🦕 Dino Math Adventure – Grade 5-6 Essential Problems

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Unit 1: Fractions

Addition, Subtraction, Multiplication & Division

🧠 Key Concepts

• Adding/Subtracting fractions: Find a common denominator first.
• Multiplying fractions: Multiply numerators × numerators, denominators × denominators.
• Dividing fractions: Multiply by the reciprocal (flip the second fraction).
• Mixed numbers: Convert to improper fractions before calculating.

🔑 MUST MEMORIZE

a/b ÷ c/d = a/b × d/c
a/b + c/b = (a+c)/b
Mixed: 2¾ = (2×4+3)/4 = 11/4

📝 EXAMPLE

Solve: 2/3 + 3/4
Step 1: LCD of 3 and 4 = 12
Step 2: 2/3 = 8/12, 3/4 = 9/12
Step 3: 8/12 + 9/12 = 17/12 = 1 5/12

✅ Answer: 1 5/12

Fractions

★★★

What is 3/4 + 2/3?

(A) 5/7
(B) 17/12
(C) 5/12
(D) 11/12

Fractions

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Calculate: 2 1/2 ÷ 5/6

(A) 12/5
(B) 3
(C) 25/12
(D) 2 1/12

🔢

Unit 2: Decimals

Operations & Place Value

🧠 Key Concepts

• Multiplying decimals: Ignore decimal points, multiply whole, then place decimal point (count total decimal places).
• Dividing decimals: Move the decimal in the divisor to make it a whole number; move dividend's decimal the same number of places.
• Rounding: Look at the digit to the RIGHT of the target place.

🔑 MUST MEMORIZE

1.2 × 3.4 → 12 × 34 = 408 → 4.08 (2 decimal places)
6.3 ÷ 0.7 → 63 ÷ 7 = 9

📝 EXAMPLE

Round 4.678 to the nearest hundredth.
Look at the thousandths digit: 8 ≥ 5, so round up.
4.678 ≈ 4.68

✅ Answer: 4.68

Decimals

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What is 3.6 × 2.5?

(A) 8.1
(B) 9.0
(C) 7.5
(D) 6.1

Decimals

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Solve: 7.56 ÷ 0.06

(A) 0.126
(B) 12.6
(C) 126
(D) 1260

⚖️

Unit 3: Ratios & Proportions

Ratios, Rates & Proportional Reasoning

🧠 Key Concepts

• A ratio compares two quantities: a:b = a/b.
• Proportion: Two equal ratios. Cross-multiply to solve: if a/b = c/d, then a×d = b×c.
• Unit rate: Rate per 1 unit (e.g., 60 km per 1 hour).

🔑 MUST MEMORIZE

a/b = c/d → a × d = b × c (cross multiplication)

📝 EXAMPLE

If 3 notebooks cost $7.50, how much do 5 notebooks cost?
3/7.50 = 5/x → 3x = 37.50 → x = $12.50

✅ Answer: $12.50

Ratios

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A recipe needs 2 cups of flour for every 3 cups of sugar. How many cups of flour are needed for 12 cups of sugar?

(A) 6
(B) 8
(C) 9
(D) 18

Ratios

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A car travels 150 km in 2.5 hours. At the same speed, how long will it take to travel 300 km?

(A) 4 hours
(B) 5 hours
(C) 6 hours
(D) 7.5 hours

💯

Unit 4: Percentages

Finding Percent, Discount & Increase

🧠 Key Concepts

• Percent means "out of 100": 35% = 35/100 = 0.35.
• Find a %: part ÷ whole × 100.
• % of a number: multiply by the decimal (30% of 80 = 0.30 × 80 = 24).
• Discount: Sale price = Original × (1 − discount rate).

🔑 MUST MEMORIZE

% change = (New − Old) / Old × 100
Sale price = Original × (1 − %discount)

📝 EXAMPLE

A jacket costs $80. It is on sale for 25% off. What is the sale price?
Discount = 0.25 × 80 = $20
Sale price = 80 − 20 = $60

✅ Answer: $60

Percentages

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What is 35% of 120?

(A) 35
(B) 40
(C) 42
(D) 48

Percentages

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A store sells a backpack for $45. The original price was $60. What is the percent discount?

(A) 15%
(B) 20%
(C) 25%
(D) 30%

📐

Unit 5: Area & Perimeter

2D Shapes – Formulas & Applications

🧠 Key Concepts

• Rectangle: Area = l × w, Perimeter = 2(l + w)
• Triangle: Area = (base × height) / 2
• Circle: Area = π × r², Circumference = 2πr
• Parallelogram: Area = base × height

🔑 MUST MEMORIZE

Circle Area = π r² (π ≈ 3.14)
Triangle Area = (b × h) / 2

📝 EXAMPLE

Find the area of a triangle with base 8 cm and height 5 cm.
Area = (8 × 5) / 2 = 40 / 2 = 20 cm²

✅ Answer: 20 cm²

Geometry

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A circle has a radius of 7 cm. What is its area? (Use π = 3.14)

(A) 43.96 cm²
(B) 49 cm²
(C) 153.86 cm²
(D) 153.94 cm²

Geometry

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A rectangular garden is 12 m long and 7 m wide. A path 1 m wide is built around the outside of the garden. What is the area of the path only?

