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5th Grade Math EOG Study Guide Place Value 1, 234, 567. 891 Rounding “Don’t forget the Poem” 5 and more add 1 more, 4 or less just ignore. Ex. Round 482 to the nearest tens place. 1. 482 480 Circle the digit in the tens place and write down any numbers before it. 2. Look to the right of your circled number. 3. Since I see a number that is four or below, I will let it go, meaning I will keep my eight and change the rest of the numbers to zeros. (if the number to the right had been five or higher, I would have given my 8 a shove and turned it into a 9). Fractions ⅝ *Remember that the numerator is the number on the top (5) and the denominator is “da” number on “da” bottom (8). When comparing fractions, use Shoot for the Stars or benchmarks (0, ½, 1, +1). o ½<⅝ * remember that the crocodile’s mouth is always open to the biggest number When ordering fractions, remember these rules: o If the denominators are the same, use the numerator to put them in order: o ⅛<⅜<⅝<⅞ If the numerators are the same, look at the denominator. The denominator that is the biggest is actually the smallest fraction. o ⅛<¼<½ You can also use benchmarks to compare and order fractions. 11 1 5 12 12 10 8 7 1 0 ½ +1 When adding or subtracting fractions, remember to find a common denominator. o Ex. ½+¼ Write down your denominators and list their multiples: 2, 4, 6, 8, 10 4, 8, 12, 16, 20 Find the least common multiple (in this case it is 4) and change any fractions to fourths using equivalent fractions. ½= Then add your new fractions and reduce if needed. When reducing fractions, list the FACTORS of the numerator and denominator. Find the greatest common factor and divide the numerator and the denominator by that number. o 10 10: 1, 2, 5, 10 10÷5= 2 15 15: 1, 3, 5, 15 15÷5= 3 Order of Operations Please Excuse My Dear Aunt Sally Parenthesis Exponents Multiplication OR Division (whichever comes first when working left to right) Addition OR Subtraction (whichever comes first when working left to right) Area and Perimeter Perimeter: the distance around a figure; add up all the sides Area: the number of square units needed to cover a flat surface; Length X Width (LxW) Measurement - *Big to small: MULTIPLY - 1 in = 2.5 cm - 1 ft = 12 in *Small to big: DIVIDE - 1 yard = 3 ft - 1 yard = 36 in - 1 kg = 2.2 lbs (a kg is bigger than a pound) - 1 lb (pound) = 16 oz (ounces) - 1 ton = 2,000 lbs - 1 mile = 1.6 km - 1 meter is about the same as 1 yard ( a meter is a little bit bigger than a yard- think of a meter stick vs. a yard stick OR Mr. Yardly vs. Mr. Meter) 1,000 Kilo kg km kl 100 Hecto hg hm hl King Milk The Land of “G” 10 Deka dKg dKm dKl Henry 1 Gram(g) Meter(m) Liter(l) Doesn’t 0.1 Deci dg dm dl Usually 0.01 Centi cg cm cl Drink Geometry Angles: right angle is exactly 90° (use the corner of a piece of paper) acute angle is less than 90° (the paper will cover the other ray) 0.001 Milli mg mm ml Chocolate obtuse angle is greater than 90° but less than 180° (the paper won’t cover the other ray) straight angle is exactly 180° (a straight line) Lines: o Intersecting lines: two lines that cross at exactly one point o Parallel lines: lines that go in the same direction and stay exactly the same distance apart. o Perpendicular lines: two lines that intersect to form right angles Polygons: o Regular shape: all sides and all angles are equal o Irregular shapes: sides are different lengths and angles are different sizes o Types of polygons: - Triangles= 3 sides, 3 angles, 180° - Quadrilaterals= 4 sides, 4 angles, 360° - Pentagons= 5 sides, 5 angles, 540° - Hexagons= 6 sides, 6 angles, 720° - Septagons= 6 sides, 6 angles, 900° - Octagons= 8 sides, 8 angles, 1080° - Nonagons= 9 sides, 9 angles, 1260° - Decagon= 10 sides, 10 angles, 1440° o Remember that you can figure out how many degrees are in a polygon by triangulating, since we know that there are 180° in a triangle. Ex. o Line symmetry: a figure has line symmetry when it can be folded about a line so that its two parts are identical o Rotational symmetry: a figure has rotational symmetry when it can be turned about a central point and still look the same in at least two positions Triangles: 3 sides, all angles