October - Open-Ended Math Problems

October Problems

Number Theory

Start out simple...

What's the Deal?

1. Mortimer wants some doughnuts. He is very cheap and likes to save even the smallest amount of money. He found a coupon in the paper for Dunkin' Donuts.The coupon was for $1 off a dozen. This week they are on sale for $3.99 a dozen without the coupon and $.35 a piece if you use the coupon. What do you think Mortimer will do and why?

Spinning

2. Tara and Sara are going to play a spinner game. These are the rules:

When it is a player's turn, you spin both spinners.
Add the 2 numbers that the spinner points to.
If the sum is odd, Tara wins even if it is not her turn.
If the sum is even, Sara wins even if it is not her turn.

Both girls think that they have a better chance of winning. Is either right? Justify your answer.

Now try to work this out...

Going Shopping

3. Mabel and her mom are going shopping on Saturday. They bought at least one item from each of the 3 departments that they visited. Mabel gave the clerk $120 and she got back $11.76 change. What items did they buy? Think about how much they spent. NO TAX TODAY!

HOUSEWARES
Dishtowels: $11.38
Curtain Rods: $12.98
Bath Mats: $29.58

CLOTHING
Shirt: $30.98
Dress: $49.90
Slacks: $39.90

TOOLS
Hammer: $17.90
Saw: $23.90
Drill: $25.78

What Time is It?

4. How many times in a 12 hour period does the sum of the digits on a digital clock equal 6? Try to think of a way to solve this without going through every single time. Describe what you did.

This will really challenge you...

Boy Scout Hike

5. Points A and C on a map are 12 km apart if you follow a certain path. A troop of Boy Scouts leaves Point A at 11:00 a.m. They travel 3 km/hr because they have heavy packs until they reach Point B at 12:45. If they want to reach Point C by 2:00, how fast will they have to go?

Measurement

Start out simple...

Baseball Trivia

6. The greatest distance that a baseball has been thrown is 445 feet, 10 inches. Is this greater or less than the length of a football field from goal line to goal line? By how much? Tell how you made your decision.

Now try to work this out...

Picture It

7. A picture that measures 12 cm by 18 cm is enlarged to 4 times its area. What are the new dimensions?

This will really challenge you...

The Nutty Squirrel - From Math Forum

8. While going for my daily run, I passed a squirrel carrying a nut in her mouth. When she saw me, she ran towards a safe place and, coming to a stone wall, easily jumped up on it and disappeared. I began to wonder how high I could jump if I were a squirrel.
If an average squirrel's back leg height from ground to hip is 3 1/2 inches, and that squirrel can jump a 2 foot high wall, what height wall could I jump if I were a giant squirrel? My leg height from ground to hip is 36 inches. Give your answer in feet and inches to the nearest inch.

Geometry

Start out simple...

9. Which of these choices contains the dimensions of a rectangle with the same perimeter as a rectangle whose dimensions are 5 m by 3 m.?

10 m by 8 m
7 m by 1 m
6 m by 4 m
8 m by 2 m

Show your work.

Now try to work this out...

A Model House

10. Choose 3 geometric solids to build a model house. What solids did you choose? How many vertices are there? From an aerial view of your structure, how many vertices can you see? Draw a picture of the aerial view.

This will really challenge you...

11. What do you need to know to solve this? You have kite ABCD. Angle B is at the top of the kite and measures 80 degrees. Angles A and C are on the sides and Angle D is at the bottom of the kite. What is the largest size that Angle A or C could be?

Patterns, Algebra, And Functions

Start out simple...

Yum

12. Determine the number of pizza combinations you could get with 4 different toppings. Each pizza must have at least 2 toppings. Make a chart to display your results.

Now try to work this out...

Ice Cream Cones

13. An ice cream stand has 9 different flavors. A group of children come to the stand and each buys a double scoop cone with 2 flavors. If none of the children chooses the same combination of flavors and every combination is chosen, how many children are there? Show how you got your answer.

This will really challenge you...

Planet Krayon - (From The Problem Solver 6)

14. Zemo, Orb, Yuko, and Sam are friends who live on neighboring space stations of the planet Krayon. They commute to school every day by space shuttle. Orb's space station is one half as far from Krayon as Zemo's space station. Yuko travels as far as the total distance traveled by Zemo and Orb. Sam travels 3 times the distance that Zemo travels. How many space miles does each friend travel to school if the friends together travel 888 space miles?
Write an algebraic equation.

Data, Statistics, And Probability

Start out simple...

Coin Toss

15. List all the possible outcomes when four coins are tossed. Determine the theoretical probability of having exactly two heads and two tails.

Now try to work this out...

Graph It!!!

16. Use the following information to make a line graph, bar graph, and circle graph. Describe how you did each one in paragraph form. Choose a title, labels, and scale.

Doritos - 20
Popcorn - 15
Candy - 12
Chips - 10
Pretzels - 3

This will really challenge you...

How Old Am I?

17. The average age of a group of teachers and students is 20. The average age of the teachers is 35. The average age of the students is 15. What is the ratio of teachers to students? Express your answer as a fraction in simplest form.

Grab Bag

18. Dominic arrived at work and went behind the counter at the north end. As he faced out over the counter, north was to his right, south to his left. While he was standing at the north end, a customer ordered a sandwich. Dominic went through these steps:

3 feet to his left to pick up the bread
2 feet to his right to put bread on the plate
4 feet to his left to get mayo and pickles
2 feet to his left to pick up knife and spoon
Returned to where the bread was on the plate
Turned around and got the salami out of the refrigerator
Put the sandwich together
3 feet to the left to serve the customer
4 feet to the left to get a soda
Back to the customer to give him the soda
To the south end of the counter to pick up the customer's money

Draw a diagram of the counter and its arrangement. Make suggestions for a more efficient arrangement.

You've reached the finish line!

October Solutions

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