(A) 40 m²
(B) 76 m²
(C) 84 m²
(D) 80 m²

📦

Unit 6: Volume

3D Shapes – Cubes, Cuboids, Cylinders

🧠 Key Concepts

• Rectangular prism (cuboid): V = l × w × h
• Cube: V = s³
• Cylinder: V = π × r² × h

🔑 MUST MEMORIZE

Cuboid: V = l × w × h
Cylinder: V = π r² h

📝 EXAMPLE

Find the volume of a cube with side length 4 cm.
V = 4³ = 4 × 4 × 4 = 64 cm³

✅ Answer: 64 cm³

Volume

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A rectangular box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?

(A) 47 cm³
(B) 60 cm³
(C) 48 cm³
(D) 56 cm³

Volume

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A cylindrical water tank has a radius of 3 m and a height of 5 m. What is its volume? (Use π = 3.14)

(A) 94.2 m³
(B) 141.3 m³
(C) 47.1 m³
(D) 28.26 m³

🌡️

Unit 7: Integers & Negative Numbers

Operations with Positive & Negative Numbers

🧠 Key Concepts

• Adding a negative = subtracting: 5 + (−3) = 5 − 3 = 2
• Subtracting a negative = adding: 5 − (−3) = 5 + 3 = 8
• Same signs → positive product; Different signs → negative product.
• Rules: (−) × (−) = (+), (+) × (−) = (−)

🔑 MUST MEMORIZE

(−) × (−) = (+)
(+) × (−) = (−)
a − (−b) = a + b

📝 EXAMPLE

Solve: −4 × (−6) ÷ 3
Step 1: −4 × −6 = +24
Step 2: 24 ÷ 3 = 8

✅ Answer: 8

Integers

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What is −8 − (−3)?

(A) −11
(B) −5
(C) 5
(D) 11

✏️

Unit 8: Algebra – Equations

Expressions, Variables & Solving Equations

🧠 Key Concepts

• A variable (e.g., x) represents an unknown number.
• Solve by doing the same operation to BOTH sides.
• Order of operations: PEMDAS – Parentheses, Exponents, Multiply/Divide (left→right), Add/Subtract (left→right).

🔑 MUST MEMORIZE

PEMDAS: P → E → M&D → A&S
Balance rule: Do the same to both sides

📝 EXAMPLE

Solve: 3x + 7 = 22
Step 1: 3x = 22 − 7 = 15
Step 2: x = 15 ÷ 3 = 5

✅ Answer: x = 5

Algebra

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Solve for x: 4x − 9 = 23

(A) x = 3.5
(B) x = 6
(C) x = 7
(D) x = 8

Algebra

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Evaluate: 3 + 4 × (6 − 2)² ÷ 8

(A) 11
(B) 3.5
(C) 10
(D) 15

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Unit 9: Data & Statistics

Mean, Median, Mode, Range

🧠 Key Concepts

• Mean: Sum of all values ÷ count of values.
• Median: Middle value when data is sorted (or average of two middle values).
• Mode: Most frequently occurring value.
• Range: Largest − Smallest value.

🔑 MUST MEMORIZE

Mean = (sum of all values) ÷ n
Range = Max − Min

📝 EXAMPLE

Data: 4, 7, 7, 10, 12
Mean = (4+7+7+10+12) ÷ 5 = 40 ÷ 5 = 8
Median = 7 (middle value)
Mode = 7 (appears most)
Range = 12 − 4 = 8

✅ Mean=8, Median=7, Mode=7, Range=8

Statistics

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Test scores: 82, 90, 75, 90, 63. What is the mean score?

(A) 78
(B) 80
(C) 82
(D) 90

Statistics

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Data set: 5, 8, 3, 8, 6, 3, 9, 3. What is the median?

(A) 3
(B) 5
(C) 5.5
(D) 6

🎲

Unit 10: Probability

Basic Probability & Simple Events

🧠 Key Concepts

• Probability = (favourable outcomes) ÷ (total possible outcomes).
• P ranges from 0 (impossible) to 1 (certain).
• Complement: P(not A) = 1 − P(A).

🔑 MUST MEMORIZE

P(event) = favourable outcomes / total outcomes
P(not A) = 1 − P(A)

📝 EXAMPLE

A bag has 3 red, 2 blue, 5 green marbles. P(red) = 3/10.
P(not red) = 1 − 3/10 = 7/10

✅ P(red) = 3/10, P(not red) = 7/10

Probability

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A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3

Probability

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A jar contains 4 yellow, 6 blue, and 10 red marbles. What is the probability of NOT picking a red marble?

(A) 1/2
(B) 2/5
(C) 1/10
(D) 3/10

🏆

Unit 11: Mixed Challenge

Word Problem – Multiple Steps

CHALLENGE

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Sarah has $200. She spends 30% on clothes, then uses 1/4 of the remaining money on food. How much money does she have left?

(A) $100
(B) $105
(C) $110
(D) $95