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Peg + Cat: The Race Car Problem Math Activities Teaching Guide

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Peg + Cat: The Race Car Problem

Peg and Cat have built an amazing car out of things they found lying around, and they plan to win the Tallapegga Twenty. If they can make it out of the junkyard, that is. It’s a good thing Peg knows the best shape to use to make wheels and how to count laps to see who is ahead. Will Peg and Cat be the first to complete twenty laps and win the Golden Cup?

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HOME > Maths > Calculations > Problem Solving

RUCSAC Problem Solving Acronym Posters (SB6628)

A set of A4- sized rucksack posters to act as visual reminders when pupils are working on problem solving activities.  The RUCSAC acronym stands for read, understand, choose, solve, answer and check.

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RACE CAR Problem Solving Acronym Posters (SB6629)

A set of A4- sized formula one racing car posters to act as visual reminders when pupils are working on problem solving activities.  The RACE CAR acronym stands for read, ask, choose, experiment, check, answer, report.

Year 6 General Maths Loop Cards (SB6630)

A set of loop cards with various number problems aimed at Year 6.  30 different cards included.  Includes multiplication, fractions, division, subtraction, addition and more.  One child calls out the start card and the pupils then match/call out the corresponding cards until the game ‘loops’ back to the original child.

Days and Months Maths Loop Cards (SB6839)

A set of loop cards with questions related to days and months - aimed at Year 3/4.  Questions include How many days in a fortnight?’, ‘How many hours in 2 days?’ and ‘How many seconds in 1 minute?’ etc.

Reception Maths Vocabulary Cards: Solving Problems (SB2122)

A set of printable cards featuring the mathematical vocabulary for ‘Solving problems’ to be used in Reception.

Year 1 Maths Vocabulary Cards: Solving Problems (SB2257)

A set of printable cards featuring the mathematical vocabulary for ‘Solving problems’ to be used in Year One.

Year 2 Maths Vocabulary Cards: Solving Problems (SB2336)

A set of printable cards featuring the mathematical vocabulary for ‘Solving problems’ to be used in Year Two.

Year 3 Maths Vocab Cards: Solving Problems (SB6883)

A set of printable cards featuring the mathematical vocabulary for ‘Solving problems’ to be used in Year 3.

Year 4 Maths Vocab Cards: Solving Problems (SB6899)

A set of printable cards featuring the mathematical vocabulary for ‘Solving problems’ to be used in Year 4.

Year 5 Maths Vocab Cards: Solving Problems (SB6906)

A set of printable cards featuring the mathematical vocabulary for ‘Solving problems’ to be used in Year 5.

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Race Car Math: Counting and Number Recognition Activity for Preschoolers

February 17, 2014, join the conversation, categories/tags:, ages 3-5 math and literacy ages 5-7 preschool, want these great ideas sent right to your inbox sign up for the newsletter..

Here’s a fun preschool math activity that teaches counting and number recognition through racing Hot Wheels cars!

For preschoolers, often the most motivating way to learn to count and recognize written numbers is through play.  The boys are STILL obsessed with Hot Wheels (if you’ve been following our blog, you’ll know that this has lasted for a long time!), and we set up a Hot Wheels car race to practice recognizing, counting, and writing the numbers 1-20.

First, we chose 20 cars to be in our race.  The boys spent a lot of time deciding which cars would race and what numbers they would be.  🙂  I labeled the cars with masking tape and a sharpie.

For the car races, we used our rain gutter ramps.  Check out our rain gutter Hot Wheels racing ramps post for more details!

I had Aidan make squares of paper with the numbers 1-20.  We put the squares in a bowl.  For each heat, I had Owen draw out two squares, and those would be the cars that would race down the ramp.

Owen had to find the cars with the correct numbers on them (number recognition!).

Then he wrote the race results in a chart that I made for him.  For each heat, Owen wrote down the numbers of the cars that were racing.  Then, he circled the number of the winner.

We had so much fun!

More math with Hot Wheels:

• Sort them by color and count the groups.
• Sort them by type of vehicle and count the groups.
• Create adding problems – red cars plus blue cars, etc.

Shekinah Kromhout Mar 1, 2014

Hello! I find your blog so underwhelming and refreshing. This idea with the cars are perfect for my girls. They adore cars as well. So thank you and please keep blogging!

Melissa Eigsti Apr 30, 2014

My boys loved this game! I did it for my kindergartner to help him read numbers 11-30. We used your rain gutter idea but my boys added masking tape at the end to create a finish line. It was easier to see which car won depending on which side broke the tape open. Also we practiced number sequencing by lining the cars up in order. If you fold the paper into 16 rectangles they are the perfect size for lining up the cars. After removing the cars for their race, we wrote the numbers on the paper in their place for record keeping. This has been a popular FB post among my boy-heaving homeschooling groups!

Robin May 25, 2014

Cars are great for the four times tables too. 4 wheels per car, 8 cars=32 wheels total. You could use motorcycles for the 2 times tables and transport trucks for 6 or 8 times tables (depending on the truck).

Sarah May 28, 2014

That's a great idea!

MypolishKiddos Mar 14, 2017

My 4 year old is obsessed with hot wheel cars so he's gonna love this activity :)

Regula Apr 28, 2020

I am a kindergarten teacher and due to COVID I write every day a letter to my little students full of ideas and games to keep them busy at home. Your idea is wonderful. I will explore your blog to find more games I can send to my students. Thank you very much.

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How Race Car Drivers Use Math

By Sheri L. Arroyo

Math Curriculum Consultant: Rhea A. Stewart, M.A., Specialist in Mathematics, Science, and Technology Education Math in the Real World: How Race Car Drivers Use Math

Copyright © 2010 by Infobase Publishing

All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval systems, without permission in writing from the publisher. For information contact:

Chelsea Clubhouse An imprint of Chelsea House Publishers 132 West 31st Street New York NY 10001

Library of Congress Cataloging-in-Publication Data Arroyo, Sheri L. How race car drivers use math / by Sheri L. Arroyo; math curriculum consultant, Rhea A. Stewart. p. cm. — (Math in the real world) Includes index. ISBN 978-1-60413-609-8 1. Mathematics—Juvenile literature. 2. Automobile racing drivers—Juvenile literature. I. Title. II. Series. QA135.6.A78 2010 510—dc22 2009021476

Chelsea Clubhouse books are available at special discounts when purchased in bulk quantities for businesses, associations, institutions, or sales promotions. Please call our Special Sales Department in New York at (212) 967-8800 or (800) 322-8755.

