Mathematics Assessment: Classifying Equations of Parallel and Perpendicular Lines

Mathematics Assessment: Classifying Equations of Parallel and Perpendicular Lines

Classifying equations of parallel and perpendicular lines focuses on the mathematical relationships between slopes. This lesson is designed for middle and high school students to enhance their understanding of geometry and algebra. It includes tasks that help identify parallel and perpendicular lines through their equations. The lesson also addresses common misconceptions and provides collaborative activities to reinforce learning. Ideal for educators seeking to improve student comprehension in geometry.

Key Points

  • Explains the relationship between slopes of parallel and perpendicular lines.
  • Includes assessment tasks for identifying equations of lines.
  • Encourages collaborative group work to enhance understanding.
  • Addresses common misconceptions in classifying line equations.
  • newtopiccyclegrowin
221
/ 24
CONCEPT DEVELOPMENT
Mathematics Assessment Project
CLASSROOM CHALLENGES
A Formative Assessment Lesson
Classifying Equations
of Parallel and
Perpendicular
Lines
Mathematics Assessment Resource Service
University of Nottingham & UC Berkeley
For more details, visit: http://map.mathshell.org
© 2015 MARS, Shell Center, University of Nottingham
May be reproduced, unmodified, for non-commercial purposes under the Creative Commons license
detailed at http://creativecommons.org/licenses/by-nc-nd/3.0/ - all other rights reserved
Teacher guide Classifying Equations of Parallel and Perpendicular Lines T-1
Classifying Equations of Parallel and
Perpendicular Lines
MATHEMATICAL GOALS
This lesson unit is intended to help you assess how well students understand the relationship between
the slopes of parallel and perpendicular lines and in particular, to help identify students who find it
difficult to:
• Find, from their equations, lines that are parallel and perpendicular.
• Identify and use intercepts.
It also aims to encourage discussion on some common misconceptions about equations of lines.
COMMON CORE STATE STANDARDS
This lesson relates to the following Standards for Mathematical Content in the Common Core State
Standards for Mathematics:
G-PE: Use coordinates to prove simple geometric theorems algebraically.
F-IF: Analyze functions using different representations.
This lesson also relates to all the Standards for Mathematical Practice in the Common Core State
Standards for Mathematics, with a particular emphasis on Practices 2, 5, and 7:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
INTRODUCTION
The lesson unit is structured in the following way:
• Before the lesson, students work individually on a task designed to reveal their current level of
understanding and their difficulties. You then review their work and create questions for students
to answer in order to improve their solutions.
• During the lesson, students work in small groups on a related task, justifying and explaining their
decisions to each other. They then re-group to critique each other’s work. Finally, in a whole-
class discussion, students explain and extend their methods and solutions.
• In a follow-up lesson, students work alone to improve their solutions to the assessment task.
MATERIALS REQUIRED
• Each student will need two copies of Parallel and Perpendicular Lines, a mini-whiteboard, pen,
and eraser.
• Each small group of students will need the Card Set: Equations (already cut up into cards), two
copies of the Properties table, and a glue stick.
• Graph paper should be kept in reserve and only used when requested.
• There is a projector resource to help introduce activities and support the whole-class discussion.
TIME NEEDED
Approximately 15 minutes before the lesson, a 1-hour lesson, and 15 minutes in a follow-up lesson.
Teacher guide Classifying Equations of Parallel and Perpendicular Lines T-2
BEFORE THE LESSON
Assessment task: Parallel and Perpendicular Lines (15 minutes)
Have students do this task, in class or for homework,
a day or more before the formative assessment
lesson. This will give you an opportunity to assess
the work and to find out the kinds of difficulties
students have with it. You should then be able to
target your help more effectively in the subsequent
lesson.
Give each student a copy of the assessment task
Parallel and Perpendicular Lines.
Read through the questions and try to answer
them as carefully as you can.
It is important that, as far as possible, students are
allowed to answer the questions without your
assistance.
Advise your students that they should not worry too
much if they cannot understand or do everything,
because there will be a lesson using a similar task
that will help them. Explain that their goal is to be able to answer questions such as these by the end
of the next lesson.
Assessing students’ responses
Collect students’ responses to the task. Make some notes on what their work reveals about their
current levels of understanding. The purpose of doing this is to forewarn you of the difficulties
students will experience during the lesson itself, so that you may prepare carefully.
We suggest that you do not score students’ work. The research shows that this will be
counterproductive, as it will encourage students to compare their scores and will distract their
attention from what they can do to improve their mathematics.
Instead, help students to make further progress by summarizing their difficulties as a series of
questions. Some suggestions for these are given in the Common issues table on the next page. These
have been drawn from common difficulties observed in trials of this lesson unit.
We suggest you make a list of your own questions, based on your students’ work. We recommend
you either:
• write one or two questions on each student’s work, or
• give each student a printed version of your list of questions and highlight the questions for each
individual student.
If you do not have time to do this, you could select a few questions that will be of help to the majority
of students and write these on the board when you return the work to the students in the follow-up
lesson.
Finding Equations of Parallel & Perpendicular Lines Student Materials Alpha Version 7 Jan 2010
© 2010 Shell Center/MARS University of Nottingham UK S-1
Parallel and Perpendicular Lines
Here are some equations of straight lines:
!
y + 2 x = 8
1. Which four lines form the four sides of a rectangle?
Explain your reasoning carefully.
2. Complete the drawing below to show the four lines and the x and y axes.
Label the lines clearly.
/ 24
End of Document
221
You May Also Like

FAQs of Mathematics Assessment: Classifying Equations of Parallel and Perpendicular Lines

What are the main objectives of the lesson on parallel and perpendicular lines?
The lesson aims to help students understand the relationship between the slopes of parallel and perpendicular lines. It focuses on identifying these lines through their equations and using intercepts effectively. Additionally, the lesson encourages discussion about common misconceptions that students may have regarding line equations. By engaging in collaborative tasks, students can justify their reasoning and improve their mathematical communication skills.
How does the lesson assess students' understanding of line equations?
Students begin with an individual assessment task that reveals their current understanding of parallel and perpendicular lines. Their responses are reviewed to identify common difficulties, which informs targeted instruction during the lesson. The collaborative group work allows students to discuss and critique each other's reasoning, further solidifying their grasp of the concepts. A follow-up lesson enables students to revise their initial responses based on what they learned.
What types of activities are included in the lesson plan?
The lesson includes individual assessment tasks, collaborative group work, and whole-class discussions. Students first work on identifying equations of lines that form a rectangle, then engage in matching tasks where they categorize equations based on properties. The lesson culminates in a whole-class discussion to address discrepancies and reinforce understanding of the material. This structured approach fosters both individual and collective learning.
What common misconceptions do students have about parallel and perpendicular lines?
Students often struggle to connect the properties of rectangles with the slopes of lines, failing to recognize that rectangles have pairs of parallel and perpendicular sides. Additionally, some students may not understand how to derive slopes from different forms of line equations. The lesson addresses these misconceptions by guiding students through reasoning and encouraging them to articulate their thought processes during collaborative activities.

Related of Mathematics Assessment: Classifying Equations of Parallel and Perpendicular Lines