Ratio Rumble Worksheet Ratio Rumble
The Quest for Proportional Harmony
Hero Name:
Date:
Welcome, Hero! To cross the Bridge of Balance and enter the central kingdom, you must master the art of Ratios and Proportions. Complete these challenges to unlock the gate.
Challenge 1: The Bridge of Balance
Maintain the ratio to keep the bridge stable. Find the missing values in the equivalent ratios.
1. A map uses a ratio of 2 inches to 15 miles. If two cities are 6 inches apart on the map, how many miles apart are they?
2. The alchemist mixes potions in a ratio of 3 parts phoenix feather to 5 parts dragon scale. If he uses 20 parts dragon scale, how many parts phoenix feather are needed?
3. A recipe for mana bread calls for 4 cups of flour for every 3 cups of water. Complete the table to show equivalent ratios.
Flour (cups) Water (cups) 4 3 8 15
4. Determine if the ratios 5:8 and 15:24 are equivalent. Show your reasoning.
Challenge 2: The Rapid River
Calculate the unit rates to navigate the river's current efficiently.
5. A hero travels 120 miles in 3 hours. What is the hero's speed in miles per hour?
6. A pack of 6 healing herbs costs 18 gold coins. What is the unit price per herb?
7. Comparing Shops: The Blacksmith sells 4 shields for 52 gold coins. The Armory sells 5 shields for 60 gold coins. Which shop has the better unit price? Show your work.
Challenge 3: The Treasure Hoard
Solve the percentage puzzles to unlock the treasure chests.
8. What is 25% of 80 gold coins?
9. 12 knights represent 30% of the army. How many total soldiers are in the army?
10. A shield originally cost 50 gold coins but is on sale for 40% off. What is the sale price?
11. In a forest of 200 trees, 45% are Oak and the rest are Pine. How many Pine trees are there?
Final Riddle: The Dragon's Gate
"To pass the gate, you must prove your mastery of the whole. If 3 dragons can eat 15 sheep in 2 days, how many sheep can 5 dragons eat in 4 days if the rate remains the same?"
Ratio Rumble Answer Key Ratio Rumble
Answer Key
6th Grade Math Review
Domain: Ratios & Proportional Relationships
Challenge 1: The Bridge of Balance
1. Map ratio 2 in : 15 mi. 6 inches apart?
Answer: 45 miles
Work: 2 × 3 = 6, so 15 × 3 = 45
2. Phoenix feather (3) to Dragon scale (5). If 20 parts dragon scale?
Answer: 12 parts phoenix feather
Work: 20 ÷ 5 = 4. 3 × 4 = 12
3. Table: Flour (4, 8, 20) vs Water (3, 6, 15)
Answer: 6 Water (for 8 Flour); 20 Flour (for 15 Water)
4. Are 5:8 and 15:24 equivalent?
Answer: Yes (5 × 3 = 15; 8 × 3 = 24)
Challenge 2: The Rapid River
5. 120 miles in 3 hours speed?
Answer: 40 miles per hour
6. 6 herbs for 18 gold coins unit price?
Answer: 3 gold coins per herb
7. Comparison: Blacksmith (13/shield) vs Armory (12/shield).
Answer: The Armory is cheaper.
Challenge 3: The Treasure Hoard
8. 25% of 80 gold coins?
Answer: 20 gold coins
9. 12 knights = 30% of army. Total?
Answer: 40 soldiers (12 ÷ 0.3)
10. 50 gold coins, 40% off sale price?
Answer: 30 gold coins (50 - 20)
11. 200 trees, 45% Oak. Pine?
Answer: 110 Pine trees (200 × 0.55)
Dragon's Riddle Answer
Answer: 50 sheep
Rate: 15 sheep ÷ (3 dragons × 2 days) = 2.5 sheep/dragon/day.
5 dragons × 4 days × 2.5 sheep = 50 sheep.
Ratio Rumble Slides Ratio Rumble
6th Grade Math Quest: Day 1
Today's Mission
01
Equivalent Ratios
Maintain balance by finding missing values in proportional relationships.