You can find Chelsea Clubhouse on the World Wide Web at http://www.chelseahouse.com

Developed for Chelsea House by RJF Publishing LLC (www.RJFpublishing.com) Text and cover design by Tammy West/Westgraphix LLC Illustrations by Spectrum Creative Inc. Photo research by Edward A. Thomas Index by Nila Glikin

Photo Credits: 4, 21, 22: Getty Images; 6: JASON REED/Reuters/Landov; 8: © Wm. Baker/GhostWorx Images/Alamy; 10: © Tony Watson/Alamy; 12: RUSSELL LABOUNTY/CSM/Landov; 14, 25: AP/Wide World Photos; 16: TIM WIMBORNE/Reuters/Landov; 18: ALESSANDRO BIANCHI/Reuters/Landov; 20: PAULO WHITAKER/Reuters /Landov; 24, 26: AFP/Getty Images.

Printed and bound in the United States of America

Bang RJF 10 9 8 7 6 5 4 3 2 1

This book is printed on acid-free paper.

All links and Web addresses were checked and verified to be correct at the time of publication. Because of the dynamic nature of the Web, some addresses and links may have changed since publication and may no longer be valid. Table of Contents

Racing and Math...... 4 Track Design...... 6 Drag Racing...... 8 E.T. Racing...... 10 Go as Fast as You Can!...... 12 NASCAR: Winning the Championship...... 14 Formula One...... 16 F1: The Driver and His Team...... 18 The Fuel...... 20 The Tires...... 22 How’s My Driving?...... 24 Driver Training...... 26 If You Want to Be a Race Car Driver...... 28 Answer Key...... 29 Glossary...... 30 To Learn More...... 31 Index...... 32

Answers and helpful hints for the You Do the Math activities are in the Answer Key. Words that are defined in the Glossary are in bold type the first time they appear in the text. Racing and

Math he drivers have suited up and Tclimbed into their cars. Engines roar. All eyes are on the checkered flag. The flag drops. The drivers roar off—challenging themselves, their teams, and other drivers to perform to the best of their ability. Math is used by the drivers, by their pit crews, and by race car designers before, during, and after a race. This is a sport where everything is measured and analyzed!

The Math of Racing Cars race around the track at the Talladega There are different kinds of racing. Superspeedway. Each has a different kind of car and

4 track. In all of the types, though, math is used in many ways. How much fuel should be put in the car before a race? How fast was the driver’s qualifying time, and how does it compare to the times of other drivers? What was the driver’s speed on the straight part of the track compared with the curves? The driver and team answer these questions and more by doing math. You Do the Math Fastest Times Before races on an oval track, drivers who want to compete in the race take 2 laps to drive as fast as they can. The amount of time it takes a driver to complete his fastest lap is his official qualifying time. How fast each driver went as he raced around the track is his qualifying speed. The bar graph shows the fastest (best) qualifying speeds recorded at 10 tracks in the years 2000–2008. Use the graph to answer the questions. 1. Which track’s best qualifying speed was fastest? Texas Motor Speedway 196 2. Which track’s best qualifying Las Vegas Motor Speedway 185 speed was slowest? Auto Club Motor Speedway 188 3. What is the difference Michigan International Speedway 194 between the fastest and Lowes Motor Speedway 193 slowest best qualifying Indianapolis Motor Speedway 186 speeds? Chicagoland Speedway 188 4. How much slower was the Atlanta Motor Speedway 195 Race Tracks Race Tracks best qualifying speed at Talladega Superspeedway 192 Daytona International Daytona International Speedway 191 Speedway than at Texas Motor Speedway?

184185 186187 188 1891 19091 192193 194195 196 1971198 99 Qualifying Speeds (in miles per hour, MPH)

5 Track Design here are special tracks for differ- Tent kinds of races. NASCAR races take place on oval tracks, such as the Indianapolis Motor Speedway. In NASCAR races, the cars look very much like regular cars. NASCAR stands for the National Association for Stock Car Auto Racing. Drag racing, or hot-rod racing, is a short but fast race between two cars at a time. Drag racing is held at special tracks with a 1 -mile-long 4 straight path for the cars to race on. Indy Car races and Formula One A view from the air of the races use extremely fast, specially Indianapolis Motor Speedway. designed race cars. Indy cars race on oval tracks. Formula One races are held on road courses.

Track Types Oval tracks are grouped by their length. The length of a track is the 6

distance around the track once, beginning and ending at a starting line. Short tracks are oval tracks that are less than 1 mile in length. Intermediate tracks are from 1 mile to 2 miles in length. Superspeedways are tracks greater than 2 miles in length. Road courses are not oval in shape. They have irregular shapes and many turns (some- thing like an actual road with many sharp curves). They are more than 2 miles long. You Do the Math Comparing Tracks Look at the table with data about different oval tracks. The table tells how long each track is and how many people it can seat.

Data about Oval Tracks Track Length Seats Dover 1.0 miles 140,000 Daytona Beach 2.5 miles 168,000 Charlotte 1.5 miles 165,000 Indianapolis 2.5 miles 250,000 Kansas City 1.5 miles 82,000 Martinsville 0.5 miles 65,000

1. Order the race tracks by spectator seats from the track that has the least number of seats to the track that has the greatest number. 2. Which tracks are superspeedways? 3. What is the difference in length between Daytona Beach and Martinsville? 4. Indianapolis has sold 135,000 seats for an upcoming race. How many seats are still available? 7 Drag Racing

drag race is a contest between A two race cars that is held on a track called a drag strip. The cars 1 drive 4 of a mile straight down the track. After a car crosses the finish line, the driver releases a parachute, which helps bring the car to a stop. A drag race event will often have many cars entered in it. As each two-car race is run, the los- ing car is eliminated. Each winning car keeps racing until only one car is left that hasn’t lost a race. That car is the winner of the event.

Elapsed Time, Speed, and Reaction Time A race begins with a signal from an electronic device called a Christmas tree. The device has different colored lights. When the green light goes on, the race begins. The device used to signal the start of a drag race is called As each car takes off, it crosses a a Christmas tree. line and starts an elapsed-time clock. The clock stops when that car cross- es the finish line. The start-to-finish

8 time is the car’s elapsed time. The car with the shortest elapsed time wins the race. Each car’s speed is also measured in a 66-foot stretch that ends at the finish line. Speed is important to win a race, but so is the driver’s reaction time. This is how quickly the driver reacts to the green light. A driver with a slower speed can still win the race if he had the fastest reaction to the green light and got his car to accelerate (pick up speed) faster at the beginning of the race. You Do the Math

Who Wins? The tables below show the elapsed time and the speed in miles per hour (mph) for two races. Use the tables to answer the questions.

Results of Race #1 Driver Elapsed Time Speed Steph 8.35 seconds 181.48 mph Tran 8.09 seconds 181.45 mph

Results of Race #2 Driver Elapsed Time Speed Jason 7.68 seconds 192.51 mph Ed 9.18 seconds 107.88 mph

1. In Race #1, which driver had the shortest elapsed time? Who had the fastest speed? Who won the race? How do you know? 2. In Race #2, who lost the race? What was the difference between his elapsed time and the winner’s elapsed time? 9 E.T. Racing

ne popular type of drag racing Ois called E.T. (elapsed time) racing. In this kind of racing, any two cars can race against each other. The slower car is given a head start.

