Reid's Math GOAT Challenge

Ancient Romans used letters to write numbers — and we still use them today for Super Bowls, clocks, and outlines! Here's how they work.

🔤 The 7 Basic Symbols

Symbol	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1,000

➕ Rule 1: Adding (Left to Right)

When a bigger number comes first, you add.

VI = V + I = 5 + 1 = 6

XV = X + V = 10 + 5 = 15

LXII = L + X + I + I = 50 + 10 + 1 + 1 = 62

➖ Rule 2: Subtracting (The Tricky Part!)

When a smaller number comes before a bigger one, you subtract it.

IV = V - I = 5 - 1 = 4

IX = X - I = 10 - 1 = 9

XL = L - X = 50 - 10 = 40

XC = C - X = 100 - 10 = 90

CD = D - C = 500 - 100 = 400

CM = M - C = 1000 - 100 = 900

🏈 Super Bowl Practice!

Super Bowls use Roman numerals. Try these:

Super Bowl III = 3

Super Bowl XX = 20

Super Bowl XLII = XL + II = 40 + 2 = 42

Super Bowl LIV = L + IV = 50 + 4 = 54

Super Bowl LVIII = L + V + III = 50 + 5 + 3 = 58

💡 Pro Tip: You never write more than 3 of the same letter in a row. That's why 4 is IV (not IIII) and 9 is IX (not VIIII).

Geometry is the math of shapes! Knowing a few key formulas will help you crush the geometry questions in this game.

📏 Key Vocabulary

Perimeter — the distance AROUND a shape (like walking around a field)

Area — the space INSIDE a shape (like how much grass covers a field)

Radius (r) — distance from the CENTER of a circle to the edge

Diameter (d) — distance ACROSS a circle through the center (d = 2 × r)

Circumference — the distance AROUND a circle (the perimeter of a circle)

Pi (π) — a special number, approximately 3.14, used in circle math

▬ Rectangles (like a basketball court!)

length (l) width (w)

Area = length × width = l × w

Perimeter = 2 × (length + width) = 2(l + w)

Example: A basketball court is 94 ft long and 50 ft wide.

Area = 94 × 50 = 4,700 sq ft

Perimeter = 2 × (94 + 50) = 2 × 144 = 288 ft

▲ Triangles

base (b) height (h)

Area = ½ × base × height = (b × h) ÷ 2

Example: A pennant flag has base 6 in and height 10 in.

Area = (6 × 10) ÷ 2 = 60 ÷ 2 = 30 sq in

⭕ Circles (like a baseball or a hockey puck!)

r

d

Circumference = π × diameter = π × d

= 2 × π × radius = 2πr

Area = π × radius × radius = πr²

Example: A pitcher's mound has radius 9 ft. (Use 3.14 for π)

Circumference = 2 × 3.14 × 9 = 56.52 ft

Area = 3.14 × 9 × 9 = 254.34 sq ft

💡 Pro Tip: When a problem says "use 3.14 for pi," do the multiplication and then round as the problem asks. Always check if it says "round to the nearest whole number"!

Decimals are everywhere in sports — batting averages, free throw percentages, and race times all use decimals! Let's learn how they work.

📍 Place Values — What Each Digit Means

Every spot after the decimal point has a name:

Tenths — the first digit after the decimal point. In 0.5, the 5 is in the tenths place (five tenths = 5/10)

Hundredths — the second digit. In 0.25, the 5 is in the hundredths place (twenty-five hundredths = 25/100)

Thousandths — the third digit. In 0.325, the 5 is in the thousandths place (three hundred twenty-five thousandths = 325/1000)

How to read decimals:

0.5 = "five tenths" = 5/10

0.25 = "twenty-five hundredths" = 25/100

0.325 = "three hundred twenty-five thousandths" = 325/1000

📏 Decimals on a Number Line

Decimals live between whole numbers. Here's 0 to 1:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1/4

1/2

3/4

Notice: 0.25 is the same spot as 1/4, 0.5 is the same as 1/2, and 0.75 is the same as 3/4!

➕ Adding Decimals — Line Up the Points!

The #1 rule for adding decimals: line up the decimal points, then add like normal!

Step 1 Write the numbers so the decimal points are stacked

Step 2 Add zeros to fill empty spots if needed

Step 3 Add from right to left, just like whole numbers

Step 4 Bring the decimal point straight down

Example: Steph Curry scored 12.5 points in the 1st half and 15.3 in the 2nd half.

