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South Austin Chess Club

 

Mathnasium of South Austin is the proud sponsor of the South Austin Chess Club. The club is open to all interested players ages 8 and up. The goal of the club is to provide a friendly environment for kids to learn and play chess while developing their mental capability.

No experience is neccessary. Instruction will be provided for novice players.

The club is free, i.e., there are no membership fees.

The South Austin Chess Club meets every Saturdayexcept the first Saturday of each month, from 3pm to 6pm.

The typical activities are as follows:

  • Chess puzzles.
  • Free play.
  • Team activity.
  • Free play.

Come and join us!
  


Problems of The Week

9/11/17 - 9/16/17

 

Pre-K to 2nd Grade
Question:  In Mrs. Olson's first grade class, math lessons start at 1:05 PM and ends 65 minutes later. At what time are Mrs. Olson's math lessons over?

 

3rd to 5th Grade
Question:  Matthew learns in history class that the first presidential election in the United States happened in 1789, the second happened in 1792, and the rest have happended every 4 years since then. The most recent election was in 2016. How many presidential elections have happend in the United States in total?

 

6th Grade to Pre-Algebra
Question:  Jack's science homework is to measure the temperature outside at 7 PM each day for a week. On Monday, his thermometer reads 77o F, but his homework askss for the temperatures in Celsius. Since the temperature in Celsius is equal to five-ninths of the quantity 32 less than the temperature in Farenheit, what should Jack write down on his homework?

 

Algebra and Up
Question:  One half of Hailey's overall English grade comes from test scores. One fifth of her grade comes from quizzes. Another fifth comes from homework. The rest comes from classroom participation. If Hailey has an average test score of 92%, an average quiz score of 80%, and average homework score of 75%, and a classroom participation score of 100%, what is her overall grade as a percentage?

 


Problems of the Week

8/28/17 - 9/2/17 

Pre-K to 2nd Grade
Question:  Jack decides to paint the walls in his bedroom with colorful stripes. The first stripe in the pattern is red, then orange, then yellow, then orange, then red, then orange, then yellow, then orange, and so on. If the pattern continues, what color will the 30th stripe be?
 

3rd to 5th Grade
Question:  Nora makes 90 homemade crayons. A small box can hold 8 crayons, and a large box can hold 24 crayons. If she fills 4 small boxes with crayons, how many large boxes will she need for the rest of the crayons?

 

6th Grade to Pre-Algebra
Question:  Micah sculpts two statues, one of a dog and one of a cat. The real-life dog weighs 20 pounds, and its statue weighs 48 pounds. The real-life cat weighs 15 pounds. If the statues are both proportional to the animals in weight, then how much does the cat’s statue weigh?
 

Algebra and Up
Question:  The value of a painting increased by 20% after the painter appeared on a popular talk show. The value of the painting increased again by 15% when the painter was featured in a magazine. If the value of the painting is now $1,242.00, what was its original value?

 

 

Answers

 

Pre-K to 2nd Grade
Answer:  Orange.
The pattern repeats every four stripes - red, orange, yellow, orage. 4 goes into 30, 7 times with 2 left over. That means the stripes repeats 7 complete times and the last two stripes are red and orange.

 

3rd to 5th Grade
Answer:  3 large boxes.
4 small boxes hold 8 x 4 = 32 crayons, leaving 90 - 32 = 58 crayons unboxed. Nora can put 24 x 2 = 48 crayons into 2 large boxes, and the rest (58 - 48 = 10 crayons) into a 3rd large box.

 

6th Grade to Pre-Algebra
Answer:  36 pounds.
The ratio of the animal's weight to their statues' is 20 / 48 = 5/12. The cat weighs 15 pounds, so it's statue weighs 15 / (5/12) = 36 pounds.

 

Algebra and Up
Answer:  $900.
The value increased by 20%, then the percent increase was compounded by another 15%. So, if we call the original value of the painting V, we have
  V(1.2)(1.15) = $1,242
  1.38V = $1,242
  V = $900.

 


Problems of the Week

8/21/17 - 8/26/17 

Pre-K to 2nd Grade
Question:  Peter’s birthdate is January 3, 1996. Hannah’s birthdate is October 30, 2008. How old will each of them be on August 25, 2017?