add up to be 180° Quadrilaterals: o Square: 4 equal sides, 4 right angles, 2 pairs of parallel sides, equal and perpendicular diagonals o Rectangle: 2 pairs of equal sides, 2 pairs of parallel sides, 4 right angles, equal diagonals o Trapezoid: 1 pair of parallel sides, diagonals are sometimes congruent o Parallelogram: 2 pairs of parallel sides, 2 obtuse angles, 2 acute angles o Rhombus: 4 equal sides; 2 pairs of parallel sides, 2 acute angles, 2 obtuse angles, perpendicular diagonals Graphing Median: the middle number in an ordered series of numbers (one for you, one for me…) 5, 6, 7, 10, 12 7 is the median Mode: the number listed most often in a set of data 6, 7, 8, 8, 8, 9, 10 Range: the difference between the greatest and least numbers in a set of data. 2, 3, 4, 7 8 is the mode 7-2=5, therefore, 5 is the range Mean: the average of a set of numbers; to find the average add all the numbers and divide by the number of numbers added (add it all up and divide it all up) 5 + 5 + 7 + 9 + 9 = 30 30÷5=6 X-axis: the horizontal axis Y-axis: the vertical axis The mean is 6. Algebra > - Greater than - Greater than or equal to - less than ≥ < - equal to - less than or equal to ≤ = - not equal to ≠ Formulas: 1. Perimeter of a rectangle: Add all sides or p= (2l + 2w) 2 times the length plus 2 times the width 2. Area of a rectangle: A= (l x w) length times width 3. Perimeter of a polygon: add the length of all sides 4. Area of a parallelogram: A= (b x h) base times height 5. Area of a triangle: A= (½ b x h) one half base times height Important Facts about Perimeter and Area: The unit of measurement for perimeter does not have an exponent. o For example: 5 cm P= 14 cm 2 cm 2 cm 5 cm The unit of measurement for area does have an exponent. It should be square units o For example: 5 cm 2 cm 2 cm A= 10 cm 2 Perimeter is the distance around a figure. The fence that goes around your yard Area is the amount of space a figure takes up. The grass that covers the area inside your yard When finding the area or perimeter of an irregular figure, be sure to break the figure into known parts like squares, and rectangles. o For example: you can break this L shape into two rectangles and calculate the perimeter and area based on the known facts. Perimeter: add all sides P= 44 m Area: find the area of each rectangle, then add them together. A= 54m 2 9m To find this missing side you should take the opposite side of 9 m and subtract the part that is cut out which is 2 m. 9m – 2m = 7m 4m 4m 7m 13 m 9m To find this missing side you should take the opposite side of 13 m and subtract the part that is cut out which is 4 m. 13m – 4m = 9m 9m 2m To find this missing side you must know that opposite sides of rectangles are equal Side - one of the line segments that make up the polygon. Vertex - point where two sides meet. Two or more of these points are called vertices. Diagonal - a line connecting two vertices that isn't a side. Interior Angle - Angle formed by two adjacent sides inside the polygon. Exterior Angle - Angle formed by two adjacent sides outside the polygon. Fractions: Adding, Subtracting and Multiplying. When adding or subtracting fractions you must find the Least Common Multiple (LCM) to get a common denominator before you can add or subtract. Remember to change improper fractions to mixed numbers and reduce your final answer. Also “Watch the sign”, many students get these questions incorrect because they add when they should subtract or subtract when they should add. o For example: Find the LCM (least common multiple) of the denominators 2 and 5. 2) 2, 4, 6, 8, 10, 12 1 2 + 2 = 5 ? Get a Common Denominator Make Equivalent fractions Add the top keep the denominator the same, and reduce if possible Fractions: Multiplying Fractions, and changing improper fractions to mixed numbers, and mixed numbers to improper fractions. You do not need a common denominator to multiply fractions, so you simply multiply: Numerator 1X2= 2 Denominator 2 X 5= 10 Use GCF (Greatest Common Factor) to reduce the fraction: 2 is a prime number. Its factors are 1, and 2. 