Deadline: Wednesday, Nov. 28

You carry a heavy load. Perhaps too heavy. Let’s figure out about how much that is. Do your best to figure out what the mean (average) weight (in pounds) of a middle school backpack is. We’ll use transport weight as our target. That is, the weight of your backpack when you arrive or leave school.

Some further questions:
• How much is too much?
• Is that the same for everyone?
• What percent of your weight is your backpack weight?
• What is it that contributes most to backpack weight?
• What can (reasonably) be done to lighten your backpack load?

Include a brief discussion of how you arrived at your estimate.
One entry per person.
Do you have an idea about how to efficiently get a reliable number to compare our estimates to? See Cris if you do.

There will be prizes for:
• Closest estimate
• Best Estimate from a Family
• Best technique for arriving at your estimate.
• Special prize for research related commentary

A Pound of Tea

Jonathan and Hazel love to drink tea. When they are both at home, a pound of tea lasts two weeks. Occasionally Hazel visits her mother in Australia. It takes six weeks for Jonathan alone to use up a pound of tea.

1) How long should a pound of tea last Hazel if she were alone?

2)In 2006 Hazel visited her mother for six weeks in the spring. In the summer Jonathan gave up drinking tea for six weeks. Their favorite tea costs $9.00 per pound. About how much did the couple spend on tea during the year? Explain.

Due Thursday, March 22nd
Return your answer to the Middle School Office
or email BethA@prospectsierra.org
Anjelica's Very Odd Magic Sweater

Anjelica was wearing her new sweater when she put her hand in the pocket and found a dime. "Look, I found a dime in my pocket," she told her mom and put the dime on the table.

She put her hand in the pocket again and this time she found three dimes.
"Wow!" Anjelica thought, "I have a magic sweater!" She put her dimes together on the table and put her hand in her pocket again, and this time she found five!

Her mom said, "If you do this 10 times total, you'll have 100 dimes!" Anjelica asked, "How did you do that in your head so fast?"
Questions: What's a shortcut her mother might have used?
How many dimes will Anjelica find when she puts her hand in her pocket for the nth time?

Due Thursday, February 15th

Basic Breakfast Buffet

Linnea's family traveled to Vancouver for a holiday and stayed in a hotel that offers a breakfast buffet.

Linnea and her brothers Joel, Karl, and Jakob each picked a cereal, juice, and bread from these choices:
• cereal - oatmeal, corn flakes, granola
• juice - orange, cranberry, apple
• bread - muffin, bagel, toast

Jakob wondered how many days they could stay at the hotel without ever eating the same breakfast.
Joel asked, "Do you mean that each of us would eat a different breakfast each day and once a breakfast combination was eaten no one else could have it?"
"Yes!" answered Jakob, "that's what I mean."

Question: How many days could they stay at the hotel before someone would have to repeat one of the breakfasts?

Due Thursday, February 8th

Bowl-O-Rama

On Tuesday nights, the Linear Lanes bowling alley offers a special called Bowl-O-Rama, to encourage people to play lots of games. You pay a cover charge to get in and get bowling shoes, and then you only pay a little bit for each game you bowl.
One Tuesday, Bo and several of his pals went to Bowl-O-Rama. At the end of the night, Bo knew that he had bowled 8 games and paid a total of $7.30. Tommy had bowled 11 games and paid a total of $8.35.
1. Write an equation that expresses the cost of playing at Bowl-O-Rama in terms of the number of games you bowl.

2. Olivia wasn't sure how many games she had bowled but her total bill was $6.60. Use your equation from question 1 to determine how many games Olivia bowled.

3. Liam said the next time they came he was going to bring ten dollars. Use your equation from question 1 to determine how many games Liam will be able to bowl.

4. On other nights, when Bowl-O-Rama is not going on, it doesn't cost anything to get into Linear Lanes. Shoe rental is $1.50, and the cost per game bowled is $1.25. At least how many games must you bowl for Bowl-O-Rama to be a better deal than bowling the same number of games on any other night?

Cyndy's Curtains - Due Thursday, January 18th
Return your answer to the Middle School Office or email Beth.
Cyndy has an extra-long pair of curtains that she wants to cut and hem to use on some shorter windows. To fit the new windows, the curtains need to be 35 inches long.

The curtains are now 114 inches long. The top sleeve was made by turning under 1/4 inch of fabric (so that the edge won't show) and then turning over another 2 inches, as shown in the picture below. Turning under 1/4 inch of fabric and then turning up 3 inches of fabric, as in the picture, made the bottom hem.

Tunnel Time - due 12/14/06
A train one kilometer long travels at 40 kph. The front of the train enters a tunnel one kilometer long at 11 am.
At what time does the rear of the train emerge from the tunnel?
What speed would it be going if the end of the train emerged at 11:02 am?
Be sure to show your work, explain how you solved the problem, and explain how you know you are correct.

Food Fractions

Damien is bigger than Declerrah, so he eats more. When they share food, Damien eats about 3/5 of the food and Declerrah eats about 2/5. The other day, they went to their favorite pizza place and small pizzas were on sale: buy one, get one free. So they ordered two smalls.

