Unit Overview

Content Area: Mathematics
Unit Title: Investigation 1 “Designing Bumper Cars”
Target Course/Grade Level: 7th grade, Special Education (Inclusion Class)
Name: Rebecca Konschak
School: Lakeside Middle
Date: July 29, 2010

Unit Summary
In the context of bumper-car rides, students study perimeter, area, and relationships between them.  This investigation involves simple shapes constructed from square tiles and leads to formulas for area and perimeter of rectangles.  Rectangles are presented in a variety of ways: on grids, off grids, and described by dimensions alone.  The students in the inclusion classes generally have specific learning disabilities, other health impairments, emotional disturbances, or multiple disabilities as well as gifted and talented students mixed in with the mainstream population.

Primary interdisciplinary connections
Science, Children’s Literature

21st century themes
Financial, Economic, Business and Entrepreneurial Literacy

Unit Rationale
Calculating volume of regular and irregular objects is a key component of 7th grade science, the Properties of Matter Unit.  It is also important that students understand the concepts of area, volume, and surface area as a life skill, required for any kind of vocation or avocation that includes planning, constructing, and ordering materials.

Learning Targets

Standards Key Ideas and Details
Geometry 7.G.6

Content Statements
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Unit Essential Questions

• How do I know whether area or perimeter of a figure is involved?
• What attributes of a shape are important to measure?
• What am I finding when I find area and when I find perimeter?
• What relationships involving area or perimeter, or both will help solve the problem?
• How can I find the area and perimeter of an irregular shape?
• Is an exact answer required?

Unit Enduring Understandings

• Perimeter is the distance around a two-dimensional figure.
• Area is the space covered by a two-dimensional figure.
• There are many strategies for finding perimeter and area including using the formulas.

Unit Learning Targets
Students will...

• Find the perimeter (number of units of length needed to surround) a 2-dimensional object.
• Find the area (number of unit squares needed to cover) a 2-dimensional object.
• Discover that two figures with the same area may have different perimeters and that two figures with the same perimeter may have different areas.
• Visually show what changes occur when tiles forming a figure are rearranged, added, or subtracted.

Evidence of Learning

Summative Assessment (5 days)
At the end of this investigation, the students will respond to the Mathematical Reflections, journal understandings, and take a short quiz.

Equipment needed
Student notebooks/journals, Covering and Surrounding text book, paper and pencils

Teacher Resources
Covering and Surrounding Teacher’s Guide

Formative Assessments

• Exit Tickets
• Mathematical Reflections
• Class work
• Discussion
• Participation
• Homework
• Visual/Kinesthetic representations
• Short Quiz

Lesson Plans
Investigation 1.1
Designing Bumper-Car Rides
1 hour

Investigation 1.2
Decoding Designs
1 hour

Investigation 1.3
Computing Costs
1 hour

Investigation 1.4
Getting Your Money’s Worth
1 hour

Assessment
Mathematical Reflections, journaling, quiz
1 hour

Teacher Notes

Curriculum Development Resources
Access the links below to access additional resources used to design this unit: www.math.msu.edu/cmp

Lesson Plan 1
Content Area: Mathematics
Grade: 7th Special Education
Lesson Title: Covering and Surrounding Investigation 1
Timeframe: 5 days

Lesson Components

21st Century Themes
Global Awareness
Financial, Economic, Business, and Entrepreneurial Literacy
Civic Literacy
Health Literacy

21st Century Skills
x  Creativity and Innovation- (see Learning Activities 1 & 2)
Media Literacy
x Critical Thinking and Problem Solving- (see Learning Activities 3 & 4)
ICT Literacy
x Communication and Collaboration-(see Learning Activities 1 & 2)
x Life and Career Skills-(see Learning Activities 1 & 2)
Information Literacy
Interdisciplinary Connections: Literature and Science
Integration of Technology: Smart Board/projector, Document Camera,                 http://www.shodor.org/interactivate/activities/AreaExplorer/,   http://www.shodor.org/interactivate/activities/PerimeterExplorer/, Students will be encouraged to use www.phschool.com (Web Code: ame-9031) for homework support and/or in class.
Equipment & materials needed:

• Centimeter grid paper (TG page 145) and Inch grid paper or one-inch tiles BLM (TG 148)
• inch square tiles (36 per student)
• Transparency (1.1, TG pages 120) page
• notebooks/journals
• calculators
• white board
• Smart Board/projector
• document camera
• Connected Mathematics: Covering and Surrounding Teacher’s Guide
• blank transparencies
• Patty Paper

Goals/Objectives/CPIs
Students will explain (orally or in writing) with 75% accuracy that:

• area of a 2-dimensional figure is the number of square units needed to cover it.
• perimeter of a 2-dimensional object is the number of units of length needed to surround it

