# Carpentry T Chart Duty Hand Tools Task Layout and

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```					Carpentry T-Chart                                          Radius = Radius
PSSA Eligible Content – M11.C.1.1.1
Duty: Hand Tools                          Identify and/or use the properties of a radius,
Task: Layout and cut patters              diameter and/or tangent of a circle (given
numbers should be whole)

MATH ASSOCIATED WORDS:
CARPENTRY ASSOCIATED WORDS:
TERM - BRACE, AUGER, BORING BIT,
PERPENDICULAR, CONCENTRIC
CIRCLES.

Formula (type purpose of formula here):   Formula (type purpose of formula here):

PDE/BCTE Math Council
TEACHER’S SCRIPT FOR BRIDGING THE GAP

In both Carpentry and in Math Class you learn about the relationship between radius and
diameter.
How are the concepts similar?
These concepts are very similar in both classes.
How do the concepts differ?
In Carpentry there are many additional terms and tools you use associated with radius and
diameter.
In Math Class we study the concept of tangent as well as radius and diameter.
A tangent touches the circle in exactly one point and is perpendicular to the radius of the circle
at that point.

Common Mistakes Students Make
A common mistake that students make in interpreting drawings in both mathematics and
carpentry is confusing the radius of a circle to the radius of a corner in a diagram.
Another common error is to include the diameter of a circle as a part of the length the
rectangular portion of an irregular figure that contains a rectangle with a semi-circle on each
end.

PDE/BCTE Math Council
Occupational (Contextual) Math Concepts

1. If a circle has a radius of 7 yards what is the diameter?

2. If a circle has a diameter of 18 feet what is the radius?

3. If the radius of a circle is 4 inches and the corner radius is 9 inches,
how far should the circle measure from the corner of the pattern?
Related, Generic Math Concepts
For the following problems use the figure below.

1. If AB = 15, then what is AC?
2. If BO = 3, and AO = 5, what is the length of AB?
3. If BO = 12, what is the length of CO?

<"http://etc.usf.edu/clipart/""Visit Clipart ETC for a great collection of clipart for students and teachers."

PSSA Math Concept Look

1. If the radius of one circle is 3 feet and the radius of another circle is 10 feet,
what is the difference in their diameters?

2. If concentric circles have diameter of 16 inches and 22 inches,
what would be the shortest distance connecting the two circles?

3. If a tangent segment to a circle with a radius of 3 feet measures 4 feet,
what is the distance from the endpoint of the tangent segment outside the circle?

PDE/BCTE Math Council
Occupational (Contextual) Math Concepts
1. If the radius of a circle is 7 yards, then the diameter is 14 yards.

D = 2r               Write formula
D = 2 (7yards)       Substitute known values
D = 14 yards         Evaluate answer including correct units

2. If the diameter radius of a circle is 18 feet, then the radius is 9 feet.

D = 2r             Write formula
18 feet = 2r            Substitute known values
9 feet = r              Divide each side of the equation by 2.

3. If the radius is 4 inches and the corner radius is 9 inches, then the distance from the
circle to the corner of the pattern would be the difference of these two radii, 5 inches.
Related, Generic Math Concepts
1. Since AC and AB are tangents to the same circle they are congruent so,
AC = 15.
2. Since BO is a radius of circle O and AB is a tangent to circle O. AO would be a leg
of a right triangle ABO. This would be a 3-4-5 right triangle. If you did not recognize it
as a 3-4-5 right triangle, you could use the Pythagorean Theorem to find the length.
Since AO is the hypotenuse of this right triangle its length would be 5.

3. CO = 12 since BO and CO are radii of the same circle.

PSSA Math Concept Look
1. First you need to find the diameters of the circle, then you need to subtract those
diameters to get the difference.
D = 2r                            D = 2r           Write formula
D = 2(3 feet)                     D = 2(10 feet) Substitute known values
D = 6 feet                        D = 20 feet      Calculate Diameters
20 feet – 6 feet = 14 feet              Subtract
The difference would be 14 feet.
2. Since concentric circles have the same center, the shortest distance between the points
would be the difference in the radii.
D = 2r                           D = 2r            Write formula
22 inches = 2r                   16 inches = 2r            Substitute known values
11 inches = r                      8 inches = r            Divide each side by 2.
11 inches – 8 inches = 3 inches                    Subtract
The difference is 3 inches.
3. Since a tangent always meets a radius at a right angle this would be a 3-4-5 right
triangle and CA = 5. If you did not recognize it as a 3-4-5 right triangle, you could use
the Pythagorean Theorem to find the length.

PDE/BCTE Math Council

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