Calculating the Head Start In order to figure out which car will receive the head start, each car is timed doing a few practice runs on Two cars race down a drag strip, the 1 -mile track. The drivers use each driver trying to achieve the 4 shortest elapsed time. those practice times to calculate how

10 much time they think they need to cover the track during the actual race. This time is called their “dial-in.” Drivers choose their own dial- ins, but they must choose a time they think is realistic. Any driver choosing too slow a dial-in to get a bigger head start can be disqualified from the race. Before a race, the two drivers’ dial-ins are compared. The difference between the times is the amount of the head start that will be given to the slower car. For example, Driver A chooses a dial-in of 17 seconds, and Driver B chooses a dial-in of 15 seconds. The difference is 2 seconds (17 – 15 = 2). So, Driver A will get a 2-second head start against Driver B. You Do the Math

Calculating the Dial-in To determine his dial-in, a driver does 3 practice runs. Then, he calculates the average elapsed time for these runs by adding the 3 times together and then dividing the sum by 3. For example, Driver C is timed at 15, 14, and 16 seconds. The average time is 15 seconds: 15 + 14 + 16 = 45 45 ÷ 3 = 15 He chooses 15 seconds as his dial-in. Calculate the dial-ins for these drivers, assuming each one uses the average of his practice times as his dial-in. 1. Driver D: practice runs of 12, 10, and 14 seconds 2. Driver E: practice runs of 14.5, 16, and 16 seconds

11 Go as Fast as You Can! ot every race car driver who Nwants to compete in a NASCAR race can do so. In the days before a race, drivers and their cars must “qualify” (earn a place in the race) by performing well enough in what are called the qualifying rounds. The first step is for a member of each driver’s race team to go to a drawing where a bingo-like machine gives each driver a number. The numbers tell drivers when it’s their turn to try to qualify. In the qualifying rounds, cars go around the track one at a time. After warming up, drivers have two laps to go as fast as they can. Each lap is timed separately, and the faster of

Racing fans watch the cars zip by during a NASCAR race.

12 the two times is the car’s qualifying time. Only drivers with the faster qualifying times will get to compete in the actual race. Those with the slower times are eliminated.

Winning the Pole Position For drivers competing in the race, qualifying time is also important in another way. It determines each car’s position on the track at the start of the race. The best qualifying time gets the best start- ing position. That is called the pole position. This position is in the first row closest to the inside of the track. The best place to start the race is from the pole position. You Do the Math

Drivers’ Records 12 Pole Position Starts and Race Wins Does the driver who starts the race 11 Pole Starts from the pole position always win 10 Race Wins the race? Not necessarily. Look at 9 the graph, which shows how often 8 5 drivers won the pole position (pole starts) and won races (race wins). 7 6 1. Which driver won the most races? 5 2. Which driver won the pole 4 position most often? Number of Wins 3 3. How many more race wins did 2 Driver B have than Driver D? 1 4. How many more pole starts did 0 Driver B Driver C Driver D Driver E Driver D have than Driver B? Driver A Drivers 13 NASCAR: Winning the Championship uring race season, there are Dregular NASCAR races each week for 26 weeks. Drivers earn points depending on how they place in each race. The driver finishing in first place gets the most points: 185. A second-place finish earns 170 points, and the driver finishing in third place gets 165 points. Decreasing numbers of points are earned for each place down to 43rd place, which earns 34 points. A driver can also earn 5 bo- nus points for leading any lap, as well A driver celebrates in as 5 more bonus points for leading Victory Lane after winning a NASCAR race. the most laps during the race.

The Championship At the end of the first 26 races, the sum of each driver’s points is calculated. The 12 drivers with the most points are eligible for the championship. These drivers take part in 10 more races to see who will win the championship. Each driver starts with 5,000 points, plus 10 points for every race he or she won during the first part of the season. Then, points are earned in each of the 10 races to determine the champion. You Do the Math

Adding the Points How are these four drivers doing so far this season? The table shows the points each one earned for each of the first 4 regular races. Points Earned by 4 Drivers in 4 Races Driver Race 1 Race 2 Race 3 Race 4 Finish Bonus Finish Bonus Finish Bonus Finish Bonus Points Points Points Points Points Points Points Points A 150 0 142 0 165 5 134 0 B 124 0 138 0 134 0 146 5 C 170 5 185 10 170 5 185 10 D 142 5 150 5 160 5 150 5 1. Calculate how many total points each driver has after 4 races. 2. How many more total points does Driver C have than Driver A? 3. Which driver has the fewest total points? 4. Which driver has earned the most bonus points? 5. Put the drivers in order from greatest to least number of total points.

15 Formula One

ormula One (F1) is another kind Fof car racing. F1 races do not take place on oval tracks. Instead, the rac- es (there are about 18 in each year’s racing season) are held on special winding tracks. About half the races are held in Europe, but F1 races take place all over the world. Driv- ers, too, come from many different countries. The cars look something like insects—long snouts, wing-like parts to help keep the car stable on the track, wheels entirely outside the body—and they cost many millions of dollars each. An F1 driver speeds down the track during a practice run. Race Strategy Cars don’t pass each other very often in F1 races because the tracks are wind- ing and narrow. This means that teams come up with strategies for get- ting ahead of other cars. They calculate fuel levels, pit stops, 16 choice of tires, and driving strategy for different parts of the track in order to try to be the first one to cross the finish line. There are practice and qualifying rounds on Friday and Saturday, where the drivers work to get a good starting position. Then, the race is held on Sunday. The Sunday race is called a Grand Prix. You Do the Math

Comparing NASCAR and Formula One How are NASCAR and Formula One races alike? How are they different? Study the Venn diagram below to answer the questions.

1. How are the race track designs different in NASCAR and Formula One? 2. How is the design of a Formula One car different from the design of a NASCAR race car? 3. Name two things that are the same in NASCAR and Formula One racing. NASCAR Formula One

Cars have long Drivers get points noses, huge tires, depending on the and wing-like Cars look like order in which parts road cars they finish Cars do not Cars pass each Teams support often pass other all the time each driver each other Race courses are Drivers compete Races are held oval tracks all season to win the on irregularly championship shaped road course tracks

17 F1: The Driver and His Team very Formula One race car is Edriven by a highly talented driver and is designed, built, and managed by an entire team of engineers, de- signers, and managers. A team is known as a “constructor.” Some well- known F1 teams, or constructors, include those of car manufacturers such as BMW, Ferrari, Honda, and McLaren. A constructor usually has two cars, and two drivers usually race for each constructor.

