Oakland Terrace Grade 5 Math

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Grade 5 Unit 4 ~ Line Plots/Measures of Central Tendency

What Does This Look Like In:

9 flowers, each with a different number of spiders.

Students in Ms. Mason's and Ms. Wine's class are given this picture of a garden with flowers. Each flower has spiders. Students are asked to collect and display data about the number of spiders on each flower. Students collect the data, finding the following number of spiders on the flowers:

8, 4, 9, 4, 7, 4, 9, 7, 2

In addition to giving students data already collected, it is important to have them organize and interpret data, in this case, with a pictorial representation.

The fifth and sixth grade objectives require students to determine the different types of data used for different graphs. This student has mixed result explaining why he did or did not choose a particular graph to reflect the data about the spiders on the flowers. He is right in explaining that a line graph shows change over time and that a stem and leaf plot does not work with single-digit numbers. For a circle graph, the data must be dealing with a whole that is partitioned into groups.

Student explanations for why they did or did not choose a circle graph, stem and leaf plot, line plot or line graph to display the data.

Line Plot using the flowers as the data points. The flowers each show the spiders.
As a class or in small groups, students can use the actual flowers from the picture as the data points in their line plots.

Line plot created by a student which uses X's as the data points on a line plot.
Students can also create a line plot using X's to represent the data points. Often, however, line plots are so abstract, from a set of data that is not meaningful, that students do not understand what the X's represent. Is it the number of flowers or the number of spiders? In the top line plot using the flowers, they can see that the data points are the number of flowers (9 total). The numbers on the number line, however, represent the number of spiders on each flower. Asking students to title the line plot can also be an issue when they do not truly understand what they are graphing. But using the line plot that uses the pictures of the flowers, it is clear to students what the data shows:
The Number of Spiders on Each Flower

Students are asked to find the measures of
central tendency for this set of data.

Mode: The number that occurs most frequently in the data.	Median: The number that occurs in the middle of the data

Mean: The mean, or average, is the number found by dividing the sum of a set of numbers by the number of addends. Students understand the mean to be the evening out of the data (imagining that the number of spiders on each flower has been evened out so that they all have the same number).

Download a copy of the picture of the flowers (PDF)	Download a copy of the line plot (PDF)	Download a copy of the worksheet that goes with this activity (PDF)	Indicators: 4.5.2.1 collect and organize data using a variety of graphic representations, including tables, stem and leaf plots, line plots, and line graphs. 4.5.2.2 select and defend the selection of particular graphic displays. 4.5.4.1 explain how mean, median, mode, and range of a data set are different. 4.5.4.3 compute and compare range, mean, median, and mode of data sets.