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Math Hoops

COACH’S MANUAL

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TABLE OF CONTENTS Basketball 101. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside front cover

Part I. Basic and Advanced Game Rules UNIT 1

Basic Game Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

UNIT 2

Advanced Game Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

UNIT 3

Keeping Score. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

UNIT 4

The Shot Clock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Part II. Creating a Math Hoops League UNIT 5

Practice Games (Pre-Season) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

UNIT 6

Organizing the League. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

UNIT 7

Keeping Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

UNIT 8

Mid-Season Review/All-Star Game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

UNIT 9

League Playoffs and Championships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Part III. Strategies and Math Explorations for Successful Coaches UNIT 10

Understanding Player Cards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

UNIT 11

Analyzing the Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

UNIT 12

Creating Teams and a Season Schedule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

UNIT 13

Winning Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

UNIT 14

Improving Your Team. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

UNIT 15

Why Do Coaches Need Statistics?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Appendix Season Schedule Template. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Game Summary Stat Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Player Season Totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Mid-Season Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 All-Star Nomination Form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Team Analysis Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Player Card Template. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside back cover Math Hoops Game created by Tim Scheidt Editorial Director James Fina Writers Rich Crowe, Tim Scheidt  Creative Director Aileen Hengeveld Additional Design & Production K-Hwa Park All player/team statistics and other references are true as of the end of the 2011–12 season. The NBA and individual NBA member team identifications reproduced on this product are trademarks and copyrighted designs, and/or other forms of intellectual property, that are the exclusive property of NBA Properties, Inc. and the respective NBA member teams and may not be used, in whole or in part, without the prior written consent of NBA Properties, Inc. © 2012 NBA Properties, Inc. All rights reserved. Copyright © 2012 by Math Hoops, Inc. All rights reserved. Printed in the U.S.


PART

I

Basic and Advanced

GAME RULES UNIT 1. Basic Game Rules UNIT 2. Advanced Game Rules UNIT 3. Keeping Score UNIT 4. The Shot Clock

UNIT 1: BASIC GAME RULES • 1


Unit

1

Basic Game Rules NBA Math Hoops is played just like real basketball. Two teams take shots to score points and the team with more points at the end of the game wins. There are two versions of the game that you can play: the Basic Game and the Advanced Game. This unit contains the rules for the Basic Game.

What You Need  Game Board

 Shot Planners

 Player Cards

 Foul Cards

 Transparent Spinners

 Game Scoresheets

 10-sided Dice

 Scoreboard

 Game Token

Setup FIND OUT MORE This Coach’s Guide gives the rules for both the Basic and Advanced Games. If you want to know how to create your own Math Hoops League with a regular season of games or even a tournament, turn to Part II on p. 22.

 Two teams play against each other. Each team should have two coaches.  Open the Game Board to the Basic Game side and put the game token in the center of the court as shown in the image on the opposite page.  The Game Board is divided so that there’s an Odd end and an Even end of the court. One team begins on the Even end and the other on the Odd end. The Even team uses the even numbers on the Game Board to shoot. The Odd team uses the odd numbers.  Notice that each end of the court has circles that are inside the 3-point line as well as a few that are outside it. Shots taken INSIDE the 3-point line are worth 2 points. Shots taken OUTSIDE the line are worth 3 points.  Timing the Game: Math Hoops is played in two halves. In the Basic Game, each half is 15 minutes long. You will need

a watch or timer to keep track of the time. For the second half, the teams will switch ends of the court so that the team that started on the Even end will now use the Odd end of the board and the team that started on the Odd end will now use the even end of the board.  Starting the Game: To determine sides, each team rolls the two dice. The team with the higher total starts the game by placing the game token on the number they rolled. If the number is even, they start the game on the even end of the court. If the number is odd they start on the odd end. (If each team has the same total, roll again.)

Choosing Teams  Each team needs to select five Player Cards — one of each color to represent each of the five player positions. The team that will start the game chooses the first player, then the other team chooses a player. The selection of players goes back and forth until each team has 5 cards in 5 different colors.  Drafting a team is part of the fun. You can decide who you want on your team based on personal favorites or based on the statistics on the cards. Each player has 3 stats: field goal shooting percentage (FG%), 3-point shooting percentage (3-PT%) and free throw

FIND OUT MORE Strategy plays an important role in Math Hoops. Part I provides the bare bones rules you need to get up and running with the game. To investigate strategies that can help you be a better coach, turn to Part III on p. 30. 2 • PART I: GAME RULES


3-point lines

Game token

The Basic Game Board

percentage (FT%). The higher the percentage, the better chance of making the shot. Look at the choices in each color and then decide which Player Cards to draft. Remember you must have at least one player in each color.  Now give your team a name! It can be creative and personal like “Hannah & Henry’s High-Flying Hoopsters” or a WNBA/NBA team name like the Seattle Storm or the New York Knicks.  You are now ready to play. Lay out your 5 Player Cards so you can easily see them. You will be using these throughout the game.

FIND OUT MORE To explore additional options for drafting players, go to EXPLORATION 12.1. HOW DO YOU MAKE A PLAYER DRAFT THAT’S FAIR? on p. 52. Check with your League Commissioner to determine what method you’ll use.

Five player cards, one in each color, make a team.

Game Play Before every game, you or another coach from your team must write your team name and players’ names on a Game Scoresheet. During a game, you exchange scoresheets with the other team to keep score for your opponents. That might seem strange at first, but there’s a big advantage to this: it keeps all coaches alert to what’s happening in the game and it helps you get to know the players on your opponent’s team, which you will need as you develop winning strategies. UNIT 1: BASIC GAME RULES • 3


First Turn: For the first turn of the game, whoever rolled the higher total places the game token on the number they rolled and simply takes a shot. No additional math is needed. No Fouls can be called on the first turn. After the first turn, each turn consists of the following steps:

Step 1: Roll the dice, record the numbers, and use the Shot Planner to figure out possible shooters. Step 2: Select a shooter and move the game token onto that number on the Game Board. The other team can call a foul before a shot is taken. Step 3: Take the shot(s) by placing the transparent spinner on the Field Goal

Circle of the Player Card and spinning OR by rolling the dice and using the Free Throw Grid.

Step 4: Opponents record the results on the Game Scoresheet and take the dice to start their turn.

Let’s look at each of these steps in a little more detail:

Step 1. Roll and Record You roll the dice each time you get the ball. You use the Shot Planner to help you determine where to move the ball. When you’re the Even team, you’ll want to get math results that are even numbers so you can place the ball onto one of the circles on your end of the board. When you’re the Odd team, you’ll want to get odd numbers. USING THE SHOT PLANNER

When it’s your turn, roll the dice and write the numbers in the ROLL boxes on the Shot Planner. Always put the larger number in the box on the left — you will see that this will make things easier later on. Look at the Basic Game Shot Planner. It shows four shaded cells containing the symbols +, −, ×, and ÷. In each shaded space, add, subtract, multiply, or divide the rolled numbers based on the symbol shown. EXAMPLE You roll a 6 and a 2. Here are the math results for each operation: 6 + 2 = 8 6 − 2 = 4 6 × 2 = 12 6 ÷ 2 = 3 And here’s what you would record on your Shot Planner. ROLL

6

2

+

8 4 12 3 –

×

÷

Depending on the numbers you roll, you can have as many as 4 different players who can take a shot. In the example above, you would have 3 choices if you were playing on the even end (8, 4, and 12) but only 1 choice if you were playing on the Odd end (3). It’s even possible to have zero choices if none of the math results match ANY number on your end of the court. [See NO MATCHING NUMBERS on p. 6.] 4 • PART I: GAME RULES


RULES FOR DIVISION

For division, you will always divide the larger number by the smaller number. If the answer is a whole number, write it down. If the answer includes a remainder, draw a diagonal line in the box.

Remainders and Notation

EXAMPLE You roll a 6 and a 5. These are the results from the four operations: 6 + 5 = 11 6 − 5 = 1 6 × 5 = 30 6 ÷ 5 = 1 R1* So here’s what you would record on your Shot Planner. ROLL

6 5

+

11

1 30 ×

÷

ROLLING A ZERO

What happens if you roll a zero? Addition, subtraction, and multiplication will be easy, but division is different. You can’t divide the larger number by the smaller number when zero is the smaller number. For example, 6 ÷ 0 has no answer. (For more information on why this is so, see the sidebar DIVISION WITH ZERO on p. 43.) So rolling a zero means you have no options for division and you draw a diagonal line in the division box. Note that rolling two zeroes is a different situation and one that will work in your favor. [See ROLLING DOUBLE ZEROES (FAST BREAK) on p. 6.]

* The notation 1 R1 is a way of

showing that the answer to “6 divided by 5” is not a whole number. It means that the answer is 1 with a remainder of 1. You may know of other ways to show quotients that aren’t whole numbers.

One way is to add a decimal and zeroes to the right of the dividend, treating each zero as another digit of the dividend: 1 . 2 5 6. 0 5 1 0 Another is to express the remainder as a fraction: 6 5

1

= 15

All these mean the same thing. 1 R1

1

1.2 1  5

STEALING THE BALL

While you’re figuring out your shot options, your opponents do the math too so they can check your answers. If you get caught making a math mistake, your turn ends and the ball is turned over to the other team. This is called a Steal. After you've completed your calculations and moved the game token to the spot on the Game Board you intend to shoot from, your opponents can challenge your math by calling out "Steal" or "Stolen Ball!". They must make the call before you take a shot. At that point, play stops and the math is checked by both teams.

Ball starts here. If the ball is stolen, it can be placed on any other red circle.

If there IS an error: Your opponents get credit for a Steal. They can select any number on their end of the court that is the same position (has the same color) as the position of the player that lost the ball. The Steal is recorded for that player on the Game Scoresheet. When a team steals a ball, they do not need to roll the dice. They can just place the game token on their player and take the shot! You can still foul that player before the shot is taken. If there ISN'T an error: You automatically get credit for a field goal. If you had placed the game token on a circle outside the 3-pt. line, you get 3 points. If you had placed the game token on a circle for a 2-pt. shot, you get 2 points.

UNIT 1: BASIC GAME RULES • 5


NO MATCHING NUMBERS (TURNOVER)

You’ve rolled the dice and worked out the math on the Shot Planner. What if none of the results match a number on your end of the court? In that case, you can’t get the ball to a shooter on your team, and the play is considered to be a turnover. Turnovers are not recorded on the Game Scoresheet. Instead, the other team immediately takes over the dice and the action continues! (If you’re using the Shot Clock, remember to reset it — the normal shot clock rules will then apply.)

Turnovers in the Pro Leagues In basketball, if your team loses possession of the ball without attempting a field goal or a free throw, it has committed a turnover. There are many ways that a player can commit a turnover, for example, by fouling a defensive player, by passing the ball out of bounds, or by passing the ball into the hands of a defender. Since a turnover kills any chance your team has to score points, committing turnovers helps your team LOSE games. That’s why coaches in the WNBA/NBA (unlike Math Hoops) keep turnover statistics for each of their players and love to have players with low turnover numbers. ROLLING DOUBLE ZEROES (FAST BREAK)

FIND OUT MORE You can pick up some tips and strategies on which player to pick to shoot the ball in Part III of this Coach’s Manual. In particular, see UNIT 10: UNDERSTANDING THE PLAYER CARDS on pp. 32–42 and EXPLORATION 13.1. WHO GETS THE BALL? on p. 58.

If you roll two zeroes, every possible operation results in zero, and there are no zeroes on the Game Board. This is a special situation called a Fast Break. If you get a Fast Break, you can take a shot from any number on your end of the Game Board and your opponents can’t call a foul!

Step 2. Pick a Shooter Each number on the court is in a circle that has one of five colors. These colors correspond to the five different types of players that make up your team. To select a player to take a shot, you use the numbers from the Shot Planner. EXAMPLE You roll a 6 and a 2, so the Shot Planner results are 8, 4, 12, and 3. If you’re the Even team, you have three different numbers you can choose: 8  purple = forward 4  red = guard 12  gold = guard Which player do you want to take the shot? That will depend on your players’ shooting percentages. Notice also that one of your options, 8 (purple forward), would be a 3-point shot. As you play, you’ll figure out which of your players you want to take a shot in different situations. What if you’re the Odd team? Well, only one of those results was an odd number, so you have only one choice: 3  red = guard After you decide which player you want to take the shot, move the game token onto that circle on the Game Board.

6 • PART I: GAME RULES


CALLING A FOUL

Before you take a shot, the other team can foul your shooter. Similarly, when the other team has the ball, you can call foul their shooter. To call a foul, the opposing team must place one of the Foul Cards on the Game Board before you spin the spinner to take your shot. When a foul is called, you no longer use the spinner and circle graph on the shooter’s Player Card. Instead, you roll the dice and use the Free Throw Grid to determine the result. Free throw shots are worth one point each. The number of shots you take will depend on the situation. [See FREE THROWS in Step 3. Take the Shot.] Use the following guidelines when calling a foul:  Each team can call no more than 5 fouls per half.  When a foul is called, the corresponding player on the defense is charged with the foul.  Each player can have no more than 3 fouls per game. Why would you want to call a foul? One reason is if a shooter has a very low free throw percentage. Fouling the shooter would reduce the player’s chance to score. Fouls can also reduce the number of points you get. If you were about to take a 2-point shot, and you are fouled, you can still get 2 points, but only if you make BOTH free throw shots. If you were about to make a 3-point shot and you are fouled, you can still get 3 points, but you would have to make ALL THREE free throw shots.

FIND OUT MORE You can explore the advantages and disadvantages of calling a foul in different situations later in this book. See EXPLORATION 13.5. FOUL PLAY: WHEN IS THE BEST TIME TO FOUL? on p. 66.