World Championships There are rankings for both drivers and A driver (center) and his team’s mechanics talk about teams throughout the racing season. their car’s performance. The top 8 finishers in each Grand Prix race score points toward both the Drivers’ World Championship and the Constructors’ World Cham- pionship. The list on page 19 shows how the points are given out. 18 Grand Prix Point System 1st place 10 points 2nd place 8 points 3rd place 6 points 4th place 5 points 5th place 4 points 6th place 3 points 7th place 2 points 8th place 1 point A constructor earns points for both of its driv- ers and cars. At the end of the season, the driver with the most points is declared Drivers’ World Champion. The constructor with the most points is the Constructors’ World Champion. You Do the Math Tallying the Points The table shows the points earned by 3 drivers in each of 7 races. Use the table to answer the questions. Points Earned by 3 Drivers in 7 Races Race Driver A Driver B Driver C 1 10 8 5 2 8 10 5 3 8 5 10 4 10 6 8 5 8 10 6 6 10 8 6 7 8 6 3 1. At the end of 7 races, how many total points does each driver have? 2. Which driver has the most first place finishes? 19 The Fuel

lthough F1 cars are highly A specialized machines, they run on fuel that is very similar to regular gasoline. Each team develops its own fuel blend designed to make the team’s cars run best.

Fueling Up: The Pit Stop During a race, a car will need more fuel, will need to have its tires changed, and may need mechanical adjustments. The car has to pull off A pit crew can refuel a car and change its tires in as little as into a special area on one side of the 7 seconds. track for a pit stop. The car stops in

20 an exact position in the pit, so that team members can very quickly refuel it, change the tires, and do anything else the car needs. Every second counts because when the An F1 car crosses car is in the pit, it’s not on the track. the finish line to win a Grand Prix race. Usually, team members need between 7 and 20 seconds before the car is ready to leave the pit and get back to racing. You Do the Math How Much Fuel Do We Need? F1 race cars use a lot of fuel. In fact, many F1 cars get only about 4 miles per gallon. A full tank means a heavier and slower car, so teams have to decide how much fuel they will start the race with. Should they start with a tank that is one-third full to get ahead right away? Or will starting with only that much fuel mean an extra pit stop for refueling, which will cost time? Answering questions like these are all part of the race strategy. Think about these questions about refueling? 1. F1 cars can usually be refueled at a rate of 3 gallons per second. If the pit crew adds 30 gallons of fuel to a car, how long will refueling take? 2. Most F1 cars use about 55 gallons of fuel in every race. If a car used that much fuel and got 4 miles per gallon, how far did it travel in the race? 3. If an F1 car begins a race with 28 gallons of fuel and needs 55 gallons to complete the race, how much more fuel will it need during a pit stop?

21 The Tires

acing tires are made from very R soft rubber that gives the best grip on the track. The tires wear out quickly, though, usually lasting only 125 miles at most. In compari- son, regular car tires can often last 20,000–30,000 miles or more. F1 race teams use a careful strat- egy to decide which tires to use in a race. If it is raining at the start of the race, they will likely put wet-weather tires on the car. With such tires, the car can’t go quite as fast, but it is less likely to aquaplane (slide across the track out of control) on a wet track. If the weather Cars need wet-weather tires for racing in the rain. improves, then when the tires are changed at a pit stop, the team might switch to softer tires. These tires are smoother than the all-weather ones and can run the fastest.

22 Things Will Go Wrong Sometimes things go wrong during a race, and a car is unable to finish. Even though the team has prepared the car and thought carefully about race strategy, the car can have mechanical prob- lems, or it may be in an accident. People who follow F1 racing talk about a team’s reliability. Measuring a team’s reliability involves comparing how many races the team completed with how many races the team entered. Often a team’s reliability is expressed as a percent. Every team wants to complete as high a percent as possible of the races it enters.

You Do the Math

Looking at Reliability The bar graph shows the reliability F1 Team Reliability of five F1 teams. Use the graph to answer the questions. TEAM A

1. Which team has the TEAM B highest level of reliability? 2. Which team has the TEAM C

lowest level of reliability? Teams TEAM D 3. Which teams have at 7:00–8:00 8:00–9:00 9:00–10:00 10:00–11:00 least 75 percent reliability TEAM E or more? 4. Did any team have less than 0210040608 30 50 700 90 100 50 percent reliability? Percent

23 How’s My Driving? lmost every part of a Formula A One race is studied mathemati- cally by a race team—tires, fuel, when to make a pit stop. However, there are some things that can’t be planned. These include an unex- pected change in the weather or a mistake by the driver. Even the most skilled and experienced drivers are human and can make mistakes.

Race Results During a race, spectators can watch a number of things. They can see

The top-three finishers on the which driver is ahead of the other podium after an F1 race. drivers and which cars are in the pit. If clouds are rolling in, they can see who is changing to rain tires and who is leaving the faster smooth tires on, hoping that the rain will hold off until after the race is finished.

24 Seeing the skill of the driv- ers is, for most people, probably the best part of watching a race. The drivers take hairpin turns at high speed and may need to react quickly to steer around an accident that’s just happened in front of them. Every driver wants to be standing on the podium (platform) at the end of the race, when medals are given to the Hairpin turns are common on F1 tracks. drivers who finished in first, second, and third place. You Do the Math

Numbers on the Drivers 10 Driver Records When you’re driving an expensive race car and you have an entire team of 9 people backing you up, you need to be 8 skilled. Records are kept on how drivers

7 Fastest Podium perform in every race. How often does Laps Appearances a driver run the fastest lap or step to the 6 podium to accept a medal? The graph shows data for four drivers. Use the 5 graph to answer the questions. 10 4 1. Which driver had the most podium Records appearances? 9 3 2. Which driver had the highest 2 8 number of fastest laps? 1

7 Fastest Podium 0 Laps Appearances Driver A Driver B Driver C Driver D 6 Drivers 25 5

0 Driver A Driver B Driver C Driver D Driver Training magine sitting in the cramped Icockpit of a Formula One race car for 2 hours. There’s no room to move. The temperature is usually high, so drivers may sweat a great deal. F1 drivers drink a lot of water before a race, so they won’t suf- fer from dehydration. Many people think that driving in an F1 race is as demanding as running a marathon. F1 drivers are well-trained ath- letes. They keep in shape by running, swimming, cycling, or even roller blading. They also need to build strong neck mus- cles. These muscles must support their head and a heavy helmet as their body shifts position when they take sharp turns at high speed.

A Driver’s Day An F1 driver needs to be What is a typical day like for F1 in top physical condition. drivers? The table on page 27 shows one driver’s typical schedule for a day. 26

Driver’s Daily Schedule Time Activity 7:00 A.M. Work out with personal trainer. Run. Ride exercise bike. 9:00 A.M. Drive laps with managers in a regular car. Identify hairpin turns and other curves in the track. Discuss driving strategy. 9:45 A.M. On the track in the race car. Test new tires. 10:15 A.M. Into the pit. Car goes up on air jacks to check tires. Engineer reviews lap times. 10:25 A.M. Drive more laps. Focus on taking the curves. 11:20 A.M. Spun out. Into the pit for a check. 11:45 A.M. Back on the track. Drive more laps. Try for better lap times. 12:30 P.M. Into the pit. Tires checked and changed. 1:00 P.M. Lunch. 1:30 P.M. Continue driving laps. Focus on time. 2:30 P.M. Into the pit. Car is checked. Meet with engineers and managers to review time data. 3:00 P.M. Back on the track. Test lap time with half load of fuel. 3:45 P.M. Into the pit. Review data with team. 5:30 P.M. Work out with personal trainer. Swim until 7:30 P.M.

