Lesson: V
Title: Inside Outside
Grade Level: 4-6
Subject: Mathematics//Geometry/ Problem Solving/ Reading Comprehension/ Listening/Speaking/ Technology/Writing/Measurement
Learner Outcomes: Student will:
Spaghetti and Meatballs for All! By Marilyn Burns
The Relatives Came: Cynthia Rylant
Rubber bands
One inch Color Tiles
Chart
Calculators
Centimeter square graph paper
Overhead copy of centimeter graph paper
Inch square graph paper
Overhead copy of the inch square graph paper
Math journal/notebook or teacher created sheet
Pencils
Scissors
Glue/tape
Crayons
Paper: Construction paper whole sheets, 1/2 sheets of 8
1/2" x 11"
Yarn or string
Rulers: dual measurement cm/inches
tape measures
centimeter cubes
geoboards and bands or geoboard graph paper
Overhead projector
Overhead centimeter cubes
Overhead Color Tiles
Overhead Geoboard and geobands
Pattern Blocks
Paper clips
Doghouse Problem Worksheet
Technology/Tools/Courseware:
Overhead projector
Calculators
Computer: Multimedia
Browser
Teacher Notes:
Prepare overhead copies of a T-Chart, centimeter graph paper and inch graph paper for group usage.
Procedures:
Perimeter:
1. Assign each child a partner to work with cooperatively. Give
each pair of children a sheet of plain paper and have them create a T-Chart.
Label one side of the paper area and the other side perimeter.
2. Partners will work cooperatively to list anything that they know
about area and perimeter. (One child will be the recorder and the other
child will be the reporter) i.e.. What it area/perimeter?, How do we measure
area/perimeter?,
Why do we need to know about area/perimeter? (everyday applications?)
3. Have the reporter from each group verbalize their statements. The teacher will make a group recording on the overhead T-Chart, discuss the statements.
4. Develop a working definition for perimeter and area. Write the definition on chart paper, display these papers in the room so as to add to or delete from the classroom definition as the lesson progress.
5. Retain each group's T-Chart and the class T-Chart for an additional lesson and assessment.
6. Pass out the geoboards/bands. Free exploration. (Classroom management tip: Demonstrate how to use the geobands. One flying band is an accident. The second flying geoband, the geoboard and bands belong to the teacher.)
7. Model creating a rectangular shape on the overhead geoboard i.e..length 4 pegs, width 3 pegs. Have the children create the same shape with you. Count the units of length and width. A unit is the distance between two pegs. What would be the perimeter of the rectangle, distance around the outside edges of the rectangle. (4 + 3 + 4 + 3 = 14 units) Repeat with other examples.
8. When the children are comfortable with this activity have them
create figures that are not rectangles. (Teacher Note:
Be sure that the children do not make any figures that have slanted
lines). Each child should compute the perimeter of their figure
and share it with a cooperative group/partner/or whole group. Check
for accuracy.
9. Give each child a copy of the centimeter graph paper. Have
each child cut a 6 x 6 centimeter square from the paper.
Discuss the perimeter of the square.
10. Have the children cut their individual square into two or three
pieces and put the pieces together to form a new shape.
Tape the pieces together. Question: Is the perimeter of your
new shape the same as the perimeter of the original shape?
Why or Why not? Children write their explanation in their math journals.
11. Have the children find other class members who have the same perimeter. Compare the new shapes with in the group. Ask the children to form some general statements that they can make about their group shapes.
12. Create a floor graph with the newly created shapes, grouping the shapes according to their perimeters. Ask the class to make generalizations about these perimeter groups i.e.. Our perimeter is less than 24 cm because..., Our perimeter is greater than 24 cm because...
13. Ask each child to cut out a random shape from a half sheet of construction paper. Question: What is the perimeter of your new shape? Children will problem solve and devise a method for finding the area of the randomly cut shape. Provide various materials for the children to explore with i.e.. centimeter cubes, rulers, yarn, string, and tape measures.
14. Each child glues their random shape to a sheet of construction paper
and writes an explanation of how they found the perimeter of the shape.
Illustrations may also be added to the explanation. Exchange only the random
shape sheet
with a partner and have him/her find the perimeter of the shape and
write about his/her solution. Compare the two
solutions and discuss. Use a calculator to check the perimeter of the
shapes.
15. Class discussion. Revisit the original T-Charts and chart definitions, add to or delete from each to come to a consensus opinion as to the definition and formula for finding the perimeter. Once the formula has been decided upon, use several shapes to find the perimeters. Show the actual formula, compare with the class created formula. (P=2w + 2l)
Area:
1. Review the class definition of area on chart
.
2. Read and discuss Spaghetti and Meatballs
for All! What is Mrs. Comfort's problem? What are the facts necessary
to solve the problem?