Step 3. Take the Shot FIELD GOALS

To see whether a field goal is successful, place a spinner on top of the circle graph on your Player Card. You should be able to align the spinner so the center of the circle graph is directly under the center of the spinner. Then spin away! For 2-pt. Shots: If the point of the spinner stops in one of the orange zones on the circle graph, congratulations! You made the shot. If the spinner point lands in one of the gray zones, too bad! You missed the shot. For 3-pt. Shots: See how some of the orange zone on a Player Card is marked with a black crosshatch? To make a 3-point shot, the point of the spinner must land in that black crosshatch zone. If it lands in the gray zone or a part of the orange zone that is outside that black crosshatch area, the shot is missed. FREE THROWS

If your player is fouled, you take free throw shots instead of field goals. Roll the dice and then look at the Free Throw Grid on your shooter’s Player Card. The top row lists numbers for the red die and the left-hand column lists numbers for the black die. Orange squares represent successful shots. Gray squares represent missed shots. EXAMPLE

Use spinner for 2-pt. and 3-pt. shots. A gray square on the Free Throw Grid means the player missed the shot.

Dirk Nowitzki is fouled before taking a 2-pt. shot. You roll a 4 on the red die and a 5 on the black die. The matching square on the Free Throw Grid is a gray square. Sorry, Dirk missed this one. UNIT 1: BASIC GAME RULES • 7


How many free throw shots you get depends on what type of shot you were attempting and what half of the game you’re in. IN THE FIRST HALF OF THE GAME:

 If your player is fouled before attempting a 2-point shot, the foul results in a “One and One” situation. Your player takes 1 shot. If they make it, they take a 2nd shot. If they miss the first shot, they do not get to take a second shot.  If your player is fouled before attempting a 3-point shot, the One and One rule does not apply. The player gets 3 free throws regardless of whether they make or miss them. IN THE SECOND HALF OF THE GAME:

 If your player is fouled when they are about to take a 2-point shot, they now always get 2 free throws.  A foul on a player about to take a 3-point shot still results in 3 free throws.

Step 4. Keep Score Your opponents will be recording the results of your turn, but you will want to watch carefully to be sure that the right player gets credit for all your shots! All statistics are kept on the Game Scoresheets. [You can read about how to use the Game Scoresheets in UNIT 3: KEEPING SCORE on p. 18.]

First Half and Second Half The first half ends when 15 minutes are up. If it’s in the middle of a turn, finish that turn. The teams will now switch which end of the Game Board they will play on. The Even team will now be the Odd team and the Odd team becomes the Even team. No need to change seats or players. Just focus on the other end of the court! The second half is also 15 minutes long. The team that did NOT start the game gets to start the second half. For the first turn, roll the dice and use the Shot Planner to get your math results. But for this turn, you’re allowed to take a shot from any of the resulting numbers. The opposing team can’t call a foul on the first turn.

Ending the Game After the 15 minutes in the second half is up, the team that has scored more points is declared the winner. If you’re in the middle of a turn when time runs out, finish the turn. The final statistics for each player are calculated and the name of the winning team is written at the bottom of the Game Scoresheet. If the score is tied, players proceed to the Lightning Round. 8 • PART I: GAME RULES


Lightning Round If the game ends in a tie, you play a lightning round to get the winner. In the lightning round, each team takes 3 shots and whoever scores the most points is declared the winner. Start with the even team and take turns attempting shots. You can try for 2-point or 3-point field goals. No fouls are allowed in the lightning round. You can choose any of your players to shoot; however, you can’t use the same player twice. You must use three different players and have each take one shot. If the score is still tied at the end of the lightning round, the game is declared a tie. FIND OUT MORE

Final Statistics You have to keep score for the other team during each game. This includes the number of points each player scored, which ones were 2-point or 3-point shots or free throws, which shots were missed, and the number of fouls and steals per player. All this information is recorded on a Game Scoresheet like the one below. At the end of the game, you give this Game Scoresheet to the other team and receive yours from them. Fill in the totals and save the sheets. You will use these later to determine the top players and teams. [For a more complete explanation of how to use the Game Scoresheet to keep score and statistics, see UNIT 3. KEEPING SCORE on p. 18.]

To find out how you can use the completed scoresheets to help develop winning strategies, see UNIT 15: WHY DO COACHES NEED STATISTICS? on pp. 72–29.

The NBA Math Hoops Game Scoresheet

UNIT 1: BASIC GAME RULES • 9


Unit

2

Advanced Game Rules The Basic Game is a good way to learn how to play NBA Math Hoops, but if you want a challenge involving more strategy, you’ll want to move to the Advanced Game. So how does the Advanced Game differ from the Basic Game?

T

o play the Advanced Game, you first need to change the Game Board and Shot Planner so that you’re using the Advanced Game sides of each. There are a number of rule changes, but here are the major differences between the Basic Game and the Advanced Game:  The Game Board has more numbers on it and some numbers have dotted line segments connecting them. After choosing a shooter, you may have the option to pass the ball to another player.  The Advanced Game Shot Planner is more complex than in the Basic Game. There are more math calculations, but you also get up to 16 results to choose from (the white boxes) instead of 4 (the gray boxes).  There are two new statistics: assists and rebounds.  Multiplication and division play a new role in the Advanced Game.

Setup  Open the Game Board to the Advanced Game side and put the game token in the center of the court.  The court in the Advanced Game is also divided into an even end and an odd end, but you’ll see that there are dotted lines connecting many of the numbers. These dotted lines represent passing lanes and they will give you more options in deciding who will shoot the ball. [See PASSING THE BALL (ASSISTS) on p. 15.] 10 • PART I: GAME RULES

 Timing the Game: Since the Advanced Game involves more math and statistics to keep track of, each half is now 20 minutes long. Switch even and odd ends of the court at half time, just as in the Basic Game. You can also choose to play in four 10-minute quarters if you wish.  Starting the Game: As in the Basic Game, each team rolls the dice to determine who starts the game. The higher total places the game token on the corresponding number and starts the game on the even end or odd end of the court depending on the number.

Choosing Teams  The Advanced Game uses the same Player Cards as the Basic Game and the method of selecting players is also the same. Refer to the Basic Game rules to review the guidelines for putting together your team. [See Choosing Teams on p. 2.]

Game Play First Turn: After preparing and exchanging Game Scoresheets, the game starts. The team that rolled the higher total moves the game token to the number they rolled and takes the first shot. The opposing team is not allowed to use any of their fouls on the first shot. To prepare for their turn, the opponents also write down the starting number on the Shot Planner in the spot labeled BALL ON.


Passing lanes

The Advanced Game Board

After the first shot, a turn follows the same steps as the Basic Game with a couple of differences:

Step 1: Roll the dice, record the numbers, and use the Shot Planner to figure

out possible shooters. There are additional calculations in the Advanced Shot Planner.

Step 2: Select a shooter that corresponds to the math results on the Shot Planner and move the game token onto that number on the Game Board. If you choose a number that has a passing lane connecting it to another number, decide if you want to pass the ball to the new player. If you do want to pass the ball, announce the new number and move the game token appropriately. Your opponents can call a foul on a player who is passing the ball or on the player who shoots the ball. Step 3: Take the shot(s) by placing the transparent spinner on the Field Goal Circle of the Player Card and spinning OR by rolling the dice and using the Free Throw Grid. If the shot is missed, determine who gets the rebound. [See REBOUNDS on p. 16.]

Step 4: Opponents record the results on the Game Scoresheet and take the dice to start their turn.

UNIT 2: ADVANCED GAME RULES • 11


Step 1: Roll and Record Working out the math in the Advanced Game can be a little more complicated than in the Basic Game, but it also allows for a lot more strategy. Let’s look at how it works with the Advanced Shot Planner. Imagine that you are the Odd team and the Even team began the game with the ball on the number 6. You then get 8 and 3 when you roll the dice. You fill out the first part of the Shot Planner just as you would in the Basic Game:

ROLL

FIND OUT MORE Does it make a difference which way you should round? You can explore that idea later in the manual. See EXPLORATION 11.3: HOW WILL THE ADVANCED DIVISION RULES AFFECT YOUR STRATEGY? on p. 49.

8

BALL ON

3

6

+ +

11

– +

5

+

24 2  or  3

×

÷

+

×

×

×

×

÷

÷

÷

÷

So far, this looks very much like the Basic Shot Planner, except for the last box in the top row. This is the box for division. There are TWO options here! That’s because division works differently in the Advanced Game. NEW DIVISION RULES

In the Basic Game, division answers (quotients) are an option only if they are whole numbers — i.e., if you can divide one number into another without getting a remainder. That means that often there are situations when division can’t be used to determine a shooter. In the Advanced Game, the rule is a little different. If division produces a quotient that is not a whole number, you round the quotient down or up to either of the two nearest whole numbers. So, for example, 9 ÷ 4 = 2.25. This number couldn’t be used in the Basic Game, but in the Advanced Game, a team can round the number up or down to either 2 or 3. So now you have results for all four operations. But there is still a block of blank squares on the Shot Planner! That’s because there are other calculations you will do to get more options to move the ball. Unlike the Basic Game, the Advanced Game has an additional step using the Ball On number to pick a shooter. Take each of the numbers you figured out in the shaded row at the top and use addition, subtraction, multiplication, and division with the Ball On number. Fill in the 16 white boxes with the appropriate result. Depending on which number you rounded to in the division box, the completed Shot Planner in our previous example would look like this:

12 • PART I: GAME RULES


If you rounded down to 2:

8

ROLL

BALL ON

3

+

11 + 17 – 5 × 66

5 24 + + 11 30 – – 1 18 × × 30 144 ÷ ÷ ÷ 1 or 2 1 or 2 4

÷

3

+

11 + 17 – 5 × 66

÷

6

×

2 + 8 – 4 × 12 ÷ 3

If you rounded up to 3:

ROLL

8

BALL ON

6

5 24 + + 11 30 – – 1 18 × × 30 144 ÷ ÷ ÷ 1 or 2 1 or 2 4 ×

3 9 – 3 × 18 ÷ 2

+

Two of the numbers have a red slash mark on them. That’s because numbers greater than 60 are meaningless in Math Hoops. They never appear on the game board. If you know that the result of one of your calculations is going to be greater than 60, don’t spend time writing it down at all! Just draw a slash mark in the box and turn your attention to one of the boxes that will give you a shot. DEALING WITH ZEROES

In the Basic Game, if any operation with the numbers you roll results in zero, you can ignore it since zero is not a number on the game board. In the Advanced Game, however, the numbers in the top row aren’t your final numbers, so you record the zero to use with the Ball On number. Write a zero even in the top division box. You can’t divide a number by zero, but you CAN divide zero by a number: 0÷x=0 On the other hand, when you’re working out the results for the 16 boxes below the top row, you can write a slash in place of a zero.

FIND OUT MORE Why can’t you divide a number by zero? Read the sidebar DIVISION WITH ZEROES on p. 43 to get more information about this.

ROLLING DOUBLE ZEROES

Since there are no zeroes on the Advanced Game Board, if you roll double zeroes, you follow the same rule as in the Basic Game. [See ROLLING DOUBLE ZEROES (FAST BREAK) on p. 6.] STEALING THE BALL

Follow the same rules as the Basic Game to determine a Steal. Be careful! Since there’s more math involved, there are more opportunities for the other team to steal the ball. [Review the rules for STEALING THE BALL on p. 5.] UNIT 2: ADVANCED GAME RULES • 13


Another Shot Planner Example

U

sing the Advanced Game Shot Planner may seem tricky at first but as you take more turns, it will become easier. Then the trick will be finding the best shots. Here’s another example to help you get the hang of it.

result in numbers that are much greater than anything on the Game Board (252 and 756). Do you see any clues that would tell you quickly that you don’t have to bother with those operations?

Imagine that you’re playing on the Even end of the court and you roll two 6’s. Your opponent left the ball on their number 21.

The box for 0 × 21 also has a slash because 0 × 21 = 0. Does this give you an idea for any other clues to watch for?

First, write down the numbers you rolled in the appropriate spaces. Then fill in the top (gray) row by performing each operation with the two numbers and writing down the answers.

Now look at the bottom row. This is the row for division. One of the boxes has a slash here also: the box for dividing 0 with 21. That’s because 0 ÷ 21 = 0. What about 21 ÷ 0? That’s a strange expression because you can’t even define an answer for it! [If you’d like to know why this is so, read the sidebar DIVISION WITH ZERO on p. xx.]

ROLL

6 6

12 0 36 1

+

×

÷

Now write down the Ball On number in the appropriate space. Use your results from the top row and add, subtract, multiply, and divide each one with the Ball On number. If you see that you’re going to get a number that isn’t on the Game Board — either a zero or any number greater than 60 — just put a slash in that box and move on.

ROLL

6

BALL ON

6

21

12

+

0 36 1 ×

÷

33 21 57 22 – – – – 9 21 15 20 × × × × 21 ÷ ÷ ÷ ÷ 2 2 21 +

+

+

+

Since you’re playing the Even end of the court, you’re looking for answers that are even numbers. There aren’t that many! You have three options: 2, 20, 22. Note that there are several boxes that have slash marks in them. The multiplication row is mostly slashes because 12 × 21 and 36 × 21

14 • PART I: GAME RULES

Here are some ways to help you figure out which operations you don’t have to do. Two of the boxes show a result of 2, one of the three even numbers you can use. The reason you can write a 2 in these boxes is because the Advanced Game has special division rules. The quotients of 21 ÷ 12 and 36 ÷ 21 aren’t whole numbers. 21 ÷ 12 = 1.75 and 36 ÷ 21 is approximately 1.7, but in the Advanced Game you don’t need to know even that much. As long as you can estimate that the answers are between 1 and 2, you can round to the nearest even number. As you can see, division can be a very powerful tool in finding a shot to take. Just be sure you estimate correctly — remember: your opponents are doing the math along with you to see if you make a mistake and let them steal the ball!