You Do the Math How Much Time? Use the driver’s daily schedule to answer the questions. 1. How much time does the driver spend exercising and working out with a personal trainer? 2. What time does the driver first start using his race car? 3. How much time is spent driving laps after lunch? 27 If YouAnswer Key:Want to Be a Race Car Driver acing is a demanding sport. R Race car drivers need to be in excellent physical condition. They should also understand how car engines work and how such things as type of tires can affect a car’s performance. Although auto racing doesn’t re- quire a college education, knowledge of math and science are important. Drivers need to know math to under- stand the analysis of data that is so important to a winning race strategy. Knowledge of science principles will also help drivers understand such things as the forces acting on a car when, for example, it takes a sharp turn at high speed. There are racing schools that of- fer driver training. Nearly all race car drivers begin by getting experience in amateur races while they develop their skills. There is also more to racing than driving the car. A race car driver is a member of a team. The driver must be able to communicate and work effectively with other people.

28 Answer Key

Pages 4-5: Racing and Math: Pages 16-17: Formula One: 1. Texas Motor Speedway: 196 mph. 2. Las Vegas 1. NASCAR tracks are oval. Formula One tracks Motor Speedway: 185 mph. 3. 11 mph are irregularly shaped road courses. 2. NASCAR (196 – 185 = 11). 4. 5 mph (196 – 191 = 5). cars look like road cars. Formula One cars have long noses, huge tires, and wing-like parts. Pages 6-7: Track Design: 3. Possible answers: Drivers get points depending 1. Martinsville, 65,000; Kansas City, 82,000; on the order in which they finish. Teams support Dover, 140,000; Charlotte, 165,000; Daytona Beach, each driver. Drivers compete all season to win 168,000; Indianapolis, 250,000. 2. Daytona Beach the championship. and Indianapolis. 3. 2 miles (2.5 – 0.5 = 2). 4. 115,000 seats (250,000 – 135,000 = 115,000). Pages 18-19: F1: The Driver and His Team: 1. Driver A: 62 points; Driver B: 53 points; Driver Pages 8-9: Drag Racing: C: 43 points. 2. Driver A. Finishing first is worth 1. Tran had the shortest elapsed time (by 10 points. Driver A got 10 points 3 times, Driver B 0.26 seconds). Steph had the fastest speed twice, and Driver C once. (by 0.03 mph). Tran is the winner because he had the shorter elapsed time. 2. Ed lost Pages 20-21: The Fuel: the race. The difference between his elapsed 1. 10 seconds (30 ÷ 3 = 10). 2. 220 miles time and Jason’s elapsed time is 1.50 seconds (55 x 4 = 220). 3. 27 gallons (55 – 28 = 27). (9.18 – 7.68 = 1.50). Pages 22-23: The Tires: Pages 10-11: E.T. Racing: 1. Team C (85%). 2. Team D (55%). 3. Team A 1. 12 seconds (12 + 10 + 14 = 36; 36 ÷ 3 = 12). (80%) and Team C (85%). 4. No, because the 2. 15.5 seconds (14.5 + 16 + 16 = 46.5; lowest reliability is 55%. 46.5 ÷ 3 = 15.5). Pages 24-25: How’s My Driving?: Pages 12-13: Go as Fast as You Can!: 1. Driver D had the most podium appearances (8). 1. Driver B with 9 race wins. 2. Driver A with 11 2. Driver A had the highest number of fastest pole starts. 3. Driver B won 8 more races than laps (4). Driver D (9 – 1 = 8). 4. Driver D won 3 more pole Pages 26-27: Driver Training: starts than Driver B (4 – 1 = 3). 1. 4 hours (2 hours from 7:00 A.M. to 9:00 A.M. Pages 14-15: NASCAR: Winning the plus 2 hours from 5:30 P.M. to 7:30 P.M.). Championship: 2. 9:45 A.M. 3. 1 hour, 45 minutes (1 hour from 1. Driver A: 596 points; Driver B: 547 points; 1:30 P.M. to 2:30 P.M. plus 45 minutes from Driver C: 740 points; Driver D: 622 points. 3:00 P.M. to 3:45 P.M.). 2. 144 points (740 – 596 = 144). 3. Driver B. 4. Driver C, with 30 bonus points (5 + 10 + 5 + 10 = 30). 5. Driver C (740), Driver D (622), Driver A (596), Driver B (547).

29 Glossary

analyze—To examine or study. pit stop—A stop a driver makes dur- average—The sum of a group of ing a race in an area (pit) alongside numbers divided by the quantity of the track, where members of the driv- numbers in the group; also called the er’s team may refuel the car, change mean. tires, and do other maintenance. bar graph—A graph that uses bars pole position—The starting position to show data. in a race on an oval track that is clos- est to the inside of the track. calculate—To figure out the exact answer to a problem. qualifying time—The fastest time that each race car goes once around cockpit—Where the driver sits and the track before a race. the controls are located inside a race car. ranking—A listing in order, often from greatest to least. data—Information. stock car—A regular car that has dehydration—A large loss of water been changed for racing. from the body, which can cause medical problems. sum—The answer when two or more numbers are added together. difference—The amount by which one number is greater than another Venn diagram—A diagram that has number. two circles that may overlap and that shows the relationships among sets elapsed time—The amount of time of things. that has gone by since the start of an event. hairpin turn—A sharp, U-shaped turn that has a shape similar to a hairpin.

30 To Learn More

Read these books: Cavin, Curt. Race Day! The Fastest Show on Earth. Excelsior, Minn.: Tradition Books, 2003. Franks, Katie. I Want to Be a Race Car Driver. New York: Rosen Publishing, 2007. Stewart, Mark, and Mike Kennedy. NASCAR in the Driver’s Seat. Minneapolis: Lerner Publishing Group, 2008. West, David. Race Car Drivers. New York: Rosen Publishing, 2008.

