Math - 2018-19
3.15 - Graphs
The student will
a) collect, organize, and represent data in pictographs or bar graphs; and
b) read and interpret data represented in pictographs and bar graphs.
- So that I can organize data in order to learn more about our class and our community
- So that I can collect, organize and represent data when I conduct a science experiment
- So that I can collect and analyze data in order to investigate and answer questions
UNDERSTANDING THE STANDARD
- Investigations involving data should occur frequently and relate to students’ experiences, interests, and environment.
- Formulating questions for investigations is student-generated at this level. For example: What is the cafeteria lunch preferred by students in the class when four lunch menus are offered? If a new student enters our class tomorrow what color eyes will she likely have?
- The purpose of a graph is to represent data gathered to answer a question.
A pictograph uses pictures or symbols to represent one or more objects.
A key should be provided for the symbol in a pictograph when the symbol represents more than one piece of data (e.g.,represents five people in a graph). The key is used in a graph to assist in the analysis of the displayed data. One-half of a symbol represents one-half of the value of the symbol being used, as indicated in the key.
Students’ prior knowledge and work with skip counting helps them to identify the number of pictures or symbols to be used in a pictograph.
Definitions for the terms picture graph and pictographs vary. Pictographs are most often defined as a pictorial representation of numerical data. The focus of instruction should be placed on reading and using the key in analyzing the graph. There is no need for students to distinguish between a picture graph and a pictograph.
- Bar graphs are used to compare counts of different categories (categorical data). Using grid paper helps to increase accuracy in graph.
- A bar graph uses horizontal or vertical parallel bars to represent counts for categories. One bar is used for each category with the length of the bar representing the count for that category. There is space before, between, and after each of the bars.
- The axis displaying the scale representing the count for the categories should begin at zero and extend one increment above the greatest recorded piece of data. Grade three students should collect data that are recorded in increments of whole numbers, limited to multiples of 1, 2, 5, or 10.
- Each axis should be labeled, and the graph should be given a title.
Statements representing an analysis and interpretation of the characteristics of the data in the graph should be written (e.g., similarities and differences, least and greatest, the categories, and total number of responses).
Statements should also express a prediction based on the analysis and interpretation of the characteristics of the data in the graph (e.g., The lunch room should serve pizza more often since that is the lunch students have liked the most.)
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
- Formulate questions to investigate. (a)
- Design data investigations to answer formulated questions, limiting the number of categories for data collection to four. (a)
- Collect and organize data, using various forms of data collections (e.g., surveys, polls, questionnaires, scientific experiments, observations). (a)
- Represent data in a pictograph (limited to 16 or fewer data points for no more than four categories). (a)
- Represent data in a bar graph (limited to 16 or fewer data points for no more than four categories). (a)
- - Label each axis on a bar graph and give the bar graph a title. Limit increments on the numerical axis to whole numbers representing multiples of 1, 2, 5, or 10. (a)
- Analyze data represented in pictographs and bar graphs, orally and in writing. (b)
- – Read the information presented on a bar or pictograph (e.g., the title, the categories, the description of the two axes). (b)
- Interpret information from pictographs and bar graphs, with up to 30 data points and up to eight categories, describe interpretation orally and by writing at least one sentence. (b)
- Describe the categories of data and the data as a whole (e.g., data were collected on preferred ways to cook or prepare eggs — scrambled, fried, hard boiled, and egg salad). (b)
- Identify parts of the data that have special characteristics, including categories with the greatest, the least, or the same (e.g., most students prefer scrambled eggs). (b)
- Select a correct interpretation of a graph from a set of interpretations, where one is correct and the remaining are incorrect. (b)