Step 2: Pick a Shooter If you perform every calculation on the Shot Planner, you can have as many as 16 different numbers to work with. Some of these won’t give you a shot either because they’re numbers that don’t match your end of the court (odd or even) or because they’re numbers that aren’t found on the Game Board. As in the Basic Game, you’ll want to get the ball to your best shooter — or maybe your best free throw shooter if you think your opponents are going to foul you! The Shot Planner results may give you a number that matches the player you were hoping to give the ball to. But even if the results don’t match your favorite player, you still might be able to get the ball to him or her.

FIND OUT MORE Want some tips on how to determine who should get the ball? Check out the explorations in UNIT 13: WINNING STRATEGIES ON p. 58.

PASSING THE BALL (ASSISTS)

In the Advanced Game, you are not always limited to selecting a shooter that matches one of your Shot Planner results. That’s because the Advanced Game Board includes passing lanes. After you’ve completed your math calculations, you can pass the ball from a player matching one of the math results to another player you prefer would take the shot as long as the two players are connected by a passing lane. EXAMPLE Suppose you’re the Even team and you are faced with the following situation: ROLL

8

BALL ON

3

9

11 5 24 + + + 20 14 31 – – – 2 4 15 × × × 45 ÷ ÷ ÷ 2 2 4

+

×

3 12 – 6 × 81 ÷ 3

÷

+

Your best 2-point shooter is Blake Griffin who is a Forward (represented by the light blue circles) If you want to get the ball to this player, none of the Shot Planner results will let you do that. But there IS a way you can pass the ball to that player. Look at the Advanced Game Board:

Completing the Shot Planner Math Hoops is a fast-paced game, much like real basketball. But you can be slowed down if you work out every calculation on the Shot Planner each time you get the ball. So what do you do? To start, you can look for calculations you don’t need to bother with. That’s where knowing about odd and even number operations works to your advantage! You can also make a conscious decision NOT to complete the Shot Planner. After all, your main objective is to get the ball to your player of choice. Remember that the faster you take a shot, the more shots you’ll be able to take.

The ball can be passed from 20 to 18.

UNIT 2: ADVANCED GAME RULES • 15


There are five numbers on the court corresponding to Blake Griffin: 18, 42, 46, 50, and 56. None of these numbers are found in your Shot Planner results. However, there is a passing lane connecting the number 20, which IS one of your Shot Planner results, to the number 18. So after you’ve worked out the possibilities on the Shot Planner, you can first give the ball to the player corresponding to number 20 and then pass the ball to Blake Griffin. When passing the ball, you must always first choose a number from your Shot Planner results and move the ball to that number. THEN you decide whether or not you want to pass the ball. If the player receiving the pass scores a field goal, the player that made the pass is awarded an Assist. This is recorded in the Assists column of the Game Scoresheet. In the example above, if Blake Griffin (number 18) makes the field goal, he gets credit for the points and number 20 gets credit for an Assist. As always, it is the responsibility of the opposing team to record these statistics. FOULS

In a situation that could involve passing, the defense has to pay very close attention. If the ball is on a number and a team is deciding whether or not to pass the ball, the defense can quickly call a foul if they feel that’s a good strategy. They can also wait to see if the ball is passed and call a foul then. The player who is fouled takes the free throws. Assists are not credited when free throws are scored. [For a complete explanation of FOULS, review the Basic Game rules on p. 6.]

Step 3: Take the Shot Once you’ve chosen which player you want to take the shot, follow the same rules as in the Basic Game. Use the spinner and the circle graph on your Player Card to attempt a field goal. If the other team has fouled your player, roll the dice and refer to the 10 x 10 grid to see if your player’s free throws are successful. [You can review the complete rules for FIELD GOALS and FREE THROWS on p. 7.] DEFENSIVE REBOUNDS

When a field goal or the final free throw of a team’s possession is unsuccessful, the player on the opposing team that first gets the ball is credited with a Defensive Rebound. This does not have to be the player who takes the shot. If the ball first goes to another player who then passes the ball to a shooter, the player who is passing the ball gets the Defensive Rebound. Rebounds are recorded on the Game Scoresheet. OFFENSIVE REBOUNDS

In professional basketball, when a team on offense misses a shot and recovers the ball, it is credited with an Offensive Rebound. Getting offensive rebounds is an important skill that is often the result of hard work and hustle. An offensive rebound allows a team to take another shot immediately after the first attempt. In Math Hoops, the team on offense doesn’t always get the chance to try for an offensive rebound. To get that opportunity, the offense must follow certain rules on their turn. Here’s how it works: 16 • PART I: GAME RULES


Remember that in a typical turn in the Advanced Game, the offense rolls the dice and works out the math on the Advanced Game Shot Planner. They can then move the ball onto any number from the 16 results that work for their end of the court.  If the offense moves the ball onto a number that matches one of the MULTIPLICATION or DIVISION results and they DON’T PASS the ball to another player, they earn the chance to try for an Offensive Rebound if the shot is missed.

FIND OUT MORE

Why only with a multiplication or division result? Because it usually takes more hard work and hustle to use multiplication and division than to rely on addition and subtraction. In a situation that allows for an Offensive Rebound, after the offense misses a shot, both teams immediately roll one die.  If the offense rolls a number greater than the defense, they retain possession of the ball. The original shooter is credited with an Offensive Rebound and it’s recorded on the Game Scoresheet. That shooter can then take a second shot or use a passing lane to pass the ball to another shooter. (If you are playing with the Shot Clock, you won’t use it for offensive rebound shots.)

Given the clear benefit of offensive rebounds, can you think of a situation where you wouldn’t try to get a usable number by multiplying or dividing? The explorations in Part III can help you see when this might be to your advantage. [See in particular EXPLORATION 13.4. CAN YOU BEAT THE SHOT CLOCK? on p. 64.]

 If the offense rolls a number less than or equal to the defense, they give up the ball to the defense who then starts their turn. The next player on defense to get the ball is credited with a Defensive Rebound as usual.

Step 4: Keep Score Keeping score in the Advanced Game is similar to keeping score in the Basic Game except there are two additional statistics to track: Assists and Rebounds. [For complete details on scorekeeping, turn to UNIT 3: KEEPING SCORE on p. 18.]

First Half and Second Half Each half in the Advanced Game is 20 minutes long. As in the Basic Game, teams switch to the other end of the court in the second half. The team that didn’t start the game takes the first turn in the second half. To determine where to place the ball, roll the dice and fill out the top shaded row of the Advanced Shot Planner. Move the ball to any number from the Shot Planner results, whether it's odd or even, and take the shot. Passing lanes are not used. The opposing team writes this number in the Ball On space on the Shot Planner and will use it on their turn. The opposing team can’t call a foul on the first shot.

Ending the Game After 20 minutes are up in the second half, the team that has scored more points is declared the winner. If you’re in the middle of a turn when time runs out, finish the turn. If the score is tied, teams play a lightning round. [See LIGHTNING ROUND in the Basic Game rules on p. 9 for details.] The final statistics for each player are calculated and the name of the winning team is written at the bottom of the Game Scoresheet.

UNIT 2: ADVANCED GAME RULES • 17


Unit

3

Keeping Score There are two methods for keeping score included in NBA Math Hoops: the Scoreboard and the Game Scoresheets. You will use both of these while you are playing.

Scoreboard The scoreboard serves two purposes:  It provides a summary of the game rules and guidelines for playing both versions of the game  It allows you to keep a running account of the score as each point is scored. This is done by manually turning the wheels on the upper ends of each side of the scoreboard. The scoreboard alone can be used in the first few games as you learn the rules and get used to how the game is played. Once you’re comfortable with game play and are ready to start official exhibition or regular season games, start using the Game Scoresheet along with the scoreboard. The

Game Scoresheet tells the complete story of what happens in a game and can be used to improve your coaching skills.

Game Scoresheet Before a game begins, each team prepares its Game Scoresheet by filling in its players’ names for each position. The scoresheets are then exchanged between teams, since teams will keep the game stats for their opponents. Along with carefully watching each spin, this keeps all coaches actively engaged throughout each game. The Game Scoresheet has eight columns:  Player  Field Goals (2-pt. and 3-pt.)  Free Throws  Steals  Fouls  Rebounds  Assists  Total Points Scoring a game is a pretty straightforward process. The coach designated to keep score for the opposing team records data as the game is played. Look at the sample player data recorded on the scoresheet on the next page.

Math Hoops Scoreboard

18 • PART I: GAME RULES


Offensive Rebound Defensive Rebound

The Game Scoresheet for NBA Math Hoops

How To Use the Game Scoresheet FIELD GOALS Make the Shot — Circle the appropriate number to represent the number of points that were scored (2 or 3) Miss the Shot — Draw a diagonal line through the appropriate number FREE THROWS Make the Shot — Draw a circle around each successful free throw shot. Miss the Shot — Draw a diagonal line through each free throw that’s missed. STEALS Circle an S next to the player who takes a shot after stealing the ball. (It doesn’t matter if the shot is made. You are recording the fact that they made the steal.) FOULS When the defending team decides to foul a player, the corresponding player on their team is charged with the foul. For example, if the defense fouls a red (guard) player on the opposing team, their red (guard) player is marked with a foul by circling the appropriate number in the FOULS column. A player can get no more than 3 fouls in one game, so you would circle the “1” for the first foul, “2” for the second foul, and “3” for the third foul. ASSISTS ADVANCED GAME When playing offense, if you decide to pass the ball to another player who then takes the shot, circle an A next to the player who made the pass ONLY IF the shooter makes the shot. If the shooter misses, no Assist is credited to the passing player. REBOUNDS

ADVANCED GAME

Defensive Rebounds — Circle an R next to the player who gets the ball after the opposing team MISSES a shot — either a field goal or the final free throw when a player is fouled. Offensive Rebounds — Draw a square around an R next to the player who attempts another field goal in an Offensive Rebound situation.

FIND OUT MORE For a complete definition of offensive rebounds, review the Advanced Game rule OFFENSIVE REBOUNDS on pp. 16–17.

UNIT 3: KEEPING SCORE • 19


At the conclusion of a game, Game Scoresheets are exchanged and coaches complete the Total Points column for each player on their team. To do this, simply add together the circled 1s, 2s and 3s for each player. After calculating each player’s total points, the totals should be added together to get the opponent’s total score. This number should match the total displayed on the scoreboard. If there are differences, the Game Scoresheet should be considered the official record. Here is what a completed Game Scoresheet looks like:

Game Scoresheets tell the story of a particular game and will prove to be useful when doing individual player and team analysis. You may want to start looking through the Math Explorations in Part III to see how this unfolds.

20 • PART I: GAME RULES


Unit

4

The Shot Clock NBA and WNBA games are played with a 24-second shot clock. Basketball games at the college level use shot clocks that give teams more time. Women’s college basketball uses a 30-second clock while men’s college basketball uses a 35-second shot clock.

E

ach NBA Math Hoops classroom kit includes 4 shot clocks. The shot clock offers two different options: a “college” level of 35 seconds and a “pro” level of 24 seconds. The rules for the shot clock are simple:

planner and calculations, the more likely it will be that you will use a shot clock in your games. Once you do, you’ll see how it takes NBA Math Hoops games to a whole new level!

 Both teams must agree in advance whether the game will be played at the Pro or College level.

When to Start the Shot Clock

 When the offense begins their turn, the defense starts the timer by pushing down on the ball.  The offense must now find a valid shooter and attempt a shot before the timer reaches 0:00. If no shot is taken before the buzzer sounds, it is considered a turnover and the ball is awarded to the other team. Work with your League Commissioner to decide when and how shot clocks will be used. Make sure you have a good handle on how the game is played before bringing in the shot clock. Set a goal to improve your shot planner skills so that you can use one as soon as possible. Start with the 35-second function and use that until you can consistently get shots off before the buzzer sounds. Once you do, you may be ready to move to the 24-second professional level. Whether you’re playing the Basic or Advanced Game, the more proficient you and your co-coach become with the shot

One of the most important things in using the shot clock is deciding when to start it. You can choose what the rule will be. A few options include:

The shot clock

 Immediately after the roll of the dice (Basic and Advanced Games)  Once the dice and Ball On numbers are recorded (Advanced Game)  Once the dice and Ball On numbers are recorded and the top row of operations on the Shot Planner are recorded (Advanced Game) Whatever option is used, be sure both teams agree on the rule prior to the start of a game. The rule will apply to both teams for the entire game. Decide what rule you will use for when to start the shot clock. If you think of additional possibilities, share them with your League Commissioner and fellow coaches. The object should be to use the shot clock at a level and in a way that pushes you to improve your skills while increasing the pace of the game.

How to Set the Shot Clock Use the toggle switch on the side of the shot clock to set it for either 35 or 24 seconds. Push down once on the top of the ball to clear the display. Pushing a second time will start the clock counting down until it reaches 0:00. Once it reaches 0:00, a 2-second buzzer will sound. To reset the clock, just push down on the ball again. You’re now ready for the next play!

