Let's master some powerful math strategies!
Topics covered:
✓ Double and Half Method
✓ Near Numbers Strategy
✓ Area, Surface Area, and Volume
The double and half method is a multiplication strategy where you double one factor and halve the other to make the problem easier to solve.
16 × 5
Instead of solving this directly:
• Double the 5 → 10
• Half the 16 → 8
• Solve the easier problem: 8 × 10 = 80
The answer stays the same, but the math becomes simpler!
When you double one number and halve the other, the product stays the same because multiplication is about equal groups.
4 × 6 = 24 (4 groups of 6)
2 × 12 = 24 (2 groups of 12)
8 × 3 = 24 (8 groups of 3)
All equal 24! We're just rearranging the groups.
This method works best when:
Great candidates: 14 × 5, 18 × 25, 32 × 15
Not as helpful: 13 × 7 (can't easily halve 13)
Problem 1: 16 × 5 = ?
Solution:
• Half of 16 = 8
• Double 5 = 10
• 8 × 10 = 80
Problem 2: 12 × 5 = ?
Solution:
• Half of 12 = 6
• Double 5 = 10
• 6 × 10 = 60
Problem 3: 18 × 5 = ?
Solution:
• Half of 18 = 9
• Double 5 = 10
• 9 × 10 = 90
Problem 4: 8 × 15 = ?
Solution:
• Half of 8 = 4
• Double 15 = 30
• 4 × 30 = 120
Problem 5: 14 × 5 = ?
Solution:
• Half of 14 = 7
• Double 5 = 10
• 7 × 10 = 70
Problem 6: 6 × 25 = ?
Solution:
• Half of 6 = 3
• Double 25 = 50
• 3 × 50 = 150
Problem 7: 24 × 15 = ?
Solution:
• Half of 24 = 12
• Double 15 = 30
• 12 × 30 = 360
Problem 8: 16 × 35 = ?
Solution:
• Half of 16 = 8
• Double 35 = 70
• 8 × 70 = 560
Problem 9: 32 × 25 = ?
Solution:
• Half of 32 = 16
• Double 25 = 50
• 16 × 50 = 800
Problem 10: 18 × 25 = ?
Solution:
• Half of 18 = 9
• Double 25 = 50
• 9 × 50 = 450
Problem 11: 28 × 15 = ?
Solution:
• Half of 28 = 14
• Double 15 = 30
• 14 × 30 = 420
Problem 12: 12 × 45 = ?
Solution:
• Half of 12 = 6
• Double 45 = 90
• 6 × 90 = 540
The near numbers strategy (also called the compensation method) is used when one number is close to a "friendly" number like 10, 100, or 1,000.
47 × 98
98 is close to 100, so:
• Multiply by 100: 47 × 100 = 4,700
• We multiplied by 2 too many (100 - 98 = 2)
• Subtract: 47 × 2 = 94
• Answer: 4,700 - 94 = 4,606
Follow these steps:
If the original number was LESS than your friendly number: Subtract
If the original number was MORE than your friendly number: Add
23 × 99
• 23 × 100 = 2,300
• We multiplied by 1 too many
• Subtract: 2,300 - 23 = 2,277
52 × 101
• 52 × 100 = 5,200
• We need 1 more group of 52
• Add: 5,200 + 52 = 5,252
Problem 1: 35 × 99 = ?
Solution:
• 35 × 100 = 3,500
• 100 - 99 = 1 (too many)
• Subtract: 3,500 - 35 = 3,465
Problem 2: 42 × 98 = ?
Solution:
• 42 × 100 = 4,200
• 100 - 98 = 2 (too many)
• 42 × 2 = 84
• Subtract: 4,200 - 84 = 4,116
Problem 3: 18 × 101 = ?
Solution:
• 18 × 100 = 1,800
• 101 - 100 = 1 (need more)
• Add: 1,800 + 18 = 1,818
Problem 4: 56 × 99 = ?
Solution:
• 56 × 100 = 5,600
• 100 - 99 = 1 (too many)
• Subtract: 5,600 - 56 = 5,544
Problem 5: 25 × 102 = ?
Solution:
• 25 × 100 = 2,500
• 102 - 100 = 2 (need more)
• 25 × 2 = 50
• Add: 2,500 + 50 = 2,550
Problem 6: 64 × 98 = ?
Solution:
• 64 × 100 = 6,400
• 100 - 98 = 2 (too many)
• 64 × 2 = 128
• Subtract: 6,400 - 128 = 6,272
Problem 7: 73 × 97 = ?
Solution:
• 73 × 100 = 7,300
• 100 - 97 = 3 (too many)
• 73 × 3 = 219
• Subtract: 7,300 - 219 = 7,081
Problem 8: 89 × 99 = ?
Solution:
• 89 × 100 = 8,900
• 100 - 99 = 1 (too many)
• Subtract: 8,900 - 89 = 8,811
Problem 9: 45 × 103 = ?
