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?
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
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. 1.25 ft
B. 12.50 ft
C. 27.60 ft
D. 125.00 ft
E. 276.00 ft
In ∆ABC at right, how many degrees are in B?
- 38o
- 42o
- 52o
- 90o
- 142o
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. $25.00
B. $21.70
C. $ 17.20
D. $ 13.30
E. $10
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?
A. 5.2 quarts
B. 2.25 quarts
C. 2.125 quarts
D. 9/4 quarts
E. 2.5 quarts
A large tube of toothpaste weighs 170 grams. Which expression tells the weight in kilograms of a dozen tubes of toothpaste?
A. (12 x 170) ÷ 1,000
B. 1000 ÷ (12 x 170)
C. (12 X 1000) ÷ 170
D. (170 x 1000) ÷ 12
E. 12 ÷ 170