UNIT 4: THE SHOT CLOCK • 21


PART

II

Creating A

MATH HOOPS LEAGUE UNIT 5. Practice Games (Pre-Season) UNIT 6. Organizing the League UNIT 7. Keeping Statistics UNIT 8. Mid-Season Review/All-Star Game UNIT 9. League Playoffs and Championships

UNIT 1: BASIC GAME RULES • 23


Unit

5

Practice Games (Pre-Season) Once your Math Hoops season begins, you will put on your game face. Every shot counts and every game affects your team’s chances of becoming champions. But before you can get so serious, you need to get your feet wet.

J

ust as NBA players have a pre-season in which they prepare themselves for league games, you have a chance to practice Math Hoops before the real season begins. Before you can even practice, you need to understand the rules of the game. Reading Part I of this manual is a good place to start; but you can get a better understanding by playing the game itself. Get out the Game Board, the cards, the spinners, and the dice, and get to work. When you play another team, don’t be surprised if you have to help each other figure out some game rules when you first play. When that happens, refer back to Part I or ask for some help from your League Commissioner. By practicing, you will also begin to gain an insider’s understanding of Math Hoops. Moving the game along, choosing between shooters, and making quick decisions will help you gain knowledge in a way that reading a manual cannot. When NBA players begin their pre-season, they look good but are not ready to play together as a team. Through practice and exercise, they get physically and mentally prepared for a long and incredibly competitive season. Treat your practice games as the way to get yourself prepared for a competitive Math Hoops season.

24 • PART II: CREATING A MATH HOOPS LEAGUE


Unit

6

Organizing the League The Game Rules in Part I give you all the information you need to create teams and play games against other teams. But if you really want to experience the energy and excitement of competitive play, you’ll want to organize your own NBA Math Hoops league!

Teams What do you need to form a Math Hoops league? Well, first you need to create teams by selecting players from the set of Player Cards. These players will be the ones you will use in every game so choose carefully. The game rules say that each team must have one player from each of these categories:

Gold Guards Red Guards

Blue Forwards Purple Forwards

Green Centers

This will give you 5 players total, but for a Math Hoops league, you’ll want to pick up some additional players. This will give you more coaching options over the course of a season. You can think of your first five players as your “starters.” Then select 3 additional players to act as substitutes. You can think of these players as your “bench.” Having a solid backup for a guard, a forward, and your center is a good strategic move. If one of your players is having an off game, you can bring in a replacement to (hopefully) give your team a boost. So how do you choose players for your team? This part of the game can be a lot of fun when you use a draft to do it. In a draft, each team in your league takes turns choosing one player for each position and then the players that will act as substitutes. When it’s your turn to pick, you’ll need to work quickly. Make sure you figure out before the draft how this is going to work. Do you and the other coaches on your team take turns picking players? Should one of your coaches make all the choices? You decide!

FIND OUT MORE To explore different ways of setting up a player draft, turn to EXPLORATION 12.1: HOW DO YOU MAKE A PLAYER DRAFT THAT’S FAIR? on page 52.

Player Positions: Center, Guard, For ward The five players on a basketball team are divided into 1 center, 2 forwards, and 2 guards. The center is usually the tallest member of a team. To get rebounds on defense, the center usually is centered near the basket on defense. On offense, a center that is close to the basket has a shooting advantage over shorter opponents.

The guards are usually the shortest members of a team. Being shorter, they have a disadvantage getting rebounds and shooting over opponents, but they usually have advantages in speed, quickness, and agility. Because of these advantages, one of the guards, called the point guard, usually dribbles the basketball up the court on offense. The point guard is always a good ball handler

and is responsible for setting up plays on offense. The other guard is called a shooting guard. As the name suggests, a shooting guard is usually an accurate shooter who is expected to score many points for his or her team. Finally, a team has its two forwards. Their height is usually between that of the guards and the center. One is called the small

forward. As you would guess, he or she is usually the smaller of the two forwards, and often has responsibilities like that of the shooting guard. The larger forward is called the power forward. A power forward is often built like a center, tall and powerful. As such, he or she plays close to the basket and is responsible for getting rebounds.

UNIT 6: ORGANIZING THE LEAGUE • 25


Maybe you’ll recognize some of the players in Math Hoops. You might even see a favorite player of yours and want to choose that player for your team. But be careful. Let the numbers guide you as well. To get an idea of how well a player will do in Math Hoops, look at the back of a player’s card:  The bigger the orange zones, the better that player is at 2-point shots.  The bigger the black crosshatch zones, the better that player is at 3-point shots.  The more orange squares in the free throw grid, the better that player is at foul shots.

League Divisions Once all the teams have been created, you can form league divisions. The number of divisions will probably be determined by the number of teams. For example, there are 12 teams in the WNBA divided into a western conference and eastern conference with 6 teams each. The NBA consists of 30 teams. Because there are so many, the NBA is first divided into a western conference and eastern conference, with 15 teams in each, then each conference is divided into three divisions, with five teams in each division. Every season, the team that finishes first in each of the six divisions is guaranteed a spot in the postseason playoffs.

FIND OUT MORE Your League Commissioner might be the one to set up your season schedule, but if the task falls to you, or if you simply want to explore ways to do it, turn to the activity in PART III: 12.3 HOW CAN YOU DESIGN A CREATIVE SEASON SCHEDULE? on p. 57.

How many teams are there in your Math Hoops league? If there are only a few, you may want to have just a single division. But if there are many, you can break the league into two divisions. For example, a league with eight teams makes it hard for every team to fight for first place. Breaking this league into two 4-team divisions could make for better competition.

Season Schedule During a regular season, an NBA team plays four games against each team in its own division: two at home and two on the road. Each team also plays 2–4 games against the 25 teams in the five other divisions. League officials map out schedules for the 30 teams long before each season begins. Given the number of teams and length of the season, it’s a complicated job. For your Math Hoops league, the job should be a bit simpler. Your main task will be to make sure that you have a fair schedule. In a single-division league, the goal should be for every team to play every other team the same number of times, and for every team to get the same number of home and road games. In a multiple-division league, you might have teams play fewer games against teams outside their division. This scheduling goal sounds straightforward but it is not always possible to achieve! When you make your Math Hoops schedule, you will see what that means.

26 • PART II: CREATING A MATH HOOPS LEAGUE


Unit

7

Keeping Statistics If you look at the different forms available in Math Hoops, you’ll see many statistics that can be compiled as you play the game. You might ask, “Why bother?” The answer is that keeping statistics and examining them regularly will make you a better coach and may even add to the fun.

H

ere are some ways you can keep track of Math Hoops data and how doing that helps you play the game.  Field goal percentages and averages for your team: You learn with real game results who has performed best for your team. That affects whom you want to shoot the ball in the future.

To help you keep track of these statistics, NBA Math Hoops contains a number of tools. You will find several in the Appendix at the back of this manual, including the following:  Game Summary Stat Sheet  Player Season Totals

 Scoring leaders around your league: Before you play another team, you want to know if they have some monster scorer. That shooter might get fouled a bit more than usual when playing against your team.

 Mid-Season Assessment

 Best free throw shooters around the league: When you play against great free throw shooters, you might want to just let them try for field goals.

In addition, the Math Hoops Classroom Kit contains a wall poster for keeping track of League Leaders and Team Standings. The poster can be used to display data pertaining to the league as a whole, not just your team.

 League standings for all the teams: Everyone wants to know what place their team is in. Even if it is not first place, you want to aim for better position with each new game.

 Team Analysis Chart These sheets are for you and your cocoach to use to analyze your team’s performance throughout the season.

FIND OUT MORE To get some ideas of useful statistics to track and how to track them, try the activities in UNIT 15: WHY DO COACHES NEED STATISTICS? starting on p. 72.

Look over all the forms that are available and decide for yourself how keeping statistics can improve your play.

UNIT 7: KEEPING STATISTICS • 27


Unit

8

Mid-Season Review/ All-Star Game After you have a number of games under your belt, you may want to step back and review individual player and team performance.

A FIND OUT MORE To help you conduct a thorough mid-season review, check out these explorations: 14.1 MID-SEASON ASSESSMENT: IS IT TIME FOR A ROSTER CHANGE? (P. 68) 15.2 PER-GAME STATISTICS (P. 74) 15.3 TEAM ANALYSIS (P. 76)

simple way to do this would be to compare your team’s record with other teams in your league. You could also pull out your regular game scoresheets and see if you can easily determine any trends that jump out at you. Do you have one player who consistently takes more shots than the others or one player who is fouled more frequently than others? This cursory review can be helpful but if you really want to raise the level of your game, you���ll need to dig a little deeper. Part III in this coaching manual is made up of in-depth math explorations that get at the core of the game. It’s possible that you’ve already completed a few — especially if you aspire to be the most knowledgeable and effective coach you can be. Many of these explorations, especially the ones listed in the Find Out More box to the left, can help you make mid-season improvements. At this point in the season, your League Commissioner may present the opportunity for you to update one or more Player Cards using simulated game data or statistics from a previous year. For instructions on how to update or create new cards, see EXPLORATION 14.2: CREATE YOUR OWN PLAYER CARDS! on p. 70.

28 • PART II: CREATING A MATH HOOPS LEAGUE

The All-Star Game One outcome of conducting a thorough mid-season review is that you will identify your team leaders. One way to recognize their performance that also provides a fun break in the regular season is to organize and play an All-Star Game. All-Star Games allow leagues to showcase their best players. The midpoint of the Math Hoops season is a great time to select the two best players from your team to play in the All-Star Game. Your League Commissioner can explain more about how to conduct the All-Star Game, but the first thing you’ll need to do is determine who the all-stars are. Use the All-Star Nomination Form on page 85 to write a few paragraphs explaining which two players on your team you think should be in the All-Star Game. You will need to back up your writing with data from a Team Analysis Chart.


Unit

9

League Playoffs & Championship You’ve coached your way to some close victories, possibly a few heartbreaking losses, and maybe even a blowout or two. The question now is, “Do you have what it takes to become a Math Hoops Champion?”

W

hen your regular Math Hoops season ends, your League Commissioner might have the teams take part in playoff games. The team that finished first in the regular season may not think this is such a good idea. But the rest of the teams should be very happy since they now have a chance to be declared league champion.

thing to do now is to forget your regular season record. If you had the best record in the league, it does not matter; you will still have to win all your games now. And, if you had the worst record in the league, it does not matter; the playoffs are a fresh start for your team.

Math Hoops playoffs use a singleelimination tournament. Simply put, this means that if you lose one game, you are out! The team that wins all of its playoff games is declared the league champion. In a single elimination tournament, you could be the worst team (according to regular season records) and still win the league championship. If you are a college basketball fan, you already know that the NCAA tournament is run in this way. Your League Commissioner will devise a schedule for the playoff games. As long as you win a game, you will always get to play another game. The most important

The Tournament Poster in the Classroom Kit provides a framework for a 16-team playoff series.

CREATING A MATH HOOPS LEAGUE• 29


STRATEGIES AND MATH

EXPLORATIO 

30


PART

III

 NS

for Successful Coaches

UNIT 10. Understanding Player Cards UNIT 11. Analyzing the Game UNIT 12. Creating Teams and a Season Schedule UNIT 13. Winning Strategies UNIT 14. Improving Your Team UNIT 15. Why Do Coaches Need Statistics?

To win Math Hoops games, you need a combination of good luck and good skills. Luck is involved when you roll the dice and spin the spinner. Skill is involved when you make decisions. As a coach, there’s not much you can do about luck, but there are a lot of decisions you can make that will influence the outcome of a game:  Who do you pick to shoot the ball?  Do you try for a two-pointer or a threepointer?  Do you pass the ball to get a better shot?  The shot clock is running out of time. Do you pick the first number that you write on your Shot Planner?  The other team picked its shooter. Do you foul them?

As you play more and more, you’ll come up with your own strategies. But do this, too:  Talk with your co-coach. Listen to each other and figure out some strategies you can use.  Watch how the other team plays the game. You might figure out new strategies by thinking about the good or bad decisions they made.  Finally, use the explorations on the following pages to help build your understanding of the game and be a more effective coach.

31


Unit

10

Understanding Player EXPLORATION

10.1

What Are Field Goal Percentages (and Why Are They Written as Decimals)?

In the 2011 WNBA basketball season, Sylvia Fowles led the league in field goal percentage. If you look up her number on the Internet, you will see her percentage written as the decimal .591. Why is it written this way? After all, aren’t percents written with a percent symbol? Of course they are, but sports statistics are sometimes written one way and named another way. There is actually an advantage to writing these percentages as decimals. You’ll see how when you compare players later on.

A. Understanding Field Goal Percentage Field goal percentage is found by dividing field goals made (FGM) by field goals attempted (FGA). The table below shows two players, with their field goal percentages (FG%) rounded to the nearest whole percent. It looks like they have equal FG%. PLAYER

FGM

FGA

FG%

Player A

203

384

53%

Player B

137

257

53%

The next table shows each player’s FG% as a decimal rounded to the nearest thousandth. You can see that Player B has a slightly higher field goal percentage. It’s not a very big difference, but if there were an award to be handed out, Player B would get it. Recording field goal percentage to the nearest thousandth allows you to obtain a higher level of precision. Notice also that the column labeled FG% does not include a zero to the left of the decimal point. It is common in sports statistics to omit that zero. PLAYER

FGM

FGA

Decimal

FG%

Player A

203

384

0.5286458

.529

Player B

137

257

0.5330739

.533

Percentages as Ratios FG% can also be thought of as the ratio of FGM to FGA. Ratio is a way to compare by division, and it is one of those concepts that you find all over the place when you are doing mathematics. When a driver calculates miles per gallon or a nutritionist calculates calories per serving, ratios are at work. Can you think of an occasion in your day where you need to know a ratio?