Solution:
• 45 × 100 = 4,500
• 103 - 100 = 3 (need more)
• 45 × 3 = 135
• Add: 4,500 + 135 = 4,635
Problem 10: 38 × 96 = ?
Solution:
• 38 × 100 = 3,800
• 100 - 96 = 4 (too many)
• 38 × 4 = 152
• Subtract: 3,800 - 152 = 3,648
Problem 11: 67 × 101 = ?
Solution:
• 67 × 100 = 6,700
• 101 - 100 = 1 (need more)
• Add: 6,700 + 67 = 6,767
Problem 12: 54 × 95 = ?
Solution:
• 54 × 100 = 5,400
• 100 - 95 = 5 (too many)
• 54 × 5 = 270
• Subtract: 5,400 - 270 = 5,130
When we measure shapes and objects, we can measure three different things:
Measures the space inside a flat shape
Units: square units (cm², m², in², ft²)
Measures the total outside surface of a 3D object
Units: square units (cm², m², in², ft²)
Measures the space inside a 3D object
Units: cubic units (cm³, m³, in³, ft³)
Area measures how much space is inside a flat (2-dimensional) shape. Think of it as how much carpet you'd need to cover a floor.
A rectangle is 8 cm long and 5 cm wide.
Area = 8 × 5 = 40 cm²
Remember: Area is always measured in square units (cm², m², in², ft²)
Surface Area measures the total area of all the surfaces (faces) of a 3D object. Think of it as how much wrapping paper you'd need to cover a box.
A box is 6 cm long, 4 cm wide, and 3 cm tall.
SA = 2(6×4 + 6×3 + 4×3)
SA = 2(24 + 18 + 12)
SA = 2(54) = 108 cm²
Remember: Surface area is measured in square units (cm², m², in², ft²)
Volume measures how much space is inside a 3D object. Think of it as how much water could fill a container.
A box is 5 cm long, 3 cm wide, and 4 cm tall.
Volume = 5 × 3 × 4 = 60 cm³
Remember: Volume is measured in cubic units (cm³, m³, in³, ft³)
Question: How much space inside?
Units: square units (cm², m²)
Example: Floor space, painting a wall
Question: How much covers the outside?
Units: square units (cm², m²)
Example: Wrapping a gift, painting a box
Question: How much fits inside?
Units: cubic units (cm³, m³)
Example: Filling a tank with water
A rectangular garden is 12 feet long and 8 feet wide.
What should you calculate, and what is the answer?
What to calculate: AREA (it's a flat surface)
Solution:
Area = length × width
Area = 12 ft × 8 ft
Area = 96 ft²
A moving box is 20 inches long, 15 inches wide, and 12 inches tall.
How much can fit inside the box?
What to calculate: VOLUME (space inside a 3D object)
Solution:
Volume = length × width × height
Volume = 20 in × 15 in × 12 in
Volume = 3,600 in³
You need to paint all six sides of a toy chest that is 4 ft long, 2 ft wide, and 3 ft tall.
What should you calculate?
What to calculate: SURFACE AREA (covering outside surfaces)
Solution:
SA = 2(lw + lh + wh)
SA = 2(4×2 + 4×3 + 2×3)
SA = 2(8 + 12 + 6)
SA = 2(26)
SA = 52 ft²
A square piece of paper has sides that are 9 inches long.
How much space does the paper cover?
What to calculate: AREA (flat surface)
Solution:
Area = side × side
Area = 9 in × 9 in
Area = 81 in²
An aquarium is 30 cm long, 20 cm wide, and 25 cm tall.
How much water can it hold?
What to calculate: VOLUME (how much fits inside)
Solution:
Volume = length × width × height
Volume = 30 cm × 20 cm × 25 cm
Volume = 15,000 cm³
You're wrapping a gift box that is 8 inches long, 6 inches wide, and 4 inches tall.
How much wrapping paper do you need to cover all sides?
What to calculate: SURFACE AREA (covering all outside surfaces)
Solution:
SA = 2(lw + lh + wh)
SA = 2(8×6 + 8×4 + 6×4)
SA = 2(48 + 32 + 24)
SA = 2(104)
SA = 208 in²
A rectangular poster is 24 inches wide and 36 inches tall.
What is the total space the poster covers on the wall?
What to calculate: AREA (flat surface)
Solution:
Area = width × height
Area = 24 in × 36 in
Area = 864 in²
A cube-shaped storage box has sides that are 5 feet long.
How much can you store inside the box?
What to calculate: VOLUME (space inside)
Solution:
Volume = side × side × side
Volume = 5 ft × 5 ft × 5 ft
Volume = 125 ft³
What you learned:
✓ Double and Half Method
✓ Near Numbers Strategy
✓ Area (2D flat shapes)
✓ Surface Area (3D outside surfaces)
✓ Volume (3D inside space)
Keep practicing these strategies to become a math master! 🌟