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## Quiz Bowl

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Quiz Bowl

- All eight students will solve problems as part of a quiz bowl.
- Students will work together to answer questions and compete head to head against other teams.
- Teams will be seated at tables.
- A moderator will ask a question using a microphone.
- Each team will write an answer to each question on the paper provided.

Team captains will hand one answer to the table runner.

- The team captain should be seated in middle of the team.
- Teams should write answers clearly and neatly so that judges can read answers. Teams with unclear answers will not receive points.
- Time will begin once I say “go”.
- Teams should NOT include computational or scratch work on the paper; only answers should be written on the paper.

Once a team turns in their paper, the team may NOT change their answer.

- Teams will be provided with scratch paper and pencils as well as their answer sheets.
- NO books, notes, calculators, or electronic devices, such as cell phones, may be used.
- Cell phones must be turned off.

Quiz BowlRound 1: Solve the Problem at Your Table

Round 1 will consist of 10 questions.

Teams will have 20 minutes to answer all 10 questions.

Each question is worth 5 points.

Teams that finish early may ask for additional questions.

This blender costs $139.99 at Bed Bath & Beyond.

You have a 20% off coupon and a $20 off coupon.

Which coupon will give you a bigger discount for this blender?

Step 2

Step 3

There are 5 squares in Step One, 9 squares in Step Two, and 13 squares in Step Three.

How many squares will be in Step 33?

A lemonade recipe calls for 7 lemons, 630 grams of sugar, and 1 ¾ quarts of water.

You only have 4 lemons. How much water and sugar should you use?

Tennis balls have a diameter of

2.7 inches. They are sold in a

cylindrical can whose height is

8.1 inches (the exact height of 3

tennis balls) and whose diameter

is 2.7 inches.

Which is bigger, the height of the can

or the circumference of the can?

Which values of A, B, C,andD complete the table below?

You must get all four correct to receive credit.

Max’s quiz scores so far were 68%, 75%, and 70%.

Ms. Smith gave back a quiz with an 80% score. Max realized Ms. Smith made a mistake and he should have gotten a 90% score.

She said, “I’ll make the change in my grade book but it won’t change your quiz average.”

Which “average” or “measure of center” is Ms. Smith more likely using, the mean or the median?

In a standard deck of 52 cards, there are 12 face cards (King, Queen, and Jack of each suit). There are 13 cards of each suit (Ace through King).

A friend offers you a bet: if you can pick a face card of any suit, or a heart of any value, from the deck, he’ll give you $1. If not, you owe him $1. What is the probability that you win the bet?

Find the value of x that makes this equation true:

2(x – 10) = 7

Quiz BowlRound 2: Multiple Answers

Round 2 will consist of 3 questions that each have multiple answers.

Each team will earn 1 point for each correct answer and 1 bonus point if the team provides all of the possible answers or the number of possible answers.

are arranged to

make a bracelet.

Here you see 3 different views of the same bracelet.

List all the different bracelets that could be made with these 4 beads (including the bracelet in the picture).

Solution

- RBYG or BRGY (this is the given bracelet)
- or BYGR or YBRG
- or YGRB or GYBR
- or GRBY or RGYB
- RYBG or YRGB
- or YBGR or BYRG
- or BGRY or GBYR
- or GRYB or RGBY
- RBGY or BRYG
- or BGYR or GBRY
- or GYRB or YGBR
- or YRBG or RYGB

The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 8 are 1, 2, 4, and 8.

List all the numbers, from 1 to 30 (including 1 and 30) that have an odd number of factors.

Solution

- 1: 1
- 4: 1, 2, 4
- 9: 1, 3, 9
- 16: 1, 2, 4, 8, 16
- 25: 1, 5, 25

- When he counts them by 2s he has 1 left over.
- When he counts them by 3s he has 2 left over.
- When he counts them by 4s he has 3 left over.
- He has fewer than 60 marbles.

How many marbles could he have. List all the possibilities.

Solution

- If he had one more marble, his number of marbles would be a multiple of 2, 3, and 4
- Multiples of 2, 3, and 4 under 60:
- 12, 24, 36, 48
- One less than each:
- 11
- 23
- 35
- 47

Quiz BowlRound 3: Speed Round with Follow Up Questions

Round 3 will consist of 5 questions.

The first team to give a correct answer to the runner will get 3 points.

The first team with the correct answer will then receive a follow-up question for 2 bonus points.

-9 • -8 • -7 • -6 • -5 • -4 • -3 • -2 • -1 • 0 • 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9

Solution

- Anything multiplied by 0 is 0, so the answer is 0.

-9 + -8 + -7 + -6 + -5 + -4 + -3 + -2 + -1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

Solution

- Still zero… just make pairs of the positive and negative numbers.

3(x + 10) = 5(x + 10)

Solution

- 3 (___) = 5 (___) can only be true when both sides equal 0
- Therefore, x + 10 must equal 0
- So x = -10

3(x + 10) + 2 = 5(x + 10)

Solution

- 3 somethings is 2 less than 5 somethings
- I know 3 ones is 2 less than 5 ones
- The statement will be true if (x + 10) = 1
- x = -9

Q: One fourth of the vehicles at Danielle’s Cycle Shop are tricycles. The rest are bicycles. Danielle counted a total of 45 wheels in her shop.

How many bicycles does she have?

Solution

- Every 4 vehicles has 9 wheels: 6 bike wheels and 3 trike wheels
- There are 5 sets of 9 wheels in 45 wheels
- She has 4 * 5 = 20 vehicles all together, 15 of which are bikes (3/4 of 20 is 15).

F: An outbreak of hoof-and-mouth disease is spreading through the land of Narnia. A vet examines each creature’s mouth and examines each hoof (4 per centaur and 2 per faun). At the end of the day the assistant says, “I need to record how many fauns and how many centaurs we checked.”

Faun

The vet replies, “I didn’t write that down, but I do know I checked 47 mouths and 122 hooves.”

How many centaurs were checked?

Centaur

Solution

- If she had checked only fauns (2 legs each) she would have checked 47 * 2 = 94 hooves
- She checked 122 – 94 = 28 extra hooves
- That’s 14 extra pairs of hooves
- Therefore she checked 14 animals with 4 hooves (centaurs).
- 14 centaurs were checked.

Solution

- 0.5 * 0.25 * 0.125 = ½ * ¼ * 1/8
- ½ * ¼ * 1/8 = 1/(2*4*8)
- 1/(2*4*8) = 1/(8*8) = 1/64
- 1/64 = 0.15625

0.1 + + 0.25 +

Q: A jacket is on sale for 25% off. The sale price is $150.00.

How much money do you save by buying the jacket on sale?

Solution

- $150 is 75% of the jacket’s original price
- $50 is 25% of the jacket’s original price
- Therefore, you save $50.

F: Monica contributes 1/3 of the total cost of a mother’s day present. Nahim contributes ½ of the total cost. Their dad pitches in $9 so they have exactly enough money. How much was Monica’s contribution?

Solution

- Total – ½(Total) – 1/3(Total) = 1/6(Total)
- $9 was 1/6 of the price.
- The total price was $54
- 1/3 of $54 = $18
- Or, $9 was 1/6 of the price, so 1/3 of the price is 2 * $9 = $18

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