Look up these Web sites: Formula One Official Website http://www.formula1.com National Association for Stock Car Auto Racing (NASCAR) http://www.nascar.com National Hot Rod Association http://www.nhra.com

Key Internet search terms: automobile racing, drag racing, Formula One, NASCAR, stock car racing

Accidents 23, 25 NASCAR races 6, 12–15 Bonus points 14 Oval tracks 6, 7 Challenges of racing 4, 26 Physical condition of drivers 26, 28 Championships 15, 18–19, 24 Pit crew 4, 20, 21 Christmas tree (device) 8 Pit stops 16, 20, 21, 22 Constructor team 18, 19, 20 Points, accumulation of 14, 15, Constructors’ World Championship 18–19 18, 19 Pole position 13 Design of cars 4, 6, 16, 18 Practice runs 10, 11, 17 Dial-in time 11 Qualifying rounds 5, 12, 13, 17 Drag racing 6, 8–11 Racing seasons 14, 16 Drag strip 8 Rankings 18 E.T. racing 10–11 Reaction time 9, 25 Elapsed time 8, 9 Records of drivers 13, 25 Elimination 8, 13 Reliability 23 Finish line 8, 9, 21 Road courses 6, 7, 16 Formula One (F1) races 6, 16–25 Skills of drivers 4, 24, 25, 28 Fuel 16, 20–21, 24 Speed 5, 9, 25 Grand Prix 17, 18, 19 Stock car 4 Strategy for races 16–17, 21, 22, 28 Hairpin turns 25 Superspeedways 7 Head start 10, 11 Hot-rod racing 6 Team 5, 12, 16, 22, 23 Tires 17, 20, 21, 22–23, 24, 28 Indy Car races 6 Track design 6–7 Kinds of races 4, 6 Training of drivers 26–27, 28 Kinds of tracks 6–7, 16 Weather 22, 24 Length of tracks 6, 7 Wet-weather tires 22 Manufacturers of cars 18 Winding tracks 15

About the Author Sheri L. Arroyo has a master of arts degree in education. She has been an elementary school teacher in San Diego, California, for more than twenty years and has taught third grade for the past thirteen years. 32

Welcome to Our Skill Will ! Today is : April 11, 2024

Math Relay Race

Math relay race: racing to arithmetic success.

Table of Contents

Introduction:

Math Relay Race is a dynamic and competitive team-based game that infuses energy into arithmetic learning. This engaging activity enhances children’s math skills and teamwork while adding an element of excitement and friendly competition. By incorporating math problems into a relay format, children can experience the thrill of a race while sharpening their arithmetic abilities.

Materials Needed:

• Math problem cards: Prepare cards with math problems appropriate for the child’s level (e.g., addition, subtraction, multiplication, division).
• Timer: Use a timer to measure each team’s completion time for the relay.
• Markers or cones: Set up markers or cones to indicate the relay race path.

Game Rules:

• Divide the children into teams, ensuring an equal distribution of math skills within each team.
• Arrange the teams in a line at the starting line, and place a set of math problem cards a few meters away.
• The first child from each team runs to the math problem cards, selects a card, solves the problem, and returns to the team to share the answer.
• If the answer is correct, the next team member repeats the process until all team members have completed a lap.
• The team that completes all laps in the shortest time wins the Math Relay Race.

Rewards and Recognition:

• Math Relay Champion: Award a “Math Relay Champion” certificate to the winning team, acknowledging their collective arithmetic skills and teamwork.
• Effort and Sportsmanship: Recognize all participants for their effort and good sportsmanship during the relay race.

Learning Objectives:

• Enhance arithmetic skills by solving math problems quickly and accurately in a relay format.
• Foster teamwork and collaboration by encouraging children to work together and support each other.
• Promote healthy competition, sportsmanship, and the joy of learning arithmetic.

Conclusion:

Math Relay Race injects enthusiasm and collaboration into the process of learning arithmetic. The combination of problem-solving and relay-style racing creates a lively environment, inspiring children to engage with math in an exciting way. This game not only cultivates arithmetic skills but also reinforces the value of teamwork and friendly competition. Through Math Relay Race, children experience that learning math can be an energetic and enjoyable adventure.

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Math Puzzles

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Problem #055 – horse racing

25 horses racing, and you have to find out the fastest ones!

Problem statement

You are in a horse racing track, and you have 25 mechanical horses in front of you. They are programmed to race around the track in a pre-programmed time that is always the same, even though you have no idea what these times are.

The racing track accommodates up to 5 horses at a time, and after the race, it gives you the relative rankings of the horses: it tells you which horse came in 1st, 2nd, 3rd, 4th, and 5th, but it doesn't tell you the times.

What is the minimum number of races you need to figure out what are the top 3 fastest horses?

Give it some thought!

If you need any clarification whatsoever, feel free to ask in the comment section below.

Congratulations to the ones that solved this problem correctly and, in particular, to the ones who sent me their correct solutions:

• David H., Taiwan;
• Luiz G., UK;
• Ashok C., India;
• Pedro G., Portugal;

Know how to solve this? Join the list of solvers by emailing me your solution!

There is a way to find the fastest three horses with seven races only. To show that 7 is the minimum number of races needed, we need to do two things:

• we need to show that there is a way to arrange the seven races in such a way that we find the three fastest horses; and
• we need to prove it is impossible to solve this in six races or less.

Typically, finding a solution in seven races is easier to do than to show it is impossible to find a solution with six races or less, so we will start with the easier thing and show how seven races work.

Seven races works

Here is how you can find the three fastest horses with only seven races.

The first thing you do is split the 25 horses in five groups of five, let's call them the groups \(A\) through \(E\) . Then, you race each of the groups, which means that now you know what is the fastest horse of each group, the second fastest horse of each group, etc. Let's use the values \(1\) through \(5\) to talk about the (ranked) horses of each group.

So, \(A1\) is the fastest horse of group \(A\) and \(C4\) is the fourth fastest horse of group \(C\) .

After determining the fastest horse of each group, you bring them together and race them. In other words, you race the horses \(A1\) , \(B1\) , \(C1\) , \(D1\) , and \(E1\) . This is the sixth race. Suppose these are the results:

• 1st place: \(A1\) ;
• 2nd place: \(B1\) ;
• 3rd place: \(C1\) ;
• 4th place: \(D1\) ;
• 5th place: \(E1\) ;

You can argue that it is unlikely that this is the actual result of the race. For example, why couldn't \(E1\) actually win the race? This is a standard procedure in mathematics: name things in an order that is useful for us. Before, I gave the names \(A\) through \(E\) to the groups of horses, but those names were arbitrary: I could've given the names in a different order. In fact, I could've given the names in the order that would later match this sixth race!

After these six races, we can write down the names of the 25 horses and draw arrows that represent the relative speeds of the several horses. Take a look at the diagram below:

The diagram above shows the 25 horses, and a blue arrow means that the start horse is faster than the end horse. For example, the top left arrow means that horse \(A1\) is faster than horse \(B1\) , which we know because of the sixth race.

Take two random horses, say, \(C1\) and \(E4\) . Do we know which one is faster? We do: \(C1\) is faster than \(E4\) . How can we know? Well, from \(C1\) to \(E4\) we can follow a path of successive arrows showing that \(C1\) is faster than \(D1\) , which is faster than \(E1\) , which is faster than \(E2\) , which is faster than \(E3\) , which in turn is faster than \(E4\) .