 

3rd to 5th Grade
Question:  Grace has 1,000 points saved up on an app. She can trade 200 for a $10 gift card. If Grace wants to use her points to get enough gift cards to buy a pair of boots that cost $75, how many more points does she need?

 

6th Grade to Pre-Algebra
Question:  Isaac can read 50 pages in an hour. Wyatt can read 90 pages in an hour and a half. How much faster can Wyatt read a 300 page book than Isaac?

 

Algebra and Up
Question:  If x is an integer, 3x + 7 < 16, and 2x – 5 ≥ –9, what are the possible values of x?

 

 Answers

 

Pre-K to 2nd Grade
Answer:  Peter will be 21 years old, and Hannah will be 8 years old.
Since Peter’s birthday will already have happened this year, he will be 2017 – 1996 = 21 years old. Hannah’s birthday hasn’t happened yet, so her last birthday was in 2016. So, Hannah will be 2016 – 2008 = 8 years old.
 

3rd to 5th Grade
Answer:  600 points.
Grace needs 8 gift cards in total to have enough money to buy the pair of boots. She has enough points for 1,000 ÷ 200 = 5 gift cards, so she needs 3 more. To get 3 more gift cards, she needs 3 × 200 = 600 points.
 

6th Grade to Pre-Algebra
Answer:  1 hour.
Isaac’s 50 pages per hour go into 300 pages 6 times (300 ÷ 50 = 6), so Isaac can finish the book in 6 hours. Since an hour and a half is 90 minutes, that means that Wyatt can read 1 page per minute, or 60 pages per hour. Wyatt’s 60 pages per hour go into 300 pages 5 times (300 ÷ 60 = 5). So, Wyatt can read a 300 page book an hour faster than Isaac.
 

Algebra and Up
Answer:  -2, -1, 0, 1, and 2.
When we solve the first inequality, we get 3x + 7 < 16, 3x < 9, x < 3. When we solve the second, we get 2x – 5 ≥ –9, 2x ≥ –4, x ≥ –2. So, x can be an integer that’s greater than or equal to –2 and less than 3. That means x can be –2, –1, 0, 1, and 2.


Problems of the Week

8/14/17 - 8/19/17 

Pre-K to 2nd Grade
Question:  The world record for the greatest number of hula hoops spun at the same time is held by Marawa Ibrahim from Australia. She can spin 200 hula hoops at once. If Aria can spin 150 hula hoops right now, how many more does she need to spin to break the world record?

 

3rd to 5th Grade
Question:  The record for the largest pizza was broken when a restaurant called NIPfood made a pizza that was 1,260 square meters in area. If that pizza were cut in half, then each piece were cut in half, then each piece were cut in half again, over and over, until the pieces had been halved 10 times, how many pieces would there be?

 

6th Grade to Pre-Algebra
Question:  There are 2,700 residents of Casey, Illinois, home of the world’s largest mailbox. The mailbox is so big that a group of people can stand inside it. If there are 135 people standing inside the mailbox, what percentage of the population of Casey is in the mailbox?

 

Algebra and Up
Question:  Sweet Pea the dog holds the world record for the fastest 100 meters walked with a can balanced on her head. (Seriously.) She traveled the 100 meters in 2 minutes and 55 seconds. What was Sweet Pea’s average speed measured in meters per second?

 

 Answers

 

Pre-K to 2nd Grade
Answer:  51 hula hoops.
To get from 150 to 200 hula hoops, Aria would need 50 more. But that would only tie her with Marawa, so to break the record, Aria would need one more. 50 + 1 = 51 hula hoops.

 

3rd to 5th Grade
Answer:  1,024 pieces.
Each time we halve the pieces, we’re doubling the number of pieces in total. So, after the pizza is cut in half once, there are 2 pieces, then 4, 8, 16, 32, 64, 128, 256, 512, and finally 1,024 pieces.

 

6th Grade to Pre-Algebra
Answer:  5%.
One way to solve this problem is to reason that a percentage is out of 100, and there are 27 hundreds in 2,700. So, to find the percentage, we want to know what number goes into 135, 27 times: 135 ÷ 27 = 5. So, there are 5 residents for each hundred, meaning there are 5% of the residents in the mailbox.