02
Unit Rates
Find the value for "one" to compare prices and speeds across the kingdom.
03
Percentages
Unlock the treasure hoard by calculating parts of a whole (100%).
Equivalent Ratios
Ratios are equivalent if they name the same relationship between quantities.
\(2:3 = 4:6 = 20:30\)
"Just like equivalent fractions!"
Scaling Up/Down
Multiply or divide both parts of the ratio by the same non-zero number.
Unit Rates
The Power of ONE
A Unit Rate compares a quantity to one unit of another quantity.
Speed
Miles per Hour
Price
Gold per Item
"Divide the numerator by the denominator to find the unit rate!"
Knight's Trial
Sir Galen rides 15 miles in 2 hours. At this rate, how far can he travel in 6 hours?
1
Unit rate: \( 15 \div 2 = 7.5 \) mph
2
Travel time: \( 7.5 \times 6 = 45 \) miles
Number Knights Worksheet Number Knights
Guardians of the Number System
Hero Name:
Date:
Welcome, Knight! You have reached the Frozen Frontier. To traverse the icy peaks, you must solve the mysteries of fractions, decimals, and integers. Keep your wits sharp and your numbers accurate!
Trial 1: The Splitting Glaciers
1. Divide the fraction: \( \frac{3}{4} \div \frac{2}{3} \). Show each step.
2. A block of ice weighs \( \frac{7}{8} \) tons. If it is split into pieces weighing \( \frac{1}{4} \) tons each, how many full pieces can be made?
3. Add: \( 14.52 + 9.876 \)
4. Multiply: \( 4.2 \times 0.15 \)
Trial 2: Common Grounds
5. Find the GCF of 24 and 36.
6. Find the LCM of 8 and 12.
Trial 3: The Frozen Map
7. The temperature was \(-8^{\circ}C\) at dawn and rose \(12^{\circ}C\) by noon. What is the noon temperature?
8. Order from least to greatest: \( -5, 2, 0, -1, 4 \)
9. Plot and label the points:
Point A: \((3, -2)\)
Point B: \((-4, 1)\)
Point C: \((0, -3)\)
10. Distance between point \((2, 5)\) and point \((2, -3)\)?
x y
-5-4-3-2-1012345
-5-4-3-2-1012345
Number Knights Answer Key Number Knights
Answer Key
Trial 1: The Splitting Glaciers
1. \( 3/4 \div 2/3 \)
Answer: 9/8 or 1 1/8
Work: 3/4 × 3/2 = 9/8
2. 7/8 tons ice, split into 1/4 ton pieces.
Answer: 3 full pieces
Work: 7/8 ÷ 1/4 = 3.5. Only 3 are FULL pieces.
3. 14.52 + 9.876
Answer: 24.396
4. 4.2 × 0.15
Answer: 0.63
Trial 2: Common Grounds
5. GCF of 24 and 36
Answer: 12
6. LCM of 8 and 12
Answer: 24
Trial 3: The Frozen Map
7. Temperature at dawn was -8°C, rose 12°C by noon.
Answer: 4°C
8. Order: -5, 2, 0, -1, 4
Answer: -5, -1, 0, 2, 4
10. Distance between (2,5) and (2,-3)?
Answer: 8 units
Number Knights Slides Number Knights
6th Grade Math Quest: Day 2
Mission: Number System
Divide Fractions by Fractions
Compute with Multi-Digit Decimals
Master GCF, LCM, and Integers
Decimal Rules
Add/Sub: Line up the dots.
Multiply: Count the total places.
Example: \( 0.2 \times 0.3 \)
1 place + 1 place = 2 places. Answer: 0.06
12.500
+ 4.234
16.734
Fill placeholders with zeros!
Variable Victory Worksheet Variable Victory
Masters of Expressions and Equations
Hero Name:
Date:
Greetings, Strategist! Decode expressions and balance the scales of equations to reveal the unknown values!