3. Distribute zip lock bags containing 32 one inch Color Tiles and 1" graph paper . Problem: Arrange the tiles in a way to seat the 32 relatives. (Teacher Note: See the back section of Spaghetti and Meatballs for All! for solutions).
4. Have the children place the Color Tiles on the one inch graph paper in various arrangements to accommodate the seating of the 32 relatives. Trace the created shapes on to the 1 inch graph paper, check to be sure that the table (s) will seat 32 people. Use smalls x's to represent each relative. (Children will need more than one sheet of graph paper for this activity.)
5. As each seating arrangement is created, have the children count the
total number of square units that are covered by
the Color Tiles. This will be the area of the seating arrangement.
6. Group activity: Have individual children demonstrate their
seating arrangements on the overhead. (Note: There are 8 different
ways to arrange the tables.) What is the area of each of the
seating arrangement? How did you figure the
area?
7. Have the children create four sided figures on the geoboards. Review the concept that a unit of area is equal to 1 square on the geoboard, the area that is within four pegs. Each child counts the number of square units within the four sided figure that he/she created.
8. Revisit the original class definition of area. Make any necessary additions or corrections to the definition. What do you think would be a good formula to find the area of an object? Use several of the arrangements to prove that the formula the class devised is correct. Write the correct formula, compare. A= l x w
Modifications:
Adjust the lesson to meet the individual needs of the students. Enlarge materials for the children with visual handicaps or develop materials that are tactile. Using glue to create raised perimeters on the graph paper is an example of a modification that could be made. MI, Multiple Handicapped, or EMI children could work with an instructional aid, parent volunteer, classroom peer/peers, or cross grade tutor to complete the unit activities.
Extensions:
Area and Perimeter:
1. Each child needs 2 sheets of centimeter graph paper. (Teacher Note: Model this activity on the overhead for the class.) Divide the graph paper into equal sections measuring 5cm by 4cm. The children will write a letter of the alphabet in each divided section of the graph paper in block print, one block wide. Color the letters shapes. Using centimeter cubes, find the area and perimeter of each letter. Record the area (A =) and the perimeter (P =) in each letter box. Partner check. Save for assessment.
2. Use pattern blocks to practice the concept of area. Designate the small triangle pattern block to equal 1 square unit. Have the children cover some of the other pattern block shapes with the 1 square unit in order to find the area of the larger shapes. What is the area of the larger shape? This activity can be done as a group on the overhead using overhead pattern blocks. A group discussion of the area of the larger pattern blocks and their relationship to the the 1 square unit (triangle) can provide an opportunity for further assessment.
3. Use this activity for developing concepts of area and perimeter and how they are related. Give each child a zip lock bag with 15-20 paper clips. Allow for free exploration with the paper clips in the creation of shapes. Give each child Doghouse Worksheet. Problem:Help this boy build a pen for his dog using paper clips to form the sides of the pen in the space below. Make the biggest space you can so the dog will have plenty of room. What is the perimeter and the area of your dog pen? Explain how you found your answers in your math journals. Additional Activities: Good number of paper clips to use are: 24, 36, 48, and 64 because of the greater number of factors available.
4. Read The Relatives Came by Cynthia Rylant. Discuss the problem of having enough room for the relatives to sleep in the house. Each child will solve the space problem by assigning the relatives a certain amount of floor space. Give each child a sheet of inch graph paper, using pencils and then crayons, the children with indicate sleeping areas on the floor. The children will write the area and perimeter in each space.
Evaluations/Assessments:
Evaluation will be taken through teacher observations of the children working in small and cooperative groups, math journal entries, worksheets, and listening to the children verbalize an explanation of the activities in which they are participating.
State Standards:
West Virginia Instructional Goals and Objectives
Listening/Speaking: 4.9, 4.11, 5.13, 6.14,
Reading Comprehension: 4.26, 4.29, 5.15, 6.16, 6.30
Writing: 4.53, 5.60, 6.54
Measurement: 4.41, 4.42, 4.43, 5.40, 5.41, 6.41
Technology: 4.50, 4.52, 5.47, 5.50, 6.48, 6.49,
References/Resources:
Math by All Means: Area and Perimeter
by Cheryl Rectanus
STRETCH-IT!
Enrichment:
Web sites:
Area
and volume
Area
Good activities for use a computer station or to use with Data Projector
or LCD Panel:
Interactive Geometric
Concentration Game
Matching Geometric
Terms Game
Interactive Wordsearch,
Geometric Terms
Flash Cards Geometric
Terms (Interactive)
Matching Interactive
Introduction to Angles
Vocabulary:
perimeter: distance around a shape measured in units of length
area: the space a shape's surface covers and is measured in
square units
formula: a rule used to solve a math problem
Literature Connection:
Jeanne Beard
Linda Hull
Connie Miragliotta
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