 

Algebra and Up
Answer:  4/7 meters per second.
First, we need to know how many seconds are in 2 minutes and 55 seconds. Two minutes is the same as 120 seconds, and 55 more makes 175 seconds in total. A hundred meters over 175 seconds is the same as is the same as 100 ÷ 175 = 4/7 meters per second.


Problems of the Week

8/7/17 - 8/12/17 

Pre-K to 2nd Grade
Question:  There are six continents on a Risk game board. If there are 12 troops in North America, 16 troops in South America, 18 troops in Europe, 22 troops in Asia, 24 troops in Africa, and 100 troops on the board in total, then how many troops are in Australia?

 

3rd to 5th Grade
Question:  Each side of a Monopoly board has 11 spaces from one corner to the next. How many spaces are there around the whole board?

 

 

6th Grade to Pre-Algebra
Question:  In each set of Scrabble tiles, there are 42 vowels, 58 consonants, and 2 blanks. Nine of the tiles are A tiles. What fractional part of the tiles are not A tiles?

 

Algebra and Up
Question:  In the game Clue, there are 6 suspect cards, 6 tool cards, and 9 location cards. A combination of 1 suspect, 1 tool, and 1 location is selected at random at the beginning of the game and put in an envelope. What is the probability that the combination in the envelope is the Candlestick, the Library, and anyone but Colonel Mustard?

 

 Answers

 

Pre-K to 2nd Grade
Answer:  8 troops.
There are 12 + 16 + 18 + 22 + 24 = 92 troops on the board that aren’t in Australia, so there must be 100 – 92 = 8 troops in Australia.

 

3rd to 5th Grade
Answer:  40 spaces. 
Even though each side has 11 spaces, there aren’t 44 spaces because we’d be counting each corner twice. To find the number of spaces around the board, we only count one of the corners for each side, leaving 10 spaces to count for each side. That’s 10 × 4 = 40 spaces.

 

6th Grade to Pre-Algebra
Answer:  31/34.
There are 42 + 58 + 2 = 102 tiles in total. If 9 of them are As, then 9/102 = 3/34 of them are A tiles. That means that 34/34 – 3/34 = 31/34 of the tiles are not A tiles.

 

Algebra and Up
Answer:  5/324.
The probability that the crime took place in the Library with the Candlestick is 1/9 × 1/6 = 1/54. There are 5 suspects who aren’t Colonel Mustard, so that means that the probability that anybody but Colonel Mustard committed the crime in the Library with the Candlestick is 1/54 × 5/6 = 5/324.


Problems of the Week

7/31/17 - 8/05/17

 

Pre-K to 2nd Grade
Question:  One robot can lift and carry 900 pounds. A second robot can lift and carry 1,800 pounds. If the robots work together, can they lift a boulder that weighs 2,500 pounds?

 

3rd to 5th Grade
Question:  A fruit punch powered robot has a box-shaped punch tank that is 10 centimeters wide, 20 centimeters long, and 30 centimeters high. If the tank already has 600 cubic centimeters of punch in it, how much more punch can the robot hold?

 

6th Grade to Pre-Algebra
Question:  There are three different types of robot batteries. A blue battery lasts as long as three green batteries. Two green batteries last as long as five yellow batteries. How many yellow batteries last as long as a blue battery?

 

Algebra and Up
Question:  A robot can run 25 meters per second. The robot’s robot dog, K9, can run 20 meters per second. If K9 runs away from the robot and the robot starts chasing it 10 seconds later, how long will it take for the robot to run and catch K9?

 

 Answers

 

Pre-K to 2nd Grade
Answer:  Yes.
Together, the robots can lift 900 + 1,800 = 2,700 pounds. Since 2,500 pounds is less than 2,700 pounds, the robots can lift the boulder.

 

3rd to 5th Grade
Answer:  5,400 cubic centimeters
The volume of a box is its length multiplied by its width multiplied by its height. So, the volume of the tank is 10 × 20 × 30 = 6,000 cubic centimeters. Since the tank already has 600 cubic centimeters of punch in it, it can hold 6,000 – 600 = 5,400 cubic centimeters more.