32 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Cards 1. Complete the chart below. Get creative and make up names for each of the players. The first one has been done for you. PLAYER

Bartholomew Dunkman

FGM

FGA

Decimal

FG%

69

145

0.4758621

0.476

143

289

176

362

94

179

259

503

226

457

111

216

179

348

2. Now rank the players from highest to lowest FG%. You will have to use the “Decimal” column above to correctly rank the players whose FG% are equal when written to three decimal places. PLAYER

FG%

UNIT 10: UNDERSTANDING PLAYER CARDS • 33


3. Complete the chart below by filling in some missing information. Make up a creative name for each player as well. PLAYER

FGM

FGA

137

271

Decimal

.506

95 150

FG%

.522 306 239

.5188285

B. Field Goal Percentage and Game Strategy So, how does knowing how to compare shooting percentages with such precision help you when you’re playing games? Let’s look at some game situations. 1. Complete the following table and use the data to explain your reasoning in the questions that follow.

PLAYER

2-pt. Shots Made

2-pt. Shots 2-pt. Attempted Percentage

Player A

90

177

Player B

111

219

Player C

140

267

Player D

99

199

Player E

151

288

.508 .507 .524

3-pt. Shots Made

3-pt. 3-pt. Shots Shooting Attempted Percentage

Free Throws Made

Free Throws Attempted

13

38

64

73

40

97

32

42

24

63

50

55

57

142

17

24

33

88

49

59

Free Throw Percentage

2. You’re down by one point with three seconds to play in the game and you have the ball. Which player would you want to take the last shot? Explain your reasoning.

3. Your opponent is down by two points with four seconds to play in the game and has the ball. Which player would you want to take their last shot? Explain your reasoning.

34 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


4. Your opponent is up by two points with six seconds to play in the game and you have the ball. Which player would you want to take the last shot? Explain your reasoning.

5. You are up by three points with two seconds to play in the game and your opponent has the ball. Which player would you want to take their last shot? Explain your reasoning.

6. You have the ball down by one point with two seconds to play in the game and your opponent elects to foul. Which player would you want them to foul? Explain your reasoning.

7. You are up by one point with four seconds to play in the first half and your opponent has the ball. You decide to call a foul. Which player on their team would you want to have the ball at this time? Explain your reasoning.

UNIT 10: UNDERSTANDING PLAYER CARDS • 35


EXPLORATION

10.2

Why Use Circle Graphs to Represent Shooting Percentages?

Spinners are used in games all the time. When you spin a spinner, you hope that it will land in some sections and dread that it will land elsewhere. On the NBA Math Hoops Player Cards, 2-pt. and 3-pt. FG% are represented on a circle graph. The circle graph is broken into sections (the fancy word for “sections” is “sectors”) and a spinner is then placed over it. In this way, you can spin the spinner to model shot attempts. Some sections of the circle graph represent a favorable outcome (you make the shot) and some represent an unfavorable outcome (you miss the shot).

A. Two-Point Shots You’ll remember that shooting percentages are written to three decimal places. For example, Tyson Chandler, New York Knicks center, led the league in 2-pt. FG% during the 2011–12 NBA season at a phenomenal .683 clip. Written as a percent, this would be 68.3%. Another way of looking at this is that for every hundred 2-pt. shots Chandler took, he could be expected to make about 68 of them! Wow!!! So how do you represent Tyson Chandler’s 68.3% success rate on a circle graph? Remember that this is called the favorable outcome. Like any other circle, a circle graph contains 360 degrees of angle measure as you rotate about it. If you divided a circle graph into four equal sections, each would represent 25% of the circle graph (since it was divided into 4 sections) and each would have a central angle measuring 90° (since 360° ÷ 4 = 90°). The picture below shows this.

25%

25%

90˚ 90˚ 90˚ 90˚

25%

25%

1. Now, Tyson Chandler had a success rate of 68.3%. Based just on the circle above, can you estimate how much of the circle you would shade to represent his favorable outcome of making a 2-pt shot? The circle graph above shows you a way to estimate a section’s size. When the NBA Math Hoops circle graphs were created, the sections were created precisely. For Tyson Chandler, you need to take the whole circle graph (360°) and assign 68.3% of it to the

36 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


favorable outcome of making a 2-pt shot. The easiest way to do this is to use what you know about finding a percent of a number. To do this, you multiply: 68.3% of 360° = 68.3% × 360°

= 0.683 × 360°

= 245.88°

≈ 246°

When you estimated earlier how much of the circle graph to shade, you probably chose a section that was bigger than two parts (180°) and smaller than three parts (270°). As you can see now, the precise answer is 245.88°, right where you’d expect it to be. The answer is rounded to 246° since measuring degrees on a cardboard circle graph is not something you can carry out to two-decimal-place precision. On the Math Hoops Player Card circle graphs, each player gets two sections for successful shots. So, instead of having one section with a central angle of 246°, Tyson Chandler gets two sections, each with a central angle of 246° ÷ 2 = 123°. The image to the right is what his circle graph would look like. Notice how orange is used for making a shot and gray is used for missing a shot. 2. Complete the chart below. The first one has been done for you. PLAYER

2-pt. FG%

360° x 2-pt. FG% (rounded)

Player A

.564

360° × .564 = 203°

Player B

.483

Player C

.525

Player D

.477

Player E

.542

Player F

.639

Successful° ÷ 2

203° ÷ 2 = 101.5°

Orange Sections

Gray Sections

101.5°

78.5°

3. Which of the players in the table above match the following circle graphs?

Player

Player

UNIT 10: UNDERSTANDING PLAYER CARDS • 37


Proportional Reasoning It isn’t immediately obvious, but the work on the previous page involves proportional reasoning. Another way of talking about Tyson Chandler's .683 FG% is to say that he was successful, on average, on 683 of 1,000 shots. You want to find how many degrees (x) out of 360° to shade on a circle graph to represent his success. 683

x

So, you want 360 to represent 1000 . To do that, you can set up and solve this equation: x 683 360 = 1000

This leads to the same solution: 245.88°

B. Three-Point Shots Three-pt. shooting percentages are also included on NBA Math Hoops Payer Cards — all but the Centers’ cards. Look at the sample card for Diana Taurasi to the right. Like most players, Diana's 3-pt. shooting percentage is less than her 2-pt. shooting percentage. So to show successful 3-pt. shots, the Player Cards are marked by a crosshatch pattern inside the 2-pt. sections.

1. Think you can create a circle graph for one of the NBA’s premier players? Use the career data below for Steve Nash and give it a try. You will need a calculator to find the degrees for each sector and a protractor to complete your graph. a. First begin with Steve Nash’s 2-pt. shooting percentage data:

Steve Nash CAREER STATS* 2-PT. FG%

360° x 2-pt. FG% (rounded)

Successful ° ÷ 2

Orange Sections

Gray Sections

.491 b. Now finish your circle graph using Nash’s 3-pt. shooting percentage data: 3-PT. FG%

360° x 3-pt. FG% (rounded)

Successful ° ÷ 2

Crosshatched Sections

.428

* 2-point and 3-point shooting percentages reflect Steve Nash’s career through the 2011–12 season.

38 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Steve Nash

FIND OUT MORE For an example of how you can put this knowledge to use, look ahead to EXPLORATION 14.2: MAKE YOUR OWN PLAYER CARDS! on pp. 70-71.

2. If you were to place a spinner over your circle graph and do 50 spins for 2-pt. shots and 50 spins for 3-pt. shots, what do you think the outcome would be? Give it a try!

Write a brief note to NBA Commissioner, David Stern explaining why circle graphs are a good tool for displaying players’ field goal shooting percentages.

UNIT 10: UNDERSTANDING PLAYER CARDS • 39


EXPLORATION

10.3

Does the Order of Shading Matter on the Free Throw Grids?

While most of the points you score in Math Hoops will be 2-point and 3-point field goal shots, free throws can also determine the outcome of a game. To the right of the Field Goal circle graph on the Player Cards is a 10-by-10 grid with orange and gray shaded squares. The orange squares represent the player’s free throw percentage. Pull out the Player Cards for Danny Granger and Kyrie Irving and look at the free throw grids on them. Who would you rather have shooting free throws for your team? The free throw grids on the Player Cards have a total of 100 squares. Each square represents one percent. DANNY GRANGER 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

KYRIE IRVING 0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

1. What similarities do you notice about the two grids? How about differences?

2. Do you think the design of the grids would have any effect on the likelihood of making a shot? Is there a grid that you would prefer to use?

40 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


3. Work with your co-coach or another partner. Roll the dice to take 20 free throw shots. Record the results by placing an X in either the Make or Miss box for each shot on both charts.

Danny Granger Successful shots: ROLL

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20

Make Miss

Kyrie Irving Successful shots: ROLL

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20

Make Miss 4. Did the design of the grids make a difference for this small sample? Do you think it would matter if the sample were larger? Explain your reasoning.

5. Try your own design. Create two sample grids for Dwight Howard representing his Free Throw % for the 2011–12 NBA season. PLAYER

FTM

FTA

FTM/FTA

FT%

Dwight Howard

281

572

281/582

.491

0 1 2 3 4 5 6 7 8 9

GRID A

GRID B

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

UNIT 10: UNDERSTANDING PLAYER CARDS • 41


6. Describe the thinking behind the two designs you created.

7. Let’s test your designs, but this time with a larger sample. Again, work with your cocoach or another partner, but now roll the dice to take 40 free throw shots. Record the results below.

Grid A Successful shots: ROLL

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20

21 22 23 24

25

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Make Miss ROLL Make Miss

Grid B Successful shots: ROLL

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20

21 22 23 24

25

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Make Miss ROLL Make Miss 8. Did the larger sample make a difference? Write a Coaching Tip for new NBA Math Hoops coaches. Your tip should help them understand possible advantages and/or disadvantages to the design of the free throw grid. Be sure to reference the results from your two trials!

42 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Unit

11

Analyzing the Game EXPLORATION

11.1

Investigating the Shot Planner

NBA and WNBA coaches often carry a dry-erase board with a drawing of a basketball court on it for mapping out plays during time-outs. When on offense, these plays are designed to show who should get the ball and take the shot. Some very exciting finishes to important games in NBA history have been planned on these boards! In NBA Math Hoops, you use a special dry erase Shot Planner to determine your shot options. The rules say to record the roll of the dice by writing the largest number first. Why do you think this rule exists?

A. Basic Game 1. Imagine you just rolled the Math Hoops dice and rolled an 8 and a 4. Complete the two charts below, operating on the numbers from left to right as indicated. 8+4

ROLL

8 4

+

ROLL

4 8

+

4 +8

8– 4

4–8

8×4

×

4× 8

×

8÷4

÷

4÷ 8

÷

Division with Zero You may have learned that division and multiplication are inverse operations — that is, one operation reverses the effect of the other. That means you can check if an answer in division is correct by using multiplication.

EXAMPLE: 15 ÷ 3 = 5 To check this, multiply the answer (quotient) by the number you’re dividing by (divisor). If it’s correct, you’ll get the number you started with (dividend):

5 × 3 = 15 Anytime the dividend is 0, the quotient will also be 0 because 0 times any number = 0.

0 ÷ 5 = 0 and 0 × 5 = 0 When the divisor is 0 however, the quotient isn’t zero. In fact, it can’t be any number — it’s undefined. Sounds a bit crazy, doesn’t it? Let’s test one out.

If 9 ÷ 0 = 0 then by using multiplication to check the answer, 0 × 0 = 9. Hmmmmm . . . puzzling you say. Want to know more? Check out http://www.mathsisfun.com/numbers/dividing-by-zero.html for more info.

UNIT 11: ANALYZING THE GAME • 43


2. Which of your answers are the same regardless of how you recorded the roll of the dice? Why do you think this is so?

3. How are the answers for subtraction similar? How are they different?

4. Do you see a relationship between your division answers? If so, how would you describe this relationship?

5. Use the dice rolls below to figure out shot options for the Basic Game. First record the roll from greatest to least, then from least to greatest.

SAMPLE 1

ROLL ROLL

SAMPLE 2

ROLL ROLL

SAMPLE 3

ROLL ROLL

SAMPLE 4

ROLL ROLL

SAMPLE 5

ROLL ROLL

2 6 6 2

9 3 3 9

5 1 1 5 7 4 4 7 8 0 0 8

+

×

÷

+

×

÷

+

×

÷

+

×

÷

+

×

÷

+

×

÷

+

×

÷

+

×

÷

+

×

÷

+

×

÷

44 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


6. What did you discover by completing the examples above?

B. Advanced Game When playing the Basic Game, division must yield a whole number answer (quotient) but when playing the Advanced Game, you’re allowed to round up or round down. 1. Both charts below show the identical dice roll and Ball On number — the difference being that the first chart lists the dice roll from largest number to smallest and the second from smallest to largest. Complete the first chart by following the Advanced Game rules and always operating from largest number to smallest. Complete the second chart by doing the opposite — operating from smallest number to largest.

ROLL

9 2

BALL ON

ROLL

15

2 9

BALL ON

15

+

×

÷

+

+

+

+

×

×

×

×

÷

÷

÷

÷

+

×

÷

+

+

+

+

×

×

×

×

÷

÷

÷

÷

2. What did you discover by completing the examples above?

The Basic and Advanced Shot Planners

Why do you think the Shot Planner rules were set up the way they are? Be sure to reference examples from your work with both the Basic and Advanced versions of the Shot Planner to explain your reasoning.

UNIT 11: ANALYZING THE GAME • 45


EXPLORATION

11.2

Would You Rather Be Odd or Even?