12.5

+ 15.3

------

27.8 points total

Example with different decimal places: A 49ers receiver ran 8.75 yards and then 3.5 more yards.

8.75

+ 3.50 ← (add a zero to fill the spot)

------

12.25 yards total

➖ Subtracting Decimals — Same Rule!

Subtracting decimals works the same way: line up the decimal points and subtract!

Example: A Giants batter's average dropped from 0.325 to 0.280. How much did it drop?

0.325

- 0.280

-------

0.045 (or 45 points)

Example: The Sharks goalie's save percentage went from 0.920 to 0.875.

0.920

- 0.875

-------

0.045

🏟️ Decimals & Fractions — The Connection

Every fraction can become a decimal! Just divide the top number by the bottom number.

Fraction	Division	Decimal
1/2	1 ÷ 2	0.5
1/4	1 ÷ 4	0.25
3/4	3 ÷ 4	0.75
1/5	1 ÷ 5	0.2
8/10	8 ÷ 10	0.8
6/12	6 ÷ 12	0.5

Sports examples:

🏀 A player makes 8 out of 10 free throws: 8 ÷ 10 = 0.8 (or 80%)

⚾ A batter gets 13 hits in 40 at-bats: 13 ÷ 40 = .325 batting average

🏒 A goalie saves 28 of 32 shots: 28 ÷ 32 = .875 save percentage

💡 Pro Tip: When a problem says "round to the nearest hundredth," look at the thousandths digit (the third one). If it's 5 or more, round up. If it's 4 or less, keep it. Example: 0.326 rounds to 0.33, but 0.324 rounds to 0.32.

Fractions show up all over sports — shooting percentages, game records, and pizza at the team party! 🍕 Let's break them down piece by piece.

🍕 What Is a Fraction?

A fraction means a part of a whole. It has two numbers:

Numerator (top number) — how many pieces you HAVE

Denominator (bottom number) — how many TOTAL equal pieces

3/4 = three out of four pieces

✓

Think of it like pizza:

Cut a pizza into 4 slices. Eat 3 of them. You ate 3/4 of the pizza!

Cut a pizza into 8 slices. Eat 5 of them. You ate 5/8 of the pizza!

🔄 Equivalent Fractions

Different fractions can show the same amount! Multiply or divide the top and bottom by the same number.

1/2

✓

2/4 (same amount!)

✓

4/8 (still the same!)

✓

1/2 = 2/4 = 3/6 = 4/8 = all mean half!

To simplify: 6/12 → divide both by 6 → 1/2

To build up: 3/4 → multiply both by 2 → 6/8

➕ Adding & Subtracting — Same Denominator

When the bottom numbers are the same, just add (or subtract) the top numbers!

Adding a/c + b/c = (a + b) / c

Subtracting a/c - b/c = (a - b) / c

Example: The Warriors won 3/8 of games in October and 4/8 in November.

3/8 + 4/8 = (3 + 4) / 8 = 7/8

Example: A 49ers kicker made 5/6 of field goals one month, then 2/6 the next.

5/6 - 2/6 = (5 - 2) / 6 = 3/6 = 1/2

🔧 Adding & Subtracting — Different Denominators

When the bottoms are different, you need a common denominator first!

Step 1 Find a common denominator (a number both bottoms go into evenly)

Step 2 Convert both fractions to use that denominator

Step 3 Add or subtract the tops, keep the bottom

Step 4 Simplify if possible

Example: 1/4 + 1/3 = ?

Common denominator of 4 and 3 = 12

1/4 = 3/12 (multiply top and bottom by 3)

1/3 = 4/12 (multiply top and bottom by 4)

3/12 + 4/12 = 7/12

Example: 3/4 - 1/3 = ?

Common denominator = 12

3/4 = 9/12 (multiply top and bottom by 3)

1/3 = 4/12 (multiply top and bottom by 4)

9/12 - 4/12 = 5/12

🏆 Sports Fraction Practice

These are the kinds of fraction problems you'll see in the game!

Finding a fraction of a total:

🏀 Draymond played 3/4 of a 48-minute game. How many minutes?