 

6th Grade to Pre-Algebra
Answer:  7.5 yellow batteries.
The ratio of blue batteries to green batteries is 1 blue to 3 green. The ratio of green batteries to yellow batteries is 2 green to 5 yellow. To compare the ratios, we’ll need to multiply each so that they have the same number of green batteries: there are 2 blues to 6 greens, and 6 greens to 15 yellows. That means that there are 2 blues to 15 yellows, which is the same as 1 blue to 7.5 yellows. So, 7.5 yellow batteries last the same amount of time as a blue battery.

Algebra and Up
Answer:  40 seconds.
By the time the robot starts running, K9 has already gone 20 × 10 = 200 meters. So, we need to know when the distance the robot can run in x seconds is equal to 200 meters more than K9 can run in the same amount of time:
25x = 200 + 20x
5x = 200
x = 40 seconds.


Problems of the Week

7/24/17 - 7/29/17 

Pre-K to 2nd Grade
Question:  John has 8 quarters. He buys a bottle of pop and gets 6 dimes in change. How much does the pop cost?

 

3rd to 5th Grade
Question:  Mila has ¾ of a pound of caramels. Nora has 0.2 pounds of caramels. How much do their caramels weigh altogether?

 

 

6th Grade to Pre-Algebra
Question:  Lucas has an average score of 40 points on his five history quizzes. He scored 35, 44, 41, and 38 on the first four quizzes. How many points did he score on the last quiz?

 

Algebra and Up
Question:  You roll two six-sided dice and add their values together. What is the probability of rolling a prime number?

 

 Answers

 

Pre-K to 2nd Grade
Answer:  $1.40.
Each quarter is worth 25¢, so 8 quarters are worth 200¢, or $2.00. Each dime is worth 10¢, so 6 of them are worth 60¢. The bottle of pop costs the difference between the amount John pays and the amount of change he gets, so the pop is worth $2.00 – $0.60 = $1.40.

 

3rd to 5th Grade
Answer:  0.95 pounds.
One way to do this problem is to convert ¾ into a decimal in order to add it to the other decimal. Mila has ¾ = 0.75. Since 0.75 + 0.2 = 0.95, Nora and Mila have 0.95 pounds of caramels altogether.

 

6th Grade to Pre-Algebra
Answer:   42 points.
Because there are five quizzes in total and Lucas scored an average of 40 points, he must have scored a total of 200 points because 40 × 5 = 200. He scored a total of 35 + 44 + 41 + 38 = 158 points on the first four quizzes, so he must have scored 200 – 158 = 42 points on the last quiz.
 

Algebra and Up
Answer:  5 out of 12.
To roll a prime, you’d need to roll a 2, 3, 5, 7, or 11. There is one way to roll a 2, two ways to roll a 3, four ways to roll a 5, six ways to roll a 7, and two ways to roll an 11. So, there are 15 total ways to roll a prime. There are 6 sides on a die, so 6 × 6 = 36 possible outcomes when you roll two dice. That means the probability of rolling a prime is 15 out of 36, which reduces to 5 out of 12.


Problems of the Week

7/10/17 - 7/15/17

 

Pre-K to 2nd Grade
Question:   Laura and Harold are repotting orchids. They plant 2 orchid plants in each pot. When they’re done, they have 3 rows of 5 pots of orchids. How many orchid plants did Laura and Harold repot?

 

3rd to 5th Grade
Question:  Christine has a cube-shaped box that is 1 foot wide that is completely filled with 1-inch cube-shaped blocks. She takes three-quarters of them out. How many blocks are left in the box?

 

6th Grade to Pre-Algebra
Question:  Noah ate 5/12 of a bowl of ice cream. Brooklyn ate 6/14of the same ice cream. Who ate more ice cream? How much more?

 

Algebra and Up
Question:  In the figure below, AG is a line and the measure of x is two times the measure of y. What is the value of y?

 Answers

 

Pre-K to 2nd Grade
Answer:  30 orchid plants.
Since there are 3 rows of 5 pots, there are 5 + 5 + 5 = 15 pots. Since there are two orchid plants in each pot, there are 15 + 15 = 30 orchid plants in total. Laura and Harold replanted 30 orchid plants.

 

3rd to 5th Grade
Answer:  432 blocks.
A foot is 12 inches, so the box is 12 blocks wide × 12 blocks long × 12 blocks tall = 1,728 cube-shaped blocks in volume. If Christine takes three-quarters of the blocks out, that means that there’ll be one-quarter of them left in the box. So, we divide: 1,728 ÷ 4 = 432. There are 432 blocks left in the box.

