Measurement and Geometry

Transcription

1 8A A Family Letter: Area Dear Family, The student will learn how to convert between units within the customary and metric measuring systems. The table below shows the conversions for the customary system. Length Weight Capacity 12 inches (in.) 1 foot (ft); 3 ft 1 yard (yd); 5,280 ft 1 mile (mi) 16 ounces (oz) 1 pound (lb); 2,000 lb 1 ton (T) 8 fluid ounces (fl oz) 1 cup (c); 2 c 1 pint (pt); 2 pt 1 quart (qt); 4 qt 1 gallon (gal) Convert 114 inches to feet. Set up a conversion factor. 114 in. 1 ft 1 ft 12 in., so multiply by 1 ft 12 in. 12 in. 114 in. 9.5 ft Cancel the common unit, in. The conversions for the metric system are below. Vocabulary These are the math words we are learning: area the number of square units needed to cover a given surface customary system a system of measurement primarily used in the United States metric system a system of measurement used all over the world whose units are related by the decimal system Length Mass 10 millimeters (mm) 1 centimeter (cm); 100 cm 1 meter (m); 1,000 m 1 kilometer (km) 1,000 milligrams (mg) 1 gram (g); 1,000 g 1 kilogram (kg) Capacity 1,000 milliliters (ml) 1 liter (L); 1,000 (L) 1 kiloliter (kl) You can use the same methods of multiplying and dividing to convert in the metric system. However, since metric measurements are based on powers of ten, there is a conversion shortcut. To convert to smaller units, move the decimal point to the right based on the number of zeros in the conversion factor. To convert to larger units, move the decimal point to the left. kg to g cm to m 1000 g in 1 kg 3 zeros 100 cm in 1 m 2 zeros Move decimal point 3 places Move decimal point 2 places right: left: kg 4,850 g 576 cm 5.76 m 8-1

2 8A A Family Letter: Area continued The student will also learn the area formulas for rectangles, parallelograms, triangles, and trapezoids. The area of a figure is defined as the number of square units needed to cover a given surface. Figure Formula Words Rectangle A Area equals length times width. A bh Area equals base times height. Parallelogram A 1 2 bh Area equals one-half the base times the height. Triangle Trapezoid A 1 2 h (b 1 b 2 ) Area equals half the product of the height and the sum of the lengths of the bases. The student will be able to use these formulas to find the areas of composite figures. For example, the composite figure below can be divided into three recognizable polygons. You can find the area of each polygon and add their areas to find the total area of the composite figure. Sincerely, 8-2

3 8A A At-Home Practice: Area Convert mi to ft L to ml oz to lb kg to g qt to gal 6. 4,391 mm to m T to lb L to ml in. to ft m to cm gal to c mg to g Find the area of each polygon Answers: 1. 21,120 ft ,000 ml 3. 3 lb 4. 3,762 g gal m 7. 4,940 lb 8. 5,681 ml 9. 5 ft cm c g cm in m mm ft m mm 2 8-3

4 8A A Family Fun: Dimension Creation Shapes may cover the same area but have different dimensions. How many different figures can you create with a certain area? Be creative! Directions Ask a family member to play this game. Cut out the 9 cards. Place the cards face down. Each player picks an area card from the pile. Each player draws and labels 3 figures with the selected area. Compare answers. You earn 2 points for each area that is correctly calculated. You lose one point for each incorrect calculation. You earn 3 points for each figure that is different than any the other player calculated. The person with the most points is the winner. 24 m 2 18 m 2 36 m cm 2 42 cm 2 12 cm 2 56 in 2 8 in 2 25 in 2 8-4

5 8B B Family Letter: Volume and Surface Area Dear Family, The student will be learning about three-dimensional figures. A special type of three-dimensional figure is a polyhedron. The sides, or faces, of a polyhedron are polygons. The edges are formed when two faces share a side, and a vertex is formed at the point where three or more edges meet. A prism is a special polyhedron that has two congruent, parallel bases and parallelogram faces. Prisms are named for the shape of their bases. A pyramid has a polygon-shaped base, but the other faces are triangles. A pyramid is also named for its base. Square Pyramid Cylinders are NOT polyhedra because not every surface is a polygon. Vocabulary These are the math words we are learning: base a face of a threedimensional object that usually determines the name of the object cylinder a threedimensional object with two parallel, congruent, circular bases connected by a curved lateral surface edge the intersection of two faces of a polyhedron face a flat polygonal side of a polyhedron net an arrangement of two-dimensional figures that folds to form a polyhedron polyhedron a threedimensional object in which all the surfaces or faces are polygons prism a polyhedron with two congruent, parallel bases, and parallelogram faces pyramid a polygonshaped base with triangular faces that come to a point; named for the shape of its base surface area the sum of the areas of the faces of a three-dimensional object vertex the point at which three or more edges meet volume the number of cubic units needed to fill a space 8-46

6 8B B Family Letter: Volume and Surface Area continued The student will use these volume formulas to find the volume of each three-dimensional object. Rectangular Prism Triangular Prism V h V Bh The student will also learn to find the surface area of threedimensional objects. To find the surface area of a prism, the student can use a net. A net is the pattern made when the surface of a three-dimensional object is layed out flat showing each face of the object. To find the surface area, add the areas of each face. The student will use these formulas to find the surface area of Rectangular prisms, pyramids, and cylinders. Rectangular Prism Pyramid S 2lw 2wh 2lh S s bh Cylinder S h(2 r) 2( r 2 ) The student will use these formulas in most math classes. These formulas are also used in many real-life situations. Sincerely, 8-47

7 8B B At-Home Practice: Volume and Surface Area Find the surface area of each figure. Round to the nearest tenth, if necessary cm 7 cm 5 in. 6 in. Find the volume of each three-dimensional figure. Round to the nearest tenth, if necessary in. 4 in. 10 in. 2.6 in. 3 in. 4.5 in. Answers: cm in cm in m cm in in

8 8B B Family Fun: Word Find Directions Unscramble the vocabulary words in the box. Find those words hidden in the puzzle. derlcyin cefa smipr xeevtr eegd oornehylpd yrmdiap tne frsucea area mlveou seba S O E I I S B C N M P R F U E M K P Y W S Y O C U P R F U L J I D N L C D U T F I L R R F X Y M S O Z N A P O S A E H Y K C D T O C S V C T E Y C E B A S E E H E R D W R O V P D L V A P E R O C T N G T E N R R V O F W I E E M K M I F E N D D I M A R Y P V U L A W T C O S T O D J B F Q R Answers: cylinder, face, prism, vertex, edge, polyhedron, pyramid, net, surface area, volume, base 8-49