A. Properties of Odd and Even Numbers When you play Math Hoops, one team works with even numbers and the other team works with odd numbers. By now, you’ve noticed that the numbers that come up when you roll the dice can affect your shot options. This is related to properties of odd and even numbers. Each of the game dice has 10 faces. Five faces contain an even number and five faces contain an odd number. That means the chance of rolling an even number is the same as the chance of rolling an odd number. But it doesn’t end there. When you add, subtract or multiply numbers, you can tell ahead of time whether the result will be even or odd. It all depends on the two numbers you start with. Complete the three tables below to see what this means.

+

EVEN

ODD

EVEN

×

ODD

EVEN

EVEN

EVEN

ODD

ODD

ODD

EVEN

ODD

1. Do you think it matters in the game that even products are much more likely than odd products? Why?

What about division? There’s no table above for division. That’s because you can’t always divide the numbers you roll and get a whole number! And when you can divide, you can’t always predict whether the quotient will be odd or even. Let’s look at this a little more closely. 2. For each of the following, list one example: a. roll of two odd numbers that can be divided b. roll of two odd numbers that can not be divided c. roll of one even and one odd number that can be divided d. roll of one even and one odd number that can not be divided e. roll of two even numbers with an even quotient f. roll of two even numbers with an odd quotient g. roll of two even numbers with a quotient that is not a whole number

46 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


3. Whatever number is rolled on the first die, what number on the second die guarantees that your quotient is a whole number? 4. A player rolled one die first and complained, “That number is the worst for division! You hardly ever get whole numbers.” What number did this player most likely roll? 5. Given what you know about properties of even and odd numbers, do you think it’s better to be on the even or odd end of the court? Explain your reasoning.

B. BASIC GAME: Odd and Even Advantages The Math Hoops Basic Game Board shows 20 numbers on the Odd end of the court and 20 numbers on the Even end. Each end of the court also has the same number of 2-pt. and 3-pt. shot options. You might think that makes the game fair. Let’s see what you think after some investigation. Most of the time when you roll the dice, you will have at least one possible shot. Sometimes, you will have more than one choice. But every now and then, you may roll two dice and not have any shot available!

1. Suppose you’re the Odd team and you roll a 4 and a 2. To get to your end of the court, you need an odd number. What are your options?

ROLL

4 2

+

×

÷

UNIT 11: ANALYZING THE GAME • 47


2. Now suppose you’re the Even team and you roll a 9 and a 6. What are your options in this case? Are you able to get to your end of the court?

ROLL

9

6

+

×

÷

3. List all the rolls you can find where there are no shots available on the Odd end of the court. Then do the same for the Even end of the court. Do you think you found them all? Check with other coaches to see if there are any you missed. ODD:

EVEN:

4. Based on your work above and discussion with your fellow coaches, do you feel there is an advantage to being Even or Odd? Explain your thinking.

Take a closer look at the Odd end of the court. The numbers 15, 35, and 63 appear twice. On the Even end of the court, no numbers appear twice. 5. Suppose you are playing on the Odd team. With less than 30 seconds left in the game and your team down by two points, you roll a 5 and 3. What choices do you have for your shot? What will you do?

6. Do you think having numbers repeated on the game board gives the Odd team an advantage? Explain your thinking.

You have been asked twice above whether either side has an advantage in Math Hoops. Now remember that teams switch sides in the middle of each game. Taking this fact into account, prepare a written response explaining why you agree with ONE of the following statements:  If I were playing Math Hoops and could be on one side for the entire game, I would choose the Even side.  If I were playing Math Hoops and could be on one side for the entire game, I would choose the Odd side.  If I were playing Math Hoops and could be on one side for the entire game, I would not care which side I was on.

48 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


EXPLORATION

11.3

How Will the Advanced Division Rules Affect Your Strategy? ADVANCED GAME

When you use division in the Basic Game, the answer or quotient must be a whole number. If you’re left with a remainder, division gives you no options to take a shot. In the Advanced Game it’s a much different story. Will understanding and using the new division rules work to your advantage? Using division in the Advanced Game allows you to round up OR down so that you always get a whole number quotient. A roll of 9 and 4 gives you a quotient of 2 OR 3 because the correct answer is between 2 and 3. The number you’d choose would most likely depend on whether you’re playing on the ODD or EVEN end of the court. Refer to the Shot Planner below when answering the questions that follow.

ROLL

9

BALL ON

4

12

13 5 36 3 + + + + 25 17 48 15 – – – – 1 7 24 9 × × × × 60 36 ÷ ÷ ÷ ÷ 2 3 3 4

+

×

÷

1. What options are there for placing the ball on the EVEN end of the court?

2. What options are there for placing the ball on the ODD end of the court?

3. Which side has more options? 

Rounding Conventions When you divide 10 by 4, you get 2.5, a number exactly halfway between 2 and 3. In textbooks, you are taught to round this number to 3. That rule is really just a convention that we all agree to use so that everyone gets the same answer. Since 2.5 is exactly as far from 2 as it is from 3, you could just as easily round it to 2. In Math Hoops you can choose to round up or down regardless of how close a decimal is to the whole number greater or less than it. This gives you a lot of options with division. How would the game be different if you followed conventional rounding rules? Try the game this way if you want to play a more challenging variation.

UNIT 11: ANALYZING THE GAME • 49


4. How do you think things might change if 9 ÷ 4 were recorded as 2 instead of 3? Complete the Shot Planner to find out.

ROLL

9 4

BALL ON

12

13 5 36 2

+

×

÷

+

+

+

+

×

×

×

×

÷

÷

÷

÷

5. What options are there for placing the ball on the EVEN end of the court?

6. What options are there for placing the ball on the ODD end of the court?

7. Which side has more options? How did the number you rounded to affect the number of options for each shot planner?

8. Imagine you are playing on the ODD end of the court. Complete the Shot Planner below so that it gives you the most shot options.

ROLL

7 2

BALL ON

25

+

×

÷

+

+

+

+

×

×

×

×

÷

÷

÷

÷

50 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


9. What strategies did you use to find the greatest number of shot options for the ODD side of the court? What would you do differently if you were playing on the EVEN side of the court?

10. You’re in a very close game with less than one minute left. The ball is on 39 when you roll an 8 and a 3. What will be your division answer in the top row of the Shot Planner so that you get the most shot options possible? Create a model to show your results and explain your reasoning.

51


Unit

12

Creating Teams and a Season EXPLORATION

12.1

How Do You Make a Player Draft That’s Fair?

In the NBA and WNBA, there is an annual “draft” where teams select prospective players to join their teams. Teams with the worst records in a league typically get to make their first draft choice before the teams with better records. This is done to help the not-so-good teams get better more quickly. Since you are starting out with a brand new league in NBA Math Hoops, the order of the draft cannot be assigned in this way. What are some possible options for designing a draft that is fair? Each NBA Math Hoops game includes a set of 32 Player Cards. (If you have a Classroom Kit, you should have 8 complete games.) Each of the five positions is represented by six or seven different players. From each of the sets of 32 cards, two teams will draft eight players apiece. Teams will need to draft at least one player for each position. The NBA uses the concept of probability when it determines the team that gets the #1 selection in its annual draft. Research the method that the NBA uses for teams to select players. How might probability play a role in your Math Hoops draft? 1. Talk with your co-coach. List 3 possible processes for conducting a player draft. For each process, explain why you think it is fair for both teams. Possible Process

This process is fair because:

1

2

3

Your League Commissioner will assign you to work with another team. Share your ideas and be open to others that are shared with you. Both teams will need to agree on a draft process that they feel is fair.

52 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Schedule

2. Write out the process you’ve agreed to in clear, concise steps. Your process should be easy for anyone to follow and, of course, fair to both teams.

3. How will you decide which position to draft first?

4. After drafting a player for each position, you can now add 3 more players to your team. How will you determine which positions you will choose for your additional players? How do you intend to use these players?

Check with other teams and ask how they decided to conduct their draft. Be sure to ask questions if you don’t understand their process or if you think their draft is unfair. Now that you’ve participated in a draft and learned about other methods, you can be a valuable resource for others. Imagine you’ve been put in charge of guiding two teams in their NBA Math Hoops player draft. What process will you suggest they follow? Explain why you feel this would be the best way for them to conduct their draft.

UNIT 12: CREATING TEAMS AND A SEASON SCHEDULE • 53


EXPLORATION

12.2

Which Players Should You Choose for Your Team?

If you’re playing in a Math Hoops league, you will be able to draft 8 players for your team. How will you decide which players to choose? This might be a challenge to figure out, so you may want to play some practice games before having a draft. Pick 5 cards — one for each position — to practice with. Try out different players. Think of yourself as a scout evaluating the talent available to you. The question you’re trying to answer is: What makes a good player and how will you use this information when choosing your team?

A. Before the Draft 1. The Player Cards display 3 statistics for each player: Field Goal %, 3-point %, and Free Throw %. After playing a few games, do you think any of these are more important than any others? Give reasons for your opinion.

2. Look through the set of 32 Player Cards. Compare the statistics for different players of the same position. If you had to choose one player right now, who would it be?

Position

My Top Choice

BLUE RED GREEN GOLD PURPLE 3. Examine the choices you made. Then summarize your own strategy for selecting the best players in a category.

54 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Now get together with your co-coach.  Did you both agree on the choices made? Discuss any different points of view you may have.  Challenge each other’s choices and ask questions of each other. As a team, devise a strategy that you will use to select a player within any given card color.  Every team wants to be the first to make a selection in a draft so that they can get their top choice. As a team, decide upon your #1 choice for the first round of the draft. 4. Obviously, players with higher numbers are more likely to score points, and scoring more points than the opposing team is what wins ball games. What percentage would you say a “good” player should have for each statistic? FIELD GOAL % 3-POINT % FREE THROW %

5. Examine the work you did above. Was mathematics involved in any way? Illustrate and explain the role mathematics plays in your draft strategy.

UNIT 12: CREATING TEAMS AND A SEASON SCHEDULE • 55


B. After the Draft

ADVANCED GAME

Review the players you selected in the draft. Refer to the Advanced Game Board below and choose EITHER the Even or Odd end of the court to record information in the chart.

  I’m using the EVEN ODD end of the game board. (circle one)

RED

GOLD

BLUE

PURPLE

GREEN

Total # of shooting spots # of 2-pt. shooting spots # of 3-pt. shooting spots # of passing (assist) opportunities # of 2-pt. shooting opportunities (Think carefully!) # of 3-pt. shooting opportunities (Think carefully!) Preferred order (1–5) for a game-ending 2-pt. shot Preferred order (1–5) for a game-ending 3-pt. shot List three things you discovered by recording the information above. 1 2 3

Coaching a championship team requires hard work, attention to detail, and an understanding and appreciation of balance. The most successful teams have a variety of exceptional team players. Explain how you will use the information you’ve gathered in this activity to increase your team’s chances for success. 56 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


EXPLORATION

12.3

How Can You Design a Creative Season Schedule?

Once your league is divided into teams, you’ll want to start your season. You could just split into pairs today and square off against each other. But that won’t help you tomorrow! You need to come up with a schedule for the league. Before you begin, discuss the task of making a league schedule for the entire season. 1. Discuss with your teammates any information you will need before you can make the schedule. List that information below.

2. Discuss with your teammates any rules that you feel the schedule must follow. List that information below.

Breaking It Down Do you have a lot of teams in your league? Or a long season with many games? These could make for a complicated schedule. If things are getting confusing, try breaking down the problem into something simpler. Start with fewer teams or fewer games and look for patterns as you increase the difficulty.

3. Discuss as a class the information your team wrote for Questions 1 and 2. Use this discussion to form a plan and rules for making a league season schedule. Write your rules below.

Now that you have your rules, it’s time to make your schedule. Use the Season Schedule form on page 81. When you finish, present your schedule to your League Commissioner for adoption. If you had no problems creating a schedule, great! But if there were problems, include an explanation that makes clear what they were and how you dealt with them.

UNIT 12: CREATING TEAMS AND A SEASON SCHEDULE • 57


Unit

13

Winning Strategies EXPLORATION

13.1

Who Gets the Ball?

The game is underway. You’ve rolled the dice, done the calculations and now need to move and shoot the ball. Which player will you select to get the ball and what will you consider when making this decision? 1. Imagine you’re playing on the Odd end of the court during a Basic Game and you roll 7 and 4. Perform the arithmetic and record the results in the blank chart below.

ROLL

7 4

+

×

÷

2. What are your options?

Probability and You During this investigation, you will find yourself using your understanding of probability. Strategies for deciding who gets the ball rely heavily on it. Remember that probability represents the chance that a specific outcome will occur. Can you think of how the statistics on your Player Cards are connected to probability? What does it mean to say that a player has a .456 shooting percentage? On any given shot attempt, are the chances favorable that this player will make it?

The options you’ve listed result in a 2-pt. shot by one of these two players.

3. Which player has the greater probability of making a 2-pt. shot? Who would you select to take the shot? Explain your reasoning.

4. What if you had a strong suspicion that your opponent was going to call a foul regardless of which player you selected. Would this alter your plan? Why or why not?

58 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


5. Playing the Advanced Game will lead to even more shot choices. Complete the Advanced Shot Planner below but now look for EVEN options. Then use the Advanced Game Board and the Player Cards shown on these two pages to answer the questions.

ROLL

7 2

BALL ON

11

+

×

÷

+

+

+

+

×

×

×

×

÷

÷

÷

÷

6. Suppose you’ve elected to take a 2 pt. shot. Considering the probability of getting a favorable outcome, which player would be your first choice? Second choice? Why did you select these players?

7. You’re down by 2 points and have one chance to try and win the game. Who would you choose to take the final shot? How does probability play into your decision?

