Date(s): March 4 ‘09 / Topic: How much personal space do I need?
Grade Level: Grade 4 / Time(s): 1 fifty minute period
Curriculum Expectations:
Measurement
Measurement Relationships - pose and solve meaningful problems that require the ability to distinguish perimeter and area
Assessment Strategies:
Rubric- I will use this as a summative evaluation because the students are currently finishing a unit involving perimeter and area. I use this assessment while students present their work and when I review their worksheets.
Accommodations and Modifications:
If students are uncomfortable working with numbers in the decimals, I will encourage them to round their numbers to the nearest whole or convert to centimeters.
The Van De Walle approach to critical thinking in mathematics allows students to demonstrate their knowledge in a variety of ways, with no single method recognized as the “best”. The Van De Walle approach also allows for cooperative learning and allows students to self-correct as they learn from one another.
Resources:
- overhead photocopies of comics and “Recommended Personal Space” pages
- I will write the questions on the blackboard
- students will complete their work on chart paper
- “One” by Kathryn Otoshi / Outline:
Students will critically think about the concept of personal space. Students will begin to explore strategies to avoid bullying.
Introduction: 10 mins
I will introduce the activity by displaying a few cartoons that deal with the concept of personal space. I will then show the overhead titled, “Recommended Personal Space”. This provides a visual display of the concept of “personal space”.
Students will work in groups of 3 or 4 to answer the following questions.
1. How many students could fit in the classroom if everyone had a personal space radius of 1.23 meters?
2. Is 1.23 meters a reasonable amount of personal space? Why, or why not?
Students will complete the worksheet attached below as “sample worksheet”. I will explain my expectations for each section of the worksheet and help them tap into prior knowledge about perimeter and area problems.
· “What do we know about the problem?” – Students must use this section to describe information they can derive from the problem. For example, each person has a 1.23 meter radius (r=1.23 m). Students may also use this section to demonstrate background knowledge on the subject. For example, students may write the equation for the area of a circle (A=3.14 * r * r), or students may choose to transform the circles to squares and write the equation for the area of a square (A= l2 or l * l).
· “The 3 BIG Questions” – this section allows opportunity for students to reflect on the problem solving process. This is written in the students own language and may be completed after completing the “work” section.
· “Show Your Work” – this is where students must show their mathematical equations. Students may use manipulatives, or draw pictures, or use another strategy to help them find the answer. Students are encouraged to demonstrate 2 different approaches to solving the problem (this helps answer the question, ‘How do you know your answer is correct?”). Student must sign their name beside their contributions to the group work to ensure group accountability.
Middle: 30 mins
Students will have about 20 minutes to complete the worksheet and arrive at an answer for the 2 questions posed at the beginning of the lesson.
After 2 minutes students will begin presenting their conclusions to the group. Encourage students to ask questions of one another and compare their answers with each another.
After 20 minutes, student groups will begin presenting their work to the class. Each group must explain their answers to the 3 BIG questions and describe the answers they arrived at for the 2 questions posed at the beginning of the lesson.
Conclusion: 10 mins
After the group presentations, I will invite the students for a discussion about bullying. It is important to recognize our own comfort level with personal space. Tapping into our feelings helps us recognize when we feel uncomfortable. I will introduce the book, “One”. This book introduces the idea that there is strength in numbers when we speak out against bullying. This book will help prepare students for upcoming lessons on strategies to combat bullying.
Follow Up:
I will teach 3 lessons on strategies to avoid bullying. The first lesson will teach anger management strategies (from the bully perspective). The next 2 lessons will teach strategies to avoid bullying from the victim and bystander perspectives.
Recommended Personal Space
1.23 m
0.46 m
Diagram of Edward T. Hall's personal reaction bubbles (1966), showing radius in feet
Overview
Two people not affecting each other's personal space.
Reaction of two people whose personal space are in conflict.
Cartoons about Personal Space
Rubric for perimeter and area activity
Categories / Level 1 / Level 2 / Level 3 / Level 4Knowledge and Understanding – Subject-specific content acquired in each grade (knowledge), and the comprehension of its meaning an significance (understanding)
Knowledge of content
(ie/ applies appropriate problem-solving procedures such as, multiplication, identifies perimeter, equations for finding area, etc. / - demonstrates limited knowledge of content / - demonstrates some knowledge of content / - demonstrates considerable knowledge of content / - demonstrates considerable knowledge of content
Thinking – The use of critical and creative thinking skills and/or processes
Use of processing skills
(ie/ carrying out a plan, collecting data, questioning, testing, revising, modeling, solving, inferring, forming conclusions) / - uses processing skills with limited effectiveness / - uses processing skills with some effectiveness / - uses processing skills with considerable effectiveness / - uses processing skills with a high degree of effectiveness
Use of processing skills
(ie/ looking back at the solution, reasoning, justifying, reflecting, etc.) / - uses processing skills with limited effectiveness / - uses processing skills with some effectiveness / - uses processing skills with considerable effectiveness / - uses processing skills with a high degree of effectiveness
Communication – The conveying of meaning through various forms
Expression and organization of ideas and mathematical thinking using oral, visual, and written forms
(ie/ is the mathematical process to arrive at an answer clear and coherent) / - expresses and organizes mathematical thinking with limited effectiveness / - expresses and organizes mathematical thinking with some effectiveness / - expresses and organizes mathematical thinking with considerable effectiveness / - expresses and organizes mathematical thinking with a high degree of effectiveness
Sample Worksheet
What do we know about the problem?(ie/ what information does the problem give us?) / The 3 BIG Questions
1. What did you do to get the answer?
2. Why did you do it that way?
3. How do you know your answer is correct? / Show Your Work
(remember to answer the problem in 2 different ways)