Middle Grade Math 4

22 terms by Balfonso Plus

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Metric Units of Length

milli - means thousandth
1mm = 0.001m
1m=1,000mm

centi - means hundredth
1cm = 0.01m
1m = 100cm

kilo - means thousand
1km = 1,000m
1m = 0.001km

Metric Units of Mass and Capacity

Metric Units of Mass:
1kg = 1,000g
0.001 kg = 1g
1g = 1,000mg
0.001g = 1mg

Metric Units of Capacity
1kL = 1.000L
0.001 kL = 1L
1L = 1,000 mL
0.001L = 1mL

Converting Units in the Customary System

Length:
1foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 mile (mi) = 5,280 feet (ft)

Weight:
1 pound (lb) = 16 ounces (oz)

Liquid Capacity:
1 gallon (gal) = 4 quarts (qt)
1 quart = 2 pints (pt)
1 pint (pt) = 2 cups (c)

Converting Between Measurement Systems

Length:
1 in ≈ 2.54 cm
1 km ≈ 0.62mi
Area:
1 in² ≈ 6.45 cm²
Volume:
1 in³ ≈ 16.39 cm³
Capacity:
1 L ≈ 1.06 qt
Weight:
1 oz ≈ 28 g
1 kg ≈ 2.2 lb

Computing with Customary Measures

When you solve problems with customary units of measure, you must change the units of measurement.

Computing with Time

When you add or subtract units of time, you must convert between the units.

Perimeter

To find the perimeter of a given geometric figure, you add the lengths of the sides.
Example:
Find missing lengths.
8 - 7 = 1
4 - 1 = 3
x = 3 ft
3 + 3 = 6
8 - 6 = 2
y = 2 ft
8 + 7 + 3 + 3 + 2 + 4 + 3 + 8 = 38
Perimeter = 38 ft

Area of Rectangles and Squares

Area = Base x Height
The area is expressed in square + unit such as square inches (in²), square feet (ft²), or square centimeter (cm²).

Area of Triangle

Area = Base x Height ÷ 2

Area of Parallelograms

Area = Base x Height

Area of Trapezoids

Area = 1/2 Height x (Base 1 + Base 2)

Area of Compound Shapes

Circle

The diameter of a circle is the distance across the circle through its center.
The radius is the distance from the center to any point on the circle.

Circumference of the Circle

The perimeter of a circle is its circumference.
C = π (3.14) x Diameter

Area of Circle

Area = π x r²

Surface Area of Rectangular Prisms

Rectangular prisms has two of the same sizes facing each other.

Surface Area of Triangular Prisms

Triangular prisms has two of the same sizes for the top and the base. Find areas of the three rectangular shape sizes. Add them together.

Surface Area of Cylinders

1. Find areas of circle. A = π x r²
2. Multiply circle's area by two. (Top + Base)
3. Find area of rectangle.
4. Add them together.
Example:
Area of circle = 3.14 x 2² = 12.56
Area of circles = 12.56 x 2 =25.12
Base of rectangle = 3.14 x 4 =12.56
Area of rectangle = 12.56 x 5 = 62.80
Area of cylinder = 25.12 + 62.80 = 87.92 in²

Volume of Rectangular Prisms

V = Area of the Base x Height
V = 3 x 2 x 5 = 30m³

Volume of Triangular Prisms

Base = Triangle
Area of Triangle = (Base x Height) ÷ 2
Volume = Area of triangle x height

Volume of Cylinders

Base = Circle
Area of Circle = π x r²
Volume = Area of circle x height

Connecting Volume, Mass, and Capacity

Mass of Water
1 cm³ = 1 mL = 1 g
Example:
What is the mass of the water that the aquarium can hold?
Find the volume. 20 x 40 x 20 = 16,000 cm³
16,000 cm³ = 16,000 mL
16,000 mL = 16,000 g
16.000 g = 16 kg
The mass of the water the aquarium
will hold is 16 kg

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