Students need to be able to create and interpret a range of representations in mathematics, including tables. There are various ways to use tables to represent information, and students should be scaffolded provided with multiple opportunities to read, interpret and construct them (Quinnell, 2014).
Sometimes tables contain only numbers, but a table can be used to compare and contrast two or more mathematical objects or ideas. When a table is used to compare or contrast, it is called a comparison table. Comparison tables are frequently used to compare the features of various products (e.g. mobile phone plans, televisions).
Understanding this strategy
The strategy below focuses on the use of comparison tables, but teachers can use the same process to support students to create any kind of table.
Creating comparison tables is a useful strategy which can be helpful in any school subject or learning area, any strand in mathematics, and even post-secondary schooling.
A key step in constructing a comparison table is deciding on the column and row names. To introduce and support students to create comparison tables, teachers can either deconstruct models of comparison tables with students or jointly construct tables with students.
Deconstructing a model table
- Teachers present a model comparison table for the topic being studied to the class.
- Teacher explains or 'thinks aloud' the naming of rows and columns:
Items being compared are headings of columns
Features being compared are headings of rows.
Sentence structures to support the comparisons can be provided and/or modelled through the teacher's think aloud. For example, using the comparison table below:
- Build comparative statements using conjunctions, such as 'while'
An equilateral triangle has three angles of 60 degrees while a right-angled triangle has one angle of 90 degrees.
- Create a statement that includes a quantifying determiner such as 'some', 'most', 'all', or 'few'
The sum of angles in all triangles is 180°.
Some triangles have an angle measuring 90°. These triangles are called right-angle triangles.
- Write statements using 'similar' or 'similarity' and 'different' or 'difference'
One difference between equilateral and scalene triangles is the number of angles less than 90°; equilateral triangles have 3 while scalene triangles have none or one.
Jointly constructing a model table
- Teacher asks students to list features or elements of the objects or items that are being compared in the topic of study.
- Teacher jointly constructs a comparison table on the board, guiding students on how to use the list to construct headings of rows and columns.
Items being compared are headings of columns.
Features being compared are headings of rows.
- Students copy down the comparison table with the headings and use it to complete the comparison.
Vocabulary items here will be specific to the table being created. Discussion and definition of the items and features can take place as the students build the list.
Example using tables
The example below shows how a comparison table can help Year 7 students make sense of terminology associated with different types of triangles is provided below (VCMMG262). The teacher could model this or jointly construct it with students.
Features
| equilateral
| scalene
| isosceles
| acute-angled
| right-angled
| obtuse-angled
|
|---|
Number of sides
| 3
| 3
| 3
| 3
| 3 | 3 |
|---|
Number of angles
| 3
| 3
| 3
| 3
| 3
| 3
|
|---|
Sum of angles
| 180°
| 180°
| 180°
| 180°
| 180°
| 180° |
|---|
Definition based on
| sides all same length
| sides all different lengths
| two sides same length
| no angles are 90°
| one angles is 90° | one angle is more than 90° |
|---|
Number of right-angles
| 0
| 0 or 1
| 0 or 1
| 0
| 1 | 0 |
|---|
Number of angles <90°
| 3
| 0 or 1
| 2 or 3
| 3
| 2
| 2
|
|---|
Number of angles >90°
| 0
| 0 or 1 | 0 or 1 | 0 | 0 | 1 |
|---|
Note: it is useful to have rows where all entries are the same (as in the example) to show how things are similar, not just different.