Trial 1: The Ancient Scroll
1. Write an algebraic expression for: "the product of 5 and the sum of a number x and 3."
2. Evaluate the expression 2y2 - 4 when y = 3.
3. Simplify the expression: 4(x + 2) + 3x. Show your work.
4. Identify the terms and coefficients in: 7a + 2b - 5.
Trial 2: The Balanced Scales
5. Solve: w + 15 = 42
6. Solve: 8k = 72
7. Solve: m / 4 = 9
8. Solve: x - 12.5 = 30
Trial 3: Battle Tactics
9. A hero earns 12 gold for every monster defeated. Let g be gold and m be monsters. Write an equation.
10. To enter the tournament, a hero must be at least 15 years old. Write an inequality for age a and graph it on the number line below.
Inequality
12
13
14
15
16
17
18
19
11. A shield costs 45 gold. A hero buys it and has 15 gold left. Write and solve an equation to find initial gold.
Variable Victory Answer Key Variable Victory
Answer Key
6th Grade Math Review
Domain: Expressions & Equations
Trial 1: The Ancient Scroll
1. "Product of 5 and the sum of \(x\) and 3"
Answer: \( 5(x + 3) \)
2. Evaluate \( 2y^2 - 4 \) when \( y = 3 \)
Answer: 14
Work: \( 2(3^2) - 4 = 2(9) - 4 = 18 - 4 = 14 \)
3. Simplify \( 4(x + 2) + 3x \)
Answer: \( 7x + 8 \)
Work: \( 4x + 8 + 3x = 7x + 8 \)
4. Terms and coefficients in \( 7a + 2b - 5 \)
Terms: \( 7a, 2b, -5 \)
Coefficients: 7, 2
Trial 2: The Balanced Scales
5. \( w + 15 = 42 \)
\( w = 27 \)
6. \( 8k = 72 \)
\( k = 9 \)
7. \( \frac{m}{4} = 9 \)
\( m = 36 \)
8. \( x - 12.5 = 30 \)
\( x = 42.5 \)
Trial 3: Battle Tactics
9. Equation for gold (\(g\)) and monsters (\(m\))
Answer: \( g = 12m \)
10. Inequality for age at least 15
Answer: \( a \ge 15 \)
Graph: Solid dot on 15, arrow pointing to the right.
11. Initial gold (\(s\)), shield costs 45, 15 left.
Equation: \( s - 45 = 15 \)
Answer: \( s = 60 \) gold coins
Variable Victory Slides Variable Victory
6th Grade Math Quest: Day 3
Plugging In
Evaluate \( 3x + 5 \) for \( x = 4 \)
1
\( 3(4) + 5 \)
2
\( 12 + 5 \)
3
17
Inequalities
Example: \( x \ge 5 \)
<
Open Circle
≥
Closed Circle
34567
"Includes 5 and all values to the right!"
Shape Shifters Worksheet Shape Shifters
Architects of the Geometric Glade
Hero Name:
Date:
Trial 1: The Garden Plots
1. Find the area of a triangle with base 10 cm and height 8 cm.
2. Find the area of a parallelogram with base 12 in and height 5 in.
3. Trapezoid bases: 6m and 10m. Height: 4m. Area?
4. Area of the complex shape:
8m 6m 4m
Trial 2: Block Masonry
5. Volume of prism: 5 cm × 3 cm × 4 cm.
6. Surface area of a cube with side length 3 inches.
Trial 3: Blueprints
7. Calculate the surface area of a cube from a net where each side is 2m.
8. Volume of sandbox: 6ft long, 4ft wide, 1.5 ft deep.
9. Use the grid below to find the area of a rectangle with vertices at (1, 2), (1, 7), (5, 7), and (5, 2).
X Y
Work Area
Shape Shifters Answer Key Shape Shifters
Answer Key
6th Grade Math Review
Domain: Geometry
Trial 1: The Garden Plots
1. Area of triangle (base 10, height 8)
Answer: 40 \( \text{cm}^2 \)
Work: \( \frac{1}{2} \times 10 \times 8 = 40 \)
2. Area of parallelogram (base 12, height 5)
Answer: 60 \( \text{in}^2 \)
Work: \( 12 \times 5 = 60 \)
3. Area of trapezoid (bases 6, 10, height 4)
Answer: 32 \( \text{m}^2 \)
Work: \( \frac{6+10}{2} \times 4 = 8 \times 4 = 32 \)
4. Complex shape (Rectangle 8x6 + Triangle 4x6)
Answer: 60 \( \text{m}^2 \)
Work: Rectangle \( 8 \times 6 = 48 \). Triangle \( \frac{1}{2} \times 4 \times 6 = 12 \). Total: \( 48 + 12 = 60 \).
