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 about how the scale affects reading and interpreting data in a graph.

• “¿Cómo decidiste qué escala usar en tu gráfica?” // “How did you choose the scale to use for your graph?”
• “¿Cuál es el número más grande que tienes que representar? ¿Cómo puedes verificar si es posible representarlo con la escala que escogiste?” // “What is the greatest number you need to represent? How can you check to see if it is possible to represent it with the scale you chose?

• 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, a scale of 2 cannot be used for this data with the given graph outline because there are only enough rows to label to 26 and the greatest data value is 40. (See the Advanced Student Thinking if students try to use a scale of 2.) Due to the larger numbers, it is likely that students will 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.

• “¿Cómo influyó 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.)