# Draw a pictograph and a bar graph (with intervals of one) to represent a data set with up to four ### Cluster

Represent and interpret data.

Evidence of Learning Statements

 Students with a level 1 understanding of this standard will most likely be able to: Students with a level 2 understanding of this standard will most likely be able to: Students with a level 3 understanding of this standard will most likely be able to: Students with a level 4 understanding of this standard will most likely be able to: Organize, represent, and interpret data with up to three categories. Ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Complete a pictograph which represents a limited data set with up to three categories. Each picture symbol represents a single element in the data set. Complete a bar graph with intervals of one which represents a limited data set with up to three categories. Draw a pictograph to represent a sorted data set with up to three categories.  Each picture symbol represents a single element in the data set. Draw a bar graph with intervals of one to represent a sorted data set with up to three categories. Solve one-step addition and subtraction problems related to the data presented in a provided pictograph or bar graph. Draw a pictograph to represent a data set with up to four categories. Solve one and simple two-step addition and subtraction problems related to the data in a graph. Draw a bar graph with intervals of one to represent a data set with up to four categories. Solve one and simple two-step addition and subtraction problems related to the data in a graph. Draw a pictograph to represent a data set with more than four categories. Create and solve one and two-step addition and subtraction contextual problems related to the data in the graph. Draw a bar graph with intervals of one to represent a data set with more than four categories. Create and solve one and two-step addition and subtraction contextual problems related to the data in the graph. Decide if a pictograph or bar graph better represents a data set and provide justification.

Instructional Focus Statements

Level 3:

In grade 1, students organized data with up to three categories and asked and answered questions about the data. In grade 2, students expand on this to collect and organize data in four categories and then represent that data specifically in pictographs and/or bar graphs with intervals of one. Additionally, students should be solving one and two-step addition and subtraction problems related to the data in the graph. This supports standard 2.OA.A.1.  Instruction should focus on how to draw a pictograph or bar graph and then on answering questions related to the graphs incorporating a variety of problem types.

Pictographs are one of the most intuitive types of graphs for grade 2 students. Due to experiences with counting and one-to-one correspondence coupled with an understanding of non-proportional representations from working with monetary value of coins, students tend to have an easier time developing a conceptual understanding of and answering questions about data represented in pictographs. That said, as this is a student’s first experience reading and drawing pictographs, students will need instruction on how to read a pictograph, how to physically represent data on the graph, what a scale is, how to use a scale, why the scale is important, and when to use a scale of one and when to use a different scale such as two. Students need opportunities to interact both with vertical and horizontal graphs. Students should experience a balance of opportunities both collecting their own data prior to creating pictographs and creating pictographs from provided data.

Bar graphs are less intuitive for students. As with pictographs, students will need instruction on how to read a bar graph, how to physically represent data on the graph, what a scale is, how the scale on bar graphs differs from the scale on pictographs, and why the scale is important. Students should discuss ways in which bar orientation (horizontal or vertical), order, thickness, spacing, shading, colors, and so forth make the bar graphs easier or more difficult to read and interpret. With bar graphs, one of the axes will have numerical meaning and will represent segments of a number line diagram. As this scale represents counts in whole numbers (sometimes called a count scale), when students answer “how many more” or “how many less” questions, they are supporting their understanding of finding differences on a number line diagram (standard 2.MD.B.6). Students should experience a balance of opportunities both collecting their own data prior to creating bar graphs and creating pictographs from provided data.

This standard integrates well with standard 2.G.A.1 as students can make graphs from sorted shapes. Additionally, it provides the opportunity to review and reinforce standard K.MD.B.3 by sorting coins into categories followed by answering addition and subtraction questions about the data (value of various sets of coins) which supports standard 2.MD.C.8.

Level 4:

Students at this level should be challenged to graphically represent a data set with more than four categories. With pictographs, students should thoughtfully choose the scale for their graph and be able to justify their choice. Additionally, students should create their own one and two-step addition and subtraction contextual problems related to the data in their graph and provide solutions for their problems. Students should also be challenged to choose which type of graph best represents their data and provide justification for their choice (MP 3).