#### Math - 2017-18

# 6.10abc and *6.7 - Area, Perimeter, Circumference

**6.10abc ** The student will

a) **define
**pi (π) as the ratio of the circumference of a circle to its diameter;

b) **solve
**practical problems involving circumference and area of a circle, given the
diameter or radius;

c) **solve **practical problems involving area and perimeter;

6.7The student willa)

deriveπ (pi);b)

solveproblems, including practical problems, involving circumference and area of a circle; andc)

solveproblems, including practical problems, involving area and perimeter of triangles and rectangles.

**Bloom's Level:** Remember, Apply

*Adopted: 2009*

### BIG IDEAS

- I can make a tent by determining the square feet of canvas needed for 4 walls and floor, how much netting is needed for the door, and how long a zipper will surround the door opening.

- I will be
able to find area, perimeter, circumference, and surface area as appropriate in
various situations.

### UNDERSTANDING THE STANDARD

- Experiences in deriving the formulas for area,
perimeter, and volume using manipulatives such as tiles, one-inch cubes, adding
machine tape, graph paper, geoboards, or tracing paper, promote an
understanding of the formulas and facility in their use.†
- The perimeter of a polygon is the measure of the
distance around the polygon.
- Circumference is the distance around or
perimeter of a circle.
- The area of a closed curve is the number of
nonoverlapping square units required to fill the region enclosed by the curve.
- The perimeter of a square whose side measures
*s*is 4 times*s*(*P*= 4*s*), and its area is side times side (A = s^{2}). - The perimeter of a rectangle is the sum of twice
the length and twice the width [
*P*= 2*l*+ 2*w*, or*P*= 2(*l*+*w*)], and its area is the product of the length and the width (*A*=*lw*). - The value of pi (π) is the ratio of the
circumference of a circle to its diameter.
- The ratio of the circumference to the diameter
of a circle is a constant value, pi (π), which can be
approximated by measuring various sizes of circles.
- The fractional approximation of pi generally
used is 22/7.
- The decimal approximation of pi generally used
is 3.14.
- The circumference of a circle is computed using
*C*=*πd*or*C*= 2*πr*, where*d*is the diameter and*r*is the radius of the circle. - The area of a circle is computed using the
formula ,
*A*=*πr*where^{2}*r*is the radius of the circle. - The surface area of a rectangular prism is the
sum of the areas of all six faces (
*SA*= 2*lw*+ 2*lh*+ 2*wh*). - The volume of a rectangular prism is computed by
multiplying the area of the base, B, (length x width) by the height of the
prism (
*V*=*lwh*=*Bh*).

2016 VDOE Curriculum Framework - 6.7 Understanding

· The value of pi (p) is the ratio of the circumference of a circle to its diameter. Thus, the circumference of a circle is proportional to its diameter.

· The calculation of determining area and circumference may vary depending upon the approximation for pi. Common approximations for π include 3.14, , or the pi (p) button on a calculator.

· Experiences in deriving the formulas for area, perimeter, and volume using manipulatives such as tiles, one-inch cubes, graph paper, geoboards, or tracing paper, promote an understanding of the formulas and their use.

· Perimeter is the path or distance around any plane figure. The perimeter of a circle is called the circumference.

· The circumference of a circle is about three times the measure of its diameter.

·
The
circumference of a circle is computed using *C*
= π*d* or C = 2π*r*, where *d* is the
diameter and *r* is the radius of the
circle.

· The area of a closed curve is the number of nonoverlapping square units required to fill the region enclosed by the curve.

·
The area of
a circle is computed using the formula *A*
= π*r*^{2}, where *r* is the radius of the circle.

·
The
perimeter of a square whose side measures *s*
can be determined by multiplying 4 by *s *(*P* = 4*s*),
and its area can be determined by squaring the length of one side (*A* = *s*^{2}).

·
The
perimeter of a rectangle can be determined by computing the sum of twice the
length and twice the width (*P* = 2*l* + 2*w*,
or *P* = 2(*l* + *w*)), and its area can
be determined by computing the product of the length and the width (*A* = *lw*).

·
The
perimeter of a triangle can be determined by computing the sum of the side
lengths (*P = a + b + c*), and its area can be determined by
computing 1/2 the product of the base and the
height (A = 1/2 bh).

### ESSENTIALS

- What is the relationship between the
circumference and diameter of a circle?

The circumference of a circle is about 3 times the measure of the diameter. - What is the difference between area and perimeter? Perimeter is the distance around the outside of a figure while area is the measure of the amount of space enclosed by the perimeter.

**The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and representations to**

6.10a_{1} **Derive**
an approximation for pi by gathering data and comparing the circumference to
the diameter of various circles, using concrete materials or computer models.

·
6.7a_{1} **Derive**
an approximation for pi (3.14 or )
by gathering data and comparing the circumference to the diameter of various
circles, using concrete materials or computer models.

6.10b_{1} **Find**
the circumference of a circle by substituting a value for the diameter or the
radius into the formula C = πd or C = 2πr

6.10b_{2} **Find**
the area of a circle by using the formula A = π

·
6.7b_{1} **Solve**
problems, including practical problems, involving circumference and area of a
circle when given the length of the diameter or radius.

6.10b_{3} **Create**
and **solve** problems that involve
finding the circumference and area of a circle when given the diameter or
radius.

6.10c_{1} **Apply**
formulas to solve practical problems involving area and perimeter of triangles and
rectangles.

·
6.7c_{1} **Solve**
problems, including practical problems, involving area and perimeter of
triangles and rectangles.

### KEY VOCABULARY

formula, area, perimeter, volume, polygon, circumference, closed curve,
sum, twice, length, width, height, product, pi, diameter, radius, relationship,
surface dimension, base

*Updated: Oct 27, 2017*