Activities on
Perimeter and Area
TABLE OF CONTENTS
Introduction
BORDER PROBLEMS:
AREAS OF OTHER
POLYGONS:
Perimeter - Circumference
Triangles, Trapezoids, and Other Shapes
5
8
9
11
13
14
16
17
18
19
Introduction to Border Problems
Fast 4!
Perimeter Patterns
Perimeter Puzzles
The Grid Game
Custom Fences
The "Min Wins" Game
Frisbee Go-Round
Circumference Dominoes
Performance Assessments
AREA STRATEGIES:
Rectangles - Parallelograms
21
24
25
26
27
28
29
30
31
Introduction to Area Strategies
Fast 4!
Exploring Rectangles
A Space-Saving Design
Rolling Rectangles Game
Parallel Play
Max/Min Problems
Dream House Design
Performance Assessments
LER 8520 — Measure and Solve: Area & Perimeter Book
32
35
36
37
38
40
41
43
45
48
Introduction to Areas Of Other
Polygons
Fast 4!
The Tangram Puzzle
Area Art
Capture the Tanks
Pattern Block Polygons
Area Bingo
Trapezoid Patterns
Quilting Bee
Performance Assessments
AREA OF CIRCLES
49
52
53
55
57
59
60
62
63
64
Introduction to Area of Circles
Fast 4!
Inner - Outer Areas
Square a Circle
Chocolate Chip Cookies
Close To 3000 Game
Performance Assessments
1/4" Grid Paper
Pattern Block Blackline Master
Color Tile Blackline Master
© Learning Resources, Inc., Vernon Hills, IL 60061 (USA)
Activities on
Perimeter and Area
INTRODUCTION
Measure and Solve: Perimeter and Area provides ideas for engaging grade 5-8 students in problem-centered activities, games, and projects involving perimeter and area. Pattern blocks, color
tiles, and tangrams are used throughout the activities of this resource book as students explore
ideas and problem-solve. Fast 4! section openers pose shorter, targeted problems to reinforce
learning on an on-going basis. Performance assessments at the end of each section suggest
tasks to help teachers profile students’ understandings. In addition, applied problems and technology integration are present throughout the book.
This resource may be used as a unit for instruction on measurement. As such, it is divided into
four sections that focus on important aspects of measuring perimeter and area.
• Border Problems: Perimeter and Circumference
• Area Strategies: Rectangles and Parallelograms
• Areas of Other Polygons: Triangles, Trapezoids, and Other Shapes
• Area of Circles
Each section begins with an introduction page which highlights the key vocabulary and important
concepts presented in the pages that follow. Most activities and games assume that students will
work collaboratively with a partner and have ready access to available technology and materials
necessary to communicate their ideas and findings. Features which recur throughout this book
to support these actions are:
A list of materials necessary for the activity.
Activities and suggestions which allow students to explore or review
understandings critical to the central TASK of a lesson.
The major problem which guides the activity or project.
Questions which might be asked by the teacher or otherwise be presented, to
provide opportunity for students to respond orally or in their math log to
communicate their mathematical understanding.
Questions or ideas posed to prompt an understanding of how or why a
concept works.
Calculator or computer alternatives that may be integrated.
Natural extensions of a game or activity.
LER 8520 — Measure and Solve: Area & Perimeter Book
© Learning Resources, Inc., Vernon Hills, IL 60061 (USA)
Perimeter
What patterns can you find?
PERIMETER PATTERNS
Generous supply of pattern blocks for each pair of students, Math Log,
writing utensil.
With a partner, make a train of six hexagons. As you add each hexagon,
record the perimeter of the train in the chart below. Then answer the questions that
follow in your math log.
# of hexagons
Perimeter of Train
1
2
3
4
5
6
n
• How did the train's perimeter grow with each additional hexagon?
• Explain why the perimeter increased as it did, not increase by 5 units each time?
• Write an expression for the perimeter of any hexagon train.
Use n to stand for the number of hexagons. P = ______
Use pattern blocks to create each of the first three steps in the triangular
number pattern. Sketch the first four steps in your Math Log.
• What type of pattern is this?
• Describe how the perimeter increases in each step.
Extra for Experts: Write a mathematical expression to describe this increase.
• What pattern do you notice with the shaded interior regions?
LER 8520 — Measure and Solve: Area & Perimeter Book
© Learning Resources, Inc., Vernon Hills, IL 60061 (USA)
Perimeters of Polygons
A Partner Game
THE GRID GAME
For each pair of students: Grid paper, 2 (1-6) dice,
two differently colored pencils.
Objective: Given an area, cover the most space on
the grid by creating polygons with the
greatest possible perimeter.
GAME RULES
•
•
•
•
Players choose a color.
Each player rolls a die. Highest roll goes first.
In turn, roll and add the numbers on two dice.
On the grid, outline and color a polygon having an area equal to
the dice sum. Polygons cannot overlap on the grid.
• Count and record the polygon’s perimeter.
• The game ends when both players have rolled areas that cannot
fit on the grid.
• The player with the higher total perimeter wins!
Player A:
Perimeter
Player B:
Perimeter
• Which strategies could be used to get the greatest possible perimeter?
• Explain the strategies you used to block your opponent.
• How can a given area have different possible perimeters?
LER 8520 — Measure and Solve: Area & Perimeter Book
© Learning Resources, Inc., Vernon Hills, IL 60061 (USA)