Each pizza comes cut into eight slices. How many whole slices of pizza should Declerrah eat so that she gets as close as possible to 2/5 of all the pizza?

Extra: Would Declerrah be able to get closer to 2/5 if each pizza comes cut into six slices?

Be sure to show your work, explain how you solved the problem, and explain how you know you are correct.

Homework-Free Fridays - Due Thursday, November 9
Every Friday the students in Roberta’s math class who have completed their homework all week long get to play Homework-Free Friday. Roberta has three 10-sided dice, each with the digits 0 through 9. Each eligible student rolls all three dice. If the sum of the three dice is equal to the day's date, the student is excused from homework for the weekend.
On one Friday, the 15th of the month, Nina rolled an 8 on the yellow die first. How many different ways can the blue and red dice land to win her a weekend free of homework?
Click Link for for Extra!

Give this week's Problem of the Week a shot! When you have solved the problem, you can either e-mail your solution to BethA or drop it off at the Avis office. Have fun with it! Winners will be announced at Friday's assembly or in Friday's announcements.

Cadence

I'm pretty tall, and one of my friends is pretty short. I think we walk at the same speed, but she claims that she walks "faster" than I do. Help us think about this by answering the following questions:

1. My step length is 38 inches. About how many steps would I need to take to travel 100 feet?

2. My friend's step length is 2/3 of my step length. About how many steps would she need to take to travel 100 feet?

3. It takes both of us 20 seconds to travel 100 feet. What is our speed in feet per minute?

4. Who has the faster cadence? (Note: Cadence is the word for the number of steps taken per minute.)

Explain how you solved the problem and show how you know you're correct

Extra: If my friend kept her same cadence but took steps the same length as mine, by what factor would her speed increase?

Scale Logic

The Math Club at Dawn's school had a Math Carnival. At her booth Dawn set up three scales with baseballs, tennis balls and soccer balls.

A baseball, a tennis ball, and a soccer ball weigh 19 ounces. Two soccer balls with two tennis balls weigh 28 ounces. Two baseballs and a soccer ball weigh 22 ounces.

Contestants at Dawn's booth had to figure out the weight of each kind of ball.

How much does each kind of ball weigh?

Note: Assume that all the soccer balls weigh the same, all the baseballs weigh the same, and all the tennis balls weigh the same.

Explain how you solved the problem and show how you know you're correct

Extra: Find all the other combinations of these kinds of balls that would weigh 22 ounces. Explain how you found them and how you know you have found them all.

A Pound of Valentine's Chocolates

When Tristan visits Isolde on Valentine's Day, he's planning to bring her a one-pound box of chocolates. He knows that when they share a one-pound box of chocolates, it usually lasts for two weeks. When he eats a one-pound box of chocolates on his own it lasts for six weeks.

How long should a one pound box of chocolates last if Isolde eats it alone?

Explain how you solved the problem and how you know you have found all solutions.

Note: Assume they don't eat faster or slower when they are alone.

Common Cents

Monique and Misty wanted to buy their mother a box of candy for Valentine's Day. They emptied their piggy banks and discovered that Monique had twice as much in her bank as Misty had in hers. Together they had a total of $10.50.

How much did each girl contribute to the total?

Explain how you solved the problem and how you know you have found all solutions.

Extra: The girls pooled their money and bought a box containing 36 pieces of candy. Mom share with dad, but she ate three times the number of pieces that dad ate.

How many pieces did mom and dad each eat?

Practicing for the Winter Olympics

Sonya is practicing for the Winter Olympics. As she hopes to be a champion figure skater, Sonya spends many hours skating on her home rink.

Her coach, Tommy, is having her skate figures on the ice. He etches a straight line in the ice using the back of his skate. This line is 30 meters long. He then tells her to skate five equal semicircles, beginning at one end of the line and ending at the other.

She will first skate one semicircle on he right foot, then the next semicircle on her left foot, and will alternate feet, continuing across the rink until she reaches the end of the line.

What is the length of the semicircular path Sonya skates across the rink?

Be sure to show how you solved the problem and explain how you know you are correct.

Wooden Legs

Wendy builds wooden dollhouse furniture. She uses the same kind of legs to make 3-legged stools and 4-legged tables.

She has a supply of 31 legs and wants to use them all to make stools and tables.

Find all the different ways she can use them.

Explain how you solved the problem and how you know you have found all solutions.

Extra: Wendy sells her furniture to the local toy store. She gets $2 for each stool and $3 for each table. Of all the ways you found which would earn her the most money?

The Goalie's Stats

A hockey goalie is credited with a save when she stops a shot from going into the goal. The goalie's save percentage is calculated by dividing the number of saves made by the number of shots faced. That answer is rounded to three decimal places.

For example, a goalie who has faced 148 shots and made 136 saves would have a save percentage of 136/148 = .9189 or .919 when rounded off.

So far this season, Annie has faced 131 shots and made 112 saves. What is her save percentage right now?

