Triangles and rectangles
0
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about the area of two triangles and two rectangles.
Task administration:
This task can be completed with pen and paper or online (with SOME auto marking).
Level:
5
Curriculum info:
Key Competencies:
Keywords:
Description of task:
Students compare the area of two different triangles.
Curriculum Links:
Key competencies
This resource involves communicating why two triangles have the same area. This relates to the Key Competency: Using language, symbols and text.
For more information see https://nzcurriculum.tki.org.nz/Keycompetencies
This resource involves communicating why two triangles have the same area. This relates to the Key Competency: Using language, symbols and text.
For more information see https://nzcurriculum.tki.org.nz/Keycompetencies
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.Answers/responses:
Y10 (04/2016)  
a) 
"The area of triangle X is the same as the area of triangle Y." [Option 2]
Explanation that is based on two key points:
Examples:

moderate
very difficult

Based on an online sample of 137 Y10 students.
Teaching and learning:
This resource is about following a line of reasoning using properties of shapes rather than using given dimensions of shapes to compare their area .
Diagnostic and formative information:
Common incomplete or incorrect response  Next Steps 
Incomplete explanation given
Correctly identifies that both triangles have the same area, but just states that the rectangles have the same area.
Examples:

Students need to include the information that a triangle is half the area of the enclosing rectangle (or parallelogram) as well as that the rectangles have the same area.
Some may have known this. These students need to learn to give a complete argument.

Thinks that there is insuffiicient information
Selects "It could be smaller, the same, or larger" [Option 4] and sees this as insufficient information.
Examples:

Students may need to explore the relationship between the area of a triangle and the enclosing rectangle/parallelogram (½ b.h compared with b.h). They then need to integrate this information across both shapes.

Students want actual dimensions of shapes
Student selects "It could be smaller, the same, or larger" [Option 4] or "They are the same" [Option 2], but thinks that actual dimensions (i.e., base and height) need to be given.
Examples:

Students need be challenged to use other information than dimensions to make inferences. They may also need to explore the relationship between the area of a triangle and of the enclosing rectangle/parallelogram (½ b.h compared with b.h). They may then retry the question.

Using visual estimation
Students base their answer on a visual comparison.
Example:

Students may need to explore multiple examples of the area of rectangles and triangles, that lead to the general rules for their areas and then to see the relationship between them.
