Module 10 Measuring Lengths, Area, Surface Area, Capacity, and Mass PDF

MEASURING LENGTHS, AREA, SURFACE AREA, CAPACITY, and MASS GRADE 7 - MATHEMATICS  OBJECTIVES Illustrate what is means to measure Identify and use the following prefixes in the metric system: kilo-, hecto-, deka-, deci-, centi-, and mili-, Convert length, cap...

MEASURING LENGTHS, AREA, SURFACE AREA, CAPACITY, and MASS GRADE 7 - MATHEMATICS  OBJECTIVES Illustrate what is means to measure Identify and use the following prefixes in the metric system: kilo-, hecto-, deka-, deci-, centi-, and mili-, Convert length, capacity, and mass measurements from one unit to another. Convert length, capacity, and mass measurements from one unit to another. Solve problems involving capacity and mass.  Engage A working drawing that shows the location and size of the rooms is called a floor plan. A floor plan shows how the rooms would look like if he ceilings were removed and you looked down from the above. Use the floor plan to answer the following: a. The dimensions of Bedroom 1 in centimeters b. The dimensions of the bathroom in meters Exploration During the ancient times, an Egyptian carpenter would never misplace his ruler because he would usually use the parts of his body for measurements. Some of the units are shown below Span Foot Palm Cubit Digit Pace  Is the distance from the tip of the Span little finger to the tip of the thumb of an outstretched hand “Dangkal” Is the distance across the base of Palm the four fingers that form the palm Is the thickness or width of the Digit index fingers Foot Is the length of a foot Is the distance from the tip of the Cubit middle finger of the outstretched hand to the front of the elbow Pace Is the distance of one full step From then on, people began to use different units of measure The inch we use at present comes from the thickness or width of a thumb, according to the Romans. A yard, as decreed by King Henry I of England, was the distance from the tip of his nose to the end of the middle finger of his outstretched arm. 1. Measure the length and width of your Math book using your thumb’s width. 2. Measure the length of your room using your foot length. 3. Measure the length of the door of your classroom using span. 4. Compare your measurements with those of your classmates. 5. Write a paragraph describing your bedroom. Use only cubits, spans, palms, foot, and digits when you describe your bedroom and the things in it.  Extension 12 inches = 1 foot 264 paces = 1 furlong 3 feet = 1 yard 8 furlongs = 1 mile 5 feet = 1 pace 24 furlongs = 1 league Extension Prefix kilo- hecto- deka- deci- centi- milli- Symbol k h da d c m 1 1 1 value 1 000 100 10 or 0.1 or 0.01 or 0.001 10 100 1000  Extension Measuring Lengths Basic unit of length for metric measurement is the meter (m) Word Symbol Meaning kilometer km 1 000 meters hectometer hm 100 meters dekameter da 10 meters meter m 1 meter decimeter dm 0.1 meter centimeter cm 0.01 meter millimeter mm 0.001 meter  Rule These rules are used to change from one metric unit to another 1. To change from a larger unit to a smaller unit (moving to the right in the diagram), multiply by a power of ten. Thus, move the decimal point in the given quantity one place to the right for each smaller unit until the decimal unit is reached. 2. To change from a smaller unit to a larger unit (moving to the left in the diagram), divide by a power of ten. Thus, move the decimal in the given quantity one place to the left for each larger unit until the decimal unit is reached.  