This path of arrows is highlighted in the diagram below:

Now, is \(C2\) faster than \(E4\) ..? Well, we don't know! \(C2\) and \(E4\) aren't connected by a path of arrows all pointing in the same direction, so we can't know which of the two is the fastest! Understanding this is key to realising what the seventh race is, and it will be important to prove that this problem is impossible to solve with six races or less.

We need to determine the three fastest horses, so which horses are we racing together now..?

The seventh race has the following horses: \(A2\) , \(A3\) , \(B1\) , \(B2\) , and \(C1\) . Why these five? Because, for all other horses, we already have 3 or more horses that are definitely faster than them, which means they can't be in the top 3. In other words, these are the only five horses that may be the 2nd fastest and the 3rd fastest.

Six races doesn't work

If you are reading this, it is because I forgot to write this part of the proof 🤦. If you could be so kind as to drop me a short email reminding me of this, I would greatly appreciate it!

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Bridging math and social justice for inclusive education

• January 13, 2022

Research and Innovation

As a mathematics educator, Ruthmae Sears has a true flair for problem solving. Her work extends far beyond using formulas and finding solutions to abstract mathematical problems. Using mathematical reasoning to examine social disparities such as poverty, literacy and structural racism, Sears develops community-centric solutions. Her work emphasizes inclusivity in all spaces, stemming from her belief that schools are microcosms of a community.

“I've always looked at education from a holistic viewpoint,” said Sears, associate professor of mathematics education in the USF College of Education and associate director for the Coalition for Science Literacy . “We have to be committed to the whole person because it's the whole person we're trying to develop so that way they can appreciate the beauty of mathematics but also be positive agents of change within their community.”

Sears’s collaborative projects are thriving. Her research has had such a profound impact that the American Association for the Advancement of Science has recognized Sears as a AAAS Fellow – one of the world's most prestigious honors for academic research. Sears works with the NSF-funded Systemic Transformation of Education through Evidence-Based Reforms (STEER) leadership team, the Center for PAInT on the USF Sarasota-Manatee campus to support arts integration in STEM and facilitates Mathematics Power Hour , a collaboration between USF, Hillsborough County Public Schools and Texas Instruments. Through her involvement in the community, Sears promotes hope and inspires her community to develop solutions together.

In 2021, Sears and her colleagues were commissioned by the city of St. Petersburg to develop recommendations on how it can address systemic racism . Sears also facilitated the NFL Huddle for Change , a six-part discussion series on racial inequalities in physical and mental health, which was hosted by a partnership between the Super Bowl LV Host Committee, NFL Inspire Change, Community Tampa Bay and USF.

“We need to find solutions that can really improve the quality of life within our communities, such that everyone can thrive,” Sears said.

As an educator, Sears thinks a lot about curriculum and about what is taken for granted, such as the implication of students’ literacy levels on their mathematical performance, and the implications of how textbooks can be used to support learning. It’s a position she first confronted after excitedly spending a summer preparing lecture materials to teach her first trigonometry class in her native country, the Bahamas, and she was stunned to learn that her secondary school students couldn’t read.

“I saw the look of deer in the headlights when I asked students to read the problem that applied aspects of trigonometry to the real world,” Sears now refers to this as the “big moment” when she realized the importance of addressing disparities and the need to support students learning to read the language of mathematics. Since her first year of teaching, she’s collaborated with interdisciplinary peers to build new strategies that would help students succeed. Sears quickly revised her lesson materials with basic reading assignments and by the end of the school year, her students’ mathematical achievement scores significantly improved.

Realizing that everyone comes from different spaces and with different experiences, Sears embraced community support from the start of her career, including getting her church to provide students from low-income families with free mathematics and English tutoring classes, and organizing small business owners to work with female high school students to improve their social skills. Sears also worked with the PACE Foundation in the Bahamas to build a school for teen mothers and enhance its curriculum. Sears acknowledged that her students needed a holistic support system that would help them succeed in math and reading.

Sears’s vision of addressing the challenges faced by students by creating sustainable support systems is a main factor in her work in and out of the classroom. By extension, she is also interested in the well-being of teachers. Sears is acutely aware of how the challenges that teachers face contribute to the national teacher shortage. Sears’s hope is that if teachers are better informed about their students and are also aware of how their own experiences may influence their curriculum, they can thrive in their careers.

“If we're serious about systemic change initiatives, we have to really reflect on all aspects of the system and consider factors that alter or transform it,” Sears said. “It's an ecosystem.”

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When it comes to math, maybe the kids aren’t the problem

The way we are teaching, testing, and requiring mathematics is damaging our society with potentially fatal results. That’s a strong statement, I know, but to get a sense of why, take a moment to think of something that you would find hard or maybe impossible to do — executing 30 pullups, playing a violin concerto, walking a tightrope over an abyss, feeding a snake, solving a complex polynomial equation. 

Now suppose our society decrees that to graduate from high school, you must be able to do that thing or be branded a failure and not earn a diploma. How are you feeling about yourself and your prospects?

Imagine trying your hardest to learn the skills, but the textbooks, online resources and sometimes even teachers confuse you, and on top of that, some exams are so badly designed they are virtually impossible to pass. 

The 2022 results from the National Assessment of Educational Progress showed only 36% of fourth graders and 26% of eighth graders were considered proficient in mathematics. The national average for high school math proficiency is just 38%.

Why are so many young people not achieving math proficiency? Consider how we define “proficiency.” 

For example, the Common Core math standards state that, among other things, high school students should “Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f (0) = f (1) = 1, f (n+1) = f (n) + f (n-1) for n ≥ 1.” And that’s just one example of many.

Suppose your child came to you with that as homework each night, possibly in tears. Now imagine that your child has special needs and deals with dyscalculia , ADD or other challenges.  

One of my sons struggles with ADD and is trying to complete an online financial algebra course offered by his school district to fulfill his mandatory “math pathway” for graduation. To help him succeed, a certified math and science tutor and I have worked with him every day through some very poorly designed online lessons provided by his district. 

We also helped him try to solve problems during a unit exam, but together, we achieved only a score of 32% on the exam. A certified math teacher, and a former statistics instructor with a Ph.D., failed a high school financial algebra exam. Why? Because the lessons were deeply flawed, the exam items were ambiguously worded, there were too many problems for the allotted time and the rules prohibited the use of resources like a financial calculator that one might enlist in real life. 

All that is not an excuse, and this column is not some reflexive “anti-testing” rant. It is, unfortunately, the truth. That leaves us asking, “If we failed the exam, how will most students, or their parents, possibly succeed?”

If you make children and their parents feel like failures, it is predictable that some are eventually going to give up on school and on themselves. Once that happens, they are far more likely to turn to behaviors that are harmful, self-destructive, and, tragically, sometimes fatal. And when significant portions of our population share those feelings, it inevitably harms our society as a whole. It is nothing less than educational and social malpractice to create unrealistic and unnecessary demands for children and then fail to provide them with the best resources to help them succeed.   