 

6th Grade to Pre-Algebra
Answer:   Brooklyn ate 1/84 of the ice cream more than Noah.
To find the difference, we’ll need to find the least common denominator of the fractions. Since the LCM of 12 and 14 is 84, we need to convert the fractions to 84ths. Noah ate 5/12 = 35/84 of the ice cream, and Brooklyn ate 6/14 = 36/84 of the ice cream. Brooklyn therefore ate 36/84 – 35/84 = 1/84 of the ice cream more than Noah.

 

Algebra and Up
Answer: 40°.
Since AG is a line, 6z = 180°. So, z = 180° ÷ 6 = 30°. We also know that x + y + 2z = 180°, or x + y + 60 = 180°, or x + y = 120°. If x = 2y, then we can conclude that 3y = 120°. So, y must be 120° ÷ 3 = 40°.

 


Problems of the Week

7/3/17 - 7/8/17

 

Pre-K to 2nd Grade
Question:  Anna picks twice as many tomatoes as Brayden. Catherine picks 12 more tomatoes than Brayden. If Catherine picks 16 tomatoes, then how many tomatoes does Anna pick?

 

3rd to 5th Grade
Question:  Francis is chopping a 10-layered onion. He first cuts the onion in half vertically, from stem to roots. He then cuts each half of the onion 5 times horizontally. How many pieces of onion does Francis have after he separates all the layers?

 

6th Grade to Pre-Algebra
Question:  John is growing broccoli in his garden. He plants the broccoli in the morning on April 1. 96,480 minutes later, he harvests the broccoli. On what date does John harvest the broccoli?
(You may look up how many days are in each month.)

 

Algebra and Up
Question:  A strawberry has 1 seed per 5 square millimeters on its surface. Use the formula for the surface area of a cone—surface area = πr(r+sqrt[h2 + r2])—to approximate the number of seeds on an almost-cone-shaped strawberry whose height is 36 mm and whose diameter at its widest is 54 mm. Round your answer to the nearest whole number.

 Answers

 

Pre-K to 2nd Grade
Answer:  8 tomatoes.
Catherine has 16 tomatoes, so Brayden must have 16 - 12 = 4 tomatoes. Anna has twice as many, so she has 4 x 2 = 8 tomatoes. 

 

3rd to 5th Grade
Answer:  100 pieces.
There are 10 layers of onion, so we can think of that as 10 pieces. When Francis cuts the onion in half, that makes twice as many pieces: 10 x 2 = 20. When he cuts each half onion horizontally 4 times, he multiplies the number of pieces by 5: 20 x 5 = 100.

 

6th Grade to Pre-Algebra
Answer:  June 7.
If we divide 96,480 minutes by 60 minutes, we find that John harvested the broccoli 1,608 hours after he planted it. 1,608 hours ÷ 24 hours = 67 days. So, John harvested the broccoli on June 7, 67 days after April 1. 

 

Algebra and Up
Answer: 1,221 seeds.
Answers may vary, depending on where in the process you round. Since the diameter of the strawberry is 54 mm, its radius is 27 mm. When we substitute those values into the equation, we find that the surface area of a cone with the same dimensions is 1,944π square millimeters. If we divide that by 5, we get 388.8π, or about 1,221. So, we can approximate that the strawberry has 1,221 seeds.

 


 

Problems of the Week

6/26/17 - 7/1/17

 

Pre-K to 2nd Grade
Question:  Martin rolls a fair, standard, six-sided die. Match each outcome with its likelihood. 

• Martin rolls an even number.
• Martin rolls an 8.
• Martin rolls a number less than 10.
• Martin rolls a 1.
• Martin doesn’t roll a 6.

• Impossible
• Unlikely
• As likely as not
• Very likely
• Certain.

 

3rd to 5th Grade
Question:  Tara gets to draw one bill at random from either of two buckets. One bucket has 30 $1 bills and 2 $100 bills. Another bucket has 80 $1 bills and 4 $100 bills. Which bucket should Tara choose? Why?