10 is a composite number its factors are 1, 10, 2, and 5. The GCF is 2, so divide by 2. Numerator 2 divide by 2 = 1 Denominator 10 divided by 2 = 5 1 2 x 2 2 = 5 2 10 1 = 10 Multiply across the top and bottom 5 Reduce the fraction Note: If you are multiplying mixed numbers you must first change them into improper fractions. Changing an Improper Fraction to a Mixed Number: 1. Divide the numerator by the denominator. 11 2. The quotient becomes the whole number and the remainder becomes the numerator. The denominator stays the same. 5 2 5 11 - 10 1 1 2 5 Changing a Mixed Number to an Improper Fraction: 1. Multiply the whole number and the denominator. 2. Add the product to the numerator. The sum becomes the new numerator. The denominator stays the same. 1 2 11 2 x 5 = 10 +1 = 11 5 5 Metric Customary Measurement: length 1 foot (ft) = 12 inches (in.) 1 yard (yd) = 3 feet (ft) 1 yard (yd) = 36 inches (in) 1 mile (mi) = 1,760 yards (yd) 1 mile (mi) = 5,280 feet (ft) Weight 1 pound (lb) = 16 ounces (oz) 1 ton (T) = 2,000 lbs 1 ton (T) = 32,000 oz capacity 1 pint (pt) = 2 cups (c) 1 quart (qt) = 2 pints (pt) 1 quart (qt) = 4 cups (c) 1 gallon (gal) = 4 quarts (qt) 1 gallon (gal) = 8 pints (pt) 1 gallon (gal) = 16 cups (c) 1 1 1 1 1 kilogram (kg) = 1,000 grams (g) 1 Liter (l) = 1,000 milliliters (mL) Big G: centimeter (cm) = 10 millimeters (mm) decimeter (dm) 10 cm or 100 mm meter (m) = 10 dm / 100 cm / 1,000 mm kilometer (km) = 1,000 m Remember: when you go from a larger unit to a smaller unit you should multiply “horse to fly multiply” but when you go from a smaller unit to a larger unit you should divide “fly to horse divide of course” Polygon Names and properties Sample questions about polygons and their properties can be found on pages 206-211 of your math text book. Number of Sides 3 Polygon Name Triangle 3 sides 3 angles Sum of interior angles 180 4 Quadrilateral 4 sides 4 angles 360 5 Pentagon 5 sides 5 angles 540 6 Hexagon 6 sides 6 angles 720 7 Heptagon 7 sides 7 angles 900 8 Octagon 8 sides 8 angles 1080 These are regular polygons, that means that all the sides and angles are equal, the shapes will not always look this way. You will need to learn the # of sides to identify the name of a polygon. Triangles: Triangles can be identified by the kind of angles and the lengths of its sides. Right Triangle: contains 1 angle that is equal to 90 degrees Obtuse Triangle: contains 1 angle is greater than 90 degrees Isosceles Triangle: two sides are the same length Acute Triangle: all angles are less than 90 degrees Equilateral Triangle: all sides are the same length Scalene Triangle: no sides are the same length Special quadrilaterals (4 sided figures) Trapezoid: 1 pair of parallel sides Parallelogram: opposite sides are equal and parallel Rectangle: a parallelogram with 4 right angles, Rhombus: a parallelogram with all sides the same length Square: a rectangle with all sides the same length Right Angle: measures exactly 90 degrees Obtuse Angle: measures more than 90 degrees Straight Angle: measures exactly 180 degrees, can be made when two right angles are put together Acute Angle: measures less than 90 degrees Math Vocabulary Numbers and Operations Place value of numbers one through hundred millions (1-100,000,000) Standard (number), word, and expanded form ex: 324= 300 + 20 + 4 NEW Expanded form ex: 324= 3 x 100 + 2 x 10 + 4 x 1 Rounding numbers: Slip to the side and look for a FIVE! If it's 5 or more we go up one more, 4 or less we AVOID the mess (stay the same)! Numbers in front stay the same and numbers behind turn to ZEROS! Decimals: standard, word, and NEW expanded form ex: 2.45= 2 x 1 + 4 x .1 + 5 x .01 Rounding decimals Comparing and ordering decimals Adding and Subtracting decimals- Line up the DOT and give it all ya GOT! Estimating Products (rounding and multiplying numbers) Multiplying two by two and three by three digit numbers Dividing by one divisor (Does McDonald's Serve Cheese Burgers?)