A good start would be to insist that policymakers, superintendents, school boards and school principals throughout our state attempt to learn each subject in math through the same texts or online resources students are required to use. I don’t mean just skimming a text or taking the word of someone else, I mean really digging in and trying to learn the material and take the tests firsthand. I doubt most people would accept the challenge and I am certain even fewer would pass the exams. 

That is not because the administrators and teachers aren’t smart, good people — it is because the materials and exams are so poorly designed, and the requirements are so profoundly detached from daily life. But if that is so, which the evidence suggests it is, why are we inflicting such things on our children and with what impacts?

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• Dismantling highly capable cohorts will hurt all students
• The ‘Great Wealth Transfer’ is a delusion
• The 4-day work week is decades away
• When it comes to math, maybe the kids aren't the problem
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The opinions expressed in reader comments are those of the author only and do not reflect the opinions of The Seattle Times.

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Math Day at the Beach 2024

On March 23, 2024, the 23rd Math Day at the Beach event was hosted on the California State University, Long Beach campus. Math Day at the Beach is a problem-solving festival for Southern California high school students who want to have fun with mathematics and enjoy a day of camaraderie with university mathematics students and professors.

A total of 34 teams of six high school students each participated in this event, 5 teams in Division A and the others in Division B.

This year's event was hosted on the campus and it was an unequivocal success. There were several parts to this event: an individual round, team round, relay, presentation by an invited speaker, teachers face-off round, and the face-off round to determine individual winners. The problems were designed by the Mathematics and Statistics Department faculty and were selected from algebra, geometry, trigonometry, number theory, combinatorics, and probability.

2024 Winners

Here is a list of the teams and individuals who placed during the competition.

Winning Teams in Division A:

• 1st Place - University High School
• 2nd Place - Sierra Canyon School
• 3rd Place - North Hollywood High School

Winning Teams in Division B:

• 1st Place - La Canada High School, Team 1
• 2nd Place - University High School, Team 1
• 3rd Place - San Marino High School
• 4th Place - Santa Fe Christian Schools, Team 1
• 5th Place - Palos Verdes Peninsula High School, Team 1

Individual Winners:

• 1st Place - Evan Li, San Marino High School
• 2nd Place - Natalie Song, Sage Hill School
• 3rd Place - Neal Frankenberg, La Canada High School
• 4th Place - Timi Fang, University High School
• 5th Place - Justin Kchao, Palos Verdes Peninsula High School

Top New Team:

• Valencia High School

Top Young Team:

• Santa Fe Christian Schools, Team 2

Invitation to 2025

An invitation to participate in the 2025 event will go out to schools in October of 2024. If your school is interested in trying its hand at tackling those math problems, email Dr. Olga Korosteleva at [email protected]  to request practice tests.

Division A schools for 2024 (in alphabetical order):

• La Canada High School
• North Hollywood High School
• Palos Verdes Peninsula High School
• San Marino High School
• Santa Fe Christian Schools
• Sierra Canyon School
• University High School

About Math Day at the Beach

This annual event was started in 2000 by the Department of Mathematics and Statistics under the directorship of Dr. Kent Merryfield, a charismatic leader with unparalleled expertise in high-school math competitions, and ran uninterrupted until Dr. Merryfield's untimely death in November of 2018.

In March 2019, the 20th Math Day at the Beach took place under the new directorship of Dr. Olga Korosteleva. Then the pandemic placed this event on hold for two years. The event returned on March 12, 2022, and has been held since.

Math Day at the Beach is completely free, thanks to our generous sponsors, the Jerry Cassaday Family and LBS Financial Credit Union.

Learn more about Math Day at the Beach.

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Ai Tutor Math Solver, the all-in-one app that empowers you to conquer any mathematical challenge. Don't just get an answer, understand the "why" behind it. Ai Tutor Math Solver breaks down each problem into clear, step-by-step explanations, allowing you to grasp the concepts and solve similar problems independently. Stuck on one approach? Ai Tutor Math Solver often provides alternative methods to solve the same problem. This flexibility helps you find the approach that best suits your learning style and understanding. Ai Tutor Math Solver identifies your strengths and weaknesses through practice sessions and quizzes. Based on this data, the app suggests personalized learning paths with targeted exercises and explanations to address your specific needs. Stuck on a particularly tricky problem? Utilize the in-app "Ask an Expert" feature. Connect with qualified math tutors who can provide personalized guidance and answer your specific questions Go beyond static explanations. Ai Tutor Math Solver incorporates interactive elements to enhance your learning experience. Visualize concepts with graphing tools, manipulate equations to see how they change, and practice your skills with built-in quizzes. From basic arithmetic (addition, subtraction, multiplication, division) to complex calculus (integrations, derivatives), Ai Tutor Math Solver tackles a vast array of mathematical topics. Need help with algebra, geometry, trigonometry, or statistics? Ai Tutor Math Solver has your back! https://sites.google.com/view/sublimationtermofuse/home https://sites.google.com/view/sublimationprivacypolicy/home

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The developer, Kiran Madad , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

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Minimization problems for the first Dirichlet Laplacian eigenvalue with volume constraint

In this presentation, we will consider a class of minimization problems for the first Dirichlet Laplacian eigenvalue with volume constraint for partitions of a given bounded domain. We will demonstrate the existence of an optimal open partition by proving the local Lipschitz continuity of the associated eigenfunctions. Our proofs rely on a weak formulation entailing the minimization of a penalized functional, where the variables are functions rather than domains. We will employ appropriate deformations, blowup techniques, and a monotonicity formula to obtain our results.

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How One Family Lost $900,000 in a Timeshare Scam

A mexican drug cartel is targeting seniors and their timeshares..

Hosted by Katrin Bennhold

Produced by Asthaa Chaturvedi and Will Reid

With Clare Toeniskoetter and Lynsea Garrison

Edited by Brendan Klinkenberg and Michael Benoist

Original music by Marion Lozano ,  Rowan Niemisto ,  Dan Powell ,  Pat McCusker and Will Reid

Engineered by Chris Wood

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Warning: this episode contains descriptions of violence.

A massive scam targeting older Americans who own timeshare properties has resulted in hundreds of millions of dollars sent to Mexico.

Maria Abi-Habib, an investigative correspondent for The Times, tells the story of a victim who lost everything, and of the criminal group making the scam calls — Jalisco New Generation, one of Mexico’s most violent cartels.

On today’s episode

Maria Abi-Habib , an investigative correspondent for The New York Times based in Mexico City.

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How a brutal Mexican drug cartel came to target seniors and their timeshares .

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The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

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Katrin Bennhold is the Berlin bureau chief. A former Nieman fellow at Harvard University, she previously reported from London and Paris, covering a range of topics from the rise of populism to gender. More about Katrin Bennhold

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