bar graphs again in the next lesson.

• Groups of 4
• “¿Cuál es su momento favorito del año?” // “What is your favorite time of the year?”
• 30 seconds: quiet think time
• Share responses.
• “Vamos a hacer una gráfica de barras con escala para representar los momentos favoritos del año de algunos estudiantes de 3er grado” // “We are going to make a scaled bar graph to represent some 3rd grade students’ favorite times of the year.”

• “Representen en una gráfica de barras con escala los datos que se muestran en la tabla. Piensen en una escala que tenga sentido para el número de estudiantes” // “Represent the data shown in the table in a scaled bar graph. Think about a scale that makes sense with the number of students.”
• 5–7 minutes: independent work time
• “Compartan sus gráficas con su grupo. Discutan por qué eligieron esas escalas” // “Share your graphs with your small-group. Discuss the scales you chose to use.”
• 2–3 minutes: small-group discussion

• “¿Cómo inflluyó la escala que escogieron en la forma como quedó su gráfica al final?” // “How did the scale you chose for your graph affect how your graph looked in the end?” (Certain scales make it easier or more difficult to read the data. For example, with a scale of 10, it might be more difficult to read the exact values from the graph.)