8. Knowing that your opponent always has the option to foul, which player would you make sure didn’t get the ball? Explain your reasoning.

9. List three things a coach may want to consider when selecting a player to get the ball: 1

2

3

UNIT 13: WINNING STRATEGIES • 59


EXPLORATION

13.2

Go for Two Points or Three Points?

Ten seconds remain in the first half of a Basic Game and your team is down by two points. After rolling the dice and doing the calculations your options are clear: your point guard (Red) can take a 2 pt. shot or a 3pt. shot. What will you do — go for two or go for three?

Expected Value When deciding whether to take a 2-point or 3-point shot, how do you know if you’ve made a good choice? Mathematicians have actually devised a tool to help figure out decisions like these. It’s called expected value, and it’s a way of assigning a numerical value to your choices. You may want to research this concept or ask your teacher to help explain it. While understanding when and how to use expected value can be challenging, it can also give you a strong competitive edge over your opponents.

1. If you go for two points, what is the likelihood the outcome will be favorable? Can you think of a way to assign a numerical value to that outcome? Explain your method.

2. If you go for three points, what is the likelihood the outcome will be favorable? Can you think of a way to assign a numerical value to that outcome? Explain your method.

3. Have you devised a way to compare values that could help you choose whether or not to take a 2 pt. shot or a 3 pt. shot? If so, explain why you feel your method makes sense.

60 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Look at the two sample player cards below:

Refer to these cards when responding to the following game play scenarios. 4. Your game has just started and your options are for your guard, Probability Brown, to take a 2 pt. shot or your forward, Stats Johnson, to take a 3 pt. shot. Who will you choose? 5. Late in the first half and you’re quickly falling behind. Your opponent hints that they are going to start fouling. You have a choice to have Stats Johnson prepare to take a 2 pt. shot or Probability Brown set up to take a 3 pt. shot. Who will you choose?

6. The halftime score is 34-26 with your team trailing. The first roll of the second half leaves you with a choice to have Probability Brown take a 2 pt. or 3pt. shot. Which will you choose? 7. Midway through the second half you’ve closed the gap and are only down by three. You now have the option of having Stats Johnson take a 2 pt. shot or Probability Brown take a 3 pt. shot. Who will you choose? 8. You trail by two with 5 seconds left in the game. Your options are having Stats Johnson take a 2 pt. shot or a 3 pt. shot. Which will you choose?

Select any three of the scenarios above and explain, in writing, the choices you made. Support your selections with strong mathematical reasoning.

What advice would you give to someone new to NBA Math Hoops regarding going for two points or going for three? Why does your advice make sense?

UNIT 13: WINNING STRATEGIES • 61


Should You Pass or Should 13.3 You Shoot? EXPLORATION

ADVANCED GAME

A unique feature of the Advanced Game is the presence of “passing lanes” that allow the ball to go back and forth between two players on the same team. As a Math Hoops coach, you will constantly be making quick decisions during the course of the game. What will determine whether you choose to pass or shoot? Refer to the Player Cards on the opposite page to respond to to the following questions. 1. Playing on the ODD end of the court: a. It’s early in the game and you select the option of placing the ball on #13. Do you pass or shoot? b. You’ve built up a six point lead midway through the half and place the ball on #55. Do you pass or shoot? c. Your opponent has fought back to tie the game with a minute to go in the half. You have the ball and place it on #45. Do you pass or shoot? d. Ten seconds left in the first half and you’re down by one. #11 gets the ball. Do you pass or shoot? 2. Now playing on the EVEN end of the court: a. After scoring at the end of the first half and taking the lead, you start the second half with the ball on #16. Do you pass or shoot? b. Opening up a ten point lead, your team is on fire. You have the ball and it goes to #34. Do you pass or shoot?

62 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


c. Your opponent will not go away quietly. They’ve fought back to within one point with two minutes to play. You move the ball to #54. Do you pass or shoot? d. Five seconds remaining in the game and you’ve lost the lead. Down by two, the ball goes to #2. Do you pass or shoot? 3. Select one of the situations when you were on the ODD end of the court where you chose to pass. Explain the reasoning behind choosing to pass.

4. Select one of the situations when you were on the EVEN end of the court and where you chose to shoot. Explain the reasoning behind choosing to shoot.

EXTENSION: Create two game scenarios — one where you would choose to “pass” and one where you would elect to “shoot.” Explain the reasoning behind each of your choices.

UNIT 13: WINNING STRATEGIES • 63


EXPLORATION

13.4

Can You Beat the Shot Clock?

As if a Math Hoops game weren't exciting enough, introducing the shot clock guarantees to step up the pace even more. Once the clock is ticking, completing all possible calculations on the shot planner can be a challenge. That said, do you really need to complete all calculations to find a good shot option? What shot clock strategies will you develop to keep you competitive and IN the game? Look at the partially completed Advanced Shot Planner below. Rather than jumping in and starting the calculations with the Ball On number, what about looking at whether outcomes will be even or odd? If you need to quickly find Even options, why take the time to do calculations that lead to an answer that is Odd?

ROLL

5 2

BALL ON

23

+

7 3 10 2 –

×

÷

+

+

+

×

×

×

×

÷

÷

÷

÷

+

Here's the chart filled out, but instead of showing numeric results, the sixteen squares show whether a calculation will yield an even (E) or odd (O) answer.

ROLL

5 2

BALL ON

23

+ +

7 3 10 2* –

+

×

÷

+

+

O – – – E E O × × × O O E E

÷

÷

E

÷

– ×

O O E

*What other number could this be? Check your division rules!

÷

E/O E/O E/O E/O

Offensive Rebounds and the Shot Clock In the Advanced Game, a team that uses multiplication or division to determine placement of the ball has the opportunity to get an offensive rebound, leading to another shot attempt. But it can require a little more thought to figure out your options with these two operations. When the shot clock is ticking, you’ll need to decide how much time to spend on multiplication and division. Is there a risk you won’t get a number you can use before the clock runs out? Will taking additional time to multiply and divide be worth the risk?

64 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


1. Why does the last row show even OR odd?

2. Complete the charts below to identify some patterns that might help you expedite the calculation and shot selection process.

+

O

E

O

×

E

O

E

÷

O

O

O

O

E

E

E

E

O

E

Now use what you know to find possible even and odd options. There’s no need to do calculations that won’t help you. Remember, the shot clock is running! 3. Looking for EVEN options:

ROLL

7 3

BALL ON

37

10 4 21 2*

+

×

÷

+

+

+

+

×

×

×

×

÷

÷

÷

÷

*What other number could this be?

4. Looking for ODD options:

ROLL

9 5

BALL ON

8

14 4 45 2*

+

×

÷

+

+

+

+

×

×

×

×

÷

÷

÷

÷

*What other number could this be?

Describe what you’ve learned from this exploration and any new shot clock strategies you can use to stay competitive in future games.

UNIT 13: WINNING STRATEGIES • 65


EXPLORATION

13.5

Foul Play: When Is the Best Time to Foul?

One point can make the difference between winning and losing a game. Onepoint shots — free throws — are taken when the opposing team elects to foul a player. Why would a coach choose to send an opposing player to the free throw line? Because it’s possible that fouling an opposing player can actually provide a strategic advantage. The trick is to know how and why fouls — whether on offense or defense — can work in your favor. How will “foul play” enter into your game plan? Review the differences between fouls committed in the first half (the “One and One” rule) and the second half on page 8.

Refer to the sample cards above when responding to the following questions: 1. If you were going to foul a player about to take a two-point shot in the first half of a game, which of these two would you want it to be? Why? Explain your reasoning.

2. If you were going to foul a player about to take a two-point shot in the second half of a game, which of these two would you want it to be? Why? Explain your reasoning.

66 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


3. If these two players were on your team, which player would you prefer your opponent foul in the first half of a game? Why? Explain your reasoning. FIND OUT MORE The concept of expected value can help you choose when to foul. See the sidebar EXPECTED VALUE on p. 60.

4. If these two players were on your team, which player would you prefer your opponent foul in the second half of a game? Why? Explain your reasoning.

What happens when a player about to take a three-point shot is fouled? They are granted three foul shots regardless of which half of the game it is! What would you do in these situations? 5. Ten seconds left in the half and a tie score. Pushy Dixon is on your team and about to take a 3-point shot. Would you rather he take the shot or be fouled by your opponent? Why? Explain your reasoning.

6. Last shot of the game and you’re up by two points. Sandy Elbows is on your opponent’s team and about to take a 3-point shot. Will you let her shoot or call a foul? Explain your reasoning.

7. What have you learned about “foul play” in NBA Math Hoops that will help you become a more successful coach?

UNIT 13: WINNING STRATEGIES • 67


Unit

14

Improving Your Team EXPLORATION

14.1

Mid-Season Assessment: Is It Time for a Roster Change?

The midway point of the Math Hoops season is a great time to review your team’s performance. Do you have a winning record? Have you lost some close games? Have you been making the most of the three additional players you selected in the draft? If so, how have these players been helping or hurting your team? If your team has been struggling, or even if it’s doing well, now is a good time to explore some additional ways to make improvements. One way to do this is to replace one of your players by drafting a new player from the set of unused Player Cards or by creating your own Player Card. Before deciding which route to go, you’ll want to take a close look at player data from the first half of the season. On p. 84 in the back of this manual, you will find a Mid-Season Assessment sheet. Complete this form with statistics from the first half of your Math Hoops season, and then use the information you gather to consider the following questions: 1. How do your players’ shooting percentages from your Math Hoops games compare to the ones on the Player Cards? Are they significantly higher? Lower? About the same?

2. Based on the data you’ve gathered, which players are your best 2-pt. shooters? Your best 3-pt. shooters? Could you use help in either of these areas?

3. Which players are taking the most shots for your team? Which are scoring the most points? When looking at shooting percentages and points scored, are these players the ones you want to continue shooting the ball?

4. Which of your players has taken the most free throw shots? Does their free throw shooting percentage come close to matching the percentage on their card? In your opinion, are your opponents fouling the right player?

68 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Mid-Season Assessment

ADVANCED GAME ONLY

5. Who is leading your team in assists? Is this a good role for them or would they provide more benefit to your team by shooting the ball?

FIND OUT MORE 6. Would it be to your advantage to create a new card using a player’s game data from the first half of the season? Would it make sense to replace one or more of your players with new ones?

If you'd like to conduct a more in-depth analysis of your team to assess its strengths and weakness, turn to EXPLORATION 15.2: PER-GAME STATISTICS and EXPLORATION 15.3: TEAM ANALYSIS on pp. 74–77.

Write a “critique” of your team. Talk about what it has done well and how you feel it could improve. Discuss the performance of specific players on your team. Explain changes you are considering and the rationale behind these changes.

EXTENSION: Another possible option for improving your team is to make a trade with another team. In order for two teams to trade players, BOTH teams must believe that the trade could benefit their team. If you have a trade in mind, make sure you think it through carefully before moving forward. And of course, you’ll want to look closely at the data!

UNIT 14: IMPROVING YOUR TEAM • 69


EXPLORATION

14.2

Create Your Own Player Cards!

If you’ve conducted a mid-season review of your Math Hoops team and decided that it’s time for new blood, you’ll be on the lookout for a player who will beef up some area of your game you feel is lacking. You can look for a different player from amongst the pack of 32 Player Cards found in the game. But there’s no need to limit yourself that way. You can expand your possibilities by making your own Player Card! There are plenty of ways to approach creating a Player Card. Here are some ideas to get you started:  If you’re playing Math Hoops while the NBA or WNBA is in season, you may want to look at how this year’s players are doing. Is one of the players on your Math Hoops team putting up better numbers in their current season? Why not update the card you have with that player’s current stats?  If you like the players on your team, you can still do some research (always a good thing) and find another season where they outperformed the year noted on the Math Hoops Player Card.  Another option is to replace one of your players with a current NBA or WNBA player who is not already in the NBA Math Hoops game. Use their current stats or find their best year.  Or go to www.nba.com or www.wnba.com and look through the archives. You may find an all-star from the past who will blow the socks off your opponents! Before you get started though, you’ll want to have a clear plan. It may help to consider the questions below for each new card you decide to make. 1. At what position could my team use the most help? What do the numbers tell me that support my thinking?

WEB EXTENSION: If you want complete control over the Player Card you

create, you’ll want to use a blank Player Card template. But that’s not your only option. You can find a cool online tool for creating cards at www.nbamathhoops.org. You’ll be able to select any player who is currently on an NBA or WNBA team. Just choose the year you want and print out the Player Card image that is created.

70 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


2. Time to rank the shooting percentages (2pt., 3pt., free throw) in the order of importance for the new card I’m about to make. Why did I choose this order? FIND OUT MORE

3. How many sections or sectors will I break the circle graph into to display 2-point and 3-point shooting percentages? Why did I choose this number? Will it make any difference in player performance?

Want some help figuring out how to make accurate circle graphs for your Player Card? Turn back to EXPLORATION 10.2: WHY USE CIRCLE GRAPHS TO REPRESENT SHOOTING PERCENTAGES? on pp. 36–39.

4. How will I shade in the free throw grid? Will I spread things out or will I make one or more “clumps” of makes and/or misses? What will I consider when making this choice?

5. How about a test run? Are you up to the challenge? Work through the questions above and then create a new Player Card for a player who is successful on 54.3% of 2-point shots, 32.8% of 3-point shots, and 84.5% of free throws. Use the blank Player Card Template found on the inside back cover of this manual to create your sample card. Compare the card you’ve created with 2 or 3 Math Hoops colleagues. Take turns talking about the choices you made and the reasoning behind them. Determine with your co-coach whether you want to create a new player card. Explain the reasoning behind your decision.