 

6th Grade to Pre-Algebra
Question:  The ratio of apples to oranges in a box is 7:18. What is the percent chance that a fruit drawn at random from the box will be an orange?

 

Algebra and Up
Question:  There are 100 marbles in a bag. They’re numbered 0, 1, 2, all the way through 99. What is the probability that if you draw three marbles out of the bag at random without replacing them, the number on the first marble will be 0, the number on the second will be 1, and the number on the third will be 2?

 

 Answers

 

Pre-K to 2nd Grade
Answer:  It’s as likely as not that Martin rolls an even number because there are 3 even numbers and 3 odd numbers on a die. It’s impossible that he rolls an 8 because there isn’t an 8 on a die. It’s certain that he rolls a number less than 10 because all the numbers on a die are less than 10. It’s unlikely that he rolls a 1 because only 1 out of 6 numbers on a die is 1. It’s very likely that he doesn’t roll a 6 because 5 out of 6 numbers on a die aren’t 6.


3rd to 5th Grade
Answer:  Tara should choose the bucket with 30 $1 bills and 2 $100 bills.
Since 2 out of 30 + 2 = 32 bills in the first bucket are $100 bills, that means that 2/32 = 1/16 of the bills are $100. In the other bucket, 4 out of 80 + 4 = 84 bills are $100, so 4/84 = 1/21 bills are $100. Since the first bucket has the greater fractional part comprising $100 bills, that’s the smarter bucket to choose.

 

6th Grade to Pre-Algebra
Answer:  72%.
There are 7 + 18 = 25 fruits in the box. Since 18 out of 25 fruits are oranges and a percentage is out of 100, we can multiply 18 and 25 each by 4 to find the number of fruits out of 100 that are oranges. 18 × 4 = 72, so 72% of the fruits are oranges. If one is chosen at random, then the percent chance that it’ll be an orange is 72%.

 

Algebra and Up
Answer: 1 out of 970,200.
 The probability of drawing the 0 first is 1/100. If the marble isn’t replaced, then the probability of drawing the 1 next is 1/99. Then, the probability of drawing the 2 next is 1/98. So, the probability of drawing exactly those numbers in that order is 1/100 × 99 × 98 = 1/970,200.

 


Problems of the Week

6/19/17 - 6/24/17

 

Pre-K to 2nd Grade
Question:  Start with 1. Add 15. Subtract 11. Double it. Add 1. Multiply by 5. Subtract 30. Take away half. What’s the new number?

 

3rd to 5th Grade
Question:  It takes Evelyn 8 minutes to jog all the way around a circular path. If Evelyn starts at 6:35 AM and jogs around the path exactly 8 times, what time will it be when she’s done?

 

6th Grade to Pre-Algebra
Question:  24–karat gold is 100% pure gold. How many ounces of pure gold are there in a 15 pound, 16–karat gold bar?

 

Algebra and Up
Question:  There are two perpendicular lines graphed on a plane. Line A goes through the points (2, 1) and (6, 3). Line B goes through (2, 1) and (x, 5). Solve for x.

 

 Answers

 

Pre-K to 2nd Grade
Answer:  12½.
After we add 15 to 1, we have 16. Then we subtract 11, so we have 16 – 11 = 5. After we double it, we have 5 × 2 = 10. One more makes 11. Next, we have 11 × 5, which makes 55. Thirty less than 55 is 25. Since 25 is odd, we can find half of it by finding half of 24 and half of 1. Half of 24 is 12, and half of 1 is ½, so that gives us a final answer of 12½.


3rd to 5th Grade
Answer:  7:39 AM.
Eight minutes, 8 times is 8 × 8 = 64 minutes. There are 60 minutes in an hour, so Evelyn jogs for 1 hour and 4 minutes because 64 minutes – 60 minutes (1 hour) = 4 minutes. One hour after 6:35 AM is 7:35 AM, and 4 minutes after that is 7:39 AM.

 

6th Grade to Pre-Algebra
Answer:  160 ounces.
16–karat gold is 16/24 pure gold, or 2/3. Since two thirds of the gold bar is pure gold, that means that there are 15 × 2/3 = 10 pounds of pure gold. There are 16 ounce in a pound, so 10 pounds of pure gold is the same as 160 ounces of pure gold.

