NCDPI -- AIG Instructional Resource: Background Information

Date Submitted:
6/26/12
Resource Title:
Dinner Party Dilemma
Subject Area/Grade Level (s):
Math/Grade 3 / Time Frame
1-2 class periods
Common Core/Essential Standard Addressed:
Measurement and Data
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding and unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
4. Model with mathematics.
6. Attend to precision.
7. Look for and make use of structure.
Additional Standards Addressed:
(integration across topics, within or across disciplines)
Brief Description of Lesson/Task/Activity:
This task requires students to understand that perimeter and area have a relationship and to recognize and apply their understanding in a real-life context. The fact that different shapes can have different areas but the same perimeter (or different perimeters but the same area) is not necessarily self-evident for students. Through the task, students will further explore this particular concept.
Type of Differentiation for AIGs (include all that apply)
X Enrichment Extension Acceleration
Adaptations for AIGs
X Content X Process Product
Explanation of How Resource is Appropriate for AIGs
This activity varies in terms of content through abstractness and complexity. The task requires the students to analyze the relationships between area and perimeter. Additionally, the task encourages many student responses through provocative questions and open-endedness.
Needed Resources/Materials
Spaghetti and Meatballs for All! by Marilyn Burns
Blackline copy of student sheet
Sources (all sources must be cited)
TEACHER NOTES

NCDPI AIG Curriculum Resource Outline

Describe processes, steps, and materials needed at each stage of the lesson/activity.

STAGE ONE: Engage
  Hook
  Prior knowledge
  Instructional input
  Modeling
Description:
Read aloud: Spaghetti and Meatballs for All! by Marilyn Burns.
Ask the students: Why didn’t adding two more tables make it so six more people could sit at the table? Would it help if they had added the tables to the ends, making a long line instead of a square? Why or why not? Will adding two more tables (for a total of six tables) solve their problem? Why (or why not)? Is there any way to add tables and gain more than two seats (while still keeping the shape a rectangle)? Explain.
Draw another way that you could seat 32 guests. You can use as many tables as you want but the same rules about elbow-room apply!
STAGE TWO: ELABORATE
  Guided and independent practice
  Guiding questions
Description:
Present the task to the students: You have been chosen to host a dinner party for 24 guests. In order for all of the guests to be able to participate in the dinner conversation, it is important that all of the guests sit at the same rectangular table. You have to rent small square tables to use for the dinner party. Each table costs $10 to rent (chairs are free).
Remind the students that this task is different from the one posed in the book. Have students work independently to solve the task (see attached student sheet).
STAGE THREE: EVALUATE
  Assessment
Description:
Facilitate discussion among the students regarding their findings and solution strategies. It is important for students to hear their peers explain their solution paths. Have the students evaluate their solution approaches for efficiency and accuracy.
Conclusion questions:
1. What patterns were useful as you worked?
2. What table arrangements are the most and least economical? Why do you suppose that is?
3. What do you notice about the areas and perimeters of the arrangements you made?
4. Can you summarize the relationships between area and perimeter?
TEACHER NOTES

Seating Arrangements

You have been chosen to host a dinner party for 24 guests. In order for all of the guests to be able to participate in the dinner conversation, it is important that all of the guests sit at the same table. You have to rent small square tables to use for the dinner party. Each table costs $10 to rent (chairs are free).

1. Find the least expensive way to seat all 24 guests. Use pictures, numbers, and words to prove you’re right. Make sure you draw a picture of your table and label the sides, perimeter and area.

2. Next, find the most expensive way to seat all 24 guests without having any extra chairs. Use pictures, numbers, and words to prove you’re right. Make sure you draw a picture of your table and label the sides, perimeter and area.

3. How do the perimeters of each table compare? How do the areas of each table compare? How does the shape of the table affect the price?