Learning Activities/Instructional Strategies

• Engagement Describe an amusement park company to the students.  The square tiles they will be working with are similar to what the designers use to make their models of bumper car floor plans.  The students will work in pairs or small groups to arrange 24 tiles in different ways so that different numbers of rail sections are required.  Information gathered will be recorded in a table with a column for the number of tiles and another column for the number of rails each arrangement makes.  The pairs/groups need to discuss their findings in experiment with tiles.
1. Exploration Next, they will use 36 tiles for the floor and 26 rails and make sketches of their possible floor plans.  This is when the terms area and perimeter will be introduced and used in describing area and perimeter of a given floor plan.
2. Explanation The class will discuss/show/present choices of designs and the advantages/disadvantages of each and how they meet the requirements.  Students should realize that they are counting the square tiles covering the figure when they are measuring area, and they are counting the number of units surrounding a figure when they are finding perimeter.  If not, possible questions may be: “What are you actually counting when you measure area?”  “What are you actually counting when you measure perimeter?”   The children should see the differences in perimeter and area and how each should be labeled.  Questions to be discussed are: “What is the greatest perimeter anyone found for a floor plan of 36 tiles?”  “What is the least perimeter for a floor plan of 36 tiles?”
3. Elaboration Centers will be set up for children to use: story books (see Multiple Means of Representation #2 below for details), computers (see Multiple Means of Action and Expression #2 below for details), or demonstrations (see Multiple Means of Engagement #2 below for details).
4. Evaluation Class discussion/participation (page 5-6 Problem 1.1), Exit Ticket, Homework (page 10 ACE #1)

Short Quiz (on the last day of Investigation 1):  1.  Create a bumper car floor with a perimeter of 12 on grid paper or with square tiles.   2.  Create a bumper car floor with an area of 12 on grid paper or with square tiles.   3.  Explain the advantages/disadvantages of several given design choices.

Universal Design for Learning Options

 Multiple Means of Representation Perception Centimeter and inch grid paper will be used as well as square tiles to manipulate.  Additionally, the document camera will be used to show/display designs along with “Geometer’s Sketch Pad” on the computer.  Designs will be discussed and explained.  (see Learning Activities # 1-3 above) Language & symbols Students will circulate to different stations and work independently, with a peer or in a small group.  (The grouping will be decided on based on student preference and skill level.)  One center will require the students to read low level children’s literature book(s) that incorporates math into the story line.  The stories explore geometry and the terminology in a fun way.  Depending on what skill/term an individual is struggling with, they will be assigned different stories.  (Focus will be on:  Terms having to do with polygon properties will read Shape Up!  Fun with Triangles and Other Polygons and then create shapes and label them on grid paper or using pretzel sticks, or write a poem, rap or song about the shapes; Finding Area and Perimeter will read Spaghetti and Meatballs for All! and then go back through the story and draw on grid paper or create with pretzel sticks each arrangement of tables and find the area and perimeter, write a poem, rap or song about how to find area and perimeter, or suppose there were going to be 12, 16, 24, 36 people at the reunion; and find the different arrangement of tables (which requires the fewest tables which requires the most tables); For fun or extra practice The Warlord’s Kites and then the students may create the kite suggested at the end of the story or create one of their own design.)  (see Learning Activities # 4 above) Comprehension Activities from the reading (see above) and the Investigations will allow the students to see the different shapes and what designs provide longer/shorter perimeter and what designs produce larger/smaller areas.  (see Learning Activities # 1-4 above)
 Multiple Means of Action and Expression Physical activity The square tiles will allow the students to manipulate the tiles to physically experience the finding of perimeter and area.  This activity is the initial activity (Investigation 1.1).  It will let me determine ability levels for the next activities.    (see Learning Activities # 1 above) Expressive skills and fluency Tile and grid designs will be shown and manipulated on the document camera.  Again, depending on skill levels, another center will have the students creating polygons on “Geometer’s Sketch Pad” on the computer where the figures can be shown, manipulated, and measured to find perimeter/area, or using http://www.shodor.org/interactivate/activities to focus on perimeter and/or area.  (see Learning Activities # 4 above) Executive functions Class presentations and discussions as well as exit tickets will allow the pupils to demonstrateknowledge/skills gained.  The exit tickets will be used to group students in the following day’s activities.  (see Learning Activities # 3-5 above)

Multiple Means of Engagement

1. Recruiting interest Working with the tiles (in Investigation 1.1) is something that most students find enjoyable.  Plus, many pupils are excited by the prospect of an amusement park.  We are using the real life problem of the size and shape of a bumper car floor to hook the students.  (see Learning Activities # 1 above)
2. Sustaining effort and persistence The classes often find that their peers have differing ideas of what floor plan is the best.  The final centers will be groups doing the investigations from Covering and Surrounding.  The desire to prove why their floor plan is the best allows the competitive nature of many middle school students to be useful.  (see Learning Activities # 3 above)   An additional center will have students using the Smart Board to demonstrate and record finding area and perimeter, or pupils may also use Flip-Video Cameras to record strategies for finding area and perimeter.  (see Learning Activities # 4 above)
3. Self-regulation Students will start with finding perimeter and area using manipulatives, move to grid paper, and then, to figures with side lengths labeled.  For advanced individuals, figures may need to be measured or side lengths discovered by using a key that indicates how long 1 unit is.  In much of this investigation, the students are assigned a task, but then are given the ability to do the assignment using the tools they like best and choose the design that works better for them.  There is no right or wrong answer as long as they stay within the assigned guidelines and are able to show/explain why/how their design fits the criteria.  (see Learning Activities # 3-4 above)

Resources