Annie wants to raise her season save percentage to at least .900. Suppose she gets hot and saves every shot for the next few games. How many shots would she have to save to raise her season save percentage to .900?

Extra: Suppose that instead of saving every shot, Annie saves 94 percent of the shots she faces in the next few games. How many shots would it take for her to raise her season percentage to .900 in that case?

In Their Prime

Part 1: Jonathan is two years younger than his wife Hazel. Their current ages are both prime numbers. Next year Hazel's age will be a multiple of 11. Jonathan's age will be the product of two consecutive numbers.
How old are Jonathan and Hazel?

Part 2: Two prime numbers that differ by two (like Jonathan and Hazel's current ages) are called twin primes. They are always separated by a single even number.
Find all the twin primes less than 100. Starting with the twin primes 5 and 7, what is the greatest common factor that those single even numbers all share?

Be sure to explain how you solved the problem and how you know you are correct.

Zelma's ZIP Code* POW: Due for Tues May 10

Zelma noticed something unusual about her ZIP Code: each consecutive pair of digits is the product of two one-digit numbers.

For example, look at this four-digit number: 1564.
15 = 5 * 3
56 = 7 * 8
64 = 8 * 8

Zelma's ZIP Code contains the digits 2, 3, 4, 6, and 7, exactly once each. What is Zelma's 5-digit ZIP Code?

Be sure to explain your strategy and show how you know you are right. Include any observations about products or digits that helped you solve the problem.
Just for fun, do you know where Zelma lives?
Extra: Arrange all the digits 1 through 9 similarly, so that each consecutive pair of digits is the product of two one-digit numbers. Include any observations that helped you solve the problem.

POW for April 26: Four Point Puzzle
On graph paper set up a 4 quadrant grid. The vertices of quadrilateral ABCD are at the points A:(1,2), B:(2,-2), C:(-5,-4), and D(-6,0). What's the most specific name you can give to this quadrilateral?
Extra: What's the area of quadrilateral ABCD?

The Gates:
In New York City: Sunday, February 27, was for the last day of Christo and Jeanne-Claude's latest art project, The Gates, Central Park, New York, 1979-2005. Here are statistics about the project:
* 1.089 million yards of orange-yellow fabric
* 23 miles of pathways
* 7,500 gates
* each gate is 16 feet high
* 165,000 bolts and an equal number of self-locking nuts to hold the gates together
* more than 1 million square feet of vinyl and 5,300 tons of steel
* 46 miles of hems in the fabric
The scenery was beautiful and so people walked as much of The Gates as they had time for. One person, Suzanne, walked at a steady pace of 4.4 feet per second (fps) and ended up walking 1/5 of the pathway.
Question: How much time did Suzanne spend walking on The Gates pathway?
Extra: If Suzanne increased her pace by 25%, how long would it take her to walk the complete pathway?

Let the Chips Fall . . .
We have three chips. A one-digit positive whole number is written on each side of each chip. The six numbers used on the chips are consecutive. Tossing the chips once, we get 6, 7 and 8, for a sum of 21. Then we shake and toss them a few more times and get the sums of 16, 17, 20 and 23.

- Which number is on the opposite side of number 6? number 7? number 8?
- Remember to explain your strategy and to show how you know your answer is correct.
- Extra: What other sums are possible? List them and tell how you know you have found them all.
- 2005 The Math Forum http://mathforum.org/pow/

Note On Last Week痴 POW:
To quickly count the number of games played in a single elimination tournament, recognize that every game has one loser that then goes home (i.e. is out of the tournament). So the number of games corresponds one-to-one with the number of losses which corresponds with the number of teams that go home, which is all but the one victor. For the men, 65 teams means 64 games; for the women, 64 teams means 63 games.

It is NCAA March Madness time.
There is a women痴 division and men痴 division.
Each is a 64-team single elimination tournament, meaning if you lose once, you are out.
(The men痴 tournament has one additional game, a 菟lay-in game�; the winner becomes
one of the 64).

The Question: How many basketball games are played in each tournament.
Hints: Check our sports page for a charting structure that can help
solve this problem, OR use number patterns.

Also, there is a simple logic way to solve it quickly, which will
be included with next week痴 question.

POW for Tues March 9
Prospect Sierra 7th grade girls placed first in the 1st Annual All-Girl Math Competition at Julia Morgan School on Saturday March 5. They successfully answered the problem below. Can you?

ABCDE
X4
=EDCBA

A=? B=? C=? D=? E=?
Each letter has a unique single-digit value. The girls worked together as a team, so if you are stuck, get a partner.

Bartering for Bananas - Byron lives where the people trade goods they produce for other things they need. He has some fish that he has caught, and he wants to trade them for bananas. He asks around to find out what is being traded and finds out the following: * Five fish are worth the same as two loaves of bread. * Six oranges are worth the same as two melons. * One loaf of bread is worth the same as one banana and three oranges. * Four loaves of bread are worth the same as fourteen oranges. Question: How many bananas can Byron get with five fish?