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5th Grade Math Note Cards I use white index cards that I single hole punched in the upper left corner and use a color marker to put a colored line across the bottom for each strand (example red- geometry, green- measurement- bluenumbers and operations, orange- data and graphing and yellow- algebra). If colored index cards are in the budget that would be easier. Have students cut out cards and glue them onto the index cards, connecting them all together on a key ring. Additional cards can be added easily and it is also easy to isolate individual strands. Hope it helps. Ann McCoy 5th Grade Teacher Hunter Elementary "Together We Can" DATA and GRAPHING Types of graphs: 4 Line graph- shows the changes in data over time, one of the axis will show a unit of time Pictograph- uses sets of pictures to represent information; look for and use the KEY Bar- uses horizontal or vertical bars to show More Types of graphs: line plot data is placed on a number line represented by symbols 4 Stem-and-leaf- larger place values (ex.10s, 100s) are the stems and numbers in the 1s place are the leaves Circle- pie chart- divides a circle to show info information. Maximum- the largest number 4 Minimum- the smallest number Range- subtract the smallest number from the largest Mode- most often used number Median- the middle number; line the numbers up from smallest to largest and cross off on each end until you reach the middle number DECIMALS: 1 Think of decimals as money to help you compare and order them; can add zeros to end of number to make all go to same place value. Line up you decimals when you add or subtract them; put zeros into empty spaces so that all numbers go to the same place value. PATTERNS: 5 * Data is often organized in T-charts * Look for relationships between the numbers or symbols: Are they increasing (addition or multiplication)? Are they decreasing (subtraction or division)? *When you think you have found the correct pattern- always check and be sure it works! LINES: 3 Line- a straight path that goes on forever in both directions; has no endpoints Line segment- a straight line between two points, called its endpoints Ray- a straight line that has one endpoint and goes on forever in the other direction Parallel lines- lines that never meet or cross, and they stay the same distance apart Intersecting lines- lines that cross or meet Perpendicular lines- lines that cross or meet at 90 angles; forming right angles ANGLES: 3 Angles- formed by 2 rays or line segments, share the same endpoint- called the vertex Three main types of angles: Acute- measures less than 90 degrees Right- measures exactly 90 degrees Obtuse- measures more than 90 but less than 180 degrees Other types of angles: 3 Straight angle- measures exactly 180 degreeslooks like a straight line Reflex angle- measures between 180 and 360 degrees Complementary angles- two angles that make a right (90 ) angle Supplementary angles- two angles that make a straight (180 ) angle Types of triangles by length of sides: 3 Scalene- all 3 side are different lengths TRIANGLES: 3 A polygon with 3 sides, 3 vertices (corners) and 3 angles. The sum of its interior angles is 180 degrees Types of triangles by angles: Acute triangle- all angles are acute (< 90 ) Obtuse- one angle is more than 90 degrees Right- one angle is exactly 90 degrees Equilateral- all angles are 60 degrees each MORE ON TRIANGLES: 3 *To find the measure of the third angle in a triangle when given the other two angles: 1. Add the two angles you are given 2. Subtract that sum from 180 3 Isosceles- at least two sides are the same length Equilateral- all 3 sides are the same length * a equilateral triangle is also an isosceles triangle because at least 2 sides are the same length *To find out if 3 lengths can make a triangle: Add the two smaller numbers together. If that sum is more than the largest number, then yes! QUADRILATERALS: 3 A polygon with 4 sides, 4 vertices (corners), and 4 angles The sum of its interior angles is 360 degrees Types of quadrilaterals: Square- all sides same length, all right angles, 2 pairs/sets of parallel lines Rectangle- opposite sides are the same length, all right angles, 2 pairs/sets of parallel lines More types of quadrilaterals: 3 Rhombus- all sides same length, opposite angles are equal, 2 pairs of parallel lines Parallelogram- have 2 pairs/sets of parallel sides, opposite sides are equal/congruent. Squares, rectangles, and rhombus are all types of parallelograms; More types of quadrilaterals: 3 Trapezoid- has exactly one pair/set of parallel lines Kite- has two pairs of equal sides. The equal sides are next to each other. All four sides can not be the same length; does not have any pairs/sets of parallel lines OTHER POLYGONS: Pentagon- 5 sides, 5 vertices and 5 angles Hexagon- 6 sides, 6 vertices and 6 angles Octagon- 8 sides, 8 vertices and 8 angles 3 You can find the sum of the interior angles of any polygon by using formula: (n-2) x 180, where n = the number of sides of the polygon. Steps to solving conversion problems: 2 1. Set up your problem - what unit are you changing to what other unit? 2. Write the conversion for the units under the problem (same unit under the same unit in problem) 3. Either a) multiply if going from a smaller to larger number or b) divide if going from a larger to a smaller number to solve Example: Sue picked 5 kilograms of apples. 