 

Algebra and Up
Answer: x = 0.
To solve for x, we need to know the slope of Line B. Line A and Line B are perpendicular, so the slope of Line B is the opposite of the reciprocal of the slope of Line A. Line A’s slope is (y2 – y1) ÷ (x2 – x1) = (3 – 1) ÷ (6 – 2) = 1/2 , so the slope of Line B must be –2. Now that we have a point on the line and its slope, we can write an equation in slope-intercept form:

y = –2x + b
y = 1 x = 2
1 = –4 + b
b = 5
y = –2x + 5

5 is the y–intercept. When y = 5, then x = 0.


Problems of the Week

6/12/17 - 6/17/17

 

Pre-K to 2nd Grade
Question:  Each soccer team has the following players: 1 goalie, 4 defenders, 4 midfielders, and 2 forwards. How many players are on 5 soccer teams?

 

3rd to 5th Grade
Question:  Jayce and Arianna are practicing their golf swings. They bring 32 golf balls to the course. Jayce hits all 32 first, then retrieves all but one. Then it’s Arianna’s turn to hit all the remaining golf balls and retrieve them, but she also loses one. If this pattern continues, who will take the 12th turn, and how many golf balls will he or she hit? Find a way to solve the problem without counting each turn.

 

6th Grade to Pre-Algebra
Question:  Chad and Michael play on the same baseball team. Last year, they both had a batting average of .240. Michael’s batting average increased by the same amount that Chad’s batting average decreased. If Michael has a batting average of .270 this season, then what fractional part of Michael’s new batting average is Chad’s new batting average?

 

Algebra and Up
Question:  Magenta and Tavia are both running toward a soccer ball. Magenta is 28 meters away and Tavia is 33 meters away. If Magenta can run 2.5 meters per second and Tavia can run 2.75 meters per second, then how much sooner does the player who reaches the ball first get there?

 

 Answers

 

Pre-K to 2nd Grade
Answer:  55 players.
Instead of adding each position individually, we can find the number of players on each team first. There are 1 + 4 + 4 + 2 = 11 players on each soccer team. So, on 5 teams, there are 11 × 5 = 55 players!


3rd to 5th Grade
Answer:  Arianna hits 21 golf balls.
Jayce has the odd numbered turns and Arianna has the even numbered turns. Since 12 is an even number, Arianna must have the 12th turn. By the 12th turn, only 11 (not 12) golf balls have gotten lost because the balls get lost at the end of the turn. So, Arianna hits 32 – 11 = 21 golf balls.

 

6th Grade to Pre-Algebra
Answer:  7/9.
Since Michael’s average goes up by .030, Chad’s must go down by .030 to .210. Next, we can find out what fractional part Chad’s batting average is of Michael’s by dividing .210 by .270. First, we multiply both numbers by 100 to get 21/27, then we can reduce the fraction to 7/9.

 

Algebra and Up
Answer:  Magenta reaches the ball 0.8 seconds before Tavia.
If Magenta runs 2.5 meters per second, then it takes her 28 meters ÷ 2.5 = 11.2 seconds to reach the ball. Tavia reaches the ball in 33 ÷ 2.75 = 12 seconds. This means that Magenta got there 12 – 11.2 = 0.8 seconds before Tavia.


Problems of the Week

6/5/17 - 6/10/17

 

Pre-K to 2nd Grade
Question: Jack builds a sand castle with 8 different sand molds. The smallest mold holds 1 1/2 cups of sand. The next mold holds 3 cups of sand. The third mold holds 6 cups of sand, and the fourth holds 12 cups of sand. If the pattern continues, then how much sand does the biggest mold hold?

 

3rd to 5th Grade
Question: Aria, Brett, and Chelsea bounce a beach ball between them 100 times. Aria bounces the ball to Brett, Brett bounces the ball to Chelsea, Chelsea bounces the ball to Aria, and the pattern continues. Who bounces the ball the 100th time?

 

6th Grade to Pre-Algebra
Question:  Ava collects 4 more than twice as many sea shells as Ben. Ben collects 1 fewer than half as many as Carla. Carla collects 200 sea shells. How many sea shells does Ava collect?

