Inchworm – The person using
inchworm solving follows a set of algorithms that tell him/her
what to do. Many times they will not understand why the
algorithm works, just that they have been told that it does.
Ex: 39 x 52 = 39
x 52
calculate 15% tip on $46.83 = $46.83 * 0.15 = $46.83
X
0.15
Grasshopper – The person solving a
problem grasshopper style will break from the algorithm and try
other solving options. They may estimate, break the problem into
smaller parts, and/or make assumptions that can make leaps in
their thinking. They make links in number sense that can help
them to process faster. They can be comfortable with not getting
the correct answer, but something close. Usually has a little more
comfort in Algebraic thinking.
Ex: 39 x 52 = (40 – 1) x (50 + 2) = 2000 + 80 – 50 – 2 = 2028
calculate 15% tip on $46.83 = $46.83 * 10% = $4.68 + ½ of 10% =
$2.34 = $7.02
An example from this summer at Tomahawk Scout Reservation:
At a logging camp, trees must be evaluated for their value in
board feet before a timber harvest.
To find the cross sectional area of a tree, measure its
circumference at breast height (CBH)
The circumference is calculated by C = 2πr, solving this equation
for r: r = C/2π. The area is calculated by A = πr2. Therefore area
can be calculated in reference to circumference by A = π(C/2π)2 or
A = C2π/4π2 or A = C2/4π. Most of us know that π = 3.14 (although
this is not exact, it is usually close enough), but for this calculation
π = 3 is close enough. So A = C2/12. If the circumference is 9 ft,
then the area would be A = 81 ft2/12 or 6 ¾ ft2 (approx. 7 ft2). If
the tree is 100 ft tall, the board feet (volume of the tree) would be
the area times the height or V ≈ 7 ft2 * 100 ft ≈ 700 ft3.
Sample problems from the GED preparation materials:
On a certain I-pod playlist, three songs have the following playtimes:
Song A: 4 minutes and 56 seconds
Song B: 2 minutes and 30 seconds
Song C: 10 minutes and 16 seconds
What is the average playtime of these three songs?
Armando is a hair stylist. He gets 40% of what his customer is
charged by the shop. If the customer leaves a tip, Armando gets
100% of the tip. How much will Armando get if he charges $19.50
and his customer tips him $5.50.
A.
B.
C.
D.
E.
A. 5 minutes and 8 seconds
B. 5 minutes and 54 seconds
C. 6 minutes
D. 6 minutes and 7 seconds
E. 17 minutes and 42 seconds
Mrs. Cabrini needs 2 quarts of tomato sauce to make a large batch
of her spaghetti. She has 1 ¼ quarts of her own. She gets ½ quart
from her neighbor and ⅜ quart from her other neighbor. How many
quarts does she now have in all?
One of the first electronic computers was in the shape of a huge
box. It was 96 feet long and 2.5 feet wide. The amount of space
inside was 3000 cubic feet. How many feet high was the computer?
A.
B.
C.
D.
E.
A.
B.
C.
D.
E.
1.25 ft
12.50 ft
27.60 ft
125.00 ft
276.00 ft
38o
42o
52o
90o
142o
B
38
A
5.2 quarts
2.25 quarts
2.125 quarts
9/4 quarts
2.5 quarts
A large tube of toothpaste weighs 170 grams. Which expression
tells the weight in kilograms of a dozen tubes of toothpaste?
In ∆ABC at right, how many degrees are in <B?
A.
B.
C.
D.
E.
$25.00
$21.70
$ 17.20
$ 13.30
$10
C
A.
B.
C.
D.
E.
(12 x 170) ÷ 1,000
1000 ÷ (12 x 170)
(12 X 1000) ÷ 170
(170 x 1000) ÷ 12
12 ÷ 170