2 About how many pounds did she pick? Diagonals: lines drawn from one 3 vertex to a non-adjacent vertex (the vertices can not be beside each other) Triangles- have no diagonals All quadrilaterals- have 2 diagonals Squares, rhombus and kites always have perpendicular diagonals Pentagons- have 5 diagonals; form a star Kids Have Dropped Under Desks Converting Metrics! Regular polygons- all sides are the 3 same length and all the angles are the same size Other terms to know: Congruent: same shape and the same size Similar: same shape but not the same size Adjacent: next to each other 2 K H D U D C M Kilo hecto deca unit deci centi milli 1000 100 10 1 .1 .01 .001 5 kg = ____ pounds (I am changing kg to lbs) meter gram liter 5 x 2.2 = 11 pounds ( I’m going from a smaller 1 kg = 2.2 pounds (this is the conversion rule) number “1” to a larger number “2.2” so I multiply to solve.) MEASUREMENT- LENGTH 2 Customary (US) 12 inches = 1 foot 3 feet = 1 yard 36 inches = 1 yard 5,280 feet = 1 mile MEASUREMENT- WEIGHT Customary (US) 16 ounces = 1 pound 2,000 pounds = 1 ton Metric- main unit is METER 10 millimeters = 1 centimeter 1000 millimeters = 100 centimeters = 1 meter 1000 meters = 1 kilometer Metric- main unit is GRAM 1000 milligrams = 1 gram 100 centigrams = 1 gram 1000 grams = 1 kilogram MEASUREMENT- CAPACITY/VOLUME Customary (US) 8 fluid (liquid) ounces = 1 cup * See the “BIG G” on back Metric- main unit is LITER 1000 milliliters = 1 liter 100 centiliters = 1 liter 1000 grams = 1 kilogram 2 CONVERSIONS BETWEEN CUSTOMARY AND METRIC: 1 inch is about 2.5 cm 1 yard is about 1 meter 1 mile is about 1.6 km 1 kilometer is about .6 mile 1 quart is about 1 liter 1 ounce is about 28 grams 1 kilogram is about 2.2 pounds 2 2 FOUR MAIN OPERATIONS: 1 Addition- the answer is called the sum Addition words: altogether, in all, sum, how many, total Subtraction- the answer is called the difference Subtraction words- how many more than, decrease, reduce, less than, are left, change, find the difference Division- the answer is called the quotient Division words: per, each 1 Divide when you are given a total and the problem asks you to separate or divide into equal parts; when you divide amounts get smaller Multiplication- the answer is called the product. 1 Multiplication words: each, per, twice, double;these words are combined with addition words. Multiply when you are given a set of something with the same amount in each set; when you multiply amounts get bigger. ESTIMATION: 1 Use rounding to help you estimate. Round to the largest place in your number, unless you are given a specific place (ex. nearest whole number). Estimation words: round, about, almost, nearest, approximately, at least ROUNDING STEPS: 1 1.Underline the place you are rounding- the number can only do 2 things- go up by 1 or stay the same. 2. Look at the number to the right- if that number is a 0,1,2,3 or 4, the number you are rounding will stay the same. If it is a 5, 6, 7, 8, 9 it’ll go up by 1 3. Everything behind the number you’re rounding becomes zeros. Everything in front of the number stays the same, unless rounding a 9 to 10. ORDER OF OPERATIONS: Please Excuse My Dear Aunt Sally P- Parenthesis E- Exponent M- Multiplication D- Division A- Addition S- Subtraction FRACTIONS 1 Numerator- top number; this number answers the question (how many are…red, shaded? Denominator- bottom number; tells how many parts your whole has been divided into Improper Fraction: Numerator is bigger than the denominator. Mixed Numbers: have a whole number and a fraction Adding and Subtracting Fractions: 1 You can only add or subtract fractions when they have the same denominator! Comparing Fractions: 1 If the NUMERATORS are the same- the larger the denominator the smaller the fraction If the DENOMINATORS are the same- just look at the numerators and put them in order To Find a Common Denominator: 1. Ask: Is my smaller denominator a factor of my larger denominator? If yes, use the larger. 2. Find the Quick Common Denominator Find the lowest common multiple- LCM 1. First ask: Is my numerator a factor of my denominator? If yes- can simplify in one step! 2. If it is not, then use you prime numbers (2, 3, 5, 7, 11) to help you simplify 1 To make equivalent fractions- multiply or divide the numerator and the denominator by the same number. Simplifying Fractions 1 Divide the numerator and the denominator by the same number until you can not anymore.