#### Math - 2019-20

# 4.14 - Graphs

**The student will **

a) **collect, organize, **and **represent **data in bar graphs and line graphs;

b)** interpret** data represented in bar graphs and line graphs; and

c) **compare **two different representations of the same data (e.g., a set of data displayed on a chart and a bar graph, a chart and a
line graph, or a pictograph and a bar graph).

*Adopted: 2016*

### BIG IDEAS

So that I can use graphs to organize data in a way that is easier to interpret and compare numbers

Accountants use graphing to show financial information

Scientists use graphing to display their data and results from experiments

So that I can identify different and similar relationships between two separate graphs

So I can determine if the graph of a set of data is properly represented

### UNDERSTANDING THE STANDARD

- Data analysis helps describe data, recognize patterns or trends, and make predictions.
- Investigations involving practical data should occur frequently, and data can be collected through brief class surveys or through more extended projects taking many days.
- Students formulate questions, predict answers to questions under investigation, collect and represent initial data, and consider whether the data answer the questions.
- There are two types of data: categorical (e.g., qualitative) and numerical (e.g., quantitative).
Categorical data are observations about characteristics that can be sorted into groups or
categories, while numerical data are values or observations that can be measured. For example,
types of fish caught would be categorical data while weights of fish caught would be numerical
data. While students need to be aware of the differences, they do not have to know the terms for
each type of data.
- Bar graphs display grouped data such as categories using rectangular bars whose length represents the quantity the bar represents. Bar graphs should be used to compare counts of different categories (categorical or qualitative data). Grid paper can assist students in creating graphs with greater accuracy.
- A bar graph uses horizontal or vertical bars to represent counts for several 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 the bars.
- The axis that displays the scale representing the count for the categories should begin at zero and extend one increment above the greatest recorded piece of data. Grade four students should collect and represent data that are recorded in increments of whole numbers, usually multiples of 1, 2, 5, 10, or 100.
- 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 (e.g., similarities and differences, least and greatest, the categories, and total number of
responses) should be written.
- Line graphs are used to show how two data sets (numerical or quantitative data) are related. Line
graphs may be used to show how one variable changes over time (numerical or quantitative data).
By looking at a line graph, it can be determined whether the change in the data set is increasing,
decreasing, or staying the same over time.
- The values along the horizontal axis represent continuous data on a given variable, usually some measure of time (e.g., time in years, months, or days). The data presented on a line graph is referred to as “continuous data,” as it represents data collected over a continuous period of time.
- The values along the vertical axis are the scale and represent the frequency with which those values occur in the data set. The values should represent equal increments of multiples of whole numbers, fractions, or decimals, depending upon the data being collected. The scale should extend one increment above the greatest recorded piece of data.
- Each axis should be labeled, and the graph should be given a title.
- A line graph tells whether something has increased, decreased, or stayed the same with the passage of time. Statements representing an analysis and interpretation of the characteristics of the data in the graph should be included (e.g., trends of increase and/or decrease, and least and greatest).

- Bar graphs should be used to compare counts of different categories (categorical data). Using grid paper ensures more accurate graphs.
- A bar graph uses parallel, horizontal or vertical bars to represent counts for several 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 the bars.
- The axis that displays the scale representing the count for the categories should extend one increment above the greatest recorded piece of data. Fourth-grade students should collect data that are recorded in increments of whole numbers, usually multiples of 1, 2, 5, 10, or 100.
- 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 (e.g., similarities and differences, least and greatest, the categories, and total number of responses) should be written.
- For example, a line graph documenting data gathered during a planting cycle might show length of time and the height of a plant at any given interval.
- Different situations call for different types of graphs. The way data are displayed is often
dependent upon what someone is trying to communicate
Comparing different types of representations (charts and graphs) provide students an opportunity to learn how different graphs can show different aspects of the same data. Following construction of graphs, students benefit from discussions around what information each graph provides.

Tables or charts organize the exact data and display numerical information. They do not show visual comparisons, which generally means it takes longer to understand or to examine trends.

Bar graphs can be used to compare data easily and see relationships. They provide a visual display comparing the numerical values of different categories. The scale of a bar graph may affect how one perceives the data.

Examples of some questions that could be explored in comparing a chart to a line graph include: In which representation do you readily see the increase or decrease of temperature over time? In which representation is it easiest to determine when the greatest rise in temperature occurred?

**Temperature Over Time**

Time | Temperature |

9 a.m. | 12 |

10 a.m. | 26 |

11 a.m. | 33 |

12 p.m. | 39 |

### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

- Collect data, using, for example, observations, measurement, surveys, scientific experiments, polls, or questionnaires. (a)
- Organize data into a chart or table. (a)
- Represent data in bar graphs, labeling one axis with equal whole number increments of 1 or more (numerical data) (e.g., 2, 5, 10, or 100) and the other axis with categories related to the title of the graph (categorical data) (e.g., swimming, fishing, boating, and water skiing as the categories of “Favorite Summer Sports”). (a)
- Represent data in line graphs, labeling the vertical axis with equal whole number increments of 1 or more and the horizontal axis with continuous data commonly related to time (e.g., hours, days, months, years, and age). Line graphs will have no more than 10 identified points along a continuum for continuous data. For example, growth charts showing age versus height place age on the horizontal axis (e.g., 1 month, 2 months, 3 months, and 4 months).
- Title the graph or identify an appropriate title. Label the axes or identify the appropriate labels. (a)
- Interpret data by making observations from bar graphs and
line graphs by describing the characteristics of the data and
the data as a whole (e.g., the time period when the
temperature increased the most, the category with the
greatest/least, categories with the same number of
responses, similarities and differences, the total number).
One set of data will be represented on a graph. (b)
- Interpret data by making inferences from bar graphs and line graphs. (b)
- Interpret the data to answer the question posed, and compare the answer to the prediction (e.g., “The summer sport preferred by most is swimming, which is what I predicted before collecting the data.”). (b)
- Write at least one sentence to describe the analysis and interpretation of the data, identifying parts of the data that have special characteristics, including categories with the greatest, the least, or the same. (b)
- Compare two different representations of the same data
(e.g., a set of data displayed on a chart and a bar graph; a
chart and a line graph; a pictograph and a bar graph). (c)

### KEY VOCABULARY

*Updated: May 29, 2019*