UNIT 14: IMPROVING YOUR TEAM • 71


Unit

15

Why Do Coaches Need EXPLORATION

15.1

Team Standings

The NBA and WNBA have a clear-cut system for determining which teams earn the right to compete in the playoffs. Teams are ranked by winning percentage in their respective conferences and divisions. The top teams are rewarded with a playoff spot. Throughout the season, team standings are kept so that each team knows exactly where they stand at all times. What about your Math Hoops league? How can Team Standings be useful to you? Let’s look at an example of how Team Standings work in the NBA. Remember that the NBA organizes their 30 teams into two conferences, and each conference has three divisions. (See LEAGUE DIVISIONS on p. 26.) Team standings are based on winning percentage in each division. The winning percentage is determined by dividing the number of wins (W) by the number of games played (total of wins and losses). Like shooting percentages, winning percentage is represented as a decimal to three places. EXAMPLE Below are the standings for the Atlantic Division after 20 games of the 2011–12 NBA season. EASTERN CONFERENCE NUMBER OF WINS TOTAL GAMES PLAYED

ATLANTIC

W

L

Philadelphia

13

6

13 + 6 = 19

13 19 =

.6842105

.684

Boston

9

9

9 + 9 = 18

9 18 =

.5

.500

New York

7

12

7 + 12 = 19

7 19

= .3684210

.368

New Jersey

7

13

7 + 13 = 20

7 20

= .35

.358

Toronto

6

14

6 + 14 = 20

6 20

= .3

.300

GAMES PLAYED

PCT.

Games Behind A more sophisticated method for determining team standings is to use the concept of Games Behind (GB). GB gives sports nuts a quick way to figure out their team’s chances of finishing first. Suppose your team is 8 games behind the team in first place. In order for your team to catch the team in first place, your team must WIN 8 games while the team in first place LOSES 8 games. You will often see GB listed in online or newspaper accounts of team standings.

72 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Statistics? Below you will find the standings for the Western Conference after 20 games of the 2011–12 NBA season. Find each team’s winning percentage (Pct.). WESTERN CONFERENCE

PACIFIC

W

L

L.A. Clippers

10

6

L.A. Lakers

11

8

Phoenix

6

12

Golden State

6

12

Sacramento

6

13

NORTHWEST

W

L

Oklahoma City

16

3

Denver

14

5

Portland

12

8

Utah

10

7

9

10

SOUTHWEST

W

L

San Antonio

12

8

Dallas

12

8

Houston

11

8

Memphis

10

8

4

15

Minnesota

New Orleans

PCT.

PCT.

PCT.

Now that you have an understanding of how Team Standings work in the NBA, you and your fellow coaches will need to track your own team standings. The number of divisions you’ll have will depend on the number of teams in your league. It works best when divisions are kept to 4–6 teams. Included in the Math Hoops Classroom Kit is a Team Standings poster. Use this to keep track of and update your Team Standings on a regular basis.

Good luck! UNIT 15: WHY DO COACHES NEED STATISTICS? • 73


EXPLORATION

15.2

Per-Game Statistics

Shooting percentages are one way to evaluate and compare players, but you can also use a “per game” approach. Per-game statistics allow you to take all player data collected from a series of games and determine, on average, how they would perform in a single game. Does this mean they will always put up the same numbers? Of course not. But it will help you see how you’ve been coaching and whether or not you need to make any adjustments. Per-game statistics represent the average of data collected over a series of games. This average is found by taking the totals of a particular statistic divided by the number of games played. Example A player scores 48 points over the course of 4 games. So the player’s average points per game (PPG) is 12. PLAYER

Total Points

Games

Points/Games

PPG

Player A

48

4

48/4

12.0

Sometimes things don’t work out quite so . . . clean. Say you have a player that has collected 13 assists in 5 games and you have another that has collected 11 assists but has only played in 4 games. Who has the better assists per-game (APG) average? Example Player C’s assists per-game average actually works out to be 2.75 and is rounded to 2.8. PLAYER

Total Assists

Games

Assists/Games

APG

Player B

13

5

13/5

2.6

Player C

11

4

11/4

2.8

Representing numbers to tenths usually provides all the precision you’ll need when comparing per-game averages.

What Averages Mean What does it mean to find an average? In the game of basketball, the average is used to determine points-per-game, assists-per-game, rebounds . . . you get the idea. One way to think of average is to think about finding “fair share.” For example, if you know that Tyson Chandler scored a total of 37 points in his last four games, what would be the “fair share” if he were to score the same number of points each game? Well, 37 points ÷ 4 games = 9 ¼ or 9.25 points per game. As you’ve already seen, basketball statisticians favor decimal notation so 9.25 would be Tyson Chandler’s average points per game for these four games. The math makes sense but what in the world does .25 of a point look like?!!

74 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


Along with points per-game (PPG) and assists per-game (APG), you can also find rebounds per game (RPG) and steals per-game (SPG). Complete the charts below to find the per-game statistics for the players listed. 1. POINTS PLAYER

Total Points

Games

Player A

57

7

Player B

59

8

Player C

63

5

Points/Games

PPG

Assists/Games

APG

TOP PLAYER IN THIS CATEGORY: Player 2. ASSISTS PLAYER

Total Assists

Games

Player A

23

6

Player B

16

5

Player C

17

6

TOP PLAYER IN THIS CATEGORY: Player 3. REBOUNDS PLAYER

Total Rebounds

Games Rebounds/Games

Player A

13

3

Player B

8

5

Player C

19

4

RPG

TOP PLAYER IN THIS CATEGORY: Player 4. STEALS PLAYER

Total Steals

Games

Player A

22

9

Player B

6

6

Player C

10

7

Steals/Games

SPG

TOP PLAYER IN THIS CATEGORY: Player 5. List in priority order, the per-game statistics you feel a Math Hoops coach should know. Write a few sentences explaining why you chose this particular order.

UNIT 15: WHY DO COACHES NEED STATISTICS? • 75


EXPLORATION

15.3

Team Analysis

The previous Exploration should give you a good handle on computing individual statistics. Now it's time to look at team performance. After all, basketball is a TEAM sport. A well-balanced team — one that passes the ball efficiently, shoots well, and of course, scores lots of points will — most likely find themselves with a winning record. As a Math Hoops coach, it will be important that you have a good handle on how your team is performing after every 5 or 10 games. Take a look at the sample (modified) Team Analysis Chart below. This data was calculated by regularly recording game data on Player Season Totals sheets (see p. 83) and using this information to complete the Team Analysis Chart. The chart allows for easy access to data useful in making coaching decisions. Refer to the sample chart when responding to the following questions: 1. Who has the “hot hand” from 2-pt. range after 10 games? What coaching strategy could you use to take better advantage of their success?

2. How important is the passing game (assists) for this team? How can you tell based on the information given?

3. What do you feel is the team’s greatest strength? Explain your reasoning.

76 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


4. What do you feel is the team’s Achilles heel (greatest weakness)? Explain your reasoning.

5. What information would help you get a more detailed snapshot of the team’s shooting performance? How could you access this information?

6. List three coaching strategies you would employ for the next 10 games and explain why you think these strategies could improve the team’s performance.

“It’s what you learn after you know it all that counts.” —Coach John Wooden, Legendary UCLA Basketball Coach

1

2

3

Now it’s time to do this kind of analysis with your own team. Fill out the blank Team Analysis Chart found on page 86. To complete this chart, you’ll need to use the data from your Player Season Totals sheets and what you learned about per-game statistics in Exploration 15.2. When you’re finished, discuss with your co-coach how you can use this information to improve your team’s performance. Regardless of how your team has performed so far, you can always make improvements!

UNIT 15: WHY DO COACHES NEED STATISTICS? • 77


EXPLORATION

15.4

League Leaders

During a regular season, the NBA and WNBA track the top players on an ongoing basis, ranking them according to various statistics. For example, if you go to http://www.nba.com/statistics/ or http://www.wnba.com/statistics/ you can get the most up-to-date league statistics in Scoring, Rebounds, Assists, Steals, 2-pt. Field Goal %, 3-pt. Field Goal % and Free Throw %. What statistics do you think would be useful to keep track of in your Math Hoops league? How will the league statistics be of value to you as a coach? League Leaders in various offensive categories can be posted on a weekly basis. The NBA Math Hoops kit contains a classroom poster for League Leaders. You may want to volunteer to keep track of the leaders in a category of particular interest to you. The chart below is from an NBA Math Hoops league after the first 5 games of a season. It shows the Math Hoops League Leaders (top 8 players) in 2-pt. Field Goal %. You’ll note that the team names include real NBA and WNBA teams and some that students created. 2-PT. FIELD GOAL % Name

Team

Position

FGM

FGA

2-pt. FG %

Candace Parker

Bank Shots

F

24

37

.649

Andrew Bynum

Pistons

C

41

65

.631

LeBron James

Fever

F

15

26

.577

Katie Douglas

Netsters

G

25

44

.568

Chris Paul

Lakers

G

22

39

.564

Dwight Howard

Desert Hawks

C

28

51

.549

Pau Gasol

Timberwolves

F

17

32

.531

Russell Westbrook

Celtics

G

26

49

.531

1. What does this League Leaders chart tell you about these players and their respective teams?

2. Look at the last two players. What do you notice about their statistics? Why would Pau Gasol be placed above Russell Westbrook?

78 • PART III: STRATEGIES AND MATH EXPLORATIONS FOR SUCCESSFUL COACHES


3. Below you will find blank League Leaders charts for the bread and butter statistics: 2-pt. Field Goal %, 3-pt. Field Goal %, and Free Throw %. Check in with the other teams in your league and rank the top 5 players in each category. Be sure you have a minimum of 5 games played before completing this task. 2-PT. FIELD GOAL % Name

Team

Position

FGM

FGA

2-pt. FG %

Position

FGM

FGA

3-pt. FG %

Position

FTM

FTA

FT %

3-PT. FIELD GOAL % Name

Team

FREE THROW % Name

Team

You should have a good handle on this by now. How can your class/league keep track of League Leaders for these and other important statistics? What type of system will you agree to in order to keep the leader board up-to-date?


Appendix SEASON SCHEDULE TEMPLATE GAME SUMMARY STAT SHEET PLAYER SEASON TOTALS MID-SEASON ASSESSMENT ALL-STAR NOMINATION FORM TEAM ANALYSIS CHART PLAYER CARD TEMPLATE

80


Season Schedule Template The grid below is a blank template that shows one way to lay out a season schedule. This sample lists 10 days and allows for up to 8 games each day, but it is up to you to decide how long the schedule needs to be and how many games will be played each day. GAME 1

GAME 2

GAME 3

GAME 4

GAME 5

GAME 6

GAME 7

GAME 8

Day 1 DATE

Day 2 DATE

Day 3 DATE

Day 4 DATE

Day 5 DATE

Day 6 DATE

Day 7 DATE

Day 8 DATE

Day 9 DATE

Day 10 DATE

When two teams play basketball, one is the Home team and one is the Away team. Figure out a way you can indicate who the home team is in each game.

81


Game Summary Stat Sheet FINAL SCORE

Date of Game Your Team Opponent

2-Pt Player/Position

FGM

3-Pt FGA

FGM

TEAM

TEAM

SCORE

SCORE

Free Throws FGA

FTM

FTA

Total Points

S

1. 2. 3. 4. 5. *6. *7. *8.

TEAM TOTALS Note: When finished, transfer player stats to the Player Season Totals sheets. *Use these rows for any mid-game player replacements.

ABBREVIATIONS FGM: Field Goals Made FGA: Field Goals Attempted

Coach's Signature 82

FTM: Free Throws Made FTA: Free Throws Attempted

S: Steals F: Fouls

Date

R: Rebounds A: Assists

F

R

A


Player Season Totals Player

Position

Team Coaches 2-Pt

Date of Game

Opponent

FGM

3-Pt

FGA

FGM

FGA

Free Throws FTM

FTA

Total Points

S

F

R

A

SEASON TOTALS TOTAL GAMES PLAYED

Note: You will need a copy of this sheet for each of your players.

ABBREVIATIONS FGM: Field Goals Made FGA: Field Goals Attempted

FTM: Free Throws Made FTA: Free Throws Attempted

S: Steals F: Fouls

R: Rebounds A: Assists 83


84

2-Pt FGM

2-Pt FGA

2-pt. FG%

3-pt. FGM

FG%: Field Goal Percentage FT%: Free Throw Percentage

PPG: Points Per Game SPG: Steals Per Game

ABBREVIATIONS

3-pt. FGA

3-pt. FG%

Games Played

RPG: Rebounds Per Game APG: Assists Per Game

Note: You will need the information from your Player Season Totals sheets to calculate the statistics in this sheet.

TEAM TOTALS

8.

7.

6.

5.

4.

3.

2.

1.

Player Name/Position

Coaches

Team

Mid-Season Assessment

FTM

FTA

FT%


All-Star Nomination Form Team Coaches

All-Star 1

窶アll-Star 2

Explain why you chose these two players:

85


86

2-Pt FG%

3-Pt FG%

FT%

FG%: Field Goal Percentage FT%: Free Throw Percentage

PPG: Points Per Game SPG: Steals Per Game

ABBREVIATIONS

PPG

SPG

Games Played

RPG: Rebounds Per Game APG: Assists Per Game

Note: You will need the information from your Player Season Totals sheets to calculate the statistics in this sheet.

TEAM TOTALS

8.

7.

6.

5.

4.

3.

2.

1.

Player Name/Position

Coaches

Team

Team Analysis Chart

RPG

APG


NBA Math Hoops Coach's Manual!