Seventh Grade Mathematics

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Seventh Grade Mathematics

• Problem 1.1

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How far is from home plate to second base?
Assume the field is a normal Little League /
softball diamond having 60 foot base paths?
Without looking it up, how can we figure the
answer?
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A mathematical model is a picture that looks
similar to the real thing. The picture does not
need to be the same size.
What is the shape of a baseball/softball diamond?
List the properties of a square 1) 1 D ,
2 D or 3 D ?
2) It has four equal sides and four
equal angles?
What is a side? How do you measure a side? What
is an angle? How do you measure and angle
Check out pages 230 , 438-439
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If a softball/baseball diamond is a square.
What do we call the path of a catchers throw to
second base?
The diagonal of a square.
Describe how a diagonal divides a square?
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Into a triangle. What is a triangle and describe
7 things true about the triangle below.
1) 2) 3) 4) 5) 6) 7)
Its green
Two sides (legs) are the same length
Two angles have the same measure
The two equal sides are perpendicular and form a
right angle.
The right angle measures
The two equal angles each measure
The hypotenuse is the long side opposite the
right angle.
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Leg
Leg
Hypotenuse
Isosceles Right Triangle
What is the relationship between the hypotenuse
and the legs?
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Fold an 8 ½ x 8 ½ piece of paper in half
diagonally.
Does this triangle have the same 7 properties
true as the triangle we drew on the baseball
diamond?
Everything is the same except this triangle isnt
green.
Does this triangle model the baseball diamonds
triangle?
Yes
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Fold this triangle a second time.
And a third time.
And a fourth time.
Are all four of these triangles models of the
baseball diamond (Do they have the same shape) ?
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What do you call triangles that have the same
shape and the same size?
Congruent triangles

These 4 triangles are not congruent.
What do you call triangles that have the same
shape but not necessarily the same size?
Similar Triangles
All four of these triangles are similar to the
baseball diamond and therefore are models.
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If we can find the pattern among these 4
triangles (models), we will be able to find the
answer to our baseball question, How far from
the catcher to second base.
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Measure your four triangles and fill in the data
chart.
3 4.25 6
8.5 4.25 6
8.5 12
Is there a pattern? If so, what is
the pattern?
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One way to discover a pattern is by graphing our
results. We will need 8 ½ x 14 paper for
this problem.
Length of hypotenuse
( 3 , 4.25 )
Plot your four data points
( 4.25 , 6 )
( 6 , 8.5 )
Now can we see a pattern. What is it?
( 8.5 , 12 )
Length of legs
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Another way to discover a pattern is to look for
either a common difference or a common ratio.
Find the difference and the ratio and fill in the
data chart.
3 4.25 6.0
8.5 4.25 6
8.5 12
1.25 1.75 2.5
3.5
1.4167 1.4118 1.4167 1.4118
1.414 1.414 1.414 1.414
What is the pattern?
( 1.4167 1.4118 1.4167 1.4118) / 4
1.41425
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How far is from home plate to second base?
Assume the field is a normal Little League /
softball diamond having 60 foot base paths?
h 1.414 L
h 1.414 (60 ) 84.84 ft
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Does 84.84 ft 84 10 ?
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The Cleveland Indians and all professional
baseball teams play on diamonds that have 90 foot
base paths.
How far does catcher Victor Martinez have to
throw the ball in order to reach second base?
h 1.414 ( 90 ft )
h 127.26 ft