Grade 4 – Mathematics: Data Analysis with Multiple Correspondences

Overview

Using a given set of data students construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions.

Activate

Students state examples  of graphs and charts they have seen where different intervals or correspondences are used. [Plan and Question] Students find  examples of such graphs and charts in electronic media and explain why that interval or correspondence was used. [Gather and Make Sense]

Teacher Tip:
Have students find examples in a familiar electronic encyclopedia.

Suggestions for Assessment:
Observe if students understand that a symbol can represent a count of more than one of something and that intervals other than one may be used to determine which students need differentiation and/or appropriate scaffolding.

With students, construct assessment criteria for what correct pictographs and bar graphs involving different intervals and correspondences look like. Throughout grade 4 data analysis, use the Focused Observation Form to focus on students' growing competence as they demonstrate their understanding of why, when and how to create and label a pictograph (with categories, title and legend) and a bar graph (with axes and title) to display a given set of data using different intervals and correspondences.

Acquire

Students view a beadwork design and enter data  into a spreadsheet where the data is represented using a one-to-one correspondence pictograph and a many-to-one correspondence pictograph. [Gather and Make Sense] Students discuss intervals and correspondences to explain how the two graphs are the same and different [Produce to Show Understanding].

Support File:
Bead Design Sample

Suggestions for Assessment:
Record Focused Observations: Determine whether students are able to explain that there are advantages when a symbol represents a count of more than one of something.

Demonstrate how to create pictographs involving many-to-one correspondence. Students construct a pictograph involving many-to-one correspondence using the following set of data. "A taste test at an ice cream store had these results: 80 people like chocolate; 60 people like vanilla; 20 people like butterscotch; 30 people like strawberry." [Produce to Show Understanding] In groups, students discuss the advantages and disadvantages of their symbols and legends and explain the intervals and correspondence used. [Communicate]

Teacher Tip:
To change one-to-one data to a "many-to-one correspondence", select a column and click on it (avoid double-clicking). Right-click on this column and select the "Format Data Point/Series" option. Select "Fill Effects" button. Select "Stack and Scale to: ratio" and change from 1 to whatever you want each image to represent (2 or 3 or 5 or.). Repeat for other columns.

Support File:
Creating Pictographs

Suggestions for Assessment:
Record Focused Observations: Determine if students correctly construct a graph involving a symbol showing a many-to-one correspondence and label the graph correctly with axes, title and legend.
Self- Assessment: Have students self- assess using the Met/Not Yet from the criteria set in Constructing Student-Generated Criteria for Quality Work.
Peer Assessment: Have students peer assess the graphs based on previously set criteria.

Apply

Students organize, and display a given set of data that is suitable for many-to-one correspondence  in a pictograph and bar graph. [Gather and Make Sense, Produce to Show Understanding] In a journal or in peer discussions, students analyze data to draw conclusions, justify the choice of correspondences used, and answer a given question from the graph [Produce to Show Understanding].

Suggestions for Assessment:
Summative strategies such as this one have many possible tagged outcomes. Target assessment on only a few of the criteria/goals such as the ones that were not addressed in your focused observations.