Rule Convert each to the indicated unit. 1) 15 hm to dm To convert from hectometer to decimeter, we start at hectometers and move three steps to the right to obtain decimeters 15 hm = 15 000 dm  Rule Convert each to the indicated unit. 2) 543 m to km To convert from meters to kilometers, we start at meters and move three steps to the left to obtain kilometers 543 m = 0.543 km  Rule Convert each to the indicated unit. 4.8 da to mm 12.3 cm to m 1) 50 mm = 5 cm 2) 9 000 km = 9 000 000 000 mm 3) 0.04 cm = 0.000 000 004 Gm 4) 6.302 mm = 0.006 302 m 5) 1 nm = 0.000 000 1 hm Dimensional Analysis 1𝑓𝑡 12𝑖𝑛 1𝑦𝑑 36𝑖𝑛 1𝑦𝑑 3𝑓𝑡 1𝑚𝑖 5280𝑓𝑡 ; ; ; ; ; ; ; 12𝑖𝑛 1𝑓𝑡 36𝑖𝑛 1𝑦𝑑 3𝑓𝑡 1𝑦𝑑 5280𝑓𝑡 1𝑚𝑖  Customary Units Conversion 8 ft= ___ in 8𝑓𝑡 12𝑖𝑛 8𝑓𝑡 = ° = 96 𝑖𝑛 1 1𝑓𝑡 144 in = ___ yd 144𝑖𝑛 1𝑦𝑑 144 144𝑖𝑛 = ° = 𝑦𝑑 = 4𝑦𝑑 1 36𝑖𝑛 36  Metric Units to Customary Units Conversion 384 400 km = _____mi 0.62𝑚𝑖 1𝑘𝑚 384400𝑘𝑚 0.62𝑚𝑖 384000𝑘𝑚 = ∙ 1 1𝑘𝑚 = 384400 0.62 𝑚𝑖 = 238 328 𝑚𝑖  Metric Units to Customary Units Conversion 2.5 m = ______ft 2.5𝑚 = 250𝑐𝑚 1𝑓𝑡 30.48𝑐𝑚 250𝑐𝑚 1𝑓𝑡 = ∙ 1 30.48𝑐𝑚 = 8.20 𝑓𝑡.  Metric Units to Customary Units Conversion 7 ft = _____ m Metric Conversion Factors (Area) To Metric When You Symbol Multiply by To find Symbol Know Square Square 𝑖𝑛 2 6.5 𝑐𝑚2 inches centimeters Square 𝑓𝑡 2 Square feet 0.09 𝑚2 meters Square 𝑦𝑑2 Square yards 0.8 𝑚2 meters Square 𝑚𝑖 2 Square miles 2.6 𝑘𝑚2 kilometers 𝑎𝑐 Acres 0.4 Hectares ha Metric Conversion Factors (Area) From Metric When You Symbol Multiply by To find Symbol Know Square Square 𝑐𝑚 2 0.16 𝑖𝑛2 centimeters inches Square 𝑚2 1.2 Square yards 𝑦𝑑2 meters Square 𝑘𝑚2 0.4 Square miles 𝑚𝑖 2 kilometers ha hectares 2.5 acres 𝑎𝑐 The sum of the lengths of the sides of a polygon is called the perimeter. Circumference – is the distance around a circle  Formula Perimeter of a Rectangle The perimeter (P) of a rectangle with length (𝑙) and width (𝑤) is given by: 𝑃 = 2𝑙 + 2𝑤 or 𝑃 = 2(𝑙 + 𝑤) Perimeter of Regular Polygons – add all sides Circumference - 𝐶 = 𝜋𝑑 or 𝐶 = 2𝜋𝑟 Area of a Rectangle = length x width 𝐴 = 𝑙𝑤 Area of Parallelogram = base x height 𝐴 = 𝑏ℎ 𝟏 Area of a Trapezoid = x height (base 1 + base 2) 𝟐 1 𝐴 = ℎ 𝑏1 + 𝑏2 2 Area of a Circle 𝐴 = 𝜋𝑟 2 Area of a Square = (length of a side)𝟐 𝐴 = 𝑠2 𝟏 Area of a Triangle = x base x height 𝟐 1 𝐴 = 𝑏ℎ 2 Area of a Rhombus = base x height 𝐴 = 𝑏ℎ Parts of a Solid 1. Faces – any flat surface 2. Edges – line segment where two faces meet 3. Vertices – point where several planes meet in a point Prism Polyhedron with two identical parallel faces called bases Named according to the shape of its bases Triangular Prism Quadrangular Prism Pentagonal Prism Hexagonal Prism Pyramid Base is a polygonal region Altitude of the pyramid is a segment from its vertex perpendicular to the plane containing the line Regular pyramid properties Base is a regular polygon Lateral faces are congruent isosceles triangles Altitude meets the base at its center Altitude of each lateral face of a regular pyramid is called the slant height of the pyramid Cylinder Has two bases, which are congruent circular regions Axis is the line segment joining the centers of the two circles Altitude is a segment perpendicular to the plane of each base Curved surface The surface area of a space figure is the sum of the areas of all the faces Formula Surface Area of a Cube Surface Area = 6 x Area of a face 𝑆𝐴 = 6𝑠 2 Surface Area of a Rectangular Solid 𝑆𝐴 = 2𝑙𝑤 + 2ℎ𝑤 + 2ℎ𝑙 Formula Lateral Area of a Regular Pyramid 𝑙 is the height and 𝑝 is the perimeter of the base 1 𝐿 = 𝑙𝑝 2 Surface Area of a Regular Pyramid L= lateral area B = Area of Base 𝑆 =𝐿+𝐵 Formula Lateral Area of a Right Circular Cylinder Circumference x height 𝐿 = 2𝜋𝑟ℎ Surface Area of a Right Circular Cylinder 𝑆 = 𝐿 + 2𝐵 = 2𝜋𝑟ℎ + 2𝜋𝑟 2 MEASURING LENGTHS, AREA, SURFACE AREA, CAPACITY, and MASS GRADE 7 - MATHEMATICS