- Divide, Multiply, Subtract, Check, Bring down! Estimating Division (finding compatible numbers and changing the rest to zeros!) Dividing by two digit divisors Measurement Length: centimeter, inch, yard, meter, kilometer, mile Customary: system used here in the United Stated Metric: system used in most other countries Mass/Weight: grams, ounces, pounds, kilograms Capacity: The big "G" and A Liter is a little bit more than a Quart Data Analysis Stem and Leaf Plot: used to organize a set of data (after it has been collected) Pictograph: graphs using pictures to display data Bar Graph: Display data by category Circle Graph: Graphs that show parts of a WHOLE Line Graph: Shows change over time Range (take the highest # in a set of data and lowest #, stack 'em, and subtract 'em) Median (number in the middle of a set of data- you may have to average the two in the middle to find this) Mode (The number that occurs the most in a data set- there may be more than one- or none at all) Midpoint (The exact # in the middle of a data set- only available with an odd # of data collected) Geometry Polygon: A closed figure made my joining line segments. Regular Polygon: A polygon with all equal sides and angles. Irregular Polygon: A polygon with one or more different sides or angles. Right Angle: An angle measuring exactly 90 degrees. Acute Angle: An angle measuring less than 90 degrees. Obtuse Angle: An angle measuring more than 90 degrees but less than 180 degrees. Straight Angle: An angle measuring exactly 180 degrees- also a straight line. Triangle: A 3 sided polygon Right Triangle: A triangle with one right angle and two acute angles. Acute Triangle: A triangle with three acute angles. (MUST have 3)! Obtuse Triangle: A triangle with one obtuse angle and two acute angles. Scalene Triangle: A triangle with no equal sides. Isosceles Triangle: A triangle with two equal sides. Equilateral Triangles: A triangle with ALL equal sides. Perimeter: distance around an object Area: space inside an object (Length X Width) Quadrilaterals: A four sided polygon Line Symmetry: When a figure can be folded ona line and match exactly on both sides. Rotational Symmetry: The figure can be rotated less than 360 degrees around a central point and still match the original figure. Pentagon: A five sided polygon Hexagon: A six sided polygon Octagon: An eight sided polygon Decagon: A ten sided polygon Dodecagon: A twelve sided polygon Supplementary angles: two angles that add up to 180 degrees or form a straight line Complementary angles: two angles that add up to 90 degrees or a right angle Fractions Fraction: Part of a whole Numerator: The top number in a fraction Denominator: The bottom number in a fraction Common or like Fractions: These are two or more fractions that may look different but represent the same amount. ex: 1/2 is 2/4 which is also 4/8 Common Denominators: Two or more fractions with the same number in the denominator spot. When adding fractions with like denominators, just add the numerator and the denominator STAYS THE SAME! Factors: The two numbers you multiply together to get a larger number. Ex: the factors of 6 are: 1,2,3,6 (1 x 6) and (2 x 3) Greatest Common Factor (GCF): The largest factor that both the numerator and the denominator have in common. Equivalent Factions: Fractions that share the same value but have different numerators and denominators. Simplest Form: When a fraction can not be reduced any further. This is the form that all answers will be in on the EOG! Improper Fractions: A fraction that has a larger numerator than denominator. Mixed Number: A value that includes a whole number and a fraction. Prime Number: A number that only has two factors- one and itself. (ex: 2, 3, 5, 7, 11) Composite Number: A number that has more than two factors. "big brother": The little brother (smaller denominator) always looks up and wants to be just like the BIG brother (larger denominator)- so we do whatever we need to to the little brother to make him the big brother! Then, whatever we did to the bottom, we must do to the top! In 5th grade we will only be adding and subtracting unlike denominators through our "fraction families" (halves, thirds, and fifths) so this concept will work every time! Adding mixed numbers with unlike denominators: Students will learn to "Prepare the Patient" (find common denominators), "Operate" (add or subtract mixed numbers- fractions first of course), and then "Recovery" (simplify)! ***Please remember that Geometry is the strand most heavily tested on the 5th grade Math EOG. The key to Geometry is mastering the vocabulary and being able to apply the terms to different scenarios.