Lesson · Grade 5 · Mathematics
Same Perimeter, Different Areas
- Grade 5
- Mathematics
- 1 min 25 s
- British Columbia
- BC5-MA-28
A 14 m fence is bent into three rectangles, 6 m by 1 m, 5 m by 2 m and 4 m by 3 m, and each time the sides add up to the same 14 m while 1 m squares fill areas of 6, 10 and 12 square metres. A table collects the three results, shows that the shape closest to a square holds the most area, and ends on the recap that the same perimeter can mean different areas.
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In one sentence
The question this lesson answers
Here is a fence that is 14 metres long.
Will every rectangle we make with it have the same area?
Transcript
What the lesson says
Here is a fence that is 14 metres long.
Will every rectangle we make with it have the same area?
Bend it into a rectangle 6 metres long and 1 metre wide.
Add the four sides to get the perimeter: 6 plus 1 plus 6 plus 1 is 14 metres.
The area is length times width: 6 times 1 is 6 square metres.
Now reshape the same fence into a rectangle 5 metres by 2 metres.
5 plus 2 plus 5 plus 2 is still 14 metres.
But the area is now 5 times 2, which is 10 square metres.
Now try a rectangle 4 metres by 3 metres.
4 plus 3 plus 4 plus 3 is 14 metres again.
Even more area: 4 times 3 is 12 square metres.
All three have the same perimeter of 14 metres, but their areas are 6, 10 and 12 square metres.
Of these three, the one closest to a square has the most area.
Rectangles with the same perimeter can have different areas.
Curriculum
Where this fits
- British Columbia, Grade 5
Mathematics, Geometry and measurement: relationships between area and perimeterBC5-MA-28
Previous: Area and Perimeter: What Is the Difference?Next: How Long Is the Movie? Counting On to Find Elapsed Time
The outcomes and strands follow the British Columbia curriculum.
Keep going
1 min 12 s3:15 p.m. or 15:15? Morning, afternoon and the 24-hour clock
Grade 4 · 1 min 12 s
1 min 26 s3D Objects: Faces, Edges and Vertices
Grade 3 · 1 min 26 s
1 min 21 sArea and Perimeter: What Is the Difference?
Grade 5 · 1 min 21 s
1 min 5 sArea of a Circle from the Radius or the Diameter
Grade 7 · 1 min 5 s
1 min 14 sArea of a Parallelogram: Cut and Slide into a Rectangle
Grade 6 · 1 min 14 s
1 min 18 sArea of a Rectangle: Count the Squares, Then Multiply
Grade 5 · 1 min 18 s
1 min 16 sArea of a Trapezoid: Two Copies Make a Parallelogram
Grade 6 · 1 min 16 s
1 min 19 sArea of a Triangle: Half of a Parallelogram
Grade 6 · 1 min 19 s
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