ME3-11 Measuring Perimeter
Goals: Students will estimate and measure perimeters using non-standard units.
Prior Knowledge Required: What measurement means
Practice and comfort with other forms of linear measurement and nonstandard unit use
How to count
Add strings of 1-digit numbers
Vocabulary: perimeter, around, area
Hold up a piece of artwork. Ask students what parts of the artwork they would need to measure in order to
frame the picture. Then, ask how many link cubes or pattern block triangles it might take those
measurements.
Draw a rectangle on the board (22 cm × 30 cm) and demonstrate how to line up the link cubes along the
border of the rectangle. Note the importance of only counting the units whose edges touch the edge of the
object being measured. Review the importance of ensuring that units are lined up in a straight line and that
they touch sides but do not overlap.
Next, ask students what they would do if they only had one link cube to measure the distance around the
rectangle. Show students how to use only one unit and make marks to show where the unit starts and
finishes so that they can keep track of what they have measured.
As you line up the link cube, create a number sentence which encompasses the length and width of each
side, e.g., ____ + ____ + ____ + ____ = ____
Ask students if they know what the mathematical term is for measuring distance around an object. If they do
not say perimeter, introduce the term and explain that when measuring perimeter, they are measuring the
“outside edge of any area.” As you explain, use the rectangle from before and with a marker/chalk, go over
the outside edge of the shape to reinforce the concept. You may also want to write this on a sentence strip
and post it somewhere in the classroom for easy student reference.
Challenge students to come up to the board to create two shapes, one which would have a smaller
perimeter, and one with a larger perimeter than the rectangle used to demonstrate the concept of perimeter.
Other students can predict what the perimeter of each is and then test and measure the shapes. Encourage
students to write corresponding number sentences to find each shape’s perimeter.
Be prepared to address concerns about half units and get students to think of solutions. Possible solutions
could be to write that the perimeter is about X units, while some students may realize that if they have two
halves, that makes a whole and they would add it to the total of units.
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Activities:
1. Have students work in partners to measure the distance around various objects in the classroom using
link and/or unit cubes and check each others measurements for discrepancies.
2. Give students link cubes and ask them to create various shapes with a perimeter of 12 cubes.
3. Have students create fences for fields by using 4 pieces from a tangram set (two small triangles, medium
triangle, and square). Challenge them to make different shaped fields with the same four pieces. Have
them measure the perimeter with a link cube. Does the P remain the same? Why or why not?
Literature/Cross Curricular Connection:
How big is a foot? R. Myller
(The King wants to order a bed for his Queen but beds have not yet been invented. Begin the story and stop
at the point of figuring out how big the bed should be. Have students brainstorm how to solve this dilemma.
They should be focusing on figuring what perimeter the bed should be. Encourage them to use actual size to
solve the problem, and then give them grid paper to record a solution with a partner. They then will write a
letter to the King’s apprentices to explain their work and thinking. Have a group discussion to compare pairs’
solutions and then finish reading the story to them to find out how the characters solved the problem.)
Extensions:
1. What unit of measurement would students use to measure the distance around the classroom? What
would be most effective and efficient? Find out the perimeter of the classroom. (Giant steps?)
2. Have students draw a square that has a perimeter of 12 cubes. Have them figure out the length of each
side. Next, tell them to draw a rectangle that has a perimeter of 12 cubes and tell what the length of each
of the sides will be. Finally, have them draw a triangle with a perimeter of 12 cubes and have them figure
out the length of each of the sides.
3. Paul bought 13 bushes to place around the perimeter of his yard (shown in the diagram below).
For each edge of the diagram, he planted one bush. He measured the perimeter before going to the
nursery but he thinks he made a mistake because he doesn’t have enough bushes. Can you help him?
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ME3-12 Perimeter
Goals: Students will estimate and measure perimeters using the standard and non-standard units.
Prior Knowledge Required: What measurement means.
Practice and comfort with linear measurement and
non-standard unit use.
How to count.
Vocabulary: perimeter, around, area, cm
Write the word “perimeter” and explain to your students that perimeter is the measurement around the
outside of a shape. Illustrate the perimeters of some classroom items; run your hand along the perimeter
of a desk, the blackboard or a chalkboard eraser. Write the phrase “the measurement around the outside
of a shape.”
Draw this figure:
1 cm
Explain that each edge of the squares represents 1 cm, and that perimeter is calculated by totalling the
outside edges. Demonstrate a method for calculating the perimeter by marking or crossing out each edge
as it is counted. Demonstrate this several times.
Examine the figure again. Squares have four sides, so why is the perimeter only 10 cm and not 16 cm
(4 × 4)? Remind your students that perimeter is the measurement around the outside of a shape.
The squares on the ends each have three outside edges. The squares in the middle have two outside
edges. The inside edges—sides that touch—are not totalled in the perimeter. Refer your students to the
definition again.
Ask them why they might want to know the perimeter of an object. (To border a picture with ribbon? To wrap
a present? To fence in a garden?)
Demonstrate another method for calculating perimeter by counting the entire length of one side, instead
of counting one edge at a time, then adding the lengths. Remind your students that addition is a quick way
of counting.
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Activity: Distribute one piece of string, about 30 cm long, and a geoboard to each student. Have them tie
the ends of the string together to form a loop, and then create a variety of shapes on the geoboard with the
string. Explain that the shapes will all have the same perimeter because the length of the string, which forms
the outside edges, is fixed. How many different shapes can all have the same perimeter?
Extension: Distribute Pentomino pieces (a set of twelve shapes each made of five squares – see the
BLM) to your students and have them calculate the perimeter of each shape. Create a table and order the
perimeters from smallest to greatest. Have students also calculate the amount of square edges inside each
shape. Can they notice a pattern emerging in the table?
Shape
Perimeter
Number of Inside Edges
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ME3-13 Exploring Perimeter
Goals: Students will measure perimeters of given and self-created shapes.
Prior Knowledge Required: Perimeter
Practice and comfort with linear measurement and
non-standard unit use
How to count
Add strings of 1-digit numbers
Vocabulary: perimeter, around, grid paper
Review the perimeter, its definition and how it is calculated by totalling the outside edges of a figure.
Demonstrate the method for calculating perimeter by counting the entire length of each side and creating an
addition statement. Write the length of each side on the picture. Draw several figures on a grid and ask your
students to find the perimeter of the shapes. Include some shapes with sides one square long, like the shape
in the assessment exercise, as students sometimes overlook these sides in calculating perimeter. Ask your
students to draw several shapes of their own design on grid paper and exchange the shapes with a partner.
For the last exercise, suggest that students draw a letter, or simple word (like CAT), or their own names.
Assessment:
Write the length of each edge beside each edge and count the perimeter of this shape.
Do not miss any sides—there are ten!
2 cm
Extensions:
1. Explain that different shapes can have the same perimeter. Have your students draw as many shapes as
they can with a given perimeter (say ten units). (From the Western Curriculum)
2.
Can a rectangle be drawn with sides that measure a whole number of units and have a perimeter…
a) of seven units?
b) with an odd number of units?
[Both are impossible.]
Students can use a geoboard rather than grid paper, if preferred.
3.
Create three rectangles with perimeters of 12 cm. (Remember: A square is a rectangle.)
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