3/4 × 48 = (3 × 48) ÷ 4 = 144 ÷ 4 = 36 minutes

Converting fractions to decimals (divide top by bottom):

🏒 Sharks goalie saved 27 of 30 shots: 27 ÷ 30 = 0.9 (or 90%)

🏈 49ers won 5 of 8 games: 5 ÷ 8 = 0.625 (or 62.5%)

Converting fractions to percentages (divide, then × 100):

⚾ Giants won 5 of 10 games: (5 ÷ 10) × 100 = 50%

🏈 Completed 12 of 20 passes: (12 ÷ 20) × 100 = 60%

💡 Pro Tip: To compare two fractions quickly, cross-multiply! For 3/4 vs 2/3: do 3 × 3 = 9 and 4 × 2 = 8. Since 9 > 8, then 3/4 is bigger! The bigger cross-product tells you which fraction wins.

Algebra is like being a sports detective! 🔍 You know some of the stats, and you need to figure out the missing number. That missing number gets a letter name — usually x.

🔤 What Is a Variable?

A variable is a letter that stands for a number we don't know yet. An equation is like a balanced scale — both sides must be equal!

Variable — a letter (like x, y, or n) that represents an unknown number

Equation — a math sentence with an equals sign (like x + 5 = 12)

Solve — find the value of the variable that makes the equation true

x + 5

=

12

The Big Rule: Whatever you do to one side, you MUST do to the other side to keep it balanced!

x + 5 = 12

x + 5 - 5 = 12 - 5 (subtract 5 from BOTH sides)

x = 7

➕➖ One-Step Equations: Add & Subtract

If something is added to x, subtract it from both sides. If something is subtracted from x, add it to both sides.

x + a = b → x = b - a (subtract a from both sides)

x - a = b → x = b + a (add a to both sides)

Example: 🏀 Steph Curry scored x points plus 5 free throws for 17 total.

x + 5 = 17

x = 17 - 5

x = 12 points

Example: 🏒 The Sharks need x more wins to reach 20. They have 13.

13 + x = 20

x = 20 - 13

x = 7 more wins

✖️➗ One-Step Equations: Multiply & Divide

If x is multiplied by something, divide both sides. If x is divided by something, multiply both sides.

a × x = b → x = b ÷ a (divide both sides by a)

x ÷ a = b → x = b × a (multiply both sides by a)

Example: 🏈 The 49ers scored x touchdowns worth 6 points each for 18 total.

6 × x = 18

x = 18 ÷ 6

x = 3 touchdowns

Example: ⚽ Messi scored 3 times as many goals as his teammate. Messi scored 12.

3 × x = 12

x = 12 ÷ 3

x = 4 goals (teammate's total)

2️⃣ Two-Step Equations

Some equations need two steps to solve. Always undo addition/subtraction first, then undo multiplication/division.

Step 1 Undo addition or subtraction (move the plain number)

Step 2 Undo multiplication or division (deal with the number next to x)

Example: 🏀 Klay made x three-pointers (3 pts each) and 4 free throws for 25 total.

3x + 4 = 25

Step 1: 3x + 4 - 4 = 25 - 4 → 3x = 21

Step 2: 3x ÷ 3 = 21 ÷ 3 → x = 7

x = 7 three-pointers

Example: 🏀 Steph scored x in the first half and 2x in the second half for 36 total.

x + 2x = 36

3x = 36 (combine like terms: x + 2x = 3x)

x = 36 ÷ 3

x = 12 points

🏟️ Word Problems → Equations

The trickiest part of algebra is turning words into math. Here are the key translations:

Words	Math Symbol
"more than" / "plus" / "added to"	+
"less than" / "minus" / "fewer"	-
"times" / "each" / "per"	×
"split" / "shared" / "divided"	÷
"is" / "equals" / "total"	=
"a number" / "unknown"	x

Practice translating:

⚾ "A player has x hits. 6 more gives him 15 total." → x + 6 = 15

🏈 "3 field goals worth x points each total 9." → 3 × x = 9

🏀 "Scored 2x + 5 points for 35 total." → 2x + 5 = 35

💡 Pro Tip: Always check your answer by plugging it back into the original equation! If x = 7 and the equation was 3x + 4 = 25, check: 3(7) + 4 = 21 + 4 = 25 ✓ It works!

🐐 Reid's Math GOAT Challenge 🐐

Welcome to the GOAT Challenge! 🏆

📚 Choose Your Math Topics:

🏆 All-Time GOAT Leaderboard

📚 Study Hall - Crash Courses