Mathematics Problems: Moving From Good to Great

Mathematics Problems: Moving From Good to Great

GoodGood GreatGreat

TypicalTypical ExceptionalExceptional

Math in the City/Akron

Baseball and Mathematics

Baseball Geometry

• How far does a catcher have to throw the ball to get from home plate to 2nd base?

• If the grounds crew had to buy sod for the inside of the diamond, and the sod cost $6.50 per square foot, how much would they need and how much would it cost?

Good/Great?Typical/Rich?Good/Great?Typical/Rich?

Rich Problems

• Nonroutine and can be solved in a variety of ways.

• Engage student thinking, conceptual development, problem solving as well as skills.

• Involve a wide range of mediums (e.g., graphs, charts, problems, symbols, equations, manipulatives, technology).

• Uses realistic contexts and truly problematic situations.

The Cost of Going to the Ball Game

• Fred Smith took his wife and two children to the Akron Aeros game. Fred purchased two regular hot dogs, two slices of pizza, two regular sodas, and two bottled waters. How much did he spend?

The Cost of Going to the Ball Game

• Fred Smith took his wife and two children to the Akron Aeros game. Fred purchased two regular hot dogs, two slices of pizza, two regular sodas, and two bottled waters. How much did he spend?

Good?Good? Typical?Typical?

The Cost of Going to the Ball Game

• Fred Smith would like to take his wife and two children to the Akron Aeros game. Fred has $80 to spend on food and Aeros merchandise for his family. What can Fred and his family purchase at the game? Explain.

The Cost of Going to the Ball Game

• Fred Smith would like to take his wife and two children to the Akron Aeros game. Fred has $80 to spend on food and Aeros merchandise for his family. What can Fred purchase at the game? Explain.

Great?Great? Exceptional (Rich)?

Exceptional (Rich)?

Baseball Geometry

• http://www.factmonster.com/math/knowledgebox/

Good/Great?Good/Great?

Baseball Math

• http://www.prongo.com/math/multiplication.html

Good/Great?Good/Great?

Aviation and Mathematics

Aviation and Mathematics

• An airplane had 8 hours of fuel at take-off. How many hours of fuel is left after the plane flies for 5 hours 18 minutes?

• The price of jet fuel was $1.40 per gallon. The price increased 10%. How much was the increase?

Good?Good? Typical?Typical?

Aviation and Mathematics• Your take off weight without fuel is 1900 lbs.

Your maximum take-off weight with fuel is 2150 lbs. Aviation fuel weighs 6 pounds per gallon. Your aircraft uses fuel at the rate of 7.7 gallon/hr and aviation fuel costs $6.01 per gallon. You have $225. If you take off from the Akron-Canton Regional Airport and have a cruising speed of 209 km/hr, where could you go? Explain.

• http://www.ourairports.com/big-map.html#lat=41.269549502842565,lon=-81.529541015625,zoom=8,type=Map,country=US

Aviation and Mathematics• Your take off weight without fuel is 1900 lbs.

Your maximum take-off weight with fuel is 2150 lbs. Aviation fuel weighs 6 pounds per gallon. Your aircraft uses fuel at the rate of 7.7 gallon/hr and aviation fuel costs $6.01 per gallon. You have $225. If you take off from the Akron-Canton Regional Airport and have a cruising speed of 209 km/hr, where could you go? Explain.

Good?Great?Good?Great?

Akron's Derby DownsAll-American Soap Box Derby and

Mathematics

Ratio and Proportion Good?Good?

Suppose that you want to build a model (smaller-sized) soap box car that is in proportion to the full-sized car (shown above). If the proportion of the car that you want to build to the full-sized care is 16:8, then what should be the dimensions of the model car?

Aviation and Mathematics

Ratio and ProportionGreat?Great?

Suppose that you want to build a model (smaller-sized) soap box car that is in proportion to the full-sized car (shown above). A)If the proportion of the car that you want to build to the full-sized care is 16:8, then what should be the dimensions of the model car?B)How many model soap box cars can you construct that are proportional to the full-sized car? Draw a blueprint for each model that you find (be prepared to explain your thinking and reasoning).

Music and Mathematics

Music and Mathematics• Music is often divided up into units called

measures or bars. • Each measure has a certain number of

beats.• The number of beats is determined by

the time signature (also called meter).

http://www.musictheory.halifax.ns.ca/6measures.html

Notes

Music—Time Signatures

€

A time signature of 4

4 states that every

measure must contain, altogether,

the equivalent of four quarter notes

Music—Beat (Time Signatures)

€

Determine which of the following measures

in 4

4 time do and don't work out

Garland, T. H, & Kahn, C. V. (1995). Math and Music: Harmonious Connections. Lebanon, IN: Dale Seymour Publications

Music—Beat (Time Signatures)

€

Using whole, half, quarter, and eighths notes,

determine all of the posssible measures in 4

4 time

National Parks and Mathematics

• We are going to have a contest to see which group can come the closest to finding the area of Cuyahoga Valley National Park (CVNP). There will be a prize for the winning group.

• Your (groups’) goal is to find the area of the CVNP, using the Cuyahoga Valley National Park map. On the map, each square represents 128 square acres.

National Parks and Mathematics

• We are going to have a contest to see which group can come the closest to finding the area of Cuyahoga Valley National Park (CVNP). There will be a prize for the winning group.

• Your (groups’) goal is to find the area of the CVNP, using the Cuyahoga Valley National Park map. On the map, each square represents 128 square acres.

Good?Great?Good?Great?