Trial 2: The Block Masonry
5. Volume of prism (5x3x4)
Answer: 60 \( \text{cm}^3 \)
6. Surface area of cube (side 3)
Answer: 54 \( \text{in}^2 \)
Work: \( 6 \times (3 \times 3) = 6 \times 9 = 54 \)
Trial 3: Folding the Blueprint
7. Figure from net (Cube, side 2m) and Surface Area
Figure: Cube
Surface Area: 24 \( \text{m}^2 \)
Work: \( 6 \times (2 \times 2) = 24 \)
8. Volume of sandbox (6 x 4 x 1.5)
Answer: 36 \( \text{ft}^3 \)
Work: \( 6 \times 4 \times 1.5 = 24 \times 1.5 = 36 \)
9. Area of rectangle (1,2), (1,7), (5,7), (5,2)
Answer: 20 square units
Work: Height is \( 7-2 = 5 \). Width is \( 5-1 = 4 \). Area is \( 5 \times 4 = 20 \).
Shape Shifters Slides Shape Shifters
6th Grade Math Quest: Day 4
Area Challenge
Calculate the area of this triangle.
Hint:
"The formula is half of base times height."
Base = 12 cm Height = 10 cm
Answer: 60 cm²
Volume Quest
Find the volume of a granite block with:
• Length = 8 m
• Width = 5 m
• Height = 4 m
V = 8 × 5 × 4
160 m³
Quest Finale Worksheet Quest Finale
The Final Siege of the Math Citadel
Hero Name:
Date:
"You have traveled through the lands of Ratios, crossed the Number Frontier, decoded the Variable Canyon, and built the Geometric Glade. Conquer the final exam!"
1. Ratio 5 knights to 2 horses. If there are 30 horses, how many knights?
2. Solve: 4.5 / 0.09
3. Solve for x: 4x + 12 = 36
4. Volume of crate: 8 ft × 3 ft × 2.5 ft?
5. What is 15% of 120?
6. Divide: 5/6 ÷ 2/3
7. Graph x > -2 on the number line below.
-4
-3
-2
-1
0
1
2
8. Trap at (-3, 4) and treasure at (-3, -2). What is the distance?
9. A triangle has an area of 24 cm² and a base of 6 cm. Find height.
The Final Boss Battle
300 miles journey. Horse speed: 15 mph. Hay costs $12 per 50 miles.
How much will the hero spend on hay, and how many hours will it take?
Quest Finale Answer Key Quest Finale
Answer Key
1. Ratio 5:2. If 30 horses?
Answer: 75 knights (30 ÷ 2 × 5)
2. \( 4.5 \div 0.09 \)
Answer: 50
3. \( 4x + 12 = 36 \)
Answer: \( x = 6 \)
4. Volume (8 × 3 × 2.5)
Answer: 60 ft³
5. 15% of 120
Answer: 18
6. Divide: 5/6 ÷ 2/3
Answer: 5/4 or 1.25
Final Boss Solution
Total Hay Cost: $72 (6 bags × $12)
Total Time: 20 hours (300 ÷ 15)
Quest Finale Slides Quest Finale
The Ultimate Math Challenge
Boss Practice
If 1 bag of dragon food costs 25 gold and feeds 2 dragons for 5 days, how much does it cost to feed 4 dragons for 10 days?
Step 1
Cost for 4 dragons (double) for 5 days: 50 gold.
Step 2
Cost for 10 days (double again): 100 gold.
Final Answer: 100 Gold
Go Forth, Hero!
The Quest Review is complete.
Area: cm²
Volume: ft³