 

Algebra and Up
Question:  A circular beach umbrella with an area of 16π square feet casts a circular shadow with a circumference of 16π feet. What is the circumference of umbrella at the same height that casts a shadow whose area is 256π square feet? (For the purposes of this exercise, pretend umbrellas are flat circles instead of domes.)

 

 Answers

 

Pre-K to 2nd Grade
Answer:  192 cups.
Each mold holds twice as much as the last. So, the fifth holds 12 + 12 = 24 cups. The sixth holds 24 + 24 = 48 cups. The seventh holds 48 + 48 = 96 cups, and the eighth holds 96 + 96 = 192 cups.


3rd to 5th Grade
Answer:  Aria.
There are three beach ball bouncers in the group, and Chelsea is the third. So, for each bounce that’s numbered a multiple of 3, Chelsea must bounce the ball. The closest multiple of 3 before 100 is 99, so Chelsea bounces the ball the 99th time. That means that Aria bounces the ball the 100th time because she’s next in the pattern.

 

6th Grade to Pre-Algebra
Answer:  202 sea shells.
Since Carla collects 200, Ben must collect 99 because half of 200 is 100 and one less than that is 99. Ava collects 4 more than twice as many as Ben. Twice as many as 99 is 198, and 4 more than that makes 202 sea shells.

 

Algebra and Up
Answer:  16π feet.
If the small umbrella has an area of 16π square feet, its radius must be 4 feet. If its shadow has a circumference of 16π feet, then its radius must be 8 feet. The radius of the shadow is double the radius of the umbrella. Since we know the area of the larger shadow is 256π square feet, its radius must be 16 feet. That means that the radius of the larger umbrella must be half of that, 8 feet, making its circumference 16π feet.


Problems of the Week

5/30/17 - 6/3/17

 

Pre-K to 2nd Grade
Question: A clown makes 11 balloon poodles, 15 balloon octopi, 4 balloon flowers, and a balloon giraffe. How many balloon animals does the clown make?

 

3rd to 5th Grade
Question:  A spinning prize wheel has four different varieties of prizes. 40% of the prizes are items from a prize case. 30% of the prizes are tickets to a concert. 20% of the prizes are cash. The other 2 prizes are all-expense-paid trips. How many total prizes are on the wheel?

 

6th Grade to Pre-Algebra
Question:  A dunk tank is 4/5 full. After Dave gets dunked, 1/4 of the water splashes out. After that, there are 450 gallons of water left. How many gallons of water does the dunk tank hold when it’s full?

 

Algebra and Up
Question:  The paper cone of a snow cone is 5 inches deep and 3 inches wide at its opening. If the cone is filled to the top with snow and then a perfect hemisphere of snow is placed on top, what is the volume of the snow in cubic inches?

 

 Answers

 

Pre-K to 2nd Grade
Answer: 27 balloon animals.
The clown makes three different kinds of animals—poodles, octopuses, and giraffes. Let’s add them together, one species at a time. There are 11 poodles and 15 octopuses, and 11 + 15 = 26. One more, the giraffe, makes 27.


3rd to 5th Grade
Answer:  20 prizes.
First we need to know what percentage of the prizes are all-expense-paid trips. The rest of the prizes add up to 40% + 30% + 20% = 90%, so the other 10% of the prizes are all-expense-paid trips. If 2 is 10%, or one tenth, of the total, then there are 2 × 10 = 20 prizes on the wheel.

 

6th Grade to Pre-Algebra
Answer:  750 gallons.
If 1/4 of the water in a 4/5–full tank leaks out, then the tank is now 3/5 full. If 450 gallons makes up 3/5 of the tank’s capacity, then 1/5 of it must be 450 ÷ 3 = 150 gallons. 150 gallons, 5 times makes 5/5 of the tank’s capacity, and 150 × 5 = 750 gallons.

 

Algebra and Up
Answer:  6π cubic inches.
The volume of the semisphere of snow is equal to half of 4/3 ⋅ πr3, or 2/3 ⋅ πr3 (we can do this because half of 4/3 is 2/3). The volume of the cone is πr2 ⋅  h/3. We know that h = 5 and r = 1.5, so altogether, the volume of the snow cone is:
(2/3 × π × 1.53) + (π × 1.52 × 5/3)
Altogether, the above equals 2.25π + 3.75π = 6π